TSTP Solution File: NUN073+2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUN073+2 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n009.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 14:40:22 EDT 2024
% Result : Theorem 0.17s 0.37s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 106
% Syntax : Number of formulae : 334 ( 66 unt; 0 def)
% Number of atoms : 969 ( 203 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 1026 ( 391 ~; 374 |; 167 &)
% ( 70 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 76 ( 74 usr; 71 prp; 0-3 aty)
% Number of functors : 25 ( 25 usr; 6 con; 0-2 aty)
% Number of variables : 465 ( 362 !; 103 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f578,plain,
$false,
inference(avatar_sat_refutation,[],[f124,f129,f134,f139,f144,f149,f153,f157,f161,f165,f169,f173,f177,f181,f185,f189,f209,f213,f218,f222,f228,f232,f236,f240,f245,f249,f253,f269,f273,f277,f282,f286,f291,f295,f303,f307,f311,f315,f346,f351,f356,f368,f372,f376,f381,f387,f396,f404,f411,f415,f421,f425,f431,f441,f451,f457,f462,f467,f471,f475,f480,f484,f488,f503,f507,f511,f515,f539,f543,f547,f577]) ).
fof(f577,plain,
( spl25_25
| ~ spl25_2
| ~ spl25_61 ),
inference(avatar_split_clause,[],[f516,f477,f126,f242]) ).
fof(f242,plain,
( spl25_25
<=> r1(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_25])]) ).
fof(f126,plain,
( spl25_2
<=> r1(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_2])]) ).
fof(f477,plain,
( spl25_61
<=> sK1 = sK2 ),
introduced(avatar_definition,[new_symbols(naming,[spl25_61])]) ).
fof(f516,plain,
( r1(sK1)
| ~ spl25_2
| ~ spl25_61 ),
inference(superposition,[],[f128,f479]) ).
fof(f479,plain,
( sK1 = sK2
| ~ spl25_61 ),
inference(avatar_component_clause,[],[f477]) ).
fof(f128,plain,
( r1(sK2)
| ~ spl25_2 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f547,plain,
( spl25_70
| ~ spl25_33
| ~ spl25_37 ),
inference(avatar_split_clause,[],[f325,f309,f289,f545]) ).
fof(f545,plain,
( spl25_70
<=> ! [X0,X1] : sK20(X0,X1) = sK23(X0,sK13(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_70])]) ).
fof(f289,plain,
( spl25_33
<=> ! [X0,X1] : r3(X0,sK13(X1),sK20(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_33])]) ).
fof(f309,plain,
( spl25_37
<=> ! [X0,X1,X3] :
( sK23(X0,X1) = X3
| ~ r3(X0,X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_37])]) ).
fof(f325,plain,
( ! [X0,X1] : sK20(X0,X1) = sK23(X0,sK13(X1))
| ~ spl25_33
| ~ spl25_37 ),
inference(resolution,[],[f310,f290]) ).
fof(f290,plain,
( ! [X0,X1] : r3(X0,sK13(X1),sK20(X0,X1))
| ~ spl25_33 ),
inference(avatar_component_clause,[],[f289]) ).
fof(f310,plain,
( ! [X3,X0,X1] :
( ~ r3(X0,X1,X3)
| sK23(X0,X1) = X3 )
| ~ spl25_37 ),
inference(avatar_component_clause,[],[f309]) ).
fof(f543,plain,
( spl25_69
| ~ spl25_31
| ~ spl25_36 ),
inference(avatar_split_clause,[],[f321,f305,f280,f541]) ).
fof(f541,plain,
( spl25_69
<=> ! [X0,X1] : sK16(X0,X1) = sK22(X0,sK13(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_69])]) ).
fof(f280,plain,
( spl25_31
<=> ! [X0,X1] : r4(X0,sK13(X1),sK16(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_31])]) ).
fof(f305,plain,
( spl25_36
<=> ! [X0,X1,X3] :
( sK22(X0,X1) = X3
| ~ r4(X0,X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_36])]) ).
fof(f321,plain,
( ! [X0,X1] : sK16(X0,X1) = sK22(X0,sK13(X1))
| ~ spl25_31
| ~ spl25_36 ),
inference(resolution,[],[f306,f281]) ).
fof(f281,plain,
( ! [X0,X1] : r4(X0,sK13(X1),sK16(X0,X1))
| ~ spl25_31 ),
inference(avatar_component_clause,[],[f280]) ).
fof(f306,plain,
( ! [X3,X0,X1] :
( ~ r4(X0,X1,X3)
| sK22(X0,X1) = X3 )
| ~ spl25_36 ),
inference(avatar_component_clause,[],[f305]) ).
fof(f539,plain,
( spl25_68
| ~ spl25_26
| ~ spl25_27 ),
inference(avatar_split_clause,[],[f264,f251,f247,f537]) ).
fof(f537,plain,
( spl25_68
<=> ! [X0,X1] : sK20(X0,X1) = sK13(sK19(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_68])]) ).
fof(f247,plain,
( spl25_26
<=> ! [X2,X0] :
( sK13(X0) = X2
| ~ r2(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_26])]) ).
fof(f251,plain,
( spl25_27
<=> ! [X0,X1] : r2(sK19(X0,X1),sK20(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_27])]) ).
fof(f264,plain,
( ! [X0,X1] : sK20(X0,X1) = sK13(sK19(X0,X1))
| ~ spl25_26
| ~ spl25_27 ),
inference(resolution,[],[f252,f248]) ).
fof(f248,plain,
( ! [X2,X0] :
( ~ r2(X0,X2)
| sK13(X0) = X2 )
| ~ spl25_26 ),
inference(avatar_component_clause,[],[f247]) ).
fof(f252,plain,
( ! [X0,X1] : r2(sK19(X0,X1),sK20(X0,X1))
| ~ spl25_27 ),
inference(avatar_component_clause,[],[f251]) ).
fof(f515,plain,
( spl25_67
| ~ spl25_11
| ~ spl25_38 ),
inference(avatar_split_clause,[],[f328,f313,f167,f513]) ).
fof(f513,plain,
( spl25_67
<=> ! [X0,X1] :
( X0 = X1
| ~ r2(X0,sK13(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_67])]) ).
fof(f167,plain,
( spl25_11
<=> ! [X0] : r2(X0,sK13(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_11])]) ).
fof(f313,plain,
( spl25_38
<=> ! [X0,X1,X3] :
( X0 = X1
| ~ r2(X1,X3)
| ~ r2(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_38])]) ).
fof(f328,plain,
( ! [X0,X1] :
( X0 = X1
| ~ r2(X0,sK13(X1)) )
| ~ spl25_11
| ~ spl25_38 ),
inference(resolution,[],[f314,f168]) ).
fof(f168,plain,
( ! [X0] : r2(X0,sK13(X0))
| ~ spl25_11 ),
inference(avatar_component_clause,[],[f167]) ).
fof(f314,plain,
( ! [X3,X0,X1] :
( ~ r2(X1,X3)
| X0 = X1
| ~ r2(X0,X3) )
| ~ spl25_38 ),
inference(avatar_component_clause,[],[f313]) ).
fof(f511,plain,
( spl25_66
| ~ spl25_18
| ~ spl25_37 ),
inference(avatar_split_clause,[],[f323,f309,f211,f509]) ).
fof(f509,plain,
( spl25_66
<=> ! [X0,X1] : sK19(X0,X1) = sK23(X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_66])]) ).
fof(f211,plain,
( spl25_18
<=> ! [X0,X1] : r3(X0,X1,sK19(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_18])]) ).
fof(f323,plain,
( ! [X0,X1] : sK19(X0,X1) = sK23(X0,X1)
| ~ spl25_18
| ~ spl25_37 ),
inference(resolution,[],[f310,f212]) ).
fof(f212,plain,
( ! [X0,X1] : r3(X0,X1,sK19(X0,X1))
| ~ spl25_18 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f507,plain,
( spl25_65
| ~ spl25_17
| ~ spl25_36 ),
inference(avatar_split_clause,[],[f319,f305,f207,f505]) ).
fof(f505,plain,
( spl25_65
<=> ! [X0,X1] : sK15(X0,X1) = sK22(X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_65])]) ).
fof(f207,plain,
( spl25_17
<=> ! [X0,X1] : r4(X0,X1,sK15(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_17])]) ).
fof(f319,plain,
( ! [X0,X1] : sK15(X0,X1) = sK22(X0,X1)
| ~ spl25_17
| ~ spl25_36 ),
inference(resolution,[],[f306,f208]) ).
fof(f208,plain,
( ! [X0,X1] : r4(X0,X1,sK15(X0,X1))
| ~ spl25_17 ),
inference(avatar_component_clause,[],[f207]) ).
fof(f503,plain,
( spl25_64
| ~ spl25_15
| ~ spl25_35 ),
inference(avatar_split_clause,[],[f317,f301,f183,f501]) ).
fof(f501,plain,
( spl25_64
<=> ! [X0] :
( sK7(X0) = X0
| ~ r1(sK6(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_64])]) ).
fof(f183,plain,
( spl25_15
<=> ! [X2,X0] :
( ~ r2(X0,X2)
| ~ r1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_15])]) ).
fof(f301,plain,
( spl25_35
<=> ! [X0] :
( r2(sK5(X0),sK6(X0))
| sK7(X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_35])]) ).
fof(f317,plain,
( ! [X0] :
( sK7(X0) = X0
| ~ r1(sK6(X0)) )
| ~ spl25_15
| ~ spl25_35 ),
inference(resolution,[],[f302,f184]) ).
fof(f184,plain,
( ! [X2,X0] :
( ~ r2(X0,X2)
| ~ r1(X2) )
| ~ spl25_15 ),
inference(avatar_component_clause,[],[f183]) ).
fof(f302,plain,
( ! [X0] :
( r2(sK5(X0),sK6(X0))
| sK7(X0) = X0 )
| ~ spl25_35 ),
inference(avatar_component_clause,[],[f301]) ).
fof(f488,plain,
( spl25_63
| ~ spl25_24
| ~ spl25_29 ),
inference(avatar_split_clause,[],[f299,f271,f238,f486]) ).
fof(f486,plain,
( spl25_63
<=> ! [X0] :
( r1(X0)
| sK6(X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_63])]) ).
fof(f238,plain,
( spl25_24
<=> ! [X0] :
( sK6(X0) = X0
| r1(sK7(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_24])]) ).
fof(f271,plain,
( spl25_29
<=> ! [X0] :
( sK6(X0) = X0
| sK7(X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_29])]) ).
fof(f299,plain,
( ! [X0] :
( r1(X0)
| sK6(X0) = X0 )
| ~ spl25_24
| ~ spl25_29 ),
inference(duplicate_literal_removal,[],[f298]) ).
fof(f298,plain,
( ! [X0] :
( r1(X0)
| sK6(X0) = X0
| sK6(X0) = X0 )
| ~ spl25_24
| ~ spl25_29 ),
inference(superposition,[],[f239,f272]) ).
fof(f272,plain,
( ! [X0] :
( sK7(X0) = X0
| sK6(X0) = X0 )
| ~ spl25_29 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f239,plain,
( ! [X0] :
( r1(sK7(X0))
| sK6(X0) = X0 )
| ~ spl25_24 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f484,plain,
( spl25_62
| ~ spl25_15
| ~ spl25_28 ),
inference(avatar_split_clause,[],[f297,f267,f183,f482]) ).
fof(f482,plain,
( spl25_62
<=> ! [X0] :
( r1(sK7(X0))
| ~ r1(sK6(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_62])]) ).
fof(f267,plain,
( spl25_28
<=> ! [X0] :
( r2(sK5(X0),sK6(X0))
| r1(sK7(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_28])]) ).
fof(f297,plain,
( ! [X0] :
( r1(sK7(X0))
| ~ r1(sK6(X0)) )
| ~ spl25_15
| ~ spl25_28 ),
inference(resolution,[],[f268,f184]) ).
fof(f268,plain,
( ! [X0] :
( r2(sK5(X0),sK6(X0))
| r1(sK7(X0)) )
| ~ spl25_28 ),
inference(avatar_component_clause,[],[f267]) ).
fof(f480,plain,
( spl25_61
| ~ spl25_4
| ~ spl25_52 ),
inference(avatar_split_clause,[],[f427,f423,f136,f477]) ).
fof(f136,plain,
( spl25_4
<=> r2(sK2,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_4])]) ).
fof(f423,plain,
( spl25_52
<=> ! [X0] :
( ~ r2(X0,sK1)
| sK1 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_52])]) ).
fof(f427,plain,
( sK1 = sK2
| ~ spl25_4
| ~ spl25_52 ),
inference(resolution,[],[f424,f138]) ).
fof(f138,plain,
( r2(sK2,sK1)
| ~ spl25_4 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f424,plain,
( ! [X0] :
( ~ r2(X0,sK1)
| sK1 = X0 )
| ~ spl25_52 ),
inference(avatar_component_clause,[],[f423]) ).
fof(f475,plain,
( spl25_60
| ~ spl25_13
| ~ spl25_26 ),
inference(avatar_split_clause,[],[f258,f247,f175,f473]) ).
fof(f473,plain,
( spl25_60
<=> ! [X0,X1] : sK13(X0) = sK21(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_60])]) ).
fof(f175,plain,
( spl25_13
<=> ! [X0,X1] : r2(X1,sK21(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_13])]) ).
fof(f258,plain,
( ! [X0,X1] : sK13(X0) = sK21(X1,X0)
| ~ spl25_13
| ~ spl25_26 ),
inference(resolution,[],[f248,f176]) ).
fof(f176,plain,
( ! [X0,X1] : r2(X1,sK21(X0,X1))
| ~ spl25_13 ),
inference(avatar_component_clause,[],[f175]) ).
fof(f471,plain,
( spl25_59
| ~ spl25_12
| ~ spl25_26 ),
inference(avatar_split_clause,[],[f257,f247,f171,f469]) ).
fof(f469,plain,
( spl25_59
<=> ! [X0,X1] : sK13(X0) = sK17(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_59])]) ).
fof(f171,plain,
( spl25_12
<=> ! [X0,X1] : r2(X1,sK17(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_12])]) ).
fof(f257,plain,
( ! [X0,X1] : sK13(X0) = sK17(X1,X0)
| ~ spl25_12
| ~ spl25_26 ),
inference(resolution,[],[f248,f172]) ).
fof(f172,plain,
( ! [X0,X1] : r2(X1,sK17(X0,X1))
| ~ spl25_12 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f467,plain,
( spl25_58
| ~ spl25_15
| ~ spl25_27 ),
inference(avatar_split_clause,[],[f265,f251,f183,f465]) ).
fof(f465,plain,
( spl25_58
<=> ! [X0,X1] : ~ r1(sK20(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_58])]) ).
fof(f265,plain,
( ! [X0,X1] : ~ r1(sK20(X0,X1))
| ~ spl25_15
| ~ spl25_27 ),
inference(resolution,[],[f252,f184]) ).
fof(f462,plain,
( spl25_57
| ~ spl25_13
| ~ spl25_15 ),
inference(avatar_split_clause,[],[f202,f183,f175,f460]) ).
fof(f460,plain,
( spl25_57
<=> ! [X0,X1] : ~ r1(sK21(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_57])]) ).
fof(f202,plain,
( ! [X0,X1] : ~ r1(sK21(X0,X1))
| ~ spl25_13
| ~ spl25_15 ),
inference(resolution,[],[f184,f176]) ).
fof(f457,plain,
( spl25_56
| ~ spl25_12
| ~ spl25_15 ),
inference(avatar_split_clause,[],[f201,f183,f171,f455]) ).
fof(f455,plain,
( spl25_56
<=> ! [X0,X1] : ~ r1(sK17(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_56])]) ).
fof(f201,plain,
( ! [X0,X1] : ~ r1(sK17(X0,X1))
| ~ spl25_12
| ~ spl25_15 ),
inference(resolution,[],[f184,f172]) ).
fof(f451,plain,
( spl25_55
| ~ spl25_11
| ~ spl25_15 ),
inference(avatar_split_clause,[],[f200,f183,f167,f449]) ).
fof(f449,plain,
( spl25_55
<=> ! [X0] : ~ r1(sK13(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_55])]) ).
fof(f200,plain,
( ! [X0] : ~ r1(sK13(X0))
| ~ spl25_11
| ~ spl25_15 ),
inference(resolution,[],[f184,f168]) ).
fof(f441,plain,
( spl25_54
| ~ spl25_4
| ~ spl25_52
| ~ spl25_53 ),
inference(avatar_split_clause,[],[f432,f429,f423,f136,f439]) ).
fof(f439,plain,
( spl25_54
<=> ! [X0] :
( sK1 = sK7(X0)
| sK6(X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_54])]) ).
fof(f429,plain,
( spl25_53
<=> ! [X0] :
( sK2 = sK7(X0)
| sK6(X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_53])]) ).
fof(f432,plain,
( ! [X0] :
( sK1 = sK7(X0)
| sK6(X0) = X0 )
| ~ spl25_4
| ~ spl25_52
| ~ spl25_53 ),
inference(forward_demodulation,[],[f430,f427]) ).
fof(f430,plain,
( ! [X0] :
( sK2 = sK7(X0)
| sK6(X0) = X0 )
| ~ spl25_53 ),
inference(avatar_component_clause,[],[f429]) ).
fof(f431,plain,
( spl25_53
| ~ spl25_2
| ~ spl25_14
| ~ spl25_24 ),
inference(avatar_split_clause,[],[f255,f238,f179,f126,f429]) ).
fof(f179,plain,
( spl25_14
<=> ! [X1] :
( sK24 = X1
| ~ r1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_14])]) ).
fof(f255,plain,
( ! [X0] :
( sK2 = sK7(X0)
| sK6(X0) = X0 )
| ~ spl25_2
| ~ spl25_14
| ~ spl25_24 ),
inference(forward_demodulation,[],[f254,f190]) ).
fof(f190,plain,
( sK2 = sK24
| ~ spl25_2
| ~ spl25_14 ),
inference(resolution,[],[f180,f128]) ).
fof(f180,plain,
( ! [X1] :
( ~ r1(X1)
| sK24 = X1 )
| ~ spl25_14 ),
inference(avatar_component_clause,[],[f179]) ).
fof(f254,plain,
( ! [X0] :
( sK6(X0) = X0
| sK7(X0) = sK24 )
| ~ spl25_14
| ~ spl25_24 ),
inference(resolution,[],[f239,f180]) ).
fof(f425,plain,
( spl25_52
| ~ spl25_1
| ~ spl25_2
| ~ spl25_3
| ~ spl25_4
| ~ spl25_5
| ~ spl25_14
| ~ spl25_26
| ~ spl25_38 ),
inference(avatar_split_clause,[],[f339,f313,f247,f179,f141,f136,f131,f126,f121,f423]) ).
fof(f121,plain,
( spl25_1
<=> r1(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_1])]) ).
fof(f131,plain,
( spl25_3
<=> r2(sK4,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_3])]) ).
fof(f141,plain,
( spl25_5
<=> r2(sK1,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_5])]) ).
fof(f339,plain,
( ! [X0] :
( ~ r2(X0,sK1)
| sK1 = X0 )
| ~ spl25_1
| ~ spl25_2
| ~ spl25_3
| ~ spl25_4
| ~ spl25_5
| ~ spl25_14
| ~ spl25_26
| ~ spl25_38 ),
inference(forward_demodulation,[],[f331,f263]) ).
fof(f263,plain,
( sK1 = sK3
| ~ spl25_1
| ~ spl25_2
| ~ spl25_3
| ~ spl25_4
| ~ spl25_14
| ~ spl25_26 ),
inference(forward_demodulation,[],[f262,f260]) ).
fof(f260,plain,
( sK1 = sK13(sK2)
| ~ spl25_4
| ~ spl25_26 ),
inference(resolution,[],[f248,f138]) ).
fof(f262,plain,
( sK3 = sK13(sK2)
| ~ spl25_1
| ~ spl25_2
| ~ spl25_3
| ~ spl25_14
| ~ spl25_26 ),
inference(forward_demodulation,[],[f261,f196]) ).
fof(f196,plain,
( sK2 = sK4
| ~ spl25_1
| ~ spl25_2
| ~ spl25_14 ),
inference(forward_demodulation,[],[f191,f190]) ).
fof(f191,plain,
( sK4 = sK24
| ~ spl25_1
| ~ spl25_14 ),
inference(resolution,[],[f180,f123]) ).
fof(f123,plain,
( r1(sK4)
| ~ spl25_1 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f261,plain,
( sK3 = sK13(sK4)
| ~ spl25_3
| ~ spl25_26 ),
inference(resolution,[],[f248,f133]) ).
fof(f133,plain,
( r2(sK4,sK3)
| ~ spl25_3 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f331,plain,
( ! [X0] :
( sK1 = X0
| ~ r2(X0,sK3) )
| ~ spl25_5
| ~ spl25_38 ),
inference(resolution,[],[f314,f143]) ).
fof(f143,plain,
( r2(sK1,sK3)
| ~ spl25_5 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f421,plain,
( spl25_51
| ~ spl25_4
| ~ spl25_38 ),
inference(avatar_split_clause,[],[f332,f313,f136,f419]) ).
fof(f419,plain,
( spl25_51
<=> ! [X0] :
( sK2 = X0
| ~ r2(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_51])]) ).
fof(f332,plain,
( ! [X0] :
( sK2 = X0
| ~ r2(X0,sK1) )
| ~ spl25_4
| ~ spl25_38 ),
inference(resolution,[],[f314,f138]) ).
fof(f415,plain,
( spl25_50
| ~ spl25_2
| ~ spl25_9
| ~ spl25_14
| ~ spl25_16
| ~ spl25_37 ),
inference(avatar_split_clause,[],[f327,f309,f187,f179,f159,f126,f413]) ).
fof(f413,plain,
( spl25_50
<=> ! [X0] : sK23(X0,sK2) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl25_50])]) ).
fof(f159,plain,
( spl25_9
<=> ! [X0] : r1(sK12(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_9])]) ).
fof(f187,plain,
( spl25_16
<=> ! [X0] : r3(X0,sK12(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_16])]) ).
fof(f327,plain,
( ! [X0] : sK23(X0,sK2) = X0
| ~ spl25_2
| ~ spl25_9
| ~ spl25_14
| ~ spl25_16
| ~ spl25_37 ),
inference(forward_demodulation,[],[f322,f199]) ).
fof(f199,plain,
( ! [X0] : sK2 = sK12(X0)
| ~ spl25_2
| ~ spl25_9
| ~ spl25_14 ),
inference(forward_demodulation,[],[f194,f190]) ).
fof(f194,plain,
( ! [X0] : sK12(X0) = sK24
| ~ spl25_9
| ~ spl25_14 ),
inference(resolution,[],[f180,f160]) ).
fof(f160,plain,
( ! [X0] : r1(sK12(X0))
| ~ spl25_9 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f322,plain,
( ! [X0] : sK23(X0,sK12(X0)) = X0
| ~ spl25_16
| ~ spl25_37 ),
inference(resolution,[],[f310,f188]) ).
fof(f188,plain,
( ! [X0] : r3(X0,sK12(X0),X0)
| ~ spl25_16 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f411,plain,
( spl25_49
| ~ spl25_21
| ~ spl25_36 ),
inference(avatar_split_clause,[],[f318,f305,f226,f409]) ).
fof(f409,plain,
( spl25_49
<=> ! [X0] : sK2 = sK22(X0,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_49])]) ).
fof(f226,plain,
( spl25_21
<=> ! [X0] : r4(X0,sK2,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_21])]) ).
fof(f318,plain,
( ! [X0] : sK2 = sK22(X0,sK2)
| ~ spl25_21
| ~ spl25_36 ),
inference(resolution,[],[f306,f227]) ).
fof(f227,plain,
( ! [X0] : r4(X0,sK2,sK2)
| ~ spl25_21 ),
inference(avatar_component_clause,[],[f226]) ).
fof(f404,plain,
( spl25_48
| ~ spl25_5
| ~ spl25_41 ),
inference(avatar_split_clause,[],[f362,f353,f141,f401]) ).
fof(f401,plain,
( spl25_48
<=> r2(sK1,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_48])]) ).
fof(f353,plain,
( spl25_41
<=> sK1 = sK3 ),
introduced(avatar_definition,[new_symbols(naming,[spl25_41])]) ).
fof(f362,plain,
( r2(sK1,sK1)
| ~ spl25_5
| ~ spl25_41 ),
inference(superposition,[],[f143,f355]) ).
fof(f355,plain,
( sK1 = sK3
| ~ spl25_41 ),
inference(avatar_component_clause,[],[f353]) ).
fof(f396,plain,
( spl25_47
| ~ spl25_41
| ~ spl25_45 ),
inference(avatar_split_clause,[],[f382,f378,f353,f393]) ).
fof(f393,plain,
( spl25_47
<=> sK1 = sK13(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_47])]) ).
fof(f378,plain,
( spl25_45
<=> sK3 = sK13(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_45])]) ).
fof(f382,plain,
( sK1 = sK13(sK1)
| ~ spl25_41
| ~ spl25_45 ),
inference(forward_demodulation,[],[f380,f355]) ).
fof(f380,plain,
( sK3 = sK13(sK1)
| ~ spl25_45 ),
inference(avatar_component_clause,[],[f378]) ).
fof(f387,plain,
( spl25_46
| ~ spl25_4
| ~ spl25_26 ),
inference(avatar_split_clause,[],[f260,f247,f136,f384]) ).
fof(f384,plain,
( spl25_46
<=> sK1 = sK13(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_46])]) ).
fof(f381,plain,
( spl25_45
| ~ spl25_5
| ~ spl25_26 ),
inference(avatar_split_clause,[],[f259,f247,f141,f378]) ).
fof(f259,plain,
( sK3 = sK13(sK1)
| ~ spl25_5
| ~ spl25_26 ),
inference(resolution,[],[f248,f143]) ).
fof(f376,plain,
( spl25_44
| ~ spl25_2
| ~ spl25_9
| ~ spl25_14 ),
inference(avatar_split_clause,[],[f199,f179,f159,f126,f374]) ).
fof(f374,plain,
( spl25_44
<=> ! [X0] : sK2 = sK12(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_44])]) ).
fof(f372,plain,
( spl25_43
| ~ spl25_2
| ~ spl25_7
| ~ spl25_14 ),
inference(avatar_split_clause,[],[f198,f179,f151,f126,f370]) ).
fof(f370,plain,
( spl25_43
<=> ! [X0] : sK2 = sK10(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_43])]) ).
fof(f151,plain,
( spl25_7
<=> ! [X0] : r1(sK10(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_7])]) ).
fof(f198,plain,
( ! [X0] : sK2 = sK10(X0)
| ~ spl25_2
| ~ spl25_7
| ~ spl25_14 ),
inference(forward_demodulation,[],[f193,f190]) ).
fof(f193,plain,
( ! [X0] : sK10(X0) = sK24
| ~ spl25_7
| ~ spl25_14 ),
inference(resolution,[],[f180,f152]) ).
fof(f152,plain,
( ! [X0] : r1(sK10(X0))
| ~ spl25_7 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f368,plain,
( spl25_42
| ~ spl25_2
| ~ spl25_8
| ~ spl25_14 ),
inference(avatar_split_clause,[],[f197,f179,f155,f126,f366]) ).
fof(f366,plain,
( spl25_42
<=> ! [X0] : sK2 = sK9(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_42])]) ).
fof(f155,plain,
( spl25_8
<=> ! [X0] : r1(sK9(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_8])]) ).
fof(f197,plain,
( ! [X0] : sK2 = sK9(X0)
| ~ spl25_2
| ~ spl25_8
| ~ spl25_14 ),
inference(forward_demodulation,[],[f192,f190]) ).
fof(f192,plain,
( ! [X0] : sK9(X0) = sK24
| ~ spl25_8
| ~ spl25_14 ),
inference(resolution,[],[f180,f156]) ).
fof(f156,plain,
( ! [X0] : r1(sK9(X0))
| ~ spl25_8 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f356,plain,
( spl25_41
| ~ spl25_1
| ~ spl25_2
| ~ spl25_3
| ~ spl25_4
| ~ spl25_14
| ~ spl25_26 ),
inference(avatar_split_clause,[],[f263,f247,f179,f136,f131,f126,f121,f353]) ).
fof(f351,plain,
( spl25_40
| ~ spl25_1
| ~ spl25_2
| ~ spl25_14 ),
inference(avatar_split_clause,[],[f196,f179,f126,f121,f348]) ).
fof(f348,plain,
( spl25_40
<=> sK2 = sK4 ),
introduced(avatar_definition,[new_symbols(naming,[spl25_40])]) ).
fof(f346,plain,
( spl25_39
| ~ spl25_2
| ~ spl25_14 ),
inference(avatar_split_clause,[],[f190,f179,f126,f343]) ).
fof(f343,plain,
( spl25_39
<=> sK2 = sK24 ),
introduced(avatar_definition,[new_symbols(naming,[spl25_39])]) ).
fof(f315,plain,
spl25_38,
inference(avatar_split_clause,[],[f112,f313]) ).
fof(f112,plain,
! [X3,X0,X1] :
( X0 = X1
| ~ r2(X1,X3)
| ~ r2(X0,X3) ),
inference(equality_resolution,[],[f82]) ).
fof(f82,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| ~ r2(X1,X2)
| X2 != X3
| ~ r2(X0,X3) ),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( X0 = X1
| ! [X2] :
( ~ r2(X1,X2)
| ! [X3] :
( X2 != X3
| ~ r2(X0,X3) ) ) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X25,X26] :
( X25 = X26
| ! [X27] :
( ~ r2(X26,X27)
| ! [X28] :
( X27 != X28
| ~ r2(X25,X28) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3a) ).
fof(f311,plain,
spl25_37,
inference(avatar_split_clause,[],[f99,f309]) ).
fof(f99,plain,
! [X3,X0,X1] :
( sK23(X0,X1) = X3
| ~ r3(X0,X1,X3) ),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0,X1,X3] :
( ( sK23(X0,X1) = X3
& r3(X0,X1,X3) )
| ( sK23(X0,X1) != X3
& ~ r3(X0,X1,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f24,f56]) ).
fof(f56,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( X2 = X3
& r3(X0,X1,X3) )
| ( X2 != X3
& ~ r3(X0,X1,X3) ) )
=> ! [X3] :
( ( sK23(X0,X1) = X3
& r3(X0,X1,X3) )
| ( sK23(X0,X1) != X3
& ~ r3(X0,X1,X3) ) ) ),
introduced(choice_axiom,[]) ).
fof(f24,plain,
! [X0,X1] :
? [X2] :
! [X3] :
( ( X2 = X3
& r3(X0,X1,X3) )
| ( X2 != X3
& ~ r3(X0,X1,X3) ) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X5,X6] :
? [X7] :
! [X8] :
( ( X7 = X8
& r3(X5,X6,X8) )
| ( X7 != X8
& ~ r3(X5,X6,X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
fof(f307,plain,
spl25_36,
inference(avatar_split_clause,[],[f95,f305]) ).
fof(f95,plain,
! [X3,X0,X1] :
( sK22(X0,X1) = X3
| ~ r4(X0,X1,X3) ),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0,X1,X3] :
( ( sK22(X0,X1) = X3
& r4(X0,X1,X3) )
| ( sK22(X0,X1) != X3
& ~ r4(X0,X1,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f23,f54]) ).
fof(f54,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( X2 = X3
& r4(X0,X1,X3) )
| ( X2 != X3
& ~ r4(X0,X1,X3) ) )
=> ! [X3] :
( ( sK22(X0,X1) = X3
& r4(X0,X1,X3) )
| ( sK22(X0,X1) != X3
& ~ r4(X0,X1,X3) ) ) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
! [X0,X1] :
? [X2] :
! [X3] :
( ( X2 = X3
& r4(X0,X1,X3) )
| ( X2 != X3
& ~ r4(X0,X1,X3) ) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X9,X10] :
? [X11] :
! [X12] :
( ( X11 = X12
& r4(X9,X10,X12) )
| ( X11 != X12
& ~ r4(X9,X10,X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
fof(f303,plain,
spl25_35,
inference(avatar_split_clause,[],[f67,f301]) ).
fof(f67,plain,
! [X0] :
( r2(sK5(X0),sK6(X0))
| sK7(X0) = X0 ),
inference(cnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0] :
( ( sK6(X0) = X0
& r2(sK5(X0),sK6(X0)) )
| ( sK7(X0) = X0
& r1(sK7(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f15,f33,f32]) ).
fof(f32,plain,
! [X0] :
( ? [X1,X2] :
( X0 = X2
& r2(X1,X2) )
=> ( sK6(X0) = X0
& r2(sK5(X0),sK6(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f33,plain,
! [X0] :
( ? [X3] :
( X0 = X3
& r1(X3) )
=> ( sK7(X0) = X0
& r1(sK7(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f15,plain,
! [X0] :
( ? [X1,X2] :
( X0 = X2
& r2(X1,X2) )
| ? [X3] :
( X0 = X3
& r1(X3) ) ),
inference(rectify,[],[f10]) ).
fof(f10,axiom,
! [X36] :
( ? [X38,X39] :
( X36 = X39
& r2(X38,X39) )
| ? [X37] :
( X36 = X37
& r1(X37) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6a) ).
fof(f295,plain,
spl25_34,
inference(avatar_split_clause,[],[f107,f293]) ).
fof(f293,plain,
( spl25_34
<=> ! [X0,X1] : r3(sK15(X0,X1),X0,sK16(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_34])]) ).
fof(f107,plain,
! [X0,X1] : r3(sK15(X0,X1),X0,sK16(X0,X1)),
inference(definition_unfolding,[],[f86,f85]) ).
fof(f85,plain,
! [X0,X1] : sK14(X0,X1) = sK16(X0,X1),
inference(cnf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0,X1] :
( r4(X0,X1,sK15(X0,X1))
& r3(sK15(X0,X1),X0,sK14(X0,X1))
& sK14(X0,X1) = sK16(X0,X1)
& r4(X0,sK17(X0,X1),sK16(X0,X1))
& r2(X1,sK17(X0,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15,sK16,sK17])],[f21,f47,f46,f45,f44]) ).
fof(f44,plain,
! [X0,X1] :
( ? [X2] :
( ? [X3] :
( r4(X0,X1,X3)
& r3(X3,X0,X2) )
& ? [X4] :
( X2 = X4
& ? [X5] :
( r4(X0,X5,X4)
& r2(X1,X5) ) ) )
=> ( ? [X3] :
( r4(X0,X1,X3)
& r3(X3,X0,sK14(X0,X1)) )
& ? [X4] :
( sK14(X0,X1) = X4
& ? [X5] :
( r4(X0,X5,X4)
& r2(X1,X5) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f45,plain,
! [X0,X1] :
( ? [X3] :
( r4(X0,X1,X3)
& r3(X3,X0,sK14(X0,X1)) )
=> ( r4(X0,X1,sK15(X0,X1))
& r3(sK15(X0,X1),X0,sK14(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f46,plain,
! [X0,X1] :
( ? [X4] :
( sK14(X0,X1) = X4
& ? [X5] :
( r4(X0,X5,X4)
& r2(X1,X5) ) )
=> ( sK14(X0,X1) = sK16(X0,X1)
& ? [X5] :
( r4(X0,X5,sK16(X0,X1))
& r2(X1,X5) ) ) ),
introduced(choice_axiom,[]) ).
fof(f47,plain,
! [X0,X1] :
( ? [X5] :
( r4(X0,X5,sK16(X0,X1))
& r2(X1,X5) )
=> ( r4(X0,sK17(X0,X1),sK16(X0,X1))
& r2(X1,sK17(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f21,plain,
! [X0,X1] :
? [X2] :
( ? [X3] :
( r4(X0,X1,X3)
& r3(X3,X0,X2) )
& ? [X4] :
( X2 = X4
& ? [X5] :
( r4(X0,X5,X4)
& r2(X1,X5) ) ) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X19,X20] :
? [X21] :
( ? [X24] :
( r4(X19,X20,X24)
& r3(X24,X19,X21) )
& ? [X22] :
( X21 = X22
& ? [X23] :
( r4(X19,X23,X22)
& r2(X20,X23) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2a) ).
fof(f86,plain,
! [X0,X1] : r3(sK15(X0,X1),X0,sK14(X0,X1)),
inference(cnf_transformation,[],[f48]) ).
fof(f291,plain,
( spl25_33
| ~ spl25_13
| ~ spl25_26
| ~ spl25_32 ),
inference(avatar_split_clause,[],[f287,f284,f247,f175,f289]) ).
fof(f284,plain,
( spl25_32
<=> ! [X0,X1] : r3(X0,sK21(X0,X1),sK20(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_32])]) ).
fof(f287,plain,
( ! [X0,X1] : r3(X0,sK13(X1),sK20(X0,X1))
| ~ spl25_13
| ~ spl25_26
| ~ spl25_32 ),
inference(forward_demodulation,[],[f285,f258]) ).
fof(f285,plain,
( ! [X0,X1] : r3(X0,sK21(X0,X1),sK20(X0,X1))
| ~ spl25_32 ),
inference(avatar_component_clause,[],[f284]) ).
fof(f286,plain,
spl25_32,
inference(avatar_split_clause,[],[f89,f284]) ).
fof(f89,plain,
! [X0,X1] : r3(X0,sK21(X0,X1),sK20(X0,X1)),
inference(cnf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0,X1] :
( r3(X0,X1,sK19(X0,X1))
& r2(sK19(X0,X1),sK18(X0,X1))
& sK18(X0,X1) = sK20(X0,X1)
& r3(X0,sK21(X0,X1),sK20(X0,X1))
& r2(X1,sK21(X0,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19,sK20,sK21])],[f22,f52,f51,f50,f49]) ).
fof(f49,plain,
! [X0,X1] :
( ? [X2] :
( ? [X3] :
( r3(X0,X1,X3)
& r2(X3,X2) )
& ? [X4] :
( X2 = X4
& ? [X5] :
( r3(X0,X5,X4)
& r2(X1,X5) ) ) )
=> ( ? [X3] :
( r3(X0,X1,X3)
& r2(X3,sK18(X0,X1)) )
& ? [X4] :
( sK18(X0,X1) = X4
& ? [X5] :
( r3(X0,X5,X4)
& r2(X1,X5) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f50,plain,
! [X0,X1] :
( ? [X3] :
( r3(X0,X1,X3)
& r2(X3,sK18(X0,X1)) )
=> ( r3(X0,X1,sK19(X0,X1))
& r2(sK19(X0,X1),sK18(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f51,plain,
! [X0,X1] :
( ? [X4] :
( sK18(X0,X1) = X4
& ? [X5] :
( r3(X0,X5,X4)
& r2(X1,X5) ) )
=> ( sK18(X0,X1) = sK20(X0,X1)
& ? [X5] :
( r3(X0,X5,sK20(X0,X1))
& r2(X1,X5) ) ) ),
introduced(choice_axiom,[]) ).
fof(f52,plain,
! [X0,X1] :
( ? [X5] :
( r3(X0,X5,sK20(X0,X1))
& r2(X1,X5) )
=> ( r3(X0,sK21(X0,X1),sK20(X0,X1))
& r2(X1,sK21(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f22,plain,
! [X0,X1] :
? [X2] :
( ? [X3] :
( r3(X0,X1,X3)
& r2(X3,X2) )
& ? [X4] :
( X2 = X4
& ? [X5] :
( r3(X0,X5,X4)
& r2(X1,X5) ) ) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X13,X14] :
? [X15] :
( ? [X18] :
( r3(X13,X14,X18)
& r2(X18,X15) )
& ? [X16] :
( X15 = X16
& ? [X17] :
( r3(X13,X17,X16)
& r2(X14,X17) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1a) ).
fof(f282,plain,
( spl25_31
| ~ spl25_12
| ~ spl25_26
| ~ spl25_30 ),
inference(avatar_split_clause,[],[f278,f275,f247,f171,f280]) ).
fof(f275,plain,
( spl25_30
<=> ! [X0,X1] : r4(X0,sK17(X0,X1),sK16(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_30])]) ).
fof(f278,plain,
( ! [X0,X1] : r4(X0,sK13(X1),sK16(X0,X1))
| ~ spl25_12
| ~ spl25_26
| ~ spl25_30 ),
inference(forward_demodulation,[],[f276,f257]) ).
fof(f276,plain,
( ! [X0,X1] : r4(X0,sK17(X0,X1),sK16(X0,X1))
| ~ spl25_30 ),
inference(avatar_component_clause,[],[f275]) ).
fof(f277,plain,
spl25_30,
inference(avatar_split_clause,[],[f84,f275]) ).
fof(f84,plain,
! [X0,X1] : r4(X0,sK17(X0,X1),sK16(X0,X1)),
inference(cnf_transformation,[],[f48]) ).
fof(f273,plain,
spl25_29,
inference(avatar_split_clause,[],[f69,f271]) ).
fof(f69,plain,
! [X0] :
( sK6(X0) = X0
| sK7(X0) = X0 ),
inference(cnf_transformation,[],[f34]) ).
fof(f269,plain,
spl25_28,
inference(avatar_split_clause,[],[f66,f267]) ).
fof(f66,plain,
! [X0] :
( r2(sK5(X0),sK6(X0))
| r1(sK7(X0)) ),
inference(cnf_transformation,[],[f34]) ).
fof(f253,plain,
spl25_27,
inference(avatar_split_clause,[],[f108,f251]) ).
fof(f108,plain,
! [X0,X1] : r2(sK19(X0,X1),sK20(X0,X1)),
inference(definition_unfolding,[],[f91,f90]) ).
fof(f90,plain,
! [X0,X1] : sK18(X0,X1) = sK20(X0,X1),
inference(cnf_transformation,[],[f53]) ).
fof(f91,plain,
! [X0,X1] : r2(sK19(X0,X1),sK18(X0,X1)),
inference(cnf_transformation,[],[f53]) ).
fof(f249,plain,
spl25_26,
inference(avatar_split_clause,[],[f79,f247]) ).
fof(f79,plain,
! [X2,X0] :
( sK13(X0) = X2
| ~ r2(X0,X2) ),
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0,X2] :
( ( sK13(X0) = X2
& r2(X0,X2) )
| ( sK13(X0) != X2
& ~ r2(X0,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f18,f42]) ).
fof(f42,plain,
! [X0] :
( ? [X1] :
! [X2] :
( ( X1 = X2
& r2(X0,X2) )
| ( X1 != X2
& ~ r2(X0,X2) ) )
=> ! [X2] :
( ( sK13(X0) = X2
& r2(X0,X2) )
| ( sK13(X0) != X2
& ~ r2(X0,X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
! [X0] :
? [X1] :
! [X2] :
( ( X1 = X2
& r2(X0,X2) )
| ( X1 != X2
& ~ r2(X0,X2) ) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X2] :
? [X3] :
! [X4] :
( ( X3 = X4
& r2(X2,X4) )
| ( X3 != X4
& ~ r2(X2,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
fof(f245,plain,
( ~ spl25_25
| ~ spl25_4
| ~ spl25_15 ),
inference(avatar_split_clause,[],[f204,f183,f136,f242]) ).
fof(f204,plain,
( ~ r1(sK1)
| ~ spl25_4
| ~ spl25_15 ),
inference(resolution,[],[f184,f138]) ).
fof(f240,plain,
spl25_24,
inference(avatar_split_clause,[],[f68,f238]) ).
fof(f68,plain,
! [X0] :
( sK6(X0) = X0
| r1(sK7(X0)) ),
inference(cnf_transformation,[],[f34]) ).
fof(f236,plain,
spl25_23,
inference(avatar_split_clause,[],[f116,f234]) ).
fof(f234,plain,
( spl25_23
<=> ! [X0,X1] : r3(X0,X1,sK23(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_23])]) ).
fof(f116,plain,
! [X0,X1] : r3(X0,X1,sK23(X0,X1)),
inference(equality_resolution,[],[f98]) ).
fof(f98,plain,
! [X3,X0,X1] :
( r3(X0,X1,X3)
| sK23(X0,X1) != X3 ),
inference(cnf_transformation,[],[f57]) ).
fof(f232,plain,
spl25_22,
inference(avatar_split_clause,[],[f114,f230]) ).
fof(f230,plain,
( spl25_22
<=> ! [X0,X1] : r4(X0,X1,sK22(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_22])]) ).
fof(f114,plain,
! [X0,X1] : r4(X0,X1,sK22(X0,X1)),
inference(equality_resolution,[],[f94]) ).
fof(f94,plain,
! [X3,X0,X1] :
( r4(X0,X1,X3)
| sK22(X0,X1) != X3 ),
inference(cnf_transformation,[],[f55]) ).
fof(f228,plain,
( spl25_21
| ~ spl25_2
| ~ spl25_7
| ~ spl25_8
| ~ spl25_14
| ~ spl25_20 ),
inference(avatar_split_clause,[],[f224,f220,f179,f155,f151,f126,f226]) ).
fof(f220,plain,
( spl25_20
<=> ! [X0] : r4(X0,sK10(X0),sK9(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_20])]) ).
fof(f224,plain,
( ! [X0] : r4(X0,sK2,sK2)
| ~ spl25_2
| ~ spl25_7
| ~ spl25_8
| ~ spl25_14
| ~ spl25_20 ),
inference(forward_demodulation,[],[f223,f198]) ).
fof(f223,plain,
( ! [X0] : r4(X0,sK10(X0),sK2)
| ~ spl25_2
| ~ spl25_8
| ~ spl25_14
| ~ spl25_20 ),
inference(forward_demodulation,[],[f221,f197]) ).
fof(f221,plain,
( ! [X0] : r4(X0,sK10(X0),sK9(X0))
| ~ spl25_20 ),
inference(avatar_component_clause,[],[f220]) ).
fof(f222,plain,
spl25_20,
inference(avatar_split_clause,[],[f106,f220]) ).
fof(f106,plain,
! [X0] : r4(X0,sK10(X0),sK9(X0)),
inference(definition_unfolding,[],[f71,f73]) ).
fof(f73,plain,
! [X0] : sK8(X0) = sK9(X0),
inference(cnf_transformation,[],[f38]) ).
fof(f38,plain,
! [X0] :
( sK8(X0) = sK9(X0)
& r1(sK9(X0))
& r4(X0,sK10(X0),sK8(X0))
& r1(sK10(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f16,f37,f36,f35]) ).
fof(f35,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( X1 = X2
& r1(X2) )
& ? [X3] :
( r4(X0,X3,X1)
& r1(X3) ) )
=> ( ? [X2] :
( sK8(X0) = X2
& r1(X2) )
& ? [X3] :
( r4(X0,X3,sK8(X0))
& r1(X3) ) ) ),
introduced(choice_axiom,[]) ).
fof(f36,plain,
! [X0] :
( ? [X2] :
( sK8(X0) = X2
& r1(X2) )
=> ( sK8(X0) = sK9(X0)
& r1(sK9(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f37,plain,
! [X0] :
( ? [X3] :
( r4(X0,X3,sK8(X0))
& r1(X3) )
=> ( r4(X0,sK10(X0),sK8(X0))
& r1(sK10(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f16,plain,
! [X0] :
? [X1] :
( ? [X2] :
( X1 = X2
& r1(X2) )
& ? [X3] :
( r4(X0,X3,X1)
& r1(X3) ) ),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X32] :
? [X33] :
( ? [X35] :
( X33 = X35
& r1(X35) )
& ? [X34] :
( r4(X32,X34,X33)
& r1(X34) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5a) ).
fof(f71,plain,
! [X0] : r4(X0,sK10(X0),sK8(X0)),
inference(cnf_transformation,[],[f38]) ).
fof(f218,plain,
( ~ spl25_19
| ~ spl25_5
| ~ spl25_15 ),
inference(avatar_split_clause,[],[f203,f183,f141,f215]) ).
fof(f215,plain,
( spl25_19
<=> r1(sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_19])]) ).
fof(f203,plain,
( ~ r1(sK3)
| ~ spl25_5
| ~ spl25_15 ),
inference(resolution,[],[f184,f143]) ).
fof(f213,plain,
spl25_18,
inference(avatar_split_clause,[],[f92,f211]) ).
fof(f92,plain,
! [X0,X1] : r3(X0,X1,sK19(X0,X1)),
inference(cnf_transformation,[],[f53]) ).
fof(f209,plain,
spl25_17,
inference(avatar_split_clause,[],[f87,f207]) ).
fof(f87,plain,
! [X0,X1] : r4(X0,X1,sK15(X0,X1)),
inference(cnf_transformation,[],[f48]) ).
fof(f189,plain,
spl25_16,
inference(avatar_split_clause,[],[f119,f187]) ).
fof(f119,plain,
! [X0] : r3(X0,sK12(X0),X0),
inference(forward_demodulation,[],[f75,f76]) ).
fof(f76,plain,
! [X0] : sK11(X0) = X0,
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0] :
( sK11(X0) = X0
& r3(X0,sK12(X0),sK11(X0))
& r1(sK12(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12])],[f17,f40,f39]) ).
fof(f39,plain,
! [X0] :
( ? [X1] :
( X0 = X1
& ? [X2] :
( r3(X0,X2,X1)
& r1(X2) ) )
=> ( sK11(X0) = X0
& ? [X2] :
( r3(X0,X2,sK11(X0))
& r1(X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f40,plain,
! [X0] :
( ? [X2] :
( r3(X0,X2,sK11(X0))
& r1(X2) )
=> ( r3(X0,sK12(X0),sK11(X0))
& r1(sK12(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f17,plain,
! [X0] :
? [X1] :
( X0 = X1
& ? [X2] :
( r3(X0,X2,X1)
& r1(X2) ) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X29] :
? [X30] :
( X29 = X30
& ? [X31] :
( r3(X29,X31,X30)
& r1(X31) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4a) ).
fof(f75,plain,
! [X0] : r3(X0,sK12(X0),sK11(X0)),
inference(cnf_transformation,[],[f41]) ).
fof(f185,plain,
spl25_15,
inference(avatar_split_clause,[],[f111,f183]) ).
fof(f111,plain,
! [X2,X0] :
( ~ r2(X0,X2)
| ~ r1(X2) ),
inference(equality_resolution,[],[f81]) ).
fof(f81,plain,
! [X2,X0,X1] :
( ~ r2(X0,X1)
| X1 != X2
| ~ r1(X2) ),
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
! [X0,X1] :
( ~ r2(X0,X1)
| ! [X2] :
( X1 != X2
| ~ r1(X2) ) ),
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X40,X41] :
( ~ r2(X40,X41)
| ! [X42] :
( X41 != X42
| ~ r1(X42) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7a) ).
fof(f181,plain,
spl25_14,
inference(avatar_split_clause,[],[f103,f179]) ).
fof(f103,plain,
! [X1] :
( sK24 = X1
| ~ r1(X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X1] :
( ( sK24 = X1
& r1(X1) )
| ( sK24 != X1
& ~ r1(X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f1,f58]) ).
fof(f58,plain,
( ? [X0] :
! [X1] :
( ( X0 = X1
& r1(X1) )
| ( X0 != X1
& ~ r1(X1) ) )
=> ! [X1] :
( ( sK24 = X1
& r1(X1) )
| ( sK24 != X1
& ~ r1(X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f1,axiom,
? [X0] :
! [X1] :
( ( X0 = X1
& r1(X1) )
| ( X0 != X1
& ~ r1(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
fof(f177,plain,
spl25_13,
inference(avatar_split_clause,[],[f88,f175]) ).
fof(f88,plain,
! [X0,X1] : r2(X1,sK21(X0,X1)),
inference(cnf_transformation,[],[f53]) ).
fof(f173,plain,
spl25_12,
inference(avatar_split_clause,[],[f83,f171]) ).
fof(f83,plain,
! [X0,X1] : r2(X1,sK17(X0,X1)),
inference(cnf_transformation,[],[f48]) ).
fof(f169,plain,
spl25_11,
inference(avatar_split_clause,[],[f110,f167]) ).
fof(f110,plain,
! [X0] : r2(X0,sK13(X0)),
inference(equality_resolution,[],[f78]) ).
fof(f78,plain,
! [X2,X0] :
( r2(X0,X2)
| sK13(X0) != X2 ),
inference(cnf_transformation,[],[f43]) ).
fof(f165,plain,
spl25_10,
inference(avatar_split_clause,[],[f76,f163]) ).
fof(f163,plain,
( spl25_10
<=> ! [X0] : sK11(X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl25_10])]) ).
fof(f161,plain,
spl25_9,
inference(avatar_split_clause,[],[f74,f159]) ).
fof(f74,plain,
! [X0] : r1(sK12(X0)),
inference(cnf_transformation,[],[f41]) ).
fof(f157,plain,
spl25_8,
inference(avatar_split_clause,[],[f72,f155]) ).
fof(f72,plain,
! [X0] : r1(sK9(X0)),
inference(cnf_transformation,[],[f38]) ).
fof(f153,plain,
spl25_7,
inference(avatar_split_clause,[],[f70,f151]) ).
fof(f70,plain,
! [X0] : r1(sK10(X0)),
inference(cnf_transformation,[],[f38]) ).
fof(f149,plain,
spl25_6,
inference(avatar_split_clause,[],[f118,f146]) ).
fof(f146,plain,
( spl25_6
<=> r1(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_6])]) ).
fof(f118,plain,
r1(sK24),
inference(equality_resolution,[],[f102]) ).
fof(f102,plain,
! [X1] :
( r1(X1)
| sK24 != X1 ),
inference(cnf_transformation,[],[f59]) ).
fof(f144,plain,
spl25_5,
inference(avatar_split_clause,[],[f105,f141]) ).
fof(f105,plain,
r2(sK1,sK3),
inference(definition_unfolding,[],[f65,f62]) ).
fof(f62,plain,
sK0 = sK3,
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
( r2(sK1,sK0)
& r2(sK2,sK1)
& r1(sK2)
& sK0 = sK3
& r2(sK4,sK3)
& r1(sK4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f25,f30,f29,f28,f27,f26]) ).
fof(f26,plain,
( ? [X0] :
( ? [X1] :
( r2(X1,X0)
& ? [X2] :
( r2(X2,X1)
& r1(X2) ) )
& ? [X3] :
( X0 = X3
& ? [X4] :
( r2(X4,X3)
& r1(X4) ) ) )
=> ( ? [X1] :
( r2(X1,sK0)
& ? [X2] :
( r2(X2,X1)
& r1(X2) ) )
& ? [X3] :
( sK0 = X3
& ? [X4] :
( r2(X4,X3)
& r1(X4) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
( ? [X1] :
( r2(X1,sK0)
& ? [X2] :
( r2(X2,X1)
& r1(X2) ) )
=> ( r2(sK1,sK0)
& ? [X2] :
( r2(X2,sK1)
& r1(X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f28,plain,
( ? [X2] :
( r2(X2,sK1)
& r1(X2) )
=> ( r2(sK2,sK1)
& r1(sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
( ? [X3] :
( sK0 = X3
& ? [X4] :
( r2(X4,X3)
& r1(X4) ) )
=> ( sK0 = sK3
& ? [X4] :
( r2(X4,sK3)
& r1(X4) ) ) ),
introduced(choice_axiom,[]) ).
fof(f30,plain,
( ? [X4] :
( r2(X4,sK3)
& r1(X4) )
=> ( r2(sK4,sK3)
& r1(sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f25,plain,
? [X0] :
( ? [X1] :
( r2(X1,X0)
& ? [X2] :
( r2(X2,X1)
& r1(X2) ) )
& ? [X3] :
( X0 = X3
& ? [X4] :
( r2(X4,X3)
& r1(X4) ) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,plain,
~ ! [X0] :
( ! [X1] :
( ~ r2(X1,X0)
| ! [X2] :
( ~ r2(X2,X1)
| ~ r1(X2) ) )
| ! [X3] :
( X0 != X3
| ! [X4] :
( ~ r2(X4,X3)
| ~ r1(X4) ) ) ),
inference(rectify,[],[f13]) ).
fof(f13,negated_conjecture,
~ ! [X38] :
( ! [X22] :
( ~ r2(X22,X38)
| ! [X16] :
( ~ r2(X16,X22)
| ~ r1(X16) ) )
| ! [X21] :
( X21 != X38
| ! [X15] :
( ~ r2(X15,X21)
| ~ r1(X15) ) ) ),
inference(negated_conjecture,[],[f12]) ).
fof(f12,conjecture,
! [X38] :
( ! [X22] :
( ~ r2(X22,X38)
| ! [X16] :
( ~ r2(X16,X22)
| ~ r1(X16) ) )
| ! [X21] :
( X21 != X38
| ! [X15] :
( ~ r2(X15,X21)
| ~ r1(X15) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oneuneqtwo) ).
fof(f65,plain,
r2(sK1,sK0),
inference(cnf_transformation,[],[f31]) ).
fof(f139,plain,
spl25_4,
inference(avatar_split_clause,[],[f64,f136]) ).
fof(f64,plain,
r2(sK2,sK1),
inference(cnf_transformation,[],[f31]) ).
fof(f134,plain,
spl25_3,
inference(avatar_split_clause,[],[f61,f131]) ).
fof(f61,plain,
r2(sK4,sK3),
inference(cnf_transformation,[],[f31]) ).
fof(f129,plain,
spl25_2,
inference(avatar_split_clause,[],[f63,f126]) ).
fof(f63,plain,
r1(sK2),
inference(cnf_transformation,[],[f31]) ).
fof(f124,plain,
spl25_1,
inference(avatar_split_clause,[],[f60,f121]) ).
fof(f60,plain,
r1(sK4),
inference(cnf_transformation,[],[f31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUN073+2 : TPTP v8.1.2. Released v7.3.0.
% 0.03/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.34 % Computer : n009.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Apr 30 02:22:41 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % (25194)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.35 % (25197)WARNING: value z3 for option sas not known
% 0.12/0.36 % (25196)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.36 % (25198)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.36 % (25199)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)
% 0.12/0.36 % (25201)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)
% 0.12/0.36 % (25200)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)
% 0.12/0.36 % (25197)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)
% 0.12/0.36 % (25195)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.36 TRYING [1]
% 0.12/0.36 TRYING [2]
% 0.12/0.36 TRYING [3]
% 0.12/0.36 TRYING [1]
% 0.12/0.36 TRYING [2]
% 0.12/0.36 % (25199)First to succeed.
% 0.12/0.36 TRYING [4]
% 0.17/0.36 TRYING [3]
% 0.17/0.37 TRYING [1]
% 0.17/0.37 % (25197)Also succeeded, but the first one will report.
% 0.17/0.37 TRYING [2]
% 0.17/0.37 % (25201)Also succeeded, but the first one will report.
% 0.17/0.37 % (25199)Refutation found. Thanks to Tanya!
% 0.17/0.37 % SZS status Theorem for theBenchmark
% 0.17/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.37 % (25199)------------------------------
% 0.17/0.37 % (25199)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.17/0.37 % (25199)Termination reason: Refutation
% 0.17/0.37
% 0.17/0.37 % (25199)Memory used [KB]: 1038
% 0.17/0.37 % (25199)Time elapsed: 0.013 s
% 0.17/0.37 % (25199)Instructions burned: 21 (million)
% 0.17/0.37 % (25199)------------------------------
% 0.17/0.37 % (25199)------------------------------
% 0.17/0.37 % (25194)Success in time 0.028 s
%------------------------------------------------------------------------------