TSTP Solution File: GEO053-3 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : GEO053-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n023.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 11:13:39 EDT 2024
% Result : Unsatisfiable 0.21s 0.52s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 244
% Syntax : Number of formulae : 582 ( 96 unt; 0 def)
% Number of atoms : 1821 ( 179 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 2224 ( 985 ~;1069 |; 0 &)
% ( 170 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 174 ( 172 usr; 171 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-6 aty)
% Number of variables : 1287 (1287 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2814,plain,
$false,
inference(avatar_sat_refutation,[],[f106,f111,f116,f121,f126,f131,f136,f141,f145,f149,f154,f158,f162,f166,f170,f174,f178,f184,f188,f192,f196,f210,f216,f221,f225,f229,f233,f237,f241,f245,f249,f290,f294,f308,f313,f317,f321,f340,f351,f355,f365,f375,f379,f383,f387,f391,f395,f417,f438,f442,f446,f465,f470,f474,f478,f518,f522,f526,f530,f534,f539,f580,f584,f588,f625,f635,f645,f662,f666,f670,f689,f700,f714,f735,f745,f768,f799,f803,f826,f840,f1000,f1005,f1009,f1014,f1018,f1022,f1044,f1048,f1052,f1086,f1090,f1094,f1098,f1102,f1106,f1110,f1161,f1278,f1292,f1296,f1320,f1324,f1328,f1332,f1364,f1372,f1381,f1396,f1400,f1427,f1431,f1435,f1439,f1443,f1473,f1477,f1481,f1515,f1559,f1563,f1567,f1650,f1656,f1684,f1688,f1692,f1798,f1810,f1814,f1826,f1834,f1839,f1843,f1899,f1903,f1932,f1936,f1940,f1944,f1948,f1952,f1956,f1978,f2127,f2131,f2135,f2139,f2143,f2275,f2279,f2283,f2321,f2325,f2329,f2333,f2337,f2341,f2345,f2349,f2353,f2357,f2361,f2366,f2370,f2652,f2701,f2705,f2808,f2812,f2813]) ).
fof(f2813,plain,
( spl0_1
| ~ spl0_108
| ~ spl0_110
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f2683,f2650,f1398,f1378,f103]) ).
fof(f103,plain,
( spl0_1
<=> v = w ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f1378,plain,
( spl0_108
<=> v = extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f1398,plain,
( spl0_110
<=> ! [X0,X1] : extension(extension(X0,X1,lower_dimension_point_1,lower_dimension_point_2),X1,X1,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f2650,plain,
( spl0_166
<=> ! [X0,X1] : extension(extension(X0,X1,lower_dimension_point_1,lower_dimension_point_2),X1,u,v) = extension(extension(X0,X1,lower_dimension_point_1,lower_dimension_point_2),X1,u,w) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f2683,plain,
( v = w
| ~ spl0_108
| ~ spl0_110
| ~ spl0_166 ),
inference(forward_demodulation,[],[f2656,f1380]) ).
fof(f1380,plain,
( v = extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v)
| ~ spl0_108 ),
inference(avatar_component_clause,[],[f1378]) ).
fof(f2656,plain,
( w = extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v)
| ~ spl0_110
| ~ spl0_166 ),
inference(superposition,[],[f2651,f1399]) ).
fof(f1399,plain,
( ! [X0,X1] : extension(extension(X0,X1,lower_dimension_point_1,lower_dimension_point_2),X1,X1,X0) = X0
| ~ spl0_110 ),
inference(avatar_component_clause,[],[f1398]) ).
fof(f2651,plain,
( ! [X0,X1] : extension(extension(X0,X1,lower_dimension_point_1,lower_dimension_point_2),X1,u,v) = extension(extension(X0,X1,lower_dimension_point_1,lower_dimension_point_2),X1,u,w)
| ~ spl0_166 ),
inference(avatar_component_clause,[],[f2650]) ).
fof(f2812,plain,
( spl0_170
| ~ spl0_20
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f589,f578,f190,f2810]) ).
fof(f2810,plain,
( spl0_170
<=> ! [X4,X0,X3,X2,X1] :
( ~ between(X0,X1,X2)
| ~ between(X3,X1,X4)
| X1 = X3
| between(euclid1(X3,X0,X1,X2,X4),X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f190,plain,
( spl0_20
<=> ! [X5,X3,X10] :
( ~ between(X10,X3,X5)
| between(X5,X3,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f578,plain,
( spl0_62
<=> ! [X10,X0,X5,X3,X1] :
( X5 = X10
| ~ between(X3,X5,X0)
| ~ between(X10,X5,X1)
| between(X10,X3,euclid1(X10,X3,X5,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f589,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ between(X0,X1,X2)
| ~ between(X3,X1,X4)
| X1 = X3
| between(euclid1(X3,X0,X1,X2,X4),X0,X3) )
| ~ spl0_20
| ~ spl0_62 ),
inference(resolution,[],[f579,f191]) ).
fof(f191,plain,
( ! [X3,X10,X5] :
( ~ between(X10,X3,X5)
| between(X5,X3,X10) )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f190]) ).
fof(f579,plain,
( ! [X3,X10,X0,X1,X5] :
( between(X10,X3,euclid1(X10,X3,X5,X0,X1))
| ~ between(X3,X5,X0)
| ~ between(X10,X5,X1)
| X5 = X10 )
| ~ spl0_62 ),
inference(avatar_component_clause,[],[f578]) ).
fof(f2808,plain,
( spl0_169
| ~ spl0_19
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f460,f444,f186,f2806]) ).
fof(f2806,plain,
( spl0_169
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ between(X0,X1,extension(X0,X2,X3,X4))
| ~ between(X2,X5,X1)
| between(X0,X5,extension(X0,X2,X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f186,plain,
( spl0_19
<=> ! [X3,X0,X5,X1] : between(X0,X1,extension(X0,X1,X5,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f444,plain,
( spl0_51
<=> ! [X5,X10,X0,X3,X1] :
( ~ between(X10,X3,X1)
| ~ between(X10,X0,X1)
| ~ between(X3,X5,X0)
| between(X10,X5,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f460,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ between(X0,X1,extension(X0,X2,X3,X4))
| ~ between(X2,X5,X1)
| between(X0,X5,extension(X0,X2,X3,X4)) )
| ~ spl0_19
| ~ spl0_51 ),
inference(resolution,[],[f445,f187]) ).
fof(f187,plain,
( ! [X3,X0,X1,X5] : between(X0,X1,extension(X0,X1,X5,X3))
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f186]) ).
fof(f445,plain,
( ! [X3,X10,X0,X1,X5] :
( ~ between(X10,X3,X1)
| ~ between(X10,X0,X1)
| ~ between(X3,X5,X0)
| between(X10,X5,X1) )
| ~ spl0_51 ),
inference(avatar_component_clause,[],[f444]) ).
fof(f2705,plain,
( spl0_168
| ~ spl0_12
| ~ spl0_72 ),
inference(avatar_split_clause,[],[f702,f698,f156,f2703]) ).
fof(f2703,plain,
( spl0_168
<=> ! [X0,X3,X2,X1] : extension(extension(X0,X1,lower_dimension_point_1,lower_dimension_point_2),X1,X2,X3) = extension(extension(X0,X1,lower_dimension_point_1,lower_dimension_point_2),X1,X3,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f156,plain,
( spl0_12
<=> ! [X0,X1] : equidistant(X0,X1,X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f698,plain,
( spl0_72
<=> ! [X3,X10,X0,X5,X2,X1] :
( ~ equidistant(X5,X0,X1,X2)
| extension(extension(X3,X10,lower_dimension_point_1,lower_dimension_point_2),X10,X5,X0) = extension(extension(X3,X10,lower_dimension_point_1,lower_dimension_point_2),X10,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f702,plain,
( ! [X2,X3,X0,X1] : extension(extension(X0,X1,lower_dimension_point_1,lower_dimension_point_2),X1,X2,X3) = extension(extension(X0,X1,lower_dimension_point_1,lower_dimension_point_2),X1,X3,X2)
| ~ spl0_12
| ~ spl0_72 ),
inference(resolution,[],[f699,f157]) ).
fof(f157,plain,
( ! [X0,X1] : equidistant(X0,X1,X1,X0)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f156]) ).
fof(f699,plain,
( ! [X2,X3,X10,X0,X1,X5] :
( ~ equidistant(X5,X0,X1,X2)
| extension(extension(X3,X10,lower_dimension_point_1,lower_dimension_point_2),X10,X5,X0) = extension(extension(X3,X10,lower_dimension_point_1,lower_dimension_point_2),X10,X1,X2) )
| ~ spl0_72 ),
inference(avatar_component_clause,[],[f698]) ).
fof(f2701,plain,
( spl0_167
| ~ spl0_19
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f421,f385,f186,f2699]) ).
fof(f2699,plain,
( spl0_167
<=> ! [X4,X0,X3,X2,X1] :
( extension(X1,X0,X2,X3) = X0
| ~ between(X0,extension(X1,X0,X2,X3),X4)
| between(X1,X0,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f385,plain,
( spl0_45
<=> ! [X10,X0,X5,X3] :
( X3 = X5
| ~ between(X10,X3,X5)
| ~ between(X3,X5,X0)
| between(X10,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f421,plain,
( ! [X2,X3,X0,X1,X4] :
( extension(X1,X0,X2,X3) = X0
| ~ between(X0,extension(X1,X0,X2,X3),X4)
| between(X1,X0,X4) )
| ~ spl0_19
| ~ spl0_45 ),
inference(resolution,[],[f386,f187]) ).
fof(f386,plain,
( ! [X3,X10,X0,X5] :
( ~ between(X10,X3,X5)
| X3 = X5
| ~ between(X3,X5,X0)
| between(X10,X3,X0) )
| ~ spl0_45 ),
inference(avatar_component_clause,[],[f385]) ).
fof(f2652,plain,
( spl0_166
| ~ spl0_11
| ~ spl0_72 ),
inference(avatar_split_clause,[],[f701,f698,f151,f2650]) ).
fof(f151,plain,
( spl0_11
<=> equidistant(u,v,u,w) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f701,plain,
( ! [X0,X1] : extension(extension(X0,X1,lower_dimension_point_1,lower_dimension_point_2),X1,u,v) = extension(extension(X0,X1,lower_dimension_point_1,lower_dimension_point_2),X1,u,w)
| ~ spl0_11
| ~ spl0_72 ),
inference(resolution,[],[f699,f153]) ).
fof(f153,plain,
( equidistant(u,v,u,w)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f2370,plain,
( spl0_165
| ~ spl0_14
| ~ spl0_70 ),
inference(avatar_split_clause,[],[f694,f668,f164,f2368]) ).
fof(f2368,plain,
( spl0_165
<=> ! [X0,X3,X2,X1] :
( between(X0,X1,X0)
| ~ between(X2,X3,X2)
| ~ equidistant(X3,X2,X1,X0)
| ~ equidistant(X2,X3,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f164,plain,
( spl0_14
<=> ! [X3,X10] : equidistant(X10,X10,X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f668,plain,
( spl0_70
<=> ! [X11,X9,X10,X12,X5,X3] :
( ~ between(X10,X3,X5)
| between(X11,X9,X12)
| ~ equidistant(X10,X5,X11,X12)
| ~ equidistant(X3,X5,X9,X12)
| ~ equidistant(X10,X3,X11,X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f694,plain,
( ! [X2,X3,X0,X1] :
( between(X0,X1,X0)
| ~ between(X2,X3,X2)
| ~ equidistant(X3,X2,X1,X0)
| ~ equidistant(X2,X3,X0,X1) )
| ~ spl0_14
| ~ spl0_70 ),
inference(resolution,[],[f669,f165]) ).
fof(f165,plain,
( ! [X3,X10] : equidistant(X10,X10,X3,X3)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f669,plain,
( ! [X3,X10,X11,X9,X5,X12] :
( ~ equidistant(X10,X5,X11,X12)
| between(X11,X9,X12)
| ~ between(X10,X3,X5)
| ~ equidistant(X3,X5,X9,X12)
| ~ equidistant(X10,X3,X11,X9) )
| ~ spl0_70 ),
inference(avatar_component_clause,[],[f668]) ).
fof(f2366,plain,
( spl0_164
| ~ spl0_88
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f1385,f1378,f1042,f2363]) ).
fof(f2363,plain,
( spl0_164
<=> between(v,u,extension(w,u,lower_dimension_point_1,lower_dimension_point_2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f1042,plain,
( spl0_88
<=> ! [X0,X3,X2,X1] : between(extension(X0,X1,X2,X3),X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f1385,plain,
( between(v,u,extension(w,u,lower_dimension_point_1,lower_dimension_point_2))
| ~ spl0_88
| ~ spl0_108 ),
inference(superposition,[],[f1043,f1380]) ).
fof(f1043,plain,
( ! [X2,X3,X0,X1] : between(extension(X0,X1,X2,X3),X1,X0)
| ~ spl0_88 ),
inference(avatar_component_clause,[],[f1042]) ).
fof(f2361,plain,
( spl0_163
| ~ spl0_13
| ~ spl0_70 ),
inference(avatar_split_clause,[],[f692,f668,f160,f2359]) ).
fof(f2359,plain,
( spl0_163
<=> ! [X0,X3,X2,X1] :
( between(X0,X1,X2)
| ~ between(X0,X3,X2)
| ~ equidistant(X3,X2,X1,X2)
| ~ equidistant(X0,X3,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f160,plain,
( spl0_13
<=> ! [X3,X10] : equidistant(X10,X3,X10,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f692,plain,
( ! [X2,X3,X0,X1] :
( between(X0,X1,X2)
| ~ between(X0,X3,X2)
| ~ equidistant(X3,X2,X1,X2)
| ~ equidistant(X0,X3,X0,X1) )
| ~ spl0_13
| ~ spl0_70 ),
inference(resolution,[],[f669,f161]) ).
fof(f161,plain,
( ! [X3,X10] : equidistant(X10,X3,X10,X3)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f160]) ).
fof(f2357,plain,
( spl0_162
| ~ spl0_12
| ~ spl0_70 ),
inference(avatar_split_clause,[],[f691,f668,f156,f2355]) ).
fof(f2355,plain,
( spl0_162
<=> ! [X0,X3,X2,X1] :
( between(X0,X1,X2)
| ~ between(X2,X3,X0)
| ~ equidistant(X3,X0,X1,X2)
| ~ equidistant(X2,X3,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f691,plain,
( ! [X2,X3,X0,X1] :
( between(X0,X1,X2)
| ~ between(X2,X3,X0)
| ~ equidistant(X3,X0,X1,X2)
| ~ equidistant(X2,X3,X0,X1) )
| ~ spl0_12
| ~ spl0_70 ),
inference(resolution,[],[f669,f157]) ).
fof(f2353,plain,
( spl0_161
| ~ spl0_13
| ~ spl0_69 ),
inference(avatar_split_clause,[],[f680,f664,f160,f2351]) ).
fof(f2351,plain,
( spl0_161
<=> ! [X0,X3,X2,X1] :
( ~ between(X0,X1,X2)
| ~ between(X0,X3,X2)
| ~ equidistant(X0,X3,X0,X1)
| equidistant(X3,X2,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f664,plain,
( spl0_69
<=> ! [X11,X9,X10,X12,X5,X3] :
( ~ between(X10,X3,X5)
| ~ between(X11,X9,X12)
| ~ equidistant(X10,X5,X11,X12)
| ~ equidistant(X10,X3,X11,X9)
| equidistant(X3,X5,X9,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f680,plain,
( ! [X2,X3,X0,X1] :
( ~ between(X0,X1,X2)
| ~ between(X0,X3,X2)
| ~ equidistant(X0,X3,X0,X1)
| equidistant(X3,X2,X1,X2) )
| ~ spl0_13
| ~ spl0_69 ),
inference(resolution,[],[f665,f161]) ).
fof(f665,plain,
( ! [X3,X10,X11,X9,X5,X12] :
( ~ equidistant(X10,X5,X11,X12)
| ~ between(X11,X9,X12)
| ~ between(X10,X3,X5)
| ~ equidistant(X10,X3,X11,X9)
| equidistant(X3,X5,X9,X12) )
| ~ spl0_69 ),
inference(avatar_component_clause,[],[f664]) ).
fof(f2349,plain,
( spl0_160
| ~ spl0_12
| ~ spl0_69 ),
inference(avatar_split_clause,[],[f679,f664,f156,f2347]) ).
fof(f2347,plain,
( spl0_160
<=> ! [X0,X3,X2,X1] :
( ~ between(X0,X1,X2)
| ~ between(X2,X3,X0)
| ~ equidistant(X2,X3,X0,X1)
| equidistant(X3,X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f679,plain,
( ! [X2,X3,X0,X1] :
( ~ between(X0,X1,X2)
| ~ between(X2,X3,X0)
| ~ equidistant(X2,X3,X0,X1)
| equidistant(X3,X0,X1,X2) )
| ~ spl0_12
| ~ spl0_69 ),
inference(resolution,[],[f665,f157]) ).
fof(f2345,plain,
( spl0_159
| ~ spl0_13
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f673,f660,f160,f2343]) ).
fof(f2343,plain,
( spl0_159
<=> ! [X0,X3,X2,X1] :
( ~ between(X0,X1,X2)
| ~ equidistant(X1,X2,X1,X3)
| ~ between(X0,X1,X3)
| equidistant(X0,X2,X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f660,plain,
( spl0_68
<=> ! [X5,X10,X11,X12,X9,X3] :
( ~ between(X11,X9,X12)
| ~ between(X10,X3,X5)
| ~ equidistant(X3,X5,X9,X12)
| ~ equidistant(X10,X3,X11,X9)
| equidistant(X10,X5,X11,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f673,plain,
( ! [X2,X3,X0,X1] :
( ~ between(X0,X1,X2)
| ~ equidistant(X1,X2,X1,X3)
| ~ between(X0,X1,X3)
| equidistant(X0,X2,X0,X3) )
| ~ spl0_13
| ~ spl0_68 ),
inference(resolution,[],[f661,f161]) ).
fof(f661,plain,
( ! [X3,X10,X11,X9,X5,X12] :
( ~ equidistant(X10,X3,X11,X9)
| ~ between(X10,X3,X5)
| ~ equidistant(X3,X5,X9,X12)
| ~ between(X11,X9,X12)
| equidistant(X10,X5,X11,X12) )
| ~ spl0_68 ),
inference(avatar_component_clause,[],[f660]) ).
fof(f2341,plain,
( spl0_158
| ~ spl0_12
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f672,f660,f156,f2339]) ).
fof(f2339,plain,
( spl0_158
<=> ! [X0,X3,X2,X1] :
( ~ between(X0,X1,X2)
| ~ equidistant(X1,X2,X0,X3)
| ~ between(X1,X0,X3)
| equidistant(X0,X2,X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f672,plain,
( ! [X2,X3,X0,X1] :
( ~ between(X0,X1,X2)
| ~ equidistant(X1,X2,X0,X3)
| ~ between(X1,X0,X3)
| equidistant(X0,X2,X1,X3) )
| ~ spl0_12
| ~ spl0_68 ),
inference(resolution,[],[f661,f157]) ).
fof(f2337,plain,
( spl0_157
| ~ spl0_22
| ~ spl0_57 ),
inference(avatar_split_clause,[],[f553,f520,f208,f2335]) ).
fof(f2335,plain,
( spl0_157
<=> ! [X2,X3,X4,X0,X5,X1] :
( X0 = X1
| extension(X1,X0,X2,extension(X3,X2,X4,X5)) = extension(X1,X0,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f208,plain,
( spl0_22
<=> ! [X3,X0,X5,X1] : equidistant(X1,extension(X0,X1,X5,X3),X5,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f520,plain,
( spl0_57
<=> ! [X5,X10,X0,X3,X2,X1] :
( X3 = X10
| ~ equidistant(X5,X0,X1,X2)
| extension(X10,X3,X5,X0) = extension(X10,X3,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f553,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( X0 = X1
| extension(X1,X0,X2,extension(X3,X2,X4,X5)) = extension(X1,X0,X4,X5) )
| ~ spl0_22
| ~ spl0_57 ),
inference(resolution,[],[f521,f209]) ).
fof(f209,plain,
( ! [X3,X0,X1,X5] : equidistant(X1,extension(X0,X1,X5,X3),X5,X3)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f208]) ).
fof(f521,plain,
( ! [X2,X3,X10,X0,X1,X5] :
( ~ equidistant(X5,X0,X1,X2)
| X3 = X10
| extension(X10,X3,X5,X0) = extension(X10,X3,X1,X2) )
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f520]) ).
fof(f2333,plain,
( spl0_156
| ~ spl0_40
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f424,f389,f353,f2331]) ).
fof(f2331,plain,
( spl0_156
<=> ! [X0,X1] :
( extension(extension(X0,X1,X1,X0),X1,extension(X0,X1,X1,X0),X1) = X0
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f353,plain,
( spl0_40
<=> ! [X3,X10] :
( X3 = X10
| extension(X10,X3,X10,X3) = extension(X10,X3,X3,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f389,plain,
( spl0_46
<=> ! [X3,X10] : extension(extension(X10,X3,X10,X3),X3,extension(X10,X3,X10,X3),X3) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f424,plain,
( ! [X0,X1] :
( extension(extension(X0,X1,X1,X0),X1,extension(X0,X1,X1,X0),X1) = X0
| X0 = X1 )
| ~ spl0_40
| ~ spl0_46 ),
inference(superposition,[],[f390,f354]) ).
fof(f354,plain,
( ! [X3,X10] :
( extension(X10,X3,X10,X3) = extension(X10,X3,X3,X10)
| X3 = X10 )
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f353]) ).
fof(f390,plain,
( ! [X3,X10] : extension(extension(X10,X3,X10,X3),X3,extension(X10,X3,X10,X3),X3) = X10
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f389]) ).
fof(f2329,plain,
( spl0_155
| ~ spl0_38
| ~ spl0_43 ),
inference(avatar_split_clause,[],[f407,f377,f338,f2327]) ).
fof(f2327,plain,
( spl0_155
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ equidistant(X0,extension(X1,X0,lower_dimension_point_1,lower_dimension_point_2),X2,X3)
| equidistant(X4,extension(X5,X4,lower_dimension_point_1,lower_dimension_point_2),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f338,plain,
( spl0_38
<=> ! [X10,X0,X5,X3] : equidistant(X3,extension(X10,X3,lower_dimension_point_1,lower_dimension_point_2),X0,extension(X5,X0,lower_dimension_point_1,lower_dimension_point_2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f377,plain,
( spl0_43
<=> ! [X2,X10,X0,X5,X3,X1] :
( ~ equidistant(X10,X3,X5,X0)
| ~ equidistant(X5,X0,X1,X2)
| equidistant(X10,X3,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f407,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ equidistant(X0,extension(X1,X0,lower_dimension_point_1,lower_dimension_point_2),X2,X3)
| equidistant(X4,extension(X5,X4,lower_dimension_point_1,lower_dimension_point_2),X2,X3) )
| ~ spl0_38
| ~ spl0_43 ),
inference(resolution,[],[f378,f339]) ).
fof(f339,plain,
( ! [X3,X10,X0,X5] : equidistant(X3,extension(X10,X3,lower_dimension_point_1,lower_dimension_point_2),X0,extension(X5,X0,lower_dimension_point_1,lower_dimension_point_2))
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f338]) ).
fof(f378,plain,
( ! [X2,X3,X10,X0,X1,X5] :
( ~ equidistant(X10,X3,X5,X0)
| ~ equidistant(X5,X0,X1,X2)
| equidistant(X10,X3,X1,X2) )
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f377]) ).
fof(f2325,plain,
( spl0_154
| ~ spl0_38
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f401,f373,f338,f2323]) ).
fof(f2323,plain,
( spl0_154
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ equidistant(X0,extension(X1,X0,lower_dimension_point_1,lower_dimension_point_2),X2,X3)
| equidistant(X2,X3,X4,extension(X5,X4,lower_dimension_point_1,lower_dimension_point_2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f373,plain,
( spl0_42
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ equidistant(X0,X1,X2,X3)
| ~ equidistant(X0,X1,X4,X5)
| equidistant(X2,X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f401,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ equidistant(X0,extension(X1,X0,lower_dimension_point_1,lower_dimension_point_2),X2,X3)
| equidistant(X2,X3,X4,extension(X5,X4,lower_dimension_point_1,lower_dimension_point_2)) )
| ~ spl0_38
| ~ spl0_42 ),
inference(resolution,[],[f374,f339]) ).
fof(f374,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ equidistant(X0,X1,X4,X5)
| ~ equidistant(X0,X1,X2,X3)
| equidistant(X2,X3,X4,X5) )
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f373]) ).
fof(f2321,plain,
( spl0_153
| ~ spl0_19
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f1383,f1378,f186,f2318]) ).
fof(f2318,plain,
( spl0_153
<=> between(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,v) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f1383,plain,
( between(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,v)
| ~ spl0_19
| ~ spl0_108 ),
inference(superposition,[],[f187,f1380]) ).
fof(f2283,plain,
( spl0_152
| ~ spl0_11
| ~ spl0_70 ),
inference(avatar_split_clause,[],[f690,f668,f151,f2281]) ).
fof(f2281,plain,
( spl0_152
<=> ! [X0,X1] :
( between(u,X0,w)
| ~ between(u,X1,v)
| ~ equidistant(X1,v,X0,w)
| ~ equidistant(u,X1,u,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f690,plain,
( ! [X0,X1] :
( between(u,X0,w)
| ~ between(u,X1,v)
| ~ equidistant(X1,v,X0,w)
| ~ equidistant(u,X1,u,X0) )
| ~ spl0_11
| ~ spl0_70 ),
inference(resolution,[],[f669,f153]) ).
fof(f2279,plain,
( spl0_151
| ~ spl0_11
| ~ spl0_69 ),
inference(avatar_split_clause,[],[f678,f664,f151,f2277]) ).
fof(f2277,plain,
( spl0_151
<=> ! [X0,X1] :
( ~ between(u,X0,w)
| ~ between(u,X1,v)
| ~ equidistant(u,X1,u,X0)
| equidistant(X1,v,X0,w) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f678,plain,
( ! [X0,X1] :
( ~ between(u,X0,w)
| ~ between(u,X1,v)
| ~ equidistant(u,X1,u,X0)
| equidistant(X1,v,X0,w) )
| ~ spl0_11
| ~ spl0_69 ),
inference(resolution,[],[f665,f153]) ).
fof(f2275,plain,
( spl0_150
| ~ spl0_11
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f671,f660,f151,f2273]) ).
fof(f2273,plain,
( spl0_150
<=> ! [X0,X1] :
( ~ between(u,v,X0)
| ~ equidistant(v,X0,w,X1)
| ~ between(u,w,X1)
| equidistant(u,X0,u,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f671,plain,
( ! [X0,X1] :
( ~ between(u,v,X0)
| ~ equidistant(v,X0,w,X1)
| ~ between(u,w,X1)
| equidistant(u,X0,u,X1) )
| ~ spl0_11
| ~ spl0_68 ),
inference(resolution,[],[f661,f153]) ).
fof(f2143,plain,
( spl0_149
| ~ spl0_19
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1374,f1370,f186,f2141]) ).
fof(f2141,plain,
( spl0_149
<=> ! [X0,X1] : between(u,v,extension(v,w,X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f1370,plain,
( spl0_107
<=> ! [X0] :
( ~ between(v,w,X0)
| between(u,v,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f1374,plain,
( ! [X0,X1] : between(u,v,extension(v,w,X0,X1))
| ~ spl0_19
| ~ spl0_107 ),
inference(resolution,[],[f1371,f187]) ).
fof(f1371,plain,
( ! [X0] :
( ~ between(v,w,X0)
| between(u,v,X0) )
| ~ spl0_107 ),
inference(avatar_component_clause,[],[f1370]) ).
fof(f2139,plain,
( spl0_148
| ~ spl0_20
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f496,f472,f190,f2137]) ).
fof(f2137,plain,
( spl0_148
<=> ! [X4,X0,X3,X2,X1] :
( ~ between(X0,X1,X2)
| ~ between(X3,X4,X2)
| between(X3,inner_pasch(X3,X4,X2,X1,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f472,plain,
( spl0_54
<=> ! [X10,X0,X5,X3,X1] :
( ~ between(X10,X3,X5)
| ~ between(X1,X0,X5)
| between(X0,inner_pasch(X10,X3,X5,X0,X1),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f496,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ between(X0,X1,X2)
| ~ between(X3,X4,X2)
| between(X3,inner_pasch(X3,X4,X2,X1,X0),X1) )
| ~ spl0_20
| ~ spl0_54 ),
inference(resolution,[],[f473,f191]) ).
fof(f473,plain,
( ! [X3,X10,X0,X1,X5] :
( between(X0,inner_pasch(X10,X3,X5,X0,X1),X10)
| ~ between(X1,X0,X5)
| ~ between(X10,X3,X5) )
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f472]) ).
fof(f2135,plain,
( spl0_147
| ~ spl0_21
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f494,f472,f194,f2133]) ).
fof(f2133,plain,
( spl0_147
<=> ! [X4,X0,X3,X2,X1] :
( ~ between(X0,X1,X2)
| ~ between(X1,X3,X2)
| between(X4,inner_pasch(X1,X3,X2,X1,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f194,plain,
( spl0_21
<=> ! [X5,X3,X10] :
( ~ between(X10,X5,X10)
| between(X3,X5,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f494,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ between(X0,X1,X2)
| ~ between(X1,X3,X2)
| between(X4,inner_pasch(X1,X3,X2,X1,X0),X1) )
| ~ spl0_21
| ~ spl0_54 ),
inference(resolution,[],[f473,f195]) ).
fof(f195,plain,
( ! [X3,X10,X5] :
( ~ between(X10,X5,X10)
| between(X3,X5,X10) )
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f194]) ).
fof(f2131,plain,
( spl0_146
| ~ spl0_20
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f481,f463,f190,f2129]) ).
fof(f2129,plain,
( spl0_146
<=> ! [X4,X0,X3,X2,X1] :
( ~ between(X0,X1,X2)
| ~ between(X3,X4,X2)
| between(X0,inner_pasch(X3,X4,X2,X1,X0),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f463,plain,
( spl0_52
<=> ! [X10,X0,X5,X3,X1] :
( ~ between(X10,X3,X5)
| ~ between(X1,X0,X5)
| between(X3,inner_pasch(X10,X3,X5,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f481,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ between(X0,X1,X2)
| ~ between(X3,X4,X2)
| between(X0,inner_pasch(X3,X4,X2,X1,X0),X4) )
| ~ spl0_20
| ~ spl0_52 ),
inference(resolution,[],[f464,f191]) ).
fof(f464,plain,
( ! [X3,X10,X0,X1,X5] :
( between(X3,inner_pasch(X10,X3,X5,X0,X1),X1)
| ~ between(X1,X0,X5)
| ~ between(X10,X3,X5) )
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f463]) ).
fof(f2127,plain,
( spl0_145
| ~ spl0_21
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f479,f463,f194,f2125]) ).
fof(f2125,plain,
( spl0_145
<=> ! [X4,X0,X3,X2,X1] :
( ~ between(X0,X1,X2)
| ~ between(X3,X0,X2)
| between(X4,inner_pasch(X3,X0,X2,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f479,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ between(X0,X1,X2)
| ~ between(X3,X0,X2)
| between(X4,inner_pasch(X3,X0,X2,X1,X0),X0) )
| ~ spl0_21
| ~ spl0_52 ),
inference(resolution,[],[f464,f195]) ).
fof(f1978,plain,
( spl0_144
| ~ spl0_19
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f1366,f1362,f186,f1976]) ).
fof(f1976,plain,
( spl0_144
<=> ! [X0,X1] : between(u,w,extension(v,w,X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f1362,plain,
( spl0_106
<=> ! [X0] :
( ~ between(v,w,X0)
| between(u,w,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f1366,plain,
( ! [X0,X1] : between(u,w,extension(v,w,X0,X1))
| ~ spl0_19
| ~ spl0_106 ),
inference(resolution,[],[f1363,f187]) ).
fof(f1363,plain,
( ! [X0] :
( ~ between(v,w,X0)
| between(u,w,X0) )
| ~ spl0_106 ),
inference(avatar_component_clause,[],[f1362]) ).
fof(f1956,plain,
( spl0_143
| ~ spl0_14
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f639,f633,f164,f1954]) ).
fof(f1954,plain,
( spl0_143
<=> ! [X2,X0,X1] :
( ~ between(X0,X1,X0)
| between(X2,extension(extension(X2,X2,lower_dimension_point_1,lower_dimension_point_2),X2,X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f633,plain,
( spl0_66
<=> ! [X11,X10,X12,X5,X3] :
( ~ between(X10,X3,X5)
| ~ equidistant(X10,X5,X11,X12)
| between(X11,extension(extension(X12,X11,lower_dimension_point_1,lower_dimension_point_2),X11,X10,X3),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f639,plain,
( ! [X2,X0,X1] :
( ~ between(X0,X1,X0)
| between(X2,extension(extension(X2,X2,lower_dimension_point_1,lower_dimension_point_2),X2,X0,X1),X2) )
| ~ spl0_14
| ~ spl0_66 ),
inference(resolution,[],[f634,f165]) ).
fof(f634,plain,
( ! [X3,X10,X11,X5,X12] :
( ~ equidistant(X10,X5,X11,X12)
| ~ between(X10,X3,X5)
| between(X11,extension(extension(X12,X11,lower_dimension_point_1,lower_dimension_point_2),X11,X10,X3),X12) )
| ~ spl0_66 ),
inference(avatar_component_clause,[],[f633]) ).
fof(f1952,plain,
( spl0_142
| ~ spl0_13
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f638,f633,f160,f1950]) ).
fof(f1950,plain,
( spl0_142
<=> ! [X2,X0,X1] :
( ~ between(X0,X1,X2)
| between(X0,extension(extension(X2,X0,lower_dimension_point_1,lower_dimension_point_2),X0,X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f638,plain,
( ! [X2,X0,X1] :
( ~ between(X0,X1,X2)
| between(X0,extension(extension(X2,X0,lower_dimension_point_1,lower_dimension_point_2),X0,X0,X1),X2) )
| ~ spl0_13
| ~ spl0_66 ),
inference(resolution,[],[f634,f161]) ).
fof(f1948,plain,
( spl0_141
| ~ spl0_12
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f637,f633,f156,f1946]) ).
fof(f1946,plain,
( spl0_141
<=> ! [X2,X0,X1] :
( ~ between(X0,X1,X2)
| between(X2,extension(extension(X0,X2,lower_dimension_point_1,lower_dimension_point_2),X2,X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f637,plain,
( ! [X2,X0,X1] :
( ~ between(X0,X1,X2)
| between(X2,extension(extension(X0,X2,lower_dimension_point_1,lower_dimension_point_2),X2,X0,X1),X0) )
| ~ spl0_12
| ~ spl0_66 ),
inference(resolution,[],[f634,f157]) ).
fof(f1944,plain,
( spl0_140
| ~ spl0_15
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f495,f472,f168,f1942]) ).
fof(f1942,plain,
( spl0_140
<=> ! [X0,X3,X2,X1] :
( ~ between(X0,X1,X2)
| ~ between(X1,X3,X2)
| inner_pasch(X1,X3,X2,X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f168,plain,
( spl0_15
<=> ! [X0,X1] :
( X0 = X1
| ~ between(X0,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f495,plain,
( ! [X2,X3,X0,X1] :
( ~ between(X0,X1,X2)
| ~ between(X1,X3,X2)
| inner_pasch(X1,X3,X2,X1,X0) = X1 )
| ~ spl0_15
| ~ spl0_54 ),
inference(resolution,[],[f473,f169]) ).
fof(f169,plain,
( ! [X0,X1] :
( ~ between(X0,X1,X0)
| X0 = X1 )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f168]) ).
fof(f1940,plain,
( spl0_139
| ~ spl0_15
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f480,f463,f168,f1938]) ).
fof(f1938,plain,
( spl0_139
<=> ! [X0,X3,X2,X1] :
( ~ between(X0,X1,X2)
| ~ between(X3,X0,X2)
| inner_pasch(X3,X0,X2,X1,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f480,plain,
( ! [X2,X3,X0,X1] :
( ~ between(X0,X1,X2)
| ~ between(X3,X0,X2)
| inner_pasch(X3,X0,X2,X1,X0) = X0 )
| ~ spl0_15
| ~ spl0_52 ),
inference(resolution,[],[f464,f169]) ).
fof(f1936,plain,
( spl0_138
| ~ spl0_19
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f450,f436,f186,f1934]) ).
fof(f1934,plain,
( spl0_138
<=> ! [X4,X0,X3,X2,X1] :
( ~ between(X0,X1,extension(X0,X2,X3,X4))
| between(X0,X2,X1)
| between(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f436,plain,
( spl0_49
<=> ! [X10,X0,X5,X3] :
( ~ between(X10,X5,X0)
| ~ between(X10,X3,X0)
| between(X10,X5,X3)
| between(X10,X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f450,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ between(X0,X1,extension(X0,X2,X3,X4))
| between(X0,X2,X1)
| between(X0,X1,X2) )
| ~ spl0_19
| ~ spl0_49 ),
inference(resolution,[],[f437,f187]) ).
fof(f437,plain,
( ! [X3,X10,X0,X5] :
( ~ between(X10,X5,X0)
| ~ between(X10,X3,X0)
| between(X10,X5,X3)
| between(X10,X3,X5) )
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f436]) ).
fof(f1932,plain,
( spl0_137
| ~ spl0_19
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f330,f315,f186,f1930]) ).
fof(f1930,plain,
( spl0_137
<=> ! [X4,X0,X3,X2,X1] :
( ~ between(X0,X1,extension(X2,X0,X3,X4))
| between(X2,X1,extension(X2,X0,X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f315,plain,
( spl0_36
<=> ! [X10,X0,X5,X3] :
( ~ between(X10,X3,X0)
| ~ between(X3,X5,X0)
| between(X10,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f330,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ between(X0,X1,extension(X2,X0,X3,X4))
| between(X2,X1,extension(X2,X0,X3,X4)) )
| ~ spl0_19
| ~ spl0_36 ),
inference(resolution,[],[f316,f187]) ).
fof(f316,plain,
( ! [X3,X10,X0,X5] :
( ~ between(X10,X3,X0)
| ~ between(X3,X5,X0)
| between(X10,X5,X0) )
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f315]) ).
fof(f1903,plain,
( spl0_136
| ~ spl0_11
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f636,f633,f151,f1901]) ).
fof(f1901,plain,
( spl0_136
<=> ! [X0] :
( ~ between(u,X0,v)
| between(u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,X0),w) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f636,plain,
( ! [X0] :
( ~ between(u,X0,v)
| between(u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,X0),w) )
| ~ spl0_11
| ~ spl0_66 ),
inference(resolution,[],[f634,f153]) ).
fof(f1899,plain,
( spl0_135
| ~ spl0_24
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f336,f319,f218,f1897]) ).
fof(f1897,plain,
( spl0_135
<=> ! [X0] :
( ~ between(w,X0,v)
| between(w,X0,u) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f218,plain,
( spl0_24
<=> between(w,v,u) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f319,plain,
( spl0_37
<=> ! [X10,X0,X5,X3] :
( ~ between(X10,X3,X5)
| ~ between(X10,X5,X0)
| between(X10,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f336,plain,
( ! [X0] :
( ~ between(w,X0,v)
| between(w,X0,u) )
| ~ spl0_24
| ~ spl0_37 ),
inference(resolution,[],[f320,f220]) ).
fof(f220,plain,
( between(w,v,u)
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f218]) ).
fof(f320,plain,
( ! [X3,X10,X0,X5] :
( ~ between(X10,X5,X0)
| ~ between(X10,X3,X5)
| between(X10,X3,X0) )
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f319]) ).
fof(f1843,plain,
( spl0_134
| ~ spl0_19
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f433,f393,f186,f1841]) ).
fof(f1841,plain,
( spl0_134
<=> ! [X0,X3,X2,X1] : extension(extension(extension(X0,X1,X2,X3),X0,lower_dimension_point_1,lower_dimension_point_2),X0,X0,X1) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f393,plain,
( spl0_47
<=> ! [X5,X3,X10] :
( ~ between(X10,X3,X5)
| extension(extension(X5,X10,lower_dimension_point_1,lower_dimension_point_2),X10,X10,X3) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f433,plain,
( ! [X2,X3,X0,X1] : extension(extension(extension(X0,X1,X2,X3),X0,lower_dimension_point_1,lower_dimension_point_2),X0,X0,X1) = X1
| ~ spl0_19
| ~ spl0_47 ),
inference(resolution,[],[f394,f187]) ).
fof(f394,plain,
( ! [X3,X10,X5] :
( ~ between(X10,X3,X5)
| extension(extension(X5,X10,lower_dimension_point_1,lower_dimension_point_2),X10,X10,X3) = X3 )
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f393]) ).
fof(f1839,plain,
( spl0_133
| ~ spl0_19
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f303,f292,f186,f1837]) ).
fof(f1837,plain,
( spl0_133
<=> ! [X0,X3,X2,X1] :
( extension(X0,X1,X2,X3) = X1
| ~ between(X0,extension(X0,X1,X2,X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f292,plain,
( spl0_33
<=> ! [X5,X3,X10] :
( X3 = X5
| ~ between(X10,X5,X3)
| ~ between(X10,X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f303,plain,
( ! [X2,X3,X0,X1] :
( extension(X0,X1,X2,X3) = X1
| ~ between(X0,extension(X0,X1,X2,X3),X1) )
| ~ spl0_19
| ~ spl0_33 ),
inference(resolution,[],[f293,f187]) ).
fof(f293,plain,
( ! [X3,X10,X5] :
( ~ between(X10,X5,X3)
| X3 = X5
| ~ between(X10,X3,X5) )
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f1834,plain,
( spl0_1
| spl0_132
| ~ spl0_11
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f626,f586,f151,f1832,f103]) ).
fof(f1832,plain,
( spl0_132
<=> ! [X0] :
( u = X0
| ~ equidistant(X0,v,X0,w)
| ~ between(u,X0,v) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f586,plain,
( spl0_64
<=> ! [X10,X12,X5,X3] :
( X5 = X12
| X3 = X10
| ~ between(X10,X3,X5)
| ~ equidistant(X3,X5,X3,X12)
| ~ equidistant(X10,X5,X10,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f626,plain,
( ! [X0] :
( u = X0
| ~ between(u,X0,v)
| ~ equidistant(X0,v,X0,w)
| v = w )
| ~ spl0_11
| ~ spl0_64 ),
inference(resolution,[],[f587,f153]) ).
fof(f587,plain,
( ! [X3,X10,X5,X12] :
( ~ equidistant(X10,X5,X10,X12)
| X3 = X10
| ~ between(X10,X3,X5)
| ~ equidistant(X3,X5,X3,X12)
| X5 = X12 )
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f586]) ).
fof(f1826,plain,
( spl0_131
| spl0_1
| ~ spl0_5
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f570,f532,f123,f103,f1824]) ).
fof(f1824,plain,
( spl0_131
<=> ! [X0] :
( ~ between(X0,v,w)
| between(u,X0,v)
| between(X0,u,v) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f123,plain,
( spl0_5
<=> between(u,v,w) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f532,plain,
( spl0_60
<=> ! [X10,X0,X5,X3] :
( X0 = X5
| ~ between(X10,X5,X0)
| ~ between(X3,X5,X0)
| between(X3,X10,X5)
| between(X10,X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f570,plain,
( ! [X0] :
( v = w
| ~ between(X0,v,w)
| between(X0,u,v)
| between(u,X0,v) )
| ~ spl0_5
| ~ spl0_60 ),
inference(resolution,[],[f533,f125]) ).
fof(f125,plain,
( between(u,v,w)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f533,plain,
( ! [X3,X10,X0,X5] :
( ~ between(X10,X5,X0)
| X0 = X5
| ~ between(X3,X5,X0)
| between(X3,X10,X5)
| between(X10,X3,X5) )
| ~ spl0_60 ),
inference(avatar_component_clause,[],[f532]) ).
fof(f1814,plain,
( spl0_130
| spl0_81
| ~ spl0_5
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f563,f528,f123,f993,f1812]) ).
fof(f1812,plain,
( spl0_130
<=> ! [X0] :
( ~ between(u,v,X0)
| between(v,w,X0)
| between(v,X0,w) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f993,plain,
( spl0_81
<=> u = v ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f528,plain,
( spl0_59
<=> ! [X10,X0,X5,X3] :
( X3 = X10
| ~ between(X10,X3,X5)
| ~ between(X10,X3,X0)
| between(X3,X0,X5)
| between(X3,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f563,plain,
( ! [X0] :
( u = v
| ~ between(u,v,X0)
| between(v,X0,w)
| between(v,w,X0) )
| ~ spl0_5
| ~ spl0_59 ),
inference(resolution,[],[f529,f125]) ).
fof(f529,plain,
( ! [X3,X10,X0,X5] :
( ~ between(X10,X3,X5)
| X3 = X10
| ~ between(X10,X3,X0)
| between(X3,X0,X5)
| between(X3,X5,X0) )
| ~ spl0_59 ),
inference(avatar_component_clause,[],[f528]) ).
fof(f1810,plain,
( spl0_129
| ~ spl0_24
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f331,f315,f218,f1808]) ).
fof(f1808,plain,
( spl0_129
<=> ! [X0] :
( ~ between(v,X0,u)
| between(w,X0,u) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f331,plain,
( ! [X0] :
( ~ between(v,X0,u)
| between(w,X0,u) )
| ~ spl0_24
| ~ spl0_36 ),
inference(resolution,[],[f316,f220]) ).
fof(f1798,plain,
( spl0_128
| spl0_81
| ~ spl0_5
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f556,f524,f123,f993,f1796]) ).
fof(f1796,plain,
( spl0_128
<=> ! [X0] :
( ~ between(u,v,X0)
| between(u,w,X0)
| between(u,X0,w) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f524,plain,
( spl0_58
<=> ! [X10,X0,X5,X3] :
( X3 = X10
| ~ between(X10,X3,X5)
| ~ between(X10,X3,X0)
| between(X10,X0,X5)
| between(X10,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f556,plain,
( ! [X0] :
( u = v
| ~ between(u,v,X0)
| between(u,X0,w)
| between(u,w,X0) )
| ~ spl0_5
| ~ spl0_58 ),
inference(resolution,[],[f525,f125]) ).
fof(f525,plain,
( ! [X3,X10,X0,X5] :
( ~ between(X10,X3,X5)
| X3 = X10
| ~ between(X10,X3,X0)
| between(X10,X0,X5)
| between(X10,X5,X0) )
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f524]) ).
fof(f1692,plain,
( spl0_127
| ~ spl0_12
| ~ spl0_57 ),
inference(avatar_split_clause,[],[f550,f520,f156,f1690]) ).
fof(f1690,plain,
( spl0_127
<=> ! [X0,X3,X2,X1] :
( X0 = X1
| extension(X1,X0,X2,X3) = extension(X1,X0,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f550,plain,
( ! [X2,X3,X0,X1] :
( X0 = X1
| extension(X1,X0,X2,X3) = extension(X1,X0,X3,X2) )
| ~ spl0_12
| ~ spl0_57 ),
inference(resolution,[],[f521,f157]) ).
fof(f1688,plain,
( spl0_126
| ~ spl0_22
| ~ spl0_43 ),
inference(avatar_split_clause,[],[f406,f377,f208,f1686]) ).
fof(f1686,plain,
( spl0_126
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ equidistant(X0,X1,X2,X3)
| equidistant(X4,extension(X5,X4,X0,X1),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f406,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ equidistant(X0,X1,X2,X3)
| equidistant(X4,extension(X5,X4,X0,X1),X2,X3) )
| ~ spl0_22
| ~ spl0_43 ),
inference(resolution,[],[f378,f209]) ).
fof(f1684,plain,
( spl0_125
| ~ spl0_22
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f400,f373,f208,f1682]) ).
fof(f1682,plain,
( spl0_125
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ equidistant(X0,extension(X1,X0,X2,X3),X4,X5)
| equidistant(X4,X5,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f400,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ equidistant(X0,extension(X1,X0,X2,X3),X4,X5)
| equidistant(X4,X5,X2,X3) )
| ~ spl0_22
| ~ spl0_42 ),
inference(resolution,[],[f374,f209]) ).
fof(f1656,plain,
( spl0_124
| ~ spl0_11
| ~ spl0_57 ),
inference(avatar_split_clause,[],[f549,f520,f151,f1654]) ).
fof(f1654,plain,
( spl0_124
<=> ! [X0,X1] :
( X0 = X1
| extension(X1,X0,u,v) = extension(X1,X0,u,w) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f549,plain,
( ! [X0,X1] :
( X0 = X1
| extension(X1,X0,u,v) = extension(X1,X0,u,w) )
| ~ spl0_11
| ~ spl0_57 ),
inference(resolution,[],[f521,f153]) ).
fof(f1650,plain,
( spl0_1
| spl0_123
| ~ spl0_11
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f540,f516,f151,f1648,f103]) ).
fof(f1648,plain,
( spl0_123
<=> ! [X0] :
( u = X0
| ~ between(X0,u,w)
| ~ between(X0,u,v) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f516,plain,
( spl0_56
<=> ! [X10,X0,X5,X3] :
( X0 = X5
| X3 = X10
| ~ between(X10,X3,X5)
| ~ between(X10,X3,X0)
| ~ equidistant(X3,X5,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f540,plain,
( ! [X0] :
( u = X0
| ~ between(X0,u,v)
| ~ between(X0,u,w)
| v = w )
| ~ spl0_11
| ~ spl0_56 ),
inference(resolution,[],[f517,f153]) ).
fof(f517,plain,
( ! [X3,X10,X0,X5] :
( ~ equidistant(X3,X5,X3,X0)
| X3 = X10
| ~ between(X10,X3,X5)
| ~ between(X10,X3,X0)
| X0 = X5 )
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f516]) ).
fof(f1567,plain,
( spl0_122
| ~ spl0_27
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f344,f338,f231,f1565]) ).
fof(f1565,plain,
( spl0_122
<=> ! [X2,X0,X1,X3] : equidistant(extension(X0,X1,lower_dimension_point_1,lower_dimension_point_2),X1,extension(X2,X3,lower_dimension_point_1,lower_dimension_point_2),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f231,plain,
( spl0_27
<=> ! [X10,X0,X5,X3] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X3,X10,X0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f344,plain,
( ! [X2,X3,X0,X1] : equidistant(extension(X0,X1,lower_dimension_point_1,lower_dimension_point_2),X1,extension(X2,X3,lower_dimension_point_1,lower_dimension_point_2),X3)
| ~ spl0_27
| ~ spl0_38 ),
inference(resolution,[],[f339,f232]) ).
fof(f232,plain,
( ! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X3,X10,X0,X5) )
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f231]) ).
fof(f1563,plain,
( spl0_121
| ~ spl0_26
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f343,f338,f227,f1561]) ).
fof(f1561,plain,
( spl0_121
<=> ! [X0,X3,X2,X1] : equidistant(X0,extension(X1,X0,lower_dimension_point_1,lower_dimension_point_2),extension(X2,X3,lower_dimension_point_1,lower_dimension_point_2),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f227,plain,
( spl0_26
<=> ! [X10,X0,X5,X3] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X10,X3,X0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f343,plain,
( ! [X2,X3,X0,X1] : equidistant(X0,extension(X1,X0,lower_dimension_point_1,lower_dimension_point_2),extension(X2,X3,lower_dimension_point_1,lower_dimension_point_2),X3)
| ~ spl0_26
| ~ spl0_38 ),
inference(resolution,[],[f339,f228]) ).
fof(f228,plain,
( ! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X10,X3,X0,X5) )
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f227]) ).
fof(f1559,plain,
( spl0_120
| ~ spl0_25
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f342,f338,f223,f1557]) ).
fof(f1557,plain,
( spl0_120
<=> ! [X2,X0,X1,X3] : equidistant(extension(X0,X1,lower_dimension_point_1,lower_dimension_point_2),X1,X2,extension(X3,X2,lower_dimension_point_1,lower_dimension_point_2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f223,plain,
( spl0_25
<=> ! [X10,X0,X5,X3] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X3,X10,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f342,plain,
( ! [X2,X3,X0,X1] : equidistant(extension(X0,X1,lower_dimension_point_1,lower_dimension_point_2),X1,X2,extension(X3,X2,lower_dimension_point_1,lower_dimension_point_2))
| ~ spl0_25
| ~ spl0_38 ),
inference(resolution,[],[f339,f224]) ).
fof(f224,plain,
( ! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X3,X10,X5,X0) )
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f223]) ).
fof(f1515,plain,
( ~ spl0_119
| ~ spl0_11
| ~ spl0_115 ),
inference(avatar_split_clause,[],[f1444,f1441,f151,f1512]) ).
fof(f1512,plain,
( spl0_119
<=> between(u,v,u) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f1441,plain,
( spl0_115
<=> ! [X0] :
( ~ between(u,v,X0)
| ~ equidistant(X0,v,X0,w) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f1444,plain,
( ~ between(u,v,u)
| ~ spl0_11
| ~ spl0_115 ),
inference(resolution,[],[f1442,f153]) ).
fof(f1442,plain,
( ! [X0] :
( ~ equidistant(X0,v,X0,w)
| ~ between(u,v,X0) )
| ~ spl0_115 ),
inference(avatar_component_clause,[],[f1441]) ).
fof(f1481,plain,
( spl0_118
| ~ spl0_9
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f458,f444,f143,f1479]) ).
fof(f1479,plain,
( spl0_118
<=> ! [X0,X3,X2,X1] :
( ~ between(X0,X1,X2)
| ~ between(X2,X3,X1)
| between(X0,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f143,plain,
( spl0_9
<=> ! [X3,X10] : between(X10,X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f458,plain,
( ! [X2,X3,X0,X1] :
( ~ between(X0,X1,X2)
| ~ between(X2,X3,X1)
| between(X0,X3,X2) )
| ~ spl0_9
| ~ spl0_51 ),
inference(resolution,[],[f445,f144]) ).
fof(f144,plain,
( ! [X3,X10] : between(X10,X3,X3)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f1477,plain,
( spl0_117
| ~ spl0_19
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f335,f319,f186,f1475]) ).
fof(f1475,plain,
( spl0_117
<=> ! [X4,X0,X3,X2,X1] :
( ~ between(X0,X1,X2)
| between(X0,X1,extension(X0,X2,X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f335,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ between(X0,X1,X2)
| between(X0,X1,extension(X0,X2,X3,X4)) )
| ~ spl0_19
| ~ spl0_37 ),
inference(resolution,[],[f320,f187]) ).
fof(f1473,plain,
( spl0_116
| ~ spl0_19
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f325,f306,f186,f1471]) ).
fof(f1471,plain,
( spl0_116
<=> ! [X4,X0,X3,X2,X1] :
( ~ between(X0,X1,X2)
| between(X1,X2,extension(X0,X2,X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f306,plain,
( spl0_34
<=> ! [X10,X0,X5,X3] :
( ~ between(X10,X3,X5)
| ~ between(X10,X5,X0)
| between(X3,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f325,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ between(X0,X1,X2)
| between(X1,X2,extension(X0,X2,X3,X4)) )
| ~ spl0_19
| ~ spl0_34 ),
inference(resolution,[],[f307,f187]) ).
fof(f307,plain,
( ! [X3,X10,X0,X5] :
( ~ between(X10,X5,X0)
| ~ between(X10,X3,X5)
| between(X3,X5,X0) )
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f306]) ).
fof(f1443,plain,
( spl0_1
| spl0_115
| ~ spl0_11
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f509,f476,f151,f1441,f103]) ).
fof(f476,plain,
( spl0_55
<=> ! [X10,X0,X5,X3] :
( X0 = X3
| ~ between(X10,X3,X5)
| ~ equidistant(X5,X3,X5,X0)
| ~ equidistant(X10,X3,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f509,plain,
( ! [X0] :
( ~ between(u,v,X0)
| ~ equidistant(X0,v,X0,w)
| v = w )
| ~ spl0_11
| ~ spl0_55 ),
inference(resolution,[],[f477,f153]) ).
fof(f477,plain,
( ! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X10,X0)
| ~ between(X10,X3,X5)
| ~ equidistant(X5,X3,X5,X0)
| X0 = X3 )
| ~ spl0_55 ),
inference(avatar_component_clause,[],[f476]) ).
fof(f1439,plain,
( spl0_114
| ~ spl0_5
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f457,f444,f123,f1437]) ).
fof(f1437,plain,
( spl0_114
<=> ! [X0,X1] :
( ~ between(u,X0,w)
| ~ between(v,X1,X0)
| between(u,X1,w) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f457,plain,
( ! [X0,X1] :
( ~ between(u,X0,w)
| ~ between(v,X1,X0)
| between(u,X1,w) )
| ~ spl0_5
| ~ spl0_51 ),
inference(resolution,[],[f445,f125]) ).
fof(f1435,plain,
( spl0_113
| ~ spl0_24
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f326,f306,f218,f1433]) ).
fof(f1433,plain,
( spl0_113
<=> ! [X0] :
( ~ between(w,X0,v)
| between(X0,v,u) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f326,plain,
( ! [X0] :
( ~ between(w,X0,v)
| between(X0,v,u) )
| ~ spl0_24
| ~ spl0_34 ),
inference(resolution,[],[f307,f220]) ).
fof(f1431,plain,
( spl0_112
| ~ spl0_5
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f452,f440,f123,f1429]) ).
fof(f1429,plain,
( spl0_112
<=> ! [X0] :
( ~ between(u,X0,w)
| between(v,X0,w)
| between(X0,v,w) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f440,plain,
( spl0_50
<=> ! [X10,X0,X5,X3] :
( ~ between(X10,X5,X0)
| ~ between(X10,X3,X0)
| between(X5,X3,X0)
| between(X3,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f452,plain,
( ! [X0] :
( ~ between(u,X0,w)
| between(v,X0,w)
| between(X0,v,w) )
| ~ spl0_5
| ~ spl0_50 ),
inference(resolution,[],[f441,f125]) ).
fof(f441,plain,
( ! [X3,X10,X0,X5] :
( ~ between(X10,X5,X0)
| ~ between(X10,X3,X0)
| between(X5,X3,X0)
| between(X3,X5,X0) )
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f440]) ).
fof(f1427,plain,
( spl0_111
| ~ spl0_5
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f447,f436,f123,f1425]) ).
fof(f1425,plain,
( spl0_111
<=> ! [X0] :
( ~ between(u,X0,w)
| between(u,v,X0)
| between(u,X0,v) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f447,plain,
( ! [X0] :
( ~ between(u,X0,w)
| between(u,v,X0)
| between(u,X0,v) )
| ~ spl0_5
| ~ spl0_49 ),
inference(resolution,[],[f437,f125]) ).
fof(f1400,plain,
( spl0_110
| ~ spl0_9
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f431,f393,f143,f1398]) ).
fof(f431,plain,
( ! [X0,X1] : extension(extension(X0,X1,lower_dimension_point_1,lower_dimension_point_2),X1,X1,X0) = X0
| ~ spl0_9
| ~ spl0_47 ),
inference(resolution,[],[f394,f144]) ).
fof(f1396,plain,
( spl0_109
| ~ spl0_19
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f298,f288,f186,f1394]) ).
fof(f1394,plain,
( spl0_109
<=> ! [X0,X3,X2,X1] :
( ~ between(X0,X1,extension(X1,X0,X2,X3))
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f288,plain,
( spl0_32
<=> ! [X5,X3,X10] :
( X3 = X10
| ~ between(X3,X10,X5)
| ~ between(X10,X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f298,plain,
( ! [X2,X3,X0,X1] :
( ~ between(X0,X1,extension(X1,X0,X2,X3))
| X0 = X1 )
| ~ spl0_19
| ~ spl0_32 ),
inference(resolution,[],[f289,f187]) ).
fof(f289,plain,
( ! [X3,X10,X5] :
( ~ between(X10,X3,X5)
| ~ between(X3,X10,X5)
| X3 = X10 )
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f288]) ).
fof(f1381,plain,
( spl0_108
| ~ spl0_5
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f430,f393,f123,f1378]) ).
fof(f430,plain,
( v = extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v)
| ~ spl0_5
| ~ spl0_47 ),
inference(resolution,[],[f394,f125]) ).
fof(f1372,plain,
( spl0_107
| spl0_1
| ~ spl0_5
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f418,f385,f123,f103,f1370]) ).
fof(f418,plain,
( ! [X0] :
( v = w
| ~ between(v,w,X0)
| between(u,v,X0) )
| ~ spl0_5
| ~ spl0_45 ),
inference(resolution,[],[f386,f125]) ).
fof(f1364,plain,
( spl0_106
| spl0_1
| ~ spl0_5
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f408,f381,f123,f103,f1362]) ).
fof(f381,plain,
( spl0_44
<=> ! [X10,X0,X5,X3] :
( X3 = X5
| ~ between(X10,X3,X5)
| ~ between(X3,X5,X0)
| between(X10,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f408,plain,
( ! [X0] :
( v = w
| ~ between(v,w,X0)
| between(u,w,X0) )
| ~ spl0_5
| ~ spl0_44 ),
inference(resolution,[],[f382,f125]) ).
fof(f382,plain,
( ! [X3,X10,X0,X5] :
( ~ between(X10,X3,X5)
| X3 = X5
| ~ between(X3,X5,X0)
| between(X10,X5,X0) )
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f381]) ).
fof(f1332,plain,
( spl0_105
| ~ spl0_31
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f427,f389,f247,f1330]) ).
fof(f1330,plain,
( spl0_105
<=> ! [X0,X1] :
( X0 != X1
| extension(X0,X1,X0,X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f247,plain,
( spl0_31
<=> ! [X3,X10] :
( X3 = X10
| extension(X10,X3,X10,X3) != X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f427,plain,
( ! [X0,X1] :
( X0 != X1
| extension(X0,X1,X0,X1) = X1 )
| ~ spl0_31
| ~ spl0_46 ),
inference(superposition,[],[f248,f390]) ).
fof(f248,plain,
( ! [X3,X10] :
( extension(X10,X3,X10,X3) != X3
| X3 = X10 )
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f247]) ).
fof(f1328,plain,
( spl0_104
| ~ spl0_14
| ~ spl0_43 ),
inference(avatar_split_clause,[],[f405,f377,f164,f1326]) ).
fof(f1326,plain,
( spl0_104
<=> ! [X0,X3,X2,X1] :
( ~ equidistant(X0,X0,X1,X2)
| equidistant(X3,X3,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f405,plain,
( ! [X2,X3,X0,X1] :
( ~ equidistant(X0,X0,X1,X2)
| equidistant(X3,X3,X1,X2) )
| ~ spl0_14
| ~ spl0_43 ),
inference(resolution,[],[f378,f165]) ).
fof(f1324,plain,
( spl0_103
| ~ spl0_14
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f399,f373,f164,f1322]) ).
fof(f1322,plain,
( spl0_103
<=> ! [X0,X3,X2,X1] :
( ~ equidistant(X0,X0,X1,X2)
| equidistant(X1,X2,X3,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f399,plain,
( ! [X2,X3,X0,X1] :
( ~ equidistant(X0,X0,X1,X2)
| equidistant(X1,X2,X3,X3) )
| ~ spl0_14
| ~ spl0_42 ),
inference(resolution,[],[f374,f165]) ).
fof(f1320,plain,
( spl0_102
| ~ spl0_31
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f371,f353,f247,f1318]) ).
fof(f1318,plain,
( spl0_102
<=> ! [X0,X1] :
( extension(X0,X1,X1,X0) != X1
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f371,plain,
( ! [X0,X1] :
( extension(X0,X1,X1,X0) != X1
| X0 = X1 )
| ~ spl0_31
| ~ spl0_40 ),
inference(duplicate_literal_removal,[],[f366]) ).
fof(f366,plain,
( ! [X0,X1] :
( extension(X0,X1,X1,X0) != X1
| X0 = X1
| X0 = X1 )
| ~ spl0_31
| ~ spl0_40 ),
inference(superposition,[],[f248,f354]) ).
fof(f1296,plain,
( spl0_101
| ~ spl0_11
| ~ spl0_43 ),
inference(avatar_split_clause,[],[f402,f377,f151,f1294]) ).
fof(f1294,plain,
( spl0_101
<=> ! [X0,X1] :
( ~ equidistant(u,w,X0,X1)
| equidistant(u,v,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f402,plain,
( ! [X0,X1] :
( ~ equidistant(u,w,X0,X1)
| equidistant(u,v,X0,X1) )
| ~ spl0_11
| ~ spl0_43 ),
inference(resolution,[],[f378,f153]) ).
fof(f1292,plain,
( spl0_100
| ~ spl0_11
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f396,f373,f151,f1290]) ).
fof(f1290,plain,
( spl0_100
<=> ! [X0,X1] :
( ~ equidistant(u,v,X0,X1)
| equidistant(X0,X1,u,w) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f396,plain,
( ! [X0,X1] :
( ~ equidistant(u,v,X0,X1)
| equidistant(X0,X1,u,w) )
| ~ spl0_11
| ~ spl0_42 ),
inference(resolution,[],[f374,f153]) ).
fof(f1278,plain,
( spl0_99
| spl0_81
| ~ spl0_5
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f356,f349,f123,f993,f1275]) ).
fof(f1275,plain,
( spl0_99
<=> w = extension(u,v,v,w) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f349,plain,
( spl0_39
<=> ! [X5,X3,X10] :
( X3 = X10
| ~ between(X10,X3,X5)
| extension(X10,X3,X3,X5) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f356,plain,
( u = v
| w = extension(u,v,v,w)
| ~ spl0_5
| ~ spl0_39 ),
inference(resolution,[],[f350,f125]) ).
fof(f350,plain,
( ! [X3,X10,X5] :
( ~ between(X10,X3,X5)
| X3 = X10
| extension(X10,X3,X3,X5) = X5 )
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f349]) ).
fof(f1161,plain,
( ~ spl0_98
| spl0_81
| ~ spl0_24
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f304,f292,f218,f993,f1158]) ).
fof(f1158,plain,
( spl0_98
<=> between(w,u,v) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f304,plain,
( u = v
| ~ between(w,u,v)
| ~ spl0_24
| ~ spl0_33 ),
inference(resolution,[],[f293,f220]) ).
fof(f1110,plain,
( spl0_97
| ~ spl0_22
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f285,f243,f208,f1108]) ).
fof(f1108,plain,
( spl0_97
<=> ! [X0,X3,X2,X1] : equidistant(X0,X1,extension(X2,X3,X1,X0),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f243,plain,
( spl0_30
<=> ! [X10,X0,X5,X3] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X0,X5,X3,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f285,plain,
( ! [X2,X3,X0,X1] : equidistant(X0,X1,extension(X2,X3,X1,X0),X3)
| ~ spl0_22
| ~ spl0_30 ),
inference(resolution,[],[f244,f209]) ).
fof(f244,plain,
( ! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X0,X5,X3,X10) )
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f1106,plain,
( spl0_96
| ~ spl0_22
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f280,f239,f208,f1104]) ).
fof(f1104,plain,
( spl0_96
<=> ! [X0,X3,X2,X1] : equidistant(X0,X1,X2,extension(X3,X2,X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f239,plain,
( spl0_29
<=> ! [X10,X0,X5,X3] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X0,X5,X10,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f280,plain,
( ! [X2,X3,X0,X1] : equidistant(X0,X1,X2,extension(X3,X2,X1,X0))
| ~ spl0_22
| ~ spl0_29 ),
inference(resolution,[],[f240,f209]) ).
fof(f240,plain,
( ! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X0,X5,X10,X3) )
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f239]) ).
fof(f1102,plain,
( spl0_95
| ~ spl0_22
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f275,f235,f208,f1100]) ).
fof(f1100,plain,
( spl0_95
<=> ! [X0,X3,X2,X1] : equidistant(X0,X1,extension(X2,X3,X0,X1),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f235,plain,
( spl0_28
<=> ! [X10,X0,X5,X3] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X5,X0,X3,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f275,plain,
( ! [X2,X3,X0,X1] : equidistant(X0,X1,extension(X2,X3,X0,X1),X3)
| ~ spl0_22
| ~ spl0_28 ),
inference(resolution,[],[f236,f209]) ).
fof(f236,plain,
( ! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X5,X0,X3,X10) )
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f1098,plain,
( spl0_94
| ~ spl0_22
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f270,f231,f208,f1096]) ).
fof(f1096,plain,
( spl0_94
<=> ! [X2,X0,X1,X3] : equidistant(extension(X0,X1,X2,X3),X1,X3,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f270,plain,
( ! [X2,X3,X0,X1] : equidistant(extension(X0,X1,X2,X3),X1,X3,X2)
| ~ spl0_22
| ~ spl0_27 ),
inference(resolution,[],[f232,f209]) ).
fof(f1094,plain,
( spl0_93
| ~ spl0_22
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f264,f227,f208,f1092]) ).
fof(f1092,plain,
( spl0_93
<=> ! [X0,X3,X2,X1] : equidistant(X0,extension(X1,X0,X2,X3),X3,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f264,plain,
( ! [X2,X3,X0,X1] : equidistant(X0,extension(X1,X0,X2,X3),X3,X2)
| ~ spl0_22
| ~ spl0_26 ),
inference(resolution,[],[f228,f209]) ).
fof(f1090,plain,
( spl0_92
| ~ spl0_22
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f259,f223,f208,f1088]) ).
fof(f1088,plain,
( spl0_92
<=> ! [X2,X0,X1,X3] : equidistant(extension(X0,X1,X2,X3),X1,X2,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f259,plain,
( ! [X2,X3,X0,X1] : equidistant(extension(X0,X1,X2,X3),X1,X2,X3)
| ~ spl0_22
| ~ spl0_25 ),
inference(resolution,[],[f224,f209]) ).
fof(f1086,plain,
( spl0_91
| ~ spl0_22
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f254,f214,f208,f1084]) ).
fof(f1084,plain,
( spl0_91
<=> ! [X0,X3,X2,X1] : equidistant(X0,X1,X2,extension(X3,X2,X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f214,plain,
( spl0_23
<=> ! [X10,X0,X5,X3] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X5,X0,X10,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f254,plain,
( ! [X2,X3,X0,X1] : equidistant(X0,X1,X2,extension(X3,X2,X0,X1))
| ~ spl0_22
| ~ spl0_23 ),
inference(resolution,[],[f215,f209]) ).
fof(f215,plain,
( ! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X5,X0,X10,X3) )
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f1052,plain,
( spl0_90
| ~ spl0_10
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f334,f319,f147,f1050]) ).
fof(f1050,plain,
( spl0_90
<=> ! [X2,X0,X1] :
( ~ between(X0,X1,X0)
| between(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f147,plain,
( spl0_10
<=> ! [X3,X10] : between(X10,X10,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f334,plain,
( ! [X2,X0,X1] :
( ~ between(X0,X1,X0)
| between(X0,X1,X2) )
| ~ spl0_10
| ~ spl0_37 ),
inference(resolution,[],[f320,f148]) ).
fof(f148,plain,
( ! [X3,X10] : between(X10,X10,X3)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f147]) ).
fof(f1048,plain,
( spl0_89
| ~ spl0_10
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f324,f306,f147,f1046]) ).
fof(f1046,plain,
( spl0_89
<=> ! [X2,X0,X1] :
( ~ between(X0,X1,X0)
| between(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f324,plain,
( ! [X2,X0,X1] :
( ~ between(X0,X1,X0)
| between(X1,X0,X2) )
| ~ spl0_10
| ~ spl0_34 ),
inference(resolution,[],[f307,f148]) ).
fof(f1044,plain,
( spl0_88
| ~ spl0_19
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f204,f190,f186,f1042]) ).
fof(f204,plain,
( ! [X2,X3,X0,X1] : between(extension(X0,X1,X2,X3),X1,X0)
| ~ spl0_19
| ~ spl0_20 ),
inference(resolution,[],[f191,f187]) ).
fof(f1022,plain,
( spl0_87
| ~ spl0_5
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f332,f319,f123,f1020]) ).
fof(f1020,plain,
( spl0_87
<=> ! [X0] :
( ~ between(u,X0,v)
| between(u,X0,w) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f332,plain,
( ! [X0] :
( ~ between(u,X0,v)
| between(u,X0,w) )
| ~ spl0_5
| ~ spl0_37 ),
inference(resolution,[],[f320,f125]) ).
fof(f1018,plain,
( spl0_86
| ~ spl0_5
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f327,f315,f123,f1016]) ).
fof(f1016,plain,
( spl0_86
<=> ! [X0] :
( ~ between(v,X0,w)
| between(u,X0,w) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f327,plain,
( ! [X0] :
( ~ between(v,X0,w)
| between(u,X0,w) )
| ~ spl0_5
| ~ spl0_36 ),
inference(resolution,[],[f316,f125]) ).
fof(f1014,plain,
( spl0_1
| ~ spl0_85
| ~ spl0_24
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f299,f288,f218,f1011,f103]) ).
fof(f1011,plain,
( spl0_85
<=> between(v,w,u) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f299,plain,
( ~ between(v,w,u)
| v = w
| ~ spl0_24
| ~ spl0_32 ),
inference(resolution,[],[f289,f220]) ).
fof(f1009,plain,
( spl0_84
| ~ spl0_5
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f322,f306,f123,f1007]) ).
fof(f1007,plain,
( spl0_84
<=> ! [X0] :
( ~ between(u,X0,v)
| between(X0,v,w) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f322,plain,
( ! [X0] :
( ~ between(u,X0,v)
| between(X0,v,w) )
| ~ spl0_5
| ~ spl0_34 ),
inference(resolution,[],[f307,f125]) ).
fof(f1005,plain,
( ~ spl0_83
| spl0_1
| ~ spl0_5
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f300,f292,f123,f103,f1002]) ).
fof(f1002,plain,
( spl0_83
<=> between(u,w,v) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f300,plain,
( v = w
| ~ between(u,w,v)
| ~ spl0_5
| ~ spl0_33 ),
inference(resolution,[],[f293,f125]) ).
fof(f1000,plain,
( spl0_81
| ~ spl0_82
| ~ spl0_5
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f295,f288,f123,f997,f993]) ).
fof(f997,plain,
( spl0_82
<=> between(v,u,w) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f295,plain,
( ~ between(v,u,w)
| u = v
| ~ spl0_5
| ~ spl0_32 ),
inference(resolution,[],[f289,f125]) ).
fof(f840,plain,
spl0_80,
inference(avatar_split_clause,[],[f65,f838]) ).
fof(f838,plain,
( spl0_80
<=> ! [X5,X11,X10,X0,X9,X3] :
( ~ between(X10,X3,X5)
| ~ between(X11,X9,X5)
| ~ between(X10,X0,X11)
| between(X0,inner_pasch(X9,inner_pasch(X10,X0,X11,X9,X5),X10,X3,X5),X5)
| between(X3,inner_pasch(X9,inner_pasch(X10,X0,X11,X9,X5),X10,X3,X5),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f65,axiom,
! [X3,X10,X0,X11,X9,X5] :
( ~ between(X10,X3,X5)
| ~ between(X11,X9,X5)
| ~ between(X10,X0,X11)
| between(X0,inner_pasch(X9,inner_pasch(X10,X0,X11,X9,X5),X10,X3,X5),X5)
| between(X3,inner_pasch(X9,inner_pasch(X10,X0,X11,X9,X5),X10,X3,X5),X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b10) ).
fof(f826,plain,
spl0_79,
inference(avatar_split_clause,[],[f6,f824]) ).
fof(f824,plain,
( spl0_79
<=> ! [X2,X3,X9,X0,X8,X6,X1,X7] :
( X0 = X1
| ~ between(X6,X7,X8)
| ~ between(X0,X1,X2)
| ~ equidistant(X1,X3,X7,X9)
| ~ equidistant(X0,X3,X6,X9)
| ~ equidistant(X1,X2,X7,X8)
| ~ equidistant(X0,X1,X6,X7)
| equidistant(X2,X3,X8,X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f6,axiom,
! [X2,X3,X0,X1,X8,X6,X9,X7] :
( X0 = X1
| ~ between(X6,X7,X8)
| ~ between(X0,X1,X2)
| ~ equidistant(X1,X3,X7,X9)
| ~ equidistant(X0,X3,X6,X9)
| ~ equidistant(X1,X2,X7,X8)
| ~ equidistant(X0,X1,X6,X7)
| equidistant(X2,X3,X8,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',outer_five_segment) ).
fof(f803,plain,
spl0_78,
inference(avatar_split_clause,[],[f69,f801]) ).
fof(f801,plain,
( spl0_78
<=> ! [X6,X11,X9,X10,X0,X12,X5,X3] :
( ~ between(X10,X3,X5)
| ~ between(X11,X9,X12)
| ~ equidistant(X10,X3,X11,X9)
| ~ equidistant(X5,X0,X12,X6)
| ~ equidistant(X10,X0,X11,X6)
| ~ equidistant(X3,X5,X9,X12)
| equidistant(X3,X0,X9,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f69,axiom,
! [X3,X10,X0,X11,X6,X9,X5,X12] :
( ~ between(X10,X3,X5)
| ~ between(X11,X9,X12)
| ~ equidistant(X10,X3,X11,X9)
| ~ equidistant(X5,X0,X12,X6)
| ~ equidistant(X10,X0,X11,X6)
| ~ equidistant(X3,X5,X9,X12)
| equidistant(X3,X0,X9,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14) ).
fof(f799,plain,
spl0_77,
inference(avatar_split_clause,[],[f67,f797]) ).
fof(f797,plain,
( spl0_77
<=> ! [X6,X11,X9,X10,X0,X12,X5,X3] :
( ~ between(X10,X3,X5)
| ~ between(X11,X9,X12)
| ~ equidistant(X10,X3,X11,X9)
| ~ equidistant(X5,X0,X12,X6)
| ~ equidistant(X10,X0,X11,X6)
| ~ equidistant(X10,X5,X11,X12)
| equidistant(X3,X0,X9,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f67,axiom,
! [X3,X10,X0,X11,X6,X9,X5,X12] :
( ~ between(X10,X3,X5)
| ~ between(X11,X9,X12)
| ~ equidistant(X10,X3,X11,X9)
| ~ equidistant(X5,X0,X12,X6)
| ~ equidistant(X10,X0,X11,X6)
| ~ equidistant(X10,X5,X11,X12)
| equidistant(X3,X0,X9,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12) ).
fof(f768,plain,
spl0_76,
inference(avatar_split_clause,[],[f13,f766]) ).
fof(f766,plain,
( spl0_76
<=> ! [X2,X3,X0,X5,X1] :
( X3 = X5
| between(X2,X0,X1)
| between(X1,X2,X0)
| between(X0,X1,X2)
| ~ equidistant(X2,X5,X2,X3)
| ~ equidistant(X1,X5,X1,X3)
| ~ equidistant(X0,X5,X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f13,axiom,
! [X2,X3,X0,X1,X5] :
( X3 = X5
| between(X2,X0,X1)
| between(X1,X2,X0)
| between(X0,X1,X2)
| ~ equidistant(X2,X5,X2,X3)
| ~ equidistant(X1,X5,X1,X3)
| ~ equidistant(X0,X5,X0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upper_dimension) ).
fof(f745,plain,
spl0_75,
inference(avatar_split_clause,[],[f18,f743]) ).
fof(f743,plain,
( spl0_75
<=> ! [X6,X10,X9,X0,X5,X3] :
( ~ between(X3,X5,X0)
| ~ between(X10,X3,X0)
| ~ equidistant(X10,X0,X10,X6)
| ~ equidistant(X10,X3,X10,X9)
| equidistant(X10,X5,X10,continuous(X10,X3,X9,X5,X0,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f18,axiom,
! [X3,X10,X0,X6,X9,X5] :
( ~ between(X3,X5,X0)
| ~ between(X10,X3,X0)
| ~ equidistant(X10,X0,X10,X6)
| ~ equidistant(X10,X3,X10,X9)
| equidistant(X10,X5,X10,continuous(X10,X3,X9,X5,X0,X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',continuity2) ).
fof(f735,plain,
spl0_74,
inference(avatar_split_clause,[],[f17,f733]) ).
fof(f733,plain,
( spl0_74
<=> ! [X6,X10,X9,X0,X5,X3] :
( ~ between(X3,X5,X0)
| ~ between(X10,X3,X0)
| ~ equidistant(X10,X0,X10,X6)
| ~ equidistant(X10,X3,X10,X9)
| between(X9,continuous(X10,X3,X9,X5,X0,X6),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f17,axiom,
! [X3,X10,X0,X6,X9,X5] :
( ~ between(X3,X5,X0)
| ~ between(X10,X3,X0)
| ~ equidistant(X10,X0,X10,X6)
| ~ equidistant(X10,X3,X10,X9)
| between(X9,continuous(X10,X3,X9,X5,X0,X6),X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',continuity1) ).
fof(f714,plain,
spl0_73,
inference(avatar_split_clause,[],[f16,f712]) ).
fof(f712,plain,
( spl0_73
<=> ! [X10,X0,X5,X3,X1] :
( X5 = X10
| ~ between(X3,X5,X0)
| ~ between(X10,X5,X1)
| between(euclid1(X10,X3,X5,X0,X1),X1,euclid2(X10,X3,X5,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f16,axiom,
! [X3,X10,X0,X1,X5] :
( X5 = X10
| ~ between(X3,X5,X0)
| ~ between(X10,X5,X1)
| between(euclid1(X10,X3,X5,X0,X1),X1,euclid2(X10,X3,X5,X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',euclid3) ).
fof(f700,plain,
spl0_72,
inference(avatar_split_clause,[],[f95,f698]) ).
fof(f95,plain,
! [X2,X3,X10,X0,X1,X5] :
( ~ equidistant(X5,X0,X1,X2)
| extension(extension(X3,X10,lower_dimension_point_1,lower_dimension_point_2),X10,X5,X0) = extension(extension(X3,X10,lower_dimension_point_1,lower_dimension_point_2),X10,X1,X2) ),
inference(definition_unfolding,[],[f75,f20,f20]) ).
fof(f20,axiom,
! [X3,X10,X11,X12] : insertion(X11,X12,X10,X3) = extension(extension(X12,X11,lower_dimension_point_1,lower_dimension_point_2),X11,X10,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',insertion) ).
fof(f75,axiom,
! [X2,X3,X10,X0,X1,X5] :
( ~ equidistant(X5,X0,X1,X2)
| insertion(X10,X3,X5,X0) = insertion(X10,X3,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i4) ).
fof(f689,plain,
( spl0_71
| ~ spl0_11
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f281,f243,f151,f686]) ).
fof(f686,plain,
( spl0_71
<=> equidistant(w,u,v,u) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f281,plain,
( equidistant(w,u,v,u)
| ~ spl0_11
| ~ spl0_30 ),
inference(resolution,[],[f244,f153]) ).
fof(f670,plain,
spl0_70,
inference(avatar_split_clause,[],[f76,f668]) ).
fof(f76,axiom,
! [X3,X10,X11,X9,X5,X12] :
( ~ between(X10,X3,X5)
| between(X11,X9,X12)
| ~ equidistant(X10,X5,X11,X12)
| ~ equidistant(X3,X5,X9,X12)
| ~ equidistant(X10,X3,X11,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b11) ).
fof(f666,plain,
spl0_69,
inference(avatar_split_clause,[],[f68,f664]) ).
fof(f68,axiom,
! [X3,X10,X11,X9,X5,X12] :
( ~ between(X10,X3,X5)
| ~ between(X11,X9,X12)
| ~ equidistant(X10,X5,X11,X12)
| ~ equidistant(X10,X3,X11,X9)
| equidistant(X3,X5,X9,X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13) ).
fof(f662,plain,
spl0_68,
inference(avatar_split_clause,[],[f38,f660]) ).
fof(f38,axiom,
! [X3,X10,X11,X9,X5,X12] :
( ~ between(X11,X9,X12)
| ~ between(X10,X3,X5)
| ~ equidistant(X3,X5,X9,X12)
| ~ equidistant(X10,X3,X11,X9)
| equidistant(X10,X5,X11,X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8) ).
fof(f645,plain,
spl0_67,
inference(avatar_split_clause,[],[f97,f643]) ).
fof(f643,plain,
( spl0_67
<=> ! [X11,X10,X12,X5,X3] :
( ~ between(X10,X3,X5)
| ~ equidistant(X10,X5,X11,X12)
| equidistant(X3,X5,extension(extension(X12,X11,lower_dimension_point_1,lower_dimension_point_2),X11,X10,X3),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f97,plain,
! [X3,X10,X11,X5,X12] :
( ~ between(X10,X3,X5)
| ~ equidistant(X10,X5,X11,X12)
| equidistant(X3,X5,extension(extension(X12,X11,lower_dimension_point_1,lower_dimension_point_2),X11,X10,X3),X12) ),
inference(definition_unfolding,[],[f73,f20]) ).
fof(f73,axiom,
! [X3,X10,X11,X5,X12] :
( ~ between(X10,X3,X5)
| ~ equidistant(X10,X5,X11,X12)
| equidistant(X3,X5,insertion(X11,X12,X10,X3),X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i2_3) ).
fof(f635,plain,
spl0_66,
inference(avatar_split_clause,[],[f96,f633]) ).
fof(f96,plain,
! [X3,X10,X11,X5,X12] :
( ~ between(X10,X3,X5)
| ~ equidistant(X10,X5,X11,X12)
| between(X11,extension(extension(X12,X11,lower_dimension_point_1,lower_dimension_point_2),X11,X10,X3),X12) ),
inference(definition_unfolding,[],[f72,f20]) ).
fof(f72,axiom,
! [X3,X10,X11,X5,X12] :
( ~ between(X10,X3,X5)
| ~ equidistant(X10,X5,X11,X12)
| between(X11,insertion(X11,X12,X10,X3),X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i2_2) ).
fof(f625,plain,
( spl0_65
| ~ spl0_11
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f276,f239,f151,f622]) ).
fof(f622,plain,
( spl0_65
<=> equidistant(w,u,u,v) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f276,plain,
( equidistant(w,u,u,v)
| ~ spl0_11
| ~ spl0_29 ),
inference(resolution,[],[f240,f153]) ).
fof(f588,plain,
spl0_64,
inference(avatar_split_clause,[],[f66,f586]) ).
fof(f66,axiom,
! [X3,X10,X5,X12] :
( X5 = X12
| X3 = X10
| ~ between(X10,X3,X5)
| ~ equidistant(X3,X5,X3,X12)
| ~ equidistant(X10,X5,X10,X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11) ).
fof(f584,plain,
spl0_63,
inference(avatar_split_clause,[],[f15,f582]) ).
fof(f582,plain,
( spl0_63
<=> ! [X10,X0,X5,X3,X1] :
( X5 = X10
| ~ between(X3,X5,X0)
| ~ between(X10,X5,X1)
| between(X10,X0,euclid2(X10,X3,X5,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f15,axiom,
! [X3,X10,X0,X1,X5] :
( X5 = X10
| ~ between(X3,X5,X0)
| ~ between(X10,X5,X1)
| between(X10,X0,euclid2(X10,X3,X5,X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',euclid2) ).
fof(f580,plain,
spl0_62,
inference(avatar_split_clause,[],[f14,f578]) ).
fof(f14,axiom,
! [X3,X10,X0,X1,X5] :
( X5 = X10
| ~ between(X3,X5,X0)
| ~ between(X10,X5,X1)
| between(X10,X3,euclid1(X10,X3,X5,X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',euclid1) ).
fof(f539,plain,
( spl0_61
| ~ spl0_11
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f271,f235,f151,f536]) ).
fof(f536,plain,
( spl0_61
<=> equidistant(u,w,v,u) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f271,plain,
( equidistant(u,w,v,u)
| ~ spl0_11
| ~ spl0_28 ),
inference(resolution,[],[f236,f153]) ).
fof(f534,plain,
spl0_60,
inference(avatar_split_clause,[],[f79,f532]) ).
fof(f79,axiom,
! [X3,X10,X0,X5] :
( X0 = X5
| ~ between(X10,X5,X0)
| ~ between(X3,X5,X0)
| between(X3,X10,X5)
| between(X10,X3,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7) ).
fof(f530,plain,
spl0_59,
inference(avatar_split_clause,[],[f78,f528]) ).
fof(f78,axiom,
! [X3,X10,X0,X5] :
( X3 = X10
| ~ between(X10,X3,X5)
| ~ between(X10,X3,X0)
| between(X3,X0,X5)
| between(X3,X5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b13) ).
fof(f526,plain,
spl0_58,
inference(avatar_split_clause,[],[f77,f524]) ).
fof(f77,axiom,
! [X3,X10,X0,X5] :
( X3 = X10
| ~ between(X10,X3,X5)
| ~ between(X10,X3,X0)
| between(X10,X0,X5)
| between(X10,X5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b12) ).
fof(f522,plain,
spl0_57,
inference(avatar_split_clause,[],[f41,f520]) ).
fof(f41,axiom,
! [X2,X3,X10,X0,X1,X5] :
( X3 = X10
| ~ equidistant(X5,X0,X1,X2)
| extension(X10,X3,X5,X0) = extension(X10,X3,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_2) ).
fof(f518,plain,
spl0_56,
inference(avatar_split_clause,[],[f39,f516]) ).
fof(f39,axiom,
! [X3,X10,X0,X5] :
( X0 = X5
| X3 = X10
| ~ between(X10,X3,X5)
| ~ between(X10,X3,X0)
| ~ equidistant(X3,X5,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9) ).
fof(f478,plain,
spl0_55,
inference(avatar_split_clause,[],[f70,f476]) ).
fof(f70,axiom,
! [X3,X10,X0,X5] :
( X0 = X3
| ~ between(X10,X3,X5)
| ~ equidistant(X5,X3,X5,X0)
| ~ equidistant(X10,X3,X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d15) ).
fof(f474,plain,
spl0_54,
inference(avatar_split_clause,[],[f9,f472]) ).
fof(f9,axiom,
! [X3,X10,X0,X1,X5] :
( ~ between(X10,X3,X5)
| ~ between(X1,X0,X5)
| between(X0,inner_pasch(X10,X3,X5,X0,X1),X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inner_pasch2) ).
fof(f470,plain,
( spl0_53
| ~ spl0_11
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f266,f231,f151,f467]) ).
fof(f467,plain,
( spl0_53
<=> equidistant(v,u,w,u) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f266,plain,
( equidistant(v,u,w,u)
| ~ spl0_11
| ~ spl0_27 ),
inference(resolution,[],[f232,f153]) ).
fof(f465,plain,
spl0_52,
inference(avatar_split_clause,[],[f8,f463]) ).
fof(f8,axiom,
! [X3,X10,X0,X1,X5] :
( ~ between(X10,X3,X5)
| ~ between(X1,X0,X5)
| between(X3,inner_pasch(X10,X3,X5,X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inner_pasch1) ).
fof(f446,plain,
spl0_51,
inference(avatar_split_clause,[],[f82,f444]) ).
fof(f82,axiom,
! [X3,X10,X0,X1,X5] :
( ~ between(X10,X3,X1)
| ~ between(X10,X0,X1)
| ~ between(X3,X5,X0)
| between(X10,X5,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8) ).
fof(f442,plain,
spl0_50,
inference(avatar_split_clause,[],[f81,f440]) ).
fof(f81,axiom,
! [X3,X10,X0,X5] :
( ~ between(X10,X5,X0)
| ~ between(X10,X3,X0)
| between(X5,X3,X0)
| between(X3,X5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b14) ).
fof(f438,plain,
spl0_49,
inference(avatar_split_clause,[],[f80,f436]) ).
fof(f80,axiom,
! [X3,X10,X0,X5] :
( ~ between(X10,X5,X0)
| ~ between(X10,X3,X0)
| between(X10,X5,X3)
| between(X10,X3,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9) ).
fof(f417,plain,
( spl0_48
| ~ spl0_11
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f260,f227,f151,f414]) ).
fof(f414,plain,
( spl0_48
<=> equidistant(u,v,w,u) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f260,plain,
( equidistant(u,v,w,u)
| ~ spl0_11
| ~ spl0_26 ),
inference(resolution,[],[f228,f153]) ).
fof(f395,plain,
spl0_47,
inference(avatar_split_clause,[],[f94,f393]) ).
fof(f94,plain,
! [X3,X10,X5] :
( ~ between(X10,X3,X5)
| extension(extension(X5,X10,lower_dimension_point_1,lower_dimension_point_2),X10,X10,X3) = X3 ),
inference(definition_unfolding,[],[f74,f20]) ).
fof(f74,axiom,
! [X3,X10,X5] :
( ~ between(X10,X3,X5)
| insertion(X10,X5,X10,X3) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i3) ).
fof(f391,plain,
spl0_46,
inference(avatar_split_clause,[],[f88,f389]) ).
fof(f88,plain,
! [X3,X10] : extension(extension(X10,X3,X10,X3),X3,extension(X10,X3,X10,X3),X3) = X10,
inference(definition_unfolding,[],[f44,f19,f19]) ).
fof(f19,axiom,
! [X3,X10] : reflection(X10,X3) = extension(X10,X3,X10,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflection) ).
fof(f44,axiom,
! [X3,X10] : reflection(reflection(X10,X3),X3) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r6) ).
fof(f387,plain,
spl0_45,
inference(avatar_split_clause,[],[f56,f385]) ).
fof(f56,axiom,
! [X3,X10,X0,X5] :
( X3 = X5
| ~ between(X10,X3,X5)
| ~ between(X3,X5,X0)
| between(X10,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b7) ).
fof(f383,plain,
spl0_44,
inference(avatar_split_clause,[],[f55,f381]) ).
fof(f55,axiom,
! [X3,X10,X0,X5] :
( X3 = X5
| ~ between(X10,X3,X5)
| ~ between(X3,X5,X0)
| between(X10,X5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b6) ).
fof(f379,plain,
spl0_43,
inference(avatar_split_clause,[],[f29,f377]) ).
fof(f29,axiom,
! [X2,X3,X10,X0,X1,X5] :
( ~ equidistant(X10,X3,X5,X0)
| ~ equidistant(X5,X0,X1,X2)
| equidistant(X10,X3,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5) ).
fof(f375,plain,
spl0_42,
inference(avatar_split_clause,[],[f2,f373]) ).
fof(f2,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ equidistant(X0,X1,X2,X3)
| ~ equidistant(X0,X1,X4,X5)
| equidistant(X2,X3,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_for_equidistance) ).
fof(f365,plain,
( spl0_41
| ~ spl0_11
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f255,f223,f151,f362]) ).
fof(f362,plain,
( spl0_41
<=> equidistant(v,u,u,w) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f255,plain,
( equidistant(v,u,u,w)
| ~ spl0_11
| ~ spl0_25 ),
inference(resolution,[],[f224,f153]) ).
fof(f355,plain,
spl0_40,
inference(avatar_split_clause,[],[f42,f353]) ).
fof(f42,axiom,
! [X3,X10] :
( X3 = X10
| extension(X10,X3,X10,X3) = extension(X10,X3,X3,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_3) ).
fof(f351,plain,
spl0_39,
inference(avatar_split_clause,[],[f40,f349]) ).
fof(f40,axiom,
! [X3,X10,X5] :
( X3 = X10
| ~ between(X10,X3,X5)
| extension(X10,X3,X3,X5) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_1) ).
fof(f340,plain,
spl0_38,
inference(avatar_split_clause,[],[f63,f338]) ).
fof(f63,axiom,
! [X3,X10,X0,X5] : equidistant(X3,extension(X10,X3,lower_dimension_point_1,lower_dimension_point_2),X0,extension(X5,X0,lower_dimension_point_1,lower_dimension_point_2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e3_2) ).
fof(f321,plain,
spl0_37,
inference(avatar_split_clause,[],[f58,f319]) ).
fof(f58,axiom,
! [X3,X10,X0,X5] :
( ~ between(X10,X3,X5)
| ~ between(X10,X5,X0)
| between(X10,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b9) ).
fof(f317,plain,
spl0_36,
inference(avatar_split_clause,[],[f57,f315]) ).
fof(f57,axiom,
! [X3,X10,X0,X5] :
( ~ between(X10,X3,X0)
| ~ between(X3,X5,X0)
| between(X10,X5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b8) ).
fof(f313,plain,
( spl0_35
| ~ spl0_11
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f250,f214,f151,f310]) ).
fof(f310,plain,
( spl0_35
<=> equidistant(u,w,u,v) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f250,plain,
( equidistant(u,w,u,v)
| ~ spl0_11
| ~ spl0_23 ),
inference(resolution,[],[f215,f153]) ).
fof(f308,plain,
spl0_34,
inference(avatar_split_clause,[],[f54,f306]) ).
fof(f54,axiom,
! [X3,X10,X0,X5] :
( ~ between(X10,X3,X5)
| ~ between(X10,X5,X0)
| between(X3,X5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b5) ).
fof(f294,plain,
spl0_33,
inference(avatar_split_clause,[],[f50,f292]) ).
fof(f50,axiom,
! [X3,X10,X5] :
( X3 = X5
| ~ between(X10,X5,X3)
| ~ between(X10,X3,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b3) ).
fof(f290,plain,
spl0_32,
inference(avatar_split_clause,[],[f49,f288]) ).
fof(f49,axiom,
! [X3,X10,X5] :
( X3 = X10
| ~ between(X3,X10,X5)
| ~ between(X10,X3,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b2) ).
fof(f249,plain,
spl0_31,
inference(avatar_split_clause,[],[f93,f247]) ).
fof(f93,plain,
! [X3,X10] :
( X3 = X10
| extension(X10,X3,X10,X3) != X3 ),
inference(definition_unfolding,[],[f36,f19]) ).
fof(f36,axiom,
! [X3,X10] :
( X3 = X10
| reflection(X10,X3) != X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r4) ).
fof(f245,plain,
spl0_30,
inference(avatar_split_clause,[],[f28,f243]) ).
fof(f28,axiom,
! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X0,X5,X3,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_5) ).
fof(f241,plain,
spl0_29,
inference(avatar_split_clause,[],[f27,f239]) ).
fof(f27,axiom,
! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X0,X5,X10,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_4) ).
fof(f237,plain,
spl0_28,
inference(avatar_split_clause,[],[f26,f235]) ).
fof(f26,axiom,
! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X5,X0,X3,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_3) ).
fof(f233,plain,
spl0_27,
inference(avatar_split_clause,[],[f25,f231]) ).
fof(f25,axiom,
! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X3,X10,X0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_2) ).
fof(f229,plain,
spl0_26,
inference(avatar_split_clause,[],[f24,f227]) ).
fof(f24,axiom,
! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X10,X3,X0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_1) ).
fof(f225,plain,
spl0_25,
inference(avatar_split_clause,[],[f23,f223]) ).
fof(f23,axiom,
! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X3,X10,X5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3) ).
fof(f221,plain,
( spl0_24
| ~ spl0_5
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f201,f190,f123,f218]) ).
fof(f201,plain,
( between(w,v,u)
| ~ spl0_5
| ~ spl0_20 ),
inference(resolution,[],[f191,f125]) ).
fof(f216,plain,
spl0_23,
inference(avatar_split_clause,[],[f22,f214]) ).
fof(f22,axiom,
! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X5,X0,X10,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2) ).
fof(f210,plain,
spl0_22,
inference(avatar_split_clause,[],[f5,f208]) ).
fof(f5,axiom,
! [X3,X0,X1,X5] : equidistant(X1,extension(X0,X1,X5,X3),X5,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',segment_construction2) ).
fof(f196,plain,
spl0_21,
inference(avatar_split_clause,[],[f100,f194]) ).
fof(f100,plain,
! [X3,X10,X5] :
( ~ between(X10,X5,X10)
| between(X3,X5,X10) ),
inference(equality_resolution,[],[f46]) ).
fof(f46,axiom,
! [X3,X10,X0,X5] :
( X0 != X10
| ~ between(X10,X5,X0)
| between(X3,X5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b1) ).
fof(f192,plain,
spl0_20,
inference(avatar_split_clause,[],[f47,f190]) ).
fof(f47,axiom,
! [X3,X10,X5] :
( ~ between(X10,X3,X5)
| between(X5,X3,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1) ).
fof(f188,plain,
spl0_19,
inference(avatar_split_clause,[],[f4,f186]) ).
fof(f4,axiom,
! [X3,X0,X1,X5] : between(X0,X1,extension(X0,X1,X5,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',segment_construction1) ).
fof(f184,plain,
spl0_18,
inference(avatar_split_clause,[],[f3,f182]) ).
fof(f182,plain,
( spl0_18
<=> ! [X2,X0,X1] :
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f3,axiom,
! [X2,X0,X1] :
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_equidistance) ).
fof(f178,plain,
spl0_17,
inference(avatar_split_clause,[],[f62,f176]) ).
fof(f176,plain,
( spl0_17
<=> ! [X3,X10] : extension(X10,X3,lower_dimension_point_1,lower_dimension_point_2) != X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f62,axiom,
! [X3,X10] : extension(X10,X3,lower_dimension_point_1,lower_dimension_point_2) != X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e3_1) ).
fof(f174,plain,
spl0_16,
inference(avatar_split_clause,[],[f30,f172]) ).
fof(f172,plain,
( spl0_16
<=> ! [X5,X3,X10] : extension(X10,X3,X5,X5) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f30,axiom,
! [X3,X10,X5] : extension(X10,X3,X5,X5) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e1) ).
fof(f170,plain,
spl0_15,
inference(avatar_split_clause,[],[f7,f168]) ).
fof(f7,axiom,
! [X0,X1] :
( X0 = X1
| ~ between(X0,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_betweeness) ).
fof(f166,plain,
spl0_14,
inference(avatar_split_clause,[],[f37,f164]) ).
fof(f37,axiom,
! [X3,X10] : equidistant(X10,X10,X3,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7) ).
fof(f162,plain,
spl0_13,
inference(avatar_split_clause,[],[f21,f160]) ).
fof(f21,axiom,
! [X3,X10] : equidistant(X10,X3,X10,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1) ).
fof(f158,plain,
spl0_12,
inference(avatar_split_clause,[],[f1,f156]) ).
fof(f1,axiom,
! [X0,X1] : equidistant(X0,X1,X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).
fof(f154,plain,
spl0_11,
inference(avatar_split_clause,[],[f84,f151]) ).
fof(f84,axiom,
equidistant(u,v,u,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_to_v_equals_u_to_w) ).
fof(f149,plain,
spl0_10,
inference(avatar_split_clause,[],[f48,f147]) ).
fof(f48,axiom,
! [X3,X10] : between(X10,X10,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2) ).
fof(f145,plain,
spl0_9,
inference(avatar_split_clause,[],[f45,f143]) ).
fof(f45,axiom,
! [X3,X10] : between(X10,X3,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3) ).
fof(f141,plain,
~ spl0_8,
inference(avatar_split_clause,[],[f12,f138]) ).
fof(f138,plain,
( spl0_8
<=> between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f12,axiom,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension3) ).
fof(f136,plain,
~ spl0_7,
inference(avatar_split_clause,[],[f11,f133]) ).
fof(f133,plain,
( spl0_7
<=> between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f11,axiom,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension2) ).
fof(f131,plain,
~ spl0_6,
inference(avatar_split_clause,[],[f10,f128]) ).
fof(f128,plain,
( spl0_6
<=> between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f10,axiom,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension1) ).
fof(f126,plain,
spl0_5,
inference(avatar_split_clause,[],[f83,f123]) ).
fof(f83,axiom,
between(u,v,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_between_u_and_w) ).
fof(f121,plain,
~ spl0_4,
inference(avatar_split_clause,[],[f61,f118]) ).
fof(f118,plain,
( spl0_4
<=> lower_dimension_point_1 = lower_dimension_point_3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f61,axiom,
lower_dimension_point_1 != lower_dimension_point_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e2_3) ).
fof(f116,plain,
~ spl0_3,
inference(avatar_split_clause,[],[f60,f113]) ).
fof(f113,plain,
( spl0_3
<=> lower_dimension_point_2 = lower_dimension_point_3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f60,axiom,
lower_dimension_point_2 != lower_dimension_point_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e2_2) ).
fof(f111,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f59,f108]) ).
fof(f108,plain,
( spl0_2
<=> lower_dimension_point_1 = lower_dimension_point_2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f59,axiom,
lower_dimension_point_1 != lower_dimension_point_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e2_1) ).
fof(f106,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f85,f103]) ).
fof(f85,axiom,
v != w,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_v_equals_w) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GEO053-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.10/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n023.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Apr 30 05:53:25 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % (16709)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (16712)WARNING: value z3 for option sas not known
% 0.14/0.38 % (16711)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (16713)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (16714)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.38 % (16716)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.38 % (16712)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.38 % (16715)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.38 % (16710)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 Detected minimum model sizes of [3]
% 0.14/0.38 Detected maximum model sizes of [max]
% 0.14/0.39 TRYING [3]
% 0.21/0.44 Detected minimum model sizes of [3]
% 0.21/0.44 Detected maximum model sizes of [max]
% 0.21/0.50 TRYING [3]
% 0.21/0.51 % (16714)First to succeed.
% 0.21/0.52 % (16714)Refutation found. Thanks to Tanya!
% 0.21/0.52 % SZS status Unsatisfiable for theBenchmark
% 0.21/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.53 % (16714)------------------------------
% 0.21/0.53 % (16714)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.53 % (16714)Termination reason: Refutation
% 0.21/0.53
% 0.21/0.53 % (16714)Memory used [KB]: 2640
% 0.21/0.53 % (16714)Time elapsed: 0.146 s
% 0.21/0.53 % (16714)Instructions burned: 307 (million)
% 0.21/0.53 % (16714)------------------------------
% 0.21/0.53 % (16714)------------------------------
% 0.21/0.53 % (16709)Success in time 0.166 s
%------------------------------------------------------------------------------