TSTP Solution File: GEO037-3 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : GEO037-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n026.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 : Sun May 5 05:14:43 EDT 2024
% Result : Unsatisfiable 0.17s 0.42s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 176
% Syntax : Number of formulae : 435 ( 68 unt; 0 def)
% Number of atoms : 1397 ( 162 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 1737 ( 775 ~; 838 |; 0 &)
% ( 124 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 128 ( 126 usr; 125 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-6 aty)
% Number of variables : 1102 (1102 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1727,plain,
$false,
inference(avatar_sat_refutation,[],[f77,f82,f87,f92,f97,f102,f106,f110,f114,f118,f122,f135,f139,f143,f149,f153,f157,f161,f167,f176,f182,f186,f190,f194,f198,f202,f206,f210,f214,f249,f253,f265,f269,f273,f285,f293,f297,f313,f317,f321,f325,f329,f359,f363,f391,f395,f399,f415,f419,f441,f449,f466,f474,f491,f500,f510,f514,f518,f522,f526,f530,f534,f648,f652,f656,f660,f690,f698,f702,f734,f738,f742,f824,f828,f837,f841,f845,f882,f886,f888,f911,f931,f951,f956,f975,f979,f984,f988,f1048,f1053,f1060,f1064,f1101,f1137,f1141,f1145,f1149,f1256,f1260,f1279,f1283,f1309,f1313,f1317,f1321,f1325,f1363,f1367,f1416,f1420,f1440,f1444,f1481,f1485,f1489,f1493,f1592,f1596,f1600,f1604,f1608,f1676,f1680,f1684,f1726]) ).
fof(f1726,plain,
( spl0_1
| ~ spl0_17
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f1615,f1323,f147,f74]) ).
fof(f74,plain,
( spl0_1
<=> lower_dimension_point_1 = lower_dimension_point_2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f147,plain,
( spl0_17
<=> ! [X2,X0,X1] :
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f1323,plain,
( spl0_106
<=> ! [X0] : equidistant(lower_dimension_point_1,lower_dimension_point_2,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f1615,plain,
( lower_dimension_point_1 = lower_dimension_point_2
| ~ spl0_17
| ~ spl0_106 ),
inference(resolution,[],[f1324,f148]) ).
fof(f148,plain,
( ! [X2,X0,X1] :
( ~ equidistant(X0,X1,X2,X2)
| X0 = X1 )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f147]) ).
fof(f1324,plain,
( ! [X0] : equidistant(lower_dimension_point_1,lower_dimension_point_2,X0,X0)
| ~ spl0_106 ),
inference(avatar_component_clause,[],[f1323]) ).
fof(f1684,plain,
( spl0_124
| ~ spl0_21
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f445,f439,f174,f1682]) ).
fof(f1682,plain,
( spl0_124
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ between(X0,extension(X1,X0,X2,X3),X4)
| ~ equidistant(extension(X1,X0,X2,X3),X4,X3,X5)
| ~ between(X2,X3,X5)
| equidistant(X0,X4,X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f174,plain,
( spl0_21
<=> ! [X3,X0,X5,X1] : equidistant(X1,extension(X0,X1,X5,X3),X5,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f439,plain,
( spl0_51
<=> ! [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_51])]) ).
fof(f445,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ between(X0,extension(X1,X0,X2,X3),X4)
| ~ equidistant(extension(X1,X0,X2,X3),X4,X3,X5)
| ~ between(X2,X3,X5)
| equidistant(X0,X4,X2,X5) )
| ~ spl0_21
| ~ spl0_51 ),
inference(resolution,[],[f440,f175]) ).
fof(f175,plain,
( ! [X3,X0,X1,X5] : equidistant(X1,extension(X0,X1,X5,X3),X5,X3)
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f440,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_51 ),
inference(avatar_component_clause,[],[f439]) ).
fof(f1680,plain,
( spl0_123
| ~ spl0_33
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f382,f361,f263,f1678]) ).
fof(f1678,plain,
( spl0_123
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ between(X0,X1,X2)
| ~ between(X3,X4,X2)
| ~ between(X1,X5,inner_pasch(X3,X4,X2,X1,X0))
| between(X5,inner_pasch(X3,X4,X2,X1,X0),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f263,plain,
( spl0_33
<=> ! [X10,X0,X5,X3] :
( ~ between(X10,X3,X5)
| ~ between(X10,X5,X0)
| between(X3,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f361,plain,
( spl0_45
<=> ! [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_45])]) ).
fof(f382,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ between(X0,X1,X2)
| ~ between(X3,X4,X2)
| ~ between(X1,X5,inner_pasch(X3,X4,X2,X1,X0))
| between(X5,inner_pasch(X3,X4,X2,X1,X0),X3) )
| ~ spl0_33
| ~ spl0_45 ),
inference(resolution,[],[f362,f264]) ).
fof(f264,plain,
( ! [X3,X10,X0,X5] :
( ~ between(X10,X5,X0)
| ~ between(X10,X3,X5)
| between(X3,X5,X0) )
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f263]) ).
fof(f362,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_45 ),
inference(avatar_component_clause,[],[f361]) ).
fof(f1676,plain,
( spl0_122
| ~ spl0_33
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f370,f357,f263,f1674]) ).
fof(f1674,plain,
( spl0_122
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ between(X0,X1,X2)
| ~ between(X3,X4,X2)
| ~ between(X4,X5,inner_pasch(X3,X4,X2,X1,X0))
| between(X5,inner_pasch(X3,X4,X2,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f357,plain,
( spl0_44
<=> ! [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_44])]) ).
fof(f370,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ between(X0,X1,X2)
| ~ between(X3,X4,X2)
| ~ between(X4,X5,inner_pasch(X3,X4,X2,X1,X0))
| between(X5,inner_pasch(X3,X4,X2,X1,X0),X0) )
| ~ spl0_33
| ~ spl0_44 ),
inference(resolution,[],[f358,f264]) ).
fof(f358,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_44 ),
inference(avatar_component_clause,[],[f357]) ).
fof(f1608,plain,
( spl0_121
| ~ spl0_19
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f454,f447,f155,f1606]) ).
fof(f1606,plain,
( spl0_121
<=> ! [X4,X0,X3,X2,X1] :
( ~ between(X0,X1,X2)
| ~ between(X3,X1,X4)
| X1 = X3
| between(euclid2(X3,X0,X1,X2,X4),X4,euclid1(X3,X0,X1,X2,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f155,plain,
( spl0_19
<=> ! [X5,X3,X10] :
( ~ between(X10,X3,X5)
| between(X5,X3,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f447,plain,
( spl0_52
<=> ! [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_52])]) ).
fof(f454,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ between(X0,X1,X2)
| ~ between(X3,X1,X4)
| X1 = X3
| between(euclid2(X3,X0,X1,X2,X4),X4,euclid1(X3,X0,X1,X2,X4)) )
| ~ spl0_19
| ~ spl0_52 ),
inference(resolution,[],[f448,f156]) ).
fof(f156,plain,
( ! [X3,X10,X5] :
( ~ between(X10,X3,X5)
| between(X5,X3,X10) )
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f448,plain,
( ! [X3,X10,X0,X1,X5] :
( between(euclid1(X10,X3,X5,X0,X1),X1,euclid2(X10,X3,X5,X0,X1))
| ~ between(X3,X5,X0)
| ~ between(X10,X5,X1)
| X5 = X10 )
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f447]) ).
fof(f1604,plain,
( spl0_120
| ~ spl0_32
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f381,f361,f251,f1602]) ).
fof(f1602,plain,
( spl0_120
<=> ! [X4,X0,X3,X2,X1] :
( ~ between(X0,X1,X2)
| ~ between(X3,X4,X2)
| inner_pasch(X3,X4,X2,X1,X0) = X3
| ~ between(X1,X3,inner_pasch(X3,X4,X2,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f251,plain,
( spl0_32
<=> ! [X5,X3,X10] :
( X3 = X5
| ~ between(X10,X5,X3)
| ~ between(X10,X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f381,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ between(X0,X1,X2)
| ~ between(X3,X4,X2)
| inner_pasch(X3,X4,X2,X1,X0) = X3
| ~ between(X1,X3,inner_pasch(X3,X4,X2,X1,X0)) )
| ~ spl0_32
| ~ spl0_45 ),
inference(resolution,[],[f362,f252]) ).
fof(f252,plain,
( ! [X3,X10,X5] :
( ~ between(X10,X5,X3)
| X3 = X5
| ~ between(X10,X3,X5) )
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f251]) ).
fof(f1600,plain,
( spl0_119
| ~ spl0_31
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f380,f361,f247,f1598]) ).
fof(f1598,plain,
( spl0_119
<=> ! [X4,X0,X3,X2,X1] :
( ~ between(X0,X1,X2)
| ~ between(X3,X4,X2)
| ~ between(inner_pasch(X3,X4,X2,X1,X0),X1,X3)
| inner_pasch(X3,X4,X2,X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f247,plain,
( spl0_31
<=> ! [X5,X3,X10] :
( X3 = X10
| ~ between(X3,X10,X5)
| ~ between(X10,X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f380,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ between(X0,X1,X2)
| ~ between(X3,X4,X2)
| ~ between(inner_pasch(X3,X4,X2,X1,X0),X1,X3)
| inner_pasch(X3,X4,X2,X1,X0) = X1 )
| ~ spl0_31
| ~ spl0_45 ),
inference(resolution,[],[f362,f248]) ).
fof(f248,plain,
( ! [X3,X10,X5] :
( ~ between(X10,X3,X5)
| ~ between(X3,X10,X5)
| X3 = X10 )
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f247]) ).
fof(f1596,plain,
( spl0_118
| ~ spl0_32
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f369,f357,f251,f1594]) ).
fof(f1594,plain,
( spl0_118
<=> ! [X4,X0,X3,X2,X1] :
( ~ between(X0,X1,X2)
| ~ between(X3,X4,X2)
| inner_pasch(X3,X4,X2,X1,X0) = X0
| ~ between(X4,X0,inner_pasch(X3,X4,X2,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f369,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ between(X0,X1,X2)
| ~ between(X3,X4,X2)
| inner_pasch(X3,X4,X2,X1,X0) = X0
| ~ between(X4,X0,inner_pasch(X3,X4,X2,X1,X0)) )
| ~ spl0_32
| ~ spl0_44 ),
inference(resolution,[],[f358,f252]) ).
fof(f1592,plain,
( spl0_117
| ~ spl0_31
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f368,f357,f247,f1590]) ).
fof(f1590,plain,
( spl0_117
<=> ! [X4,X0,X3,X2,X1] :
( ~ between(X0,X1,X2)
| ~ between(X3,X4,X2)
| ~ between(inner_pasch(X3,X4,X2,X1,X0),X4,X0)
| inner_pasch(X3,X4,X2,X1,X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f368,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ between(X0,X1,X2)
| ~ between(X3,X4,X2)
| ~ between(inner_pasch(X3,X4,X2,X1,X0),X4,X0)
| inner_pasch(X3,X4,X2,X1,X0) = X4 )
| ~ spl0_31
| ~ spl0_44 ),
inference(resolution,[],[f358,f248]) ).
fof(f1493,plain,
( spl0_116
| ~ spl0_35
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f434,f417,f271,f1491]) ).
fof(f1491,plain,
( spl0_116
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ between(X0,X1,X2)
| ~ between(X3,X1,X4)
| X1 = X3
| ~ between(X3,X5,X2)
| between(X3,X5,euclid2(X3,X0,X1,X2,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f271,plain,
( spl0_35
<=> ! [X10,X0,X5,X3] :
( ~ between(X10,X3,X5)
| ~ between(X10,X5,X0)
| between(X10,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f417,plain,
( spl0_50
<=> ! [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_50])]) ).
fof(f434,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ between(X0,X1,X2)
| ~ between(X3,X1,X4)
| X1 = X3
| ~ between(X3,X5,X2)
| between(X3,X5,euclid2(X3,X0,X1,X2,X4)) )
| ~ spl0_35
| ~ spl0_50 ),
inference(resolution,[],[f418,f272]) ).
fof(f272,plain,
( ! [X3,X10,X0,X5] :
( ~ between(X10,X5,X0)
| ~ between(X10,X3,X5)
| between(X10,X3,X0) )
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f418,plain,
( ! [X3,X10,X0,X1,X5] :
( between(X10,X0,euclid2(X10,X3,X5,X0,X1))
| ~ between(X3,X5,X0)
| ~ between(X10,X5,X1)
| X5 = X10 )
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f417]) ).
fof(f1489,plain,
( spl0_115
| ~ spl0_33
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f432,f417,f263,f1487]) ).
fof(f1487,plain,
( spl0_115
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ between(X0,X1,X2)
| ~ between(X3,X1,X4)
| X1 = X3
| ~ between(X3,X5,X2)
| between(X5,X2,euclid2(X3,X0,X1,X2,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f432,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ between(X0,X1,X2)
| ~ between(X3,X1,X4)
| X1 = X3
| ~ between(X3,X5,X2)
| between(X5,X2,euclid2(X3,X0,X1,X2,X4)) )
| ~ spl0_33
| ~ spl0_50 ),
inference(resolution,[],[f418,f264]) ).
fof(f1485,plain,
( spl0_114
| ~ spl0_35
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f425,f413,f271,f1483]) ).
fof(f1483,plain,
( spl0_114
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ between(X0,X1,X2)
| ~ between(X3,X1,X4)
| X1 = X3
| ~ between(X3,X5,X0)
| between(X3,X5,euclid1(X3,X0,X1,X2,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f413,plain,
( spl0_49
<=> ! [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_49])]) ).
fof(f425,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ between(X0,X1,X2)
| ~ between(X3,X1,X4)
| X1 = X3
| ~ between(X3,X5,X0)
| between(X3,X5,euclid1(X3,X0,X1,X2,X4)) )
| ~ spl0_35
| ~ spl0_49 ),
inference(resolution,[],[f414,f272]) ).
fof(f414,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_49 ),
inference(avatar_component_clause,[],[f413]) ).
fof(f1481,plain,
( spl0_113
| ~ spl0_33
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f423,f413,f263,f1479]) ).
fof(f1479,plain,
( spl0_113
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ between(X0,X1,X2)
| ~ between(X3,X1,X4)
| X1 = X3
| ~ between(X3,X5,X0)
| between(X5,X0,euclid1(X3,X0,X1,X2,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f423,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ between(X0,X1,X2)
| ~ between(X3,X1,X4)
| X1 = X3
| ~ between(X3,X5,X0)
| between(X5,X0,euclid1(X3,X0,X1,X2,X4)) )
| ~ spl0_33
| ~ spl0_49 ),
inference(resolution,[],[f414,f264]) ).
fof(f1444,plain,
( spl0_112
| ~ spl0_10
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f468,f464,f116,f1442]) ).
fof(f1442,plain,
( spl0_112
<=> ! [X4,X0,X3,X2,X1] :
( ~ between(X0,X1,X2)
| ~ equidistant(X0,X2,X0,X3)
| ~ between(X1,X4,X2)
| between(X1,continuous(X0,X1,X1,X4,X2,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f116,plain,
( spl0_10
<=> ! [X3,X10] : equidistant(X10,X3,X10,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f464,plain,
( spl0_53
<=> ! [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_53])]) ).
fof(f468,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ between(X0,X1,X2)
| ~ equidistant(X0,X2,X0,X3)
| ~ between(X1,X4,X2)
| between(X1,continuous(X0,X1,X1,X4,X2,X3),X3) )
| ~ spl0_10
| ~ spl0_53 ),
inference(resolution,[],[f465,f117]) ).
fof(f117,plain,
( ! [X3,X10] : equidistant(X10,X3,X10,X3)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f465,plain,
( ! [X3,X10,X0,X6,X9,X5] :
( ~ equidistant(X10,X3,X10,X9)
| ~ between(X10,X3,X0)
| ~ equidistant(X10,X0,X10,X6)
| ~ between(X3,X5,X0)
| between(X9,continuous(X10,X3,X9,X5,X0,X6),X6) )
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f464]) ).
fof(f1440,plain,
( spl0_111
| ~ spl0_31
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f430,f417,f247,f1438]) ).
fof(f1438,plain,
( spl0_111
<=> ! [X4,X0,X3,X2,X1] :
( ~ between(X0,X1,X2)
| ~ between(X3,X1,X4)
| X1 = X3
| ~ between(X2,X3,euclid2(X3,X0,X1,X2,X4))
| X2 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f430,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ between(X0,X1,X2)
| ~ between(X3,X1,X4)
| X1 = X3
| ~ between(X2,X3,euclid2(X3,X0,X1,X2,X4))
| X2 = X3 )
| ~ spl0_31
| ~ spl0_50 ),
inference(resolution,[],[f418,f248]) ).
fof(f1420,plain,
( spl0_110
| ~ spl0_31
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f421,f413,f247,f1418]) ).
fof(f1418,plain,
( spl0_110
<=> ! [X4,X0,X3,X2,X1] :
( ~ between(X0,X1,X2)
| ~ between(X3,X1,X4)
| X1 = X3
| ~ between(X0,X3,euclid1(X3,X0,X1,X2,X4))
| X0 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f421,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ between(X0,X1,X2)
| ~ between(X3,X1,X4)
| X1 = X3
| ~ between(X0,X3,euclid1(X3,X0,X1,X2,X4))
| X0 = X3 )
| ~ spl0_31
| ~ spl0_49 ),
inference(resolution,[],[f414,f248]) ).
fof(f1416,plain,
( spl0_109
| ~ spl0_18
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f342,f319,f151,f1414]) ).
fof(f1414,plain,
( spl0_109
<=> ! [X4,X0,X3,X2,X1] :
( extension(X1,X0,X2,X3) = X0
| ~ between(X0,extension(X1,X0,X2,X3),X4)
| between(X1,extension(X1,X0,X2,X3),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f151,plain,
( spl0_18
<=> ! [X3,X0,X5,X1] : between(X0,X1,extension(X0,X1,X5,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f319,plain,
( spl0_41
<=> ! [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_41])]) ).
fof(f342,plain,
( ! [X2,X3,X0,X1,X4] :
( extension(X1,X0,X2,X3) = X0
| ~ between(X0,extension(X1,X0,X2,X3),X4)
| between(X1,extension(X1,X0,X2,X3),X4) )
| ~ spl0_18
| ~ spl0_41 ),
inference(resolution,[],[f320,f152]) ).
fof(f152,plain,
( ! [X3,X0,X1,X5] : between(X0,X1,extension(X0,X1,X5,X3))
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f320,plain,
( ! [X3,X10,X0,X5] :
( ~ between(X10,X3,X5)
| X3 = X5
| ~ between(X3,X5,X0)
| between(X10,X5,X0) )
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f319]) ).
fof(f1367,plain,
( spl0_108
| ~ spl0_21
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f403,f389,f174,f1365]) ).
fof(f1365,plain,
( spl0_108
<=> ! [X0,X3,X2,X1] :
( X0 = X1
| ~ between(X1,X0,extension(X2,X0,X0,X3))
| ~ between(X1,X0,X3)
| extension(X2,X0,X0,X3) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f389,plain,
( spl0_46
<=> ! [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_46])]) ).
fof(f403,plain,
( ! [X2,X3,X0,X1] :
( X0 = X1
| ~ between(X1,X0,extension(X2,X0,X0,X3))
| ~ between(X1,X0,X3)
| extension(X2,X0,X0,X3) = X3 )
| ~ spl0_21
| ~ spl0_46 ),
inference(resolution,[],[f390,f175]) ).
fof(f390,plain,
( ! [X3,X10,X0,X5] :
( ~ equidistant(X3,X5,X3,X0)
| X3 = X10
| ~ between(X10,X3,X5)
| ~ between(X10,X3,X0)
| X0 = X5 )
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f389]) ).
fof(f1363,plain,
( spl0_107
| ~ spl0_38
| ~ spl0_43 ),
inference(avatar_split_clause,[],[f350,f327,f295,f1361]) ).
fof(f1361,plain,
( spl0_107
<=> ! [X0,X1] :
( extension(extension(X0,X1,X0,X1),X1,X1,extension(X0,X1,X0,X1)) = X0
| extension(X0,X1,X0,X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f295,plain,
( spl0_38
<=> ! [X3,X10] :
( X3 = X10
| extension(X10,X3,X10,X3) = extension(X10,X3,X3,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f327,plain,
( spl0_43
<=> ! [X3,X10] : extension(extension(X10,X3,X10,X3),X3,extension(X10,X3,X10,X3),X3) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f350,plain,
( ! [X0,X1] :
( extension(extension(X0,X1,X0,X1),X1,X1,extension(X0,X1,X0,X1)) = X0
| extension(X0,X1,X0,X1) = X1 )
| ~ spl0_38
| ~ spl0_43 ),
inference(superposition,[],[f328,f296]) ).
fof(f296,plain,
( ! [X3,X10] :
( extension(X10,X3,X10,X3) = extension(X10,X3,X3,X10)
| X3 = X10 )
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f328,plain,
( ! [X3,X10] : extension(extension(X10,X3,X10,X3),X3,extension(X10,X3,X10,X3),X3) = X10
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f327]) ).
fof(f1325,plain,
( spl0_106
| ~ spl0_65
| ~ spl0_82 ),
inference(avatar_split_clause,[],[f945,f928,f650,f1323]) ).
fof(f650,plain,
( spl0_65
<=> ! [X0,X3,X2,X1] :
( ~ equidistant(X0,X0,X1,X2)
| equidistant(X1,X2,X3,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f928,plain,
( spl0_82
<=> equidistant(v,v,lower_dimension_point_1,lower_dimension_point_2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f945,plain,
( ! [X0] : equidistant(lower_dimension_point_1,lower_dimension_point_2,X0,X0)
| ~ spl0_65
| ~ spl0_82 ),
inference(resolution,[],[f930,f651]) ).
fof(f651,plain,
( ! [X2,X3,X0,X1] :
( ~ equidistant(X0,X0,X1,X2)
| equidistant(X1,X2,X3,X3) )
| ~ spl0_65 ),
inference(avatar_component_clause,[],[f650]) ).
fof(f930,plain,
( equidistant(v,v,lower_dimension_point_1,lower_dimension_point_2)
| ~ spl0_82 ),
inference(avatar_component_clause,[],[f928]) ).
fof(f1321,plain,
( spl0_105
| ~ spl0_35
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f384,f361,f271,f1319]) ).
fof(f1319,plain,
( spl0_105
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ between(X0,X1,X2)
| ~ between(X3,X4,X2)
| ~ between(X1,X5,inner_pasch(X3,X4,X2,X1,X0))
| between(X1,X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f384,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ between(X0,X1,X2)
| ~ between(X3,X4,X2)
| ~ between(X1,X5,inner_pasch(X3,X4,X2,X1,X0))
| between(X1,X5,X3) )
| ~ spl0_35
| ~ spl0_45 ),
inference(resolution,[],[f362,f272]) ).
fof(f1317,plain,
( spl0_104
| ~ spl0_34
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f383,f361,f267,f1315]) ).
fof(f1315,plain,
( spl0_104
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ between(X0,X1,X2)
| ~ between(X3,X4,X2)
| ~ between(inner_pasch(X3,X4,X2,X1,X0),X5,X3)
| between(X1,X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f267,plain,
( spl0_34
<=> ! [X10,X0,X5,X3] :
( ~ between(X10,X3,X0)
| ~ between(X3,X5,X0)
| between(X10,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f383,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ between(X0,X1,X2)
| ~ between(X3,X4,X2)
| ~ between(inner_pasch(X3,X4,X2,X1,X0),X5,X3)
| between(X1,X5,X3) )
| ~ spl0_34
| ~ spl0_45 ),
inference(resolution,[],[f362,f268]) ).
fof(f268,plain,
( ! [X3,X10,X0,X5] :
( ~ between(X10,X3,X0)
| ~ between(X3,X5,X0)
| between(X10,X5,X0) )
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f267]) ).
fof(f1313,plain,
( spl0_103
| ~ spl0_35
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f372,f357,f271,f1311]) ).
fof(f1311,plain,
( spl0_103
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ between(X0,X1,X2)
| ~ between(X3,X4,X2)
| ~ between(X4,X5,inner_pasch(X3,X4,X2,X1,X0))
| between(X4,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f372,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ between(X0,X1,X2)
| ~ between(X3,X4,X2)
| ~ between(X4,X5,inner_pasch(X3,X4,X2,X1,X0))
| between(X4,X5,X0) )
| ~ spl0_35
| ~ spl0_44 ),
inference(resolution,[],[f358,f272]) ).
fof(f1309,plain,
( spl0_102
| ~ spl0_34
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f371,f357,f267,f1307]) ).
fof(f1307,plain,
( spl0_102
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ between(X0,X1,X2)
| ~ between(X3,X4,X2)
| ~ between(inner_pasch(X3,X4,X2,X1,X0),X5,X0)
| between(X4,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f371,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ between(X0,X1,X2)
| ~ between(X3,X4,X2)
| ~ between(inner_pasch(X3,X4,X2,X1,X0),X5,X0)
| between(X4,X5,X0) )
| ~ spl0_34
| ~ spl0_44 ),
inference(resolution,[],[f358,f268]) ).
fof(f1283,plain,
( spl0_101
| ~ spl0_19
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f429,f417,f155,f1281]) ).
fof(f1281,plain,
( spl0_101
<=> ! [X4,X0,X3,X2,X1] :
( ~ between(X0,X1,X2)
| ~ between(X3,X1,X4)
| X1 = X3
| between(euclid2(X3,X0,X1,X2,X4),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f429,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ between(X0,X1,X2)
| ~ between(X3,X1,X4)
| X1 = X3
| between(euclid2(X3,X0,X1,X2,X4),X2,X3) )
| ~ spl0_19
| ~ spl0_50 ),
inference(resolution,[],[f418,f156]) ).
fof(f1279,plain,
( spl0_100
| ~ spl0_19
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f420,f413,f155,f1277]) ).
fof(f1277,plain,
( spl0_100
<=> ! [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_100])]) ).
fof(f420,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_19
| ~ spl0_49 ),
inference(resolution,[],[f414,f156]) ).
fof(f1260,plain,
( spl0_99
| ~ spl0_18
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f346,f323,f151,f1258]) ).
fof(f1258,plain,
( spl0_99
<=> ! [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_99])]) ).
fof(f323,plain,
( spl0_42
<=> ! [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_42])]) ).
fof(f346,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_18
| ~ spl0_42 ),
inference(resolution,[],[f324,f152]) ).
fof(f324,plain,
( ! [X3,X10,X0,X5] :
( ~ between(X10,X3,X5)
| X3 = X5
| ~ between(X3,X5,X0)
| between(X10,X3,X0) )
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f323]) ).
fof(f1256,plain,
( spl0_98
| ~ spl0_66
| ~ spl0_82 ),
inference(avatar_split_clause,[],[f944,f928,f654,f1254]) ).
fof(f1254,plain,
( spl0_98
<=> ! [X0] : equidistant(X0,X0,lower_dimension_point_1,lower_dimension_point_2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f654,plain,
( spl0_66
<=> ! [X0,X3,X2,X1] :
( ~ equidistant(X0,X0,X1,X2)
| equidistant(X3,X3,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f944,plain,
( ! [X0] : equidistant(X0,X0,lower_dimension_point_1,lower_dimension_point_2)
| ~ spl0_66
| ~ spl0_82 ),
inference(resolution,[],[f930,f655]) ).
fof(f655,plain,
( ! [X2,X3,X0,X1] :
( ~ equidistant(X0,X0,X1,X2)
| equidistant(X3,X3,X1,X2) )
| ~ spl0_66 ),
inference(avatar_component_clause,[],[f654]) ).
fof(f1149,plain,
( spl0_97
| ~ spl0_10
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f443,f439,f116,f1147]) ).
fof(f1147,plain,
( spl0_97
<=> ! [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_97])]) ).
fof(f443,plain,
( ! [X2,X3,X0,X1] :
( ~ between(X0,X1,X2)
| ~ equidistant(X1,X2,X1,X3)
| ~ between(X0,X1,X3)
| equidistant(X0,X2,X0,X3) )
| ~ spl0_10
| ~ spl0_51 ),
inference(resolution,[],[f440,f117]) ).
fof(f1145,plain,
( spl0_96
| ~ spl0_9
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f442,f439,f112,f1143]) ).
fof(f1143,plain,
( spl0_96
<=> ! [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_96])]) ).
fof(f112,plain,
( spl0_9
<=> ! [X0,X1] : equidistant(X0,X1,X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f442,plain,
( ! [X2,X3,X0,X1] :
( ~ between(X0,X1,X2)
| ~ equidistant(X1,X2,X0,X3)
| ~ between(X1,X0,X3)
| equidistant(X0,X2,X1,X3) )
| ~ spl0_9
| ~ spl0_51 ),
inference(resolution,[],[f440,f113]) ).
fof(f113,plain,
( ! [X0,X1] : equidistant(X0,X1,X1,X0)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f1141,plain,
( spl0_95
| ~ spl0_21
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f410,f397,f174,f1139]) ).
fof(f1139,plain,
( spl0_95
<=> ! [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_95])]) ).
fof(f397,plain,
( spl0_48
<=> ! [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_48])]) ).
fof(f410,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( X0 = X1
| extension(X1,X0,X2,extension(X3,X2,X4,X5)) = extension(X1,X0,X4,X5) )
| ~ spl0_21
| ~ spl0_48 ),
inference(resolution,[],[f398,f175]) ).
fof(f398,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_48 ),
inference(avatar_component_clause,[],[f397]) ).
fof(f1137,plain,
( spl0_94
| ~ spl0_38
| ~ spl0_43 ),
inference(avatar_split_clause,[],[f349,f327,f295,f1135]) ).
fof(f1135,plain,
( spl0_94
<=> ! [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_94])]) ).
fof(f349,plain,
( ! [X0,X1] :
( extension(extension(X0,X1,X1,X0),X1,extension(X0,X1,X1,X0),X1) = X0
| X0 = X1 )
| ~ spl0_38
| ~ spl0_43 ),
inference(superposition,[],[f328,f296]) ).
fof(f1101,plain,
( spl0_93
| ~ spl0_14
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f898,f528,f132,f1098]) ).
fof(f1098,plain,
( spl0_93
<=> equidistant(lower_dimension_point_2,lower_dimension_point_1,v,v) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f132,plain,
( spl0_14
<=> v = extension(u,v,lower_dimension_point_1,lower_dimension_point_2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f528,plain,
( spl0_62
<=> ! [X0,X3,X2,X1] : equidistant(X0,X1,X2,extension(X3,X2,X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f898,plain,
( equidistant(lower_dimension_point_2,lower_dimension_point_1,v,v)
| ~ spl0_14
| ~ spl0_62 ),
inference(superposition,[],[f529,f134]) ).
fof(f134,plain,
( v = extension(u,v,lower_dimension_point_1,lower_dimension_point_2)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f529,plain,
( ! [X2,X3,X0,X1] : equidistant(X0,X1,X2,extension(X3,X2,X1,X0))
| ~ spl0_62 ),
inference(avatar_component_clause,[],[f528]) ).
fof(f1064,plain,
( spl0_92
| ~ spl0_19
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f379,f361,f155,f1062]) ).
fof(f1062,plain,
( spl0_92
<=> ! [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_92])]) ).
fof(f379,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_19
| ~ spl0_45 ),
inference(resolution,[],[f362,f156]) ).
fof(f1060,plain,
( spl0_91
| ~ spl0_20
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f377,f361,f159,f1058]) ).
fof(f1058,plain,
( spl0_91
<=> ! [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_91])]) ).
fof(f159,plain,
( spl0_20
<=> ! [X5,X3,X10] :
( ~ between(X10,X5,X10)
| between(X3,X5,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f377,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_20
| ~ spl0_45 ),
inference(resolution,[],[f362,f160]) ).
fof(f160,plain,
( ! [X3,X10,X5] :
( ~ between(X10,X5,X10)
| between(X3,X5,X10) )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f1053,plain,
( spl0_90
| ~ spl0_56
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f923,f908,f498,f1051]) ).
fof(f1051,plain,
( spl0_90
<=> ! [X0,X3,X2,X1] :
( ~ between(X0,x,X1)
| ~ between(X2,v,X3)
| v = X2
| ~ equidistant(X2,v,X0,extension(w,x,lower_dimension_point_1,lower_dimension_point_2))
| ~ equidistant(v,X3,x,X1)
| ~ equidistant(X2,v,X0,x)
| equidistant(X3,v,X1,extension(w,x,lower_dimension_point_1,lower_dimension_point_2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f498,plain,
( spl0_56
<=> ! [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_56])]) ).
fof(f908,plain,
( spl0_81
<=> equidistant(v,v,x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f923,plain,
( ! [X2,X3,X0,X1] :
( ~ between(X0,x,X1)
| ~ between(X2,v,X3)
| v = X2
| ~ equidistant(X2,v,X0,extension(w,x,lower_dimension_point_1,lower_dimension_point_2))
| ~ equidistant(v,X3,x,X1)
| ~ equidistant(X2,v,X0,x)
| equidistant(X3,v,X1,extension(w,x,lower_dimension_point_1,lower_dimension_point_2)) )
| ~ spl0_56
| ~ spl0_81 ),
inference(resolution,[],[f910,f499]) ).
fof(f499,plain,
( ! [X2,X3,X0,X1,X8,X6,X9,X7] :
( ~ equidistant(X1,X3,X7,X9)
| ~ between(X6,X7,X8)
| ~ between(X0,X1,X2)
| X0 = X1
| ~ equidistant(X0,X3,X6,X9)
| ~ equidistant(X1,X2,X7,X8)
| ~ equidistant(X0,X1,X6,X7)
| equidistant(X2,X3,X8,X9) )
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f498]) ).
fof(f910,plain,
( equidistant(v,v,x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2))
| ~ spl0_81 ),
inference(avatar_component_clause,[],[f908]) ).
fof(f1048,plain,
( spl0_89
| ~ spl0_51
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f922,f908,f439,f1046]) ).
fof(f1046,plain,
( spl0_89
<=> ! [X0,X1] :
( ~ between(v,v,X0)
| ~ equidistant(v,X0,extension(w,x,lower_dimension_point_1,lower_dimension_point_2),X1)
| ~ between(x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2),X1)
| equidistant(v,X0,x,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f922,plain,
( ! [X0,X1] :
( ~ between(v,v,X0)
| ~ equidistant(v,X0,extension(w,x,lower_dimension_point_1,lower_dimension_point_2),X1)
| ~ between(x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2),X1)
| equidistant(v,X0,x,X1) )
| ~ spl0_51
| ~ spl0_81 ),
inference(resolution,[],[f910,f440]) ).
fof(f988,plain,
( spl0_88
| ~ spl0_16
| ~ spl0_48
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f926,f908,f397,f141,f986]) ).
fof(f986,plain,
( spl0_88
<=> ! [X0,X1] :
( extension(X1,X0,x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2)) = X0
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f141,plain,
( spl0_16
<=> ! [X5,X3,X10] : extension(X10,X3,X5,X5) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f926,plain,
( ! [X0,X1] :
( extension(X1,X0,x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2)) = X0
| X0 = X1 )
| ~ spl0_16
| ~ spl0_48
| ~ spl0_81 ),
inference(forward_demodulation,[],[f921,f142]) ).
fof(f142,plain,
( ! [X3,X10,X5] : extension(X10,X3,X5,X5) = X3
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f921,plain,
( ! [X0,X1] :
( X0 = X1
| extension(X1,X0,v,v) = extension(X1,X0,x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2)) )
| ~ spl0_48
| ~ spl0_81 ),
inference(resolution,[],[f910,f398]) ).
fof(f984,plain,
( spl0_87
| ~ spl0_14
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f895,f516,f132,f981]) ).
fof(f981,plain,
( spl0_87
<=> equidistant(v,v,lower_dimension_point_2,lower_dimension_point_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f516,plain,
( spl0_59
<=> ! [X0,X3,X2,X1] : equidistant(X0,extension(X1,X0,X2,X3),X3,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f895,plain,
( equidistant(v,v,lower_dimension_point_2,lower_dimension_point_1)
| ~ spl0_14
| ~ spl0_59 ),
inference(superposition,[],[f517,f134]) ).
fof(f517,plain,
( ! [X2,X3,X0,X1] : equidistant(X0,extension(X1,X0,X2,X3),X3,X2)
| ~ spl0_59 ),
inference(avatar_component_clause,[],[f516]) ).
fof(f979,plain,
( spl0_86
| ~ spl0_40
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f920,f908,f315,f977]) ).
fof(f977,plain,
( spl0_86
<=> ! [X0,X1] :
( ~ equidistant(x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2),X0,X1)
| equidistant(v,v,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f315,plain,
( spl0_40
<=> ! [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_40])]) ).
fof(f920,plain,
( ! [X0,X1] :
( ~ equidistant(x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2),X0,X1)
| equidistant(v,v,X0,X1) )
| ~ spl0_40
| ~ spl0_81 ),
inference(resolution,[],[f910,f316]) ).
fof(f316,plain,
( ! [X2,X3,X10,X0,X1,X5] :
( ~ equidistant(X10,X3,X5,X0)
| ~ equidistant(X5,X0,X1,X2)
| equidistant(X10,X3,X1,X2) )
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f315]) ).
fof(f975,plain,
( spl0_85
| ~ spl0_39
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f919,f908,f311,f973]) ).
fof(f973,plain,
( spl0_85
<=> ! [X0,X1] :
( ~ equidistant(v,v,X0,X1)
| equidistant(X0,X1,x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f311,plain,
( spl0_39
<=> ! [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_39])]) ).
fof(f919,plain,
( ! [X0,X1] :
( ~ equidistant(v,v,X0,X1)
| equidistant(X0,X1,x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2)) )
| ~ spl0_39
| ~ spl0_81 ),
inference(resolution,[],[f910,f312]) ).
fof(f312,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ equidistant(X0,X1,X4,X5)
| ~ equidistant(X0,X1,X2,X3)
| equidistant(X2,X3,X4,X5) )
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f311]) ).
fof(f956,plain,
( spl0_84
| ~ spl0_28
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f917,f908,f204,f953]) ).
fof(f953,plain,
( spl0_84
<=> equidistant(extension(w,x,lower_dimension_point_1,lower_dimension_point_2),x,v,v) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f204,plain,
( spl0_28
<=> ! [X10,X0,X5,X3] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X0,X5,X10,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f917,plain,
( equidistant(extension(w,x,lower_dimension_point_1,lower_dimension_point_2),x,v,v)
| ~ spl0_28
| ~ spl0_81 ),
inference(resolution,[],[f910,f205]) ).
fof(f205,plain,
( ! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X0,X5,X10,X3) )
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f204]) ).
fof(f951,plain,
( spl0_83
| ~ spl0_24
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f914,f908,f188,f948]) ).
fof(f948,plain,
( spl0_83
<=> equidistant(v,v,extension(w,x,lower_dimension_point_1,lower_dimension_point_2),x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f188,plain,
( spl0_24
<=> ! [X10,X0,X5,X3] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X10,X3,X0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f914,plain,
( equidistant(v,v,extension(w,x,lower_dimension_point_1,lower_dimension_point_2),x)
| ~ spl0_24
| ~ spl0_81 ),
inference(resolution,[],[f910,f189]) ).
fof(f189,plain,
( ! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X10,X3,X0,X5) )
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f188]) ).
fof(f931,plain,
( spl0_82
| ~ spl0_14
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f891,f174,f132,f928]) ).
fof(f891,plain,
( equidistant(v,v,lower_dimension_point_1,lower_dimension_point_2)
| ~ spl0_14
| ~ spl0_21 ),
inference(superposition,[],[f175,f134]) ).
fof(f911,plain,
( spl0_81
| ~ spl0_12
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f889,f132,f124,f908]) ).
fof(f124,plain,
( spl0_12
<=> equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f889,plain,
( equidistant(v,v,x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2))
| ~ spl0_12
| ~ spl0_14 ),
inference(forward_demodulation,[],[f125,f134]) ).
fof(f125,plain,
( equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2))
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f888,plain,
( ~ spl0_57
| spl0_74 ),
inference(avatar_contradiction_clause,[],[f887]) ).
fof(f887,plain,
( $false
| ~ spl0_57
| spl0_74 ),
inference(resolution,[],[f823,f509]) ).
fof(f509,plain,
( ! [X2,X3,X0,X1] : equidistant(X0,X1,X2,extension(X3,X2,X0,X1))
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f508]) ).
fof(f508,plain,
( spl0_57
<=> ! [X0,X3,X2,X1] : equidistant(X0,X1,X2,extension(X3,X2,X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f823,plain,
( ~ equidistant(lower_dimension_point_1,lower_dimension_point_2,x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2))
| spl0_74 ),
inference(avatar_component_clause,[],[f821]) ).
fof(f821,plain,
( spl0_74
<=> equidistant(lower_dimension_point_1,lower_dimension_point_2,x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f886,plain,
( spl0_80
| ~ spl0_19
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f367,f357,f155,f884]) ).
fof(f884,plain,
( spl0_80
<=> ! [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_80])]) ).
fof(f367,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_19
| ~ spl0_44 ),
inference(resolution,[],[f358,f156]) ).
fof(f882,plain,
( spl0_79
| ~ spl0_20
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f365,f357,f159,f880]) ).
fof(f880,plain,
( spl0_79
<=> ! [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_79])]) ).
fof(f365,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_20
| ~ spl0_44 ),
inference(resolution,[],[f358,f160]) ).
fof(f845,plain,
( spl0_78
| ~ spl0_15
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f378,f361,f137,f843]) ).
fof(f843,plain,
( spl0_78
<=> ! [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_78])]) ).
fof(f137,plain,
( spl0_15
<=> ! [X0,X1] :
( X0 = X1
| ~ between(X0,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f378,plain,
( ! [X2,X3,X0,X1] :
( ~ between(X0,X1,X2)
| ~ between(X1,X3,X2)
| inner_pasch(X1,X3,X2,X1,X0) = X1 )
| ~ spl0_15
| ~ spl0_45 ),
inference(resolution,[],[f362,f138]) ).
fof(f138,plain,
( ! [X0,X1] :
( ~ between(X0,X1,X0)
| X0 = X1 )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f841,plain,
( spl0_77
| ~ spl0_15
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f366,f357,f137,f839]) ).
fof(f839,plain,
( spl0_77
<=> ! [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_77])]) ).
fof(f366,plain,
( ! [X2,X3,X0,X1] :
( ~ between(X0,X1,X2)
| ~ between(X3,X0,X2)
| inner_pasch(X3,X0,X2,X1,X0) = X0 )
| ~ spl0_15
| ~ spl0_44 ),
inference(resolution,[],[f358,f138]) ).
fof(f837,plain,
( spl0_76
| ~ spl0_18
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f280,f267,f151,f835]) ).
fof(f835,plain,
( spl0_76
<=> ! [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_76])]) ).
fof(f280,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ between(X0,X1,extension(X2,X0,X3,X4))
| between(X2,X1,extension(X2,X0,X3,X4)) )
| ~ spl0_18
| ~ spl0_34 ),
inference(resolution,[],[f268,f152]) ).
fof(f828,plain,
( spl0_75
| ~ spl0_18
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f260,f251,f151,f826]) ).
fof(f826,plain,
( spl0_75
<=> ! [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_75])]) ).
fof(f260,plain,
( ! [X2,X3,X0,X1] :
( extension(X0,X1,X2,X3) = X1
| ~ between(X0,extension(X0,X1,X2,X3),X1) )
| ~ spl0_18
| ~ spl0_32 ),
inference(resolution,[],[f252,f152]) ).
fof(f824,plain,
( ~ spl0_74
| spl0_12
| ~ spl0_72 ),
inference(avatar_split_clause,[],[f754,f736,f124,f821]) ).
fof(f736,plain,
( spl0_72
<=> ! [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_72])]) ).
fof(f754,plain,
( ~ equidistant(lower_dimension_point_1,lower_dimension_point_2,x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2))
| spl0_12
| ~ spl0_72 ),
inference(resolution,[],[f737,f126]) ).
fof(f126,plain,
( ~ equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2))
| spl0_12 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f737,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( equidistant(X4,extension(X5,X4,X0,X1),X2,X3)
| ~ equidistant(X0,X1,X2,X3) )
| ~ spl0_72 ),
inference(avatar_component_clause,[],[f736]) ).
fof(f742,plain,
( spl0_73
| ~ spl0_9
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f407,f397,f112,f740]) ).
fof(f740,plain,
( spl0_73
<=> ! [X0,X3,X2,X1] :
( X0 = X1
| extension(X1,X0,X2,X3) = extension(X1,X0,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f407,plain,
( ! [X2,X3,X0,X1] :
( X0 = X1
| extension(X1,X0,X2,X3) = extension(X1,X0,X3,X2) )
| ~ spl0_9
| ~ spl0_48 ),
inference(resolution,[],[f398,f113]) ).
fof(f738,plain,
( spl0_72
| ~ spl0_21
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f339,f315,f174,f736]) ).
fof(f339,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ equidistant(X0,X1,X2,X3)
| equidistant(X4,extension(X5,X4,X0,X1),X2,X3) )
| ~ spl0_21
| ~ spl0_40 ),
inference(resolution,[],[f316,f175]) ).
fof(f734,plain,
( spl0_71
| ~ spl0_21
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f335,f311,f174,f732]) ).
fof(f732,plain,
( spl0_71
<=> ! [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_71])]) ).
fof(f335,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ equidistant(X0,extension(X1,X0,X2,X3),X4,X5)
| equidistant(X4,X5,X2,X3) )
| ~ spl0_21
| ~ spl0_39 ),
inference(resolution,[],[f312,f175]) ).
fof(f702,plain,
( spl0_70
| ~ spl0_18
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f288,f271,f151,f700]) ).
fof(f700,plain,
( spl0_70
<=> ! [X4,X0,X3,X2,X1] :
( ~ between(X0,X1,X2)
| between(X0,X1,extension(X0,X2,X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f288,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ between(X0,X1,X2)
| between(X0,X1,extension(X0,X2,X3,X4)) )
| ~ spl0_18
| ~ spl0_35 ),
inference(resolution,[],[f272,f152]) ).
fof(f698,plain,
( spl0_69
| ~ spl0_18
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f276,f263,f151,f696]) ).
fof(f696,plain,
( spl0_69
<=> ! [X4,X0,X3,X2,X1] :
( ~ between(X0,X1,X2)
| between(X1,X2,extension(X0,X2,X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f276,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ between(X0,X1,X2)
| between(X1,X2,extension(X0,X2,X3,X4)) )
| ~ spl0_18
| ~ spl0_33 ),
inference(resolution,[],[f264,f152]) ).
fof(f690,plain,
( spl0_68
| ~ spl0_18
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f256,f247,f151,f688]) ).
fof(f688,plain,
( spl0_68
<=> ! [X0,X3,X2,X1] :
( ~ between(X0,X1,extension(X1,X0,X2,X3))
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f256,plain,
( ! [X2,X3,X0,X1] :
( ~ between(X0,X1,extension(X1,X0,X2,X3))
| X0 = X1 )
| ~ spl0_18
| ~ spl0_31 ),
inference(resolution,[],[f248,f152]) ).
fof(f660,plain,
( spl0_67
| ~ spl0_30
| ~ spl0_43 ),
inference(avatar_split_clause,[],[f352,f327,f212,f658]) ).
fof(f658,plain,
( spl0_67
<=> ! [X0,X1] :
( X0 != X1
| extension(X0,X1,X0,X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f212,plain,
( spl0_30
<=> ! [X3,X10] :
( X3 = X10
| extension(X10,X3,X10,X3) != X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f352,plain,
( ! [X0,X1] :
( X0 != X1
| extension(X0,X1,X0,X1) = X1 )
| ~ spl0_30
| ~ spl0_43 ),
inference(superposition,[],[f213,f328]) ).
fof(f213,plain,
( ! [X3,X10] :
( extension(X10,X3,X10,X3) != X3
| X3 = X10 )
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f212]) ).
fof(f656,plain,
( spl0_66
| ~ spl0_11
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f338,f315,f120,f654]) ).
fof(f120,plain,
( spl0_11
<=> ! [X3,X10] : equidistant(X10,X10,X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f338,plain,
( ! [X2,X3,X0,X1] :
( ~ equidistant(X0,X0,X1,X2)
| equidistant(X3,X3,X1,X2) )
| ~ spl0_11
| ~ spl0_40 ),
inference(resolution,[],[f316,f121]) ).
fof(f121,plain,
( ! [X3,X10] : equidistant(X10,X10,X3,X3)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f652,plain,
( spl0_65
| ~ spl0_11
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f334,f311,f120,f650]) ).
fof(f334,plain,
( ! [X2,X3,X0,X1] :
( ~ equidistant(X0,X0,X1,X2)
| equidistant(X1,X2,X3,X3) )
| ~ spl0_11
| ~ spl0_39 ),
inference(resolution,[],[f312,f121]) ).
fof(f648,plain,
( spl0_64
| ~ spl0_30
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f309,f295,f212,f646]) ).
fof(f646,plain,
( spl0_64
<=> ! [X0,X1] :
( extension(X0,X1,X1,X0) != X1
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f309,plain,
( ! [X0,X1] :
( extension(X0,X1,X1,X0) != X1
| X0 = X1 )
| ~ spl0_30
| ~ spl0_38 ),
inference(duplicate_literal_removal,[],[f302]) ).
fof(f302,plain,
( ! [X0,X1] :
( extension(X0,X1,X1,X0) != X1
| X0 = X1
| X0 = X1 )
| ~ spl0_30
| ~ spl0_38 ),
inference(superposition,[],[f213,f296]) ).
fof(f534,plain,
( spl0_63
| ~ spl0_21
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f242,f208,f174,f532]) ).
fof(f532,plain,
( spl0_63
<=> ! [X0,X3,X2,X1] : equidistant(X0,X1,extension(X2,X3,X1,X0),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f208,plain,
( spl0_29
<=> ! [X10,X0,X5,X3] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X0,X5,X3,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f242,plain,
( ! [X2,X3,X0,X1] : equidistant(X0,X1,extension(X2,X3,X1,X0),X3)
| ~ spl0_21
| ~ spl0_29 ),
inference(resolution,[],[f209,f175]) ).
fof(f209,plain,
( ! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X0,X5,X3,X10) )
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f208]) ).
fof(f530,plain,
( spl0_62
| ~ spl0_21
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f238,f204,f174,f528]) ).
fof(f238,plain,
( ! [X2,X3,X0,X1] : equidistant(X0,X1,X2,extension(X3,X2,X1,X0))
| ~ spl0_21
| ~ spl0_28 ),
inference(resolution,[],[f205,f175]) ).
fof(f526,plain,
( spl0_61
| ~ spl0_21
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f234,f196,f174,f524]) ).
fof(f524,plain,
( spl0_61
<=> ! [X0,X3,X2,X1] : equidistant(X0,X1,extension(X2,X3,X0,X1),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f196,plain,
( spl0_26
<=> ! [X10,X0,X5,X3] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X5,X0,X3,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f234,plain,
( ! [X2,X3,X0,X1] : equidistant(X0,X1,extension(X2,X3,X0,X1),X3)
| ~ spl0_21
| ~ spl0_26 ),
inference(resolution,[],[f197,f175]) ).
fof(f197,plain,
( ! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X5,X0,X3,X10) )
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f196]) ).
fof(f522,plain,
( spl0_60
| ~ spl0_21
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f230,f192,f174,f520]) ).
fof(f520,plain,
( spl0_60
<=> ! [X2,X0,X1,X3] : equidistant(extension(X0,X1,X2,X3),X1,X3,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f192,plain,
( spl0_25
<=> ! [X10,X0,X5,X3] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X3,X10,X0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f230,plain,
( ! [X2,X3,X0,X1] : equidistant(extension(X0,X1,X2,X3),X1,X3,X2)
| ~ spl0_21
| ~ spl0_25 ),
inference(resolution,[],[f193,f175]) ).
fof(f193,plain,
( ! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X3,X10,X0,X5) )
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f192]) ).
fof(f518,plain,
( spl0_59
| ~ spl0_21
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f226,f188,f174,f516]) ).
fof(f226,plain,
( ! [X2,X3,X0,X1] : equidistant(X0,extension(X1,X0,X2,X3),X3,X2)
| ~ spl0_21
| ~ spl0_24 ),
inference(resolution,[],[f189,f175]) ).
fof(f514,plain,
( spl0_58
| ~ spl0_21
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f222,f184,f174,f512]) ).
fof(f512,plain,
( spl0_58
<=> ! [X2,X0,X1,X3] : equidistant(extension(X0,X1,X2,X3),X1,X2,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f184,plain,
( spl0_23
<=> ! [X10,X0,X5,X3] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X3,X10,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f222,plain,
( ! [X2,X3,X0,X1] : equidistant(extension(X0,X1,X2,X3),X1,X2,X3)
| ~ spl0_21
| ~ spl0_23 ),
inference(resolution,[],[f185,f175]) ).
fof(f185,plain,
( ! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X3,X10,X5,X0) )
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f510,plain,
( spl0_57
| ~ spl0_21
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f218,f180,f174,f508]) ).
fof(f180,plain,
( spl0_22
<=> ! [X10,X0,X5,X3] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X5,X0,X10,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f218,plain,
( ! [X2,X3,X0,X1] : equidistant(X0,X1,X2,extension(X3,X2,X0,X1))
| ~ spl0_21
| ~ spl0_22 ),
inference(resolution,[],[f181,f175]) ).
fof(f181,plain,
( ! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X5,X0,X10,X3) )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f180]) ).
fof(f500,plain,
spl0_56,
inference(avatar_split_clause,[],[f6,f498]) ).
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(f491,plain,
spl0_55,
inference(avatar_split_clause,[],[f13,f489]) ).
fof(f489,plain,
( spl0_55
<=> ! [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_55])]) ).
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(f474,plain,
spl0_54,
inference(avatar_split_clause,[],[f18,f472]) ).
fof(f472,plain,
( spl0_54
<=> ! [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_54])]) ).
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(f466,plain,
spl0_53,
inference(avatar_split_clause,[],[f17,f464]) ).
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(f449,plain,
spl0_52,
inference(avatar_split_clause,[],[f16,f447]) ).
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(f441,plain,
spl0_51,
inference(avatar_split_clause,[],[f37,f439]) ).
fof(f37,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(f419,plain,
spl0_50,
inference(avatar_split_clause,[],[f15,f417]) ).
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(f415,plain,
spl0_49,
inference(avatar_split_clause,[],[f14,f413]) ).
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(f399,plain,
spl0_48,
inference(avatar_split_clause,[],[f40,f397]) ).
fof(f40,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(f395,plain,
( spl0_47
| ~ spl0_8
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f287,f271,f108,f393]) ).
fof(f393,plain,
( spl0_47
<=> ! [X2,X0,X1] :
( ~ between(X0,X1,X0)
| between(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f108,plain,
( spl0_8
<=> ! [X3,X10] : between(X10,X10,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f287,plain,
( ! [X2,X0,X1] :
( ~ between(X0,X1,X0)
| between(X0,X1,X2) )
| ~ spl0_8
| ~ spl0_35 ),
inference(resolution,[],[f272,f109]) ).
fof(f109,plain,
( ! [X3,X10] : between(X10,X10,X3)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f391,plain,
spl0_46,
inference(avatar_split_clause,[],[f38,f389]) ).
fof(f38,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(f363,plain,
spl0_45,
inference(avatar_split_clause,[],[f9,f361]) ).
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(f359,plain,
spl0_44,
inference(avatar_split_clause,[],[f8,f357]) ).
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(f329,plain,
spl0_43,
inference(avatar_split_clause,[],[f64,f327]) ).
fof(f64,plain,
! [X3,X10] : extension(extension(X10,X3,X10,X3),X3,extension(X10,X3,X10,X3),X3) = X10,
inference(definition_unfolding,[],[f43,f19,f19]) ).
fof(f19,axiom,
! [X3,X10] : reflection(X10,X3) = extension(X10,X3,X10,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflection) ).
fof(f43,axiom,
! [X3,X10] : reflection(reflection(X10,X3),X3) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r6) ).
fof(f325,plain,
spl0_42,
inference(avatar_split_clause,[],[f55,f323]) ).
fof(f55,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(f321,plain,
spl0_41,
inference(avatar_split_clause,[],[f54,f319]) ).
fof(f54,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(f317,plain,
spl0_40,
inference(avatar_split_clause,[],[f28,f315]) ).
fof(f28,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(f313,plain,
spl0_39,
inference(avatar_split_clause,[],[f2,f311]) ).
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(f297,plain,
spl0_38,
inference(avatar_split_clause,[],[f41,f295]) ).
fof(f41,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(f293,plain,
spl0_37,
inference(avatar_split_clause,[],[f39,f291]) ).
fof(f291,plain,
( spl0_37
<=> ! [X5,X3,X10] :
( X3 = X10
| ~ between(X10,X3,X5)
| extension(X10,X3,X3,X5) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f39,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(f285,plain,
( spl0_36
| ~ spl0_8
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f275,f263,f108,f283]) ).
fof(f283,plain,
( spl0_36
<=> ! [X2,X0,X1] :
( ~ between(X0,X1,X0)
| between(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f275,plain,
( ! [X2,X0,X1] :
( ~ between(X0,X1,X0)
| between(X1,X0,X2) )
| ~ spl0_8
| ~ spl0_33 ),
inference(resolution,[],[f264,f109]) ).
fof(f273,plain,
spl0_35,
inference(avatar_split_clause,[],[f57,f271]) ).
fof(f57,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(f269,plain,
spl0_34,
inference(avatar_split_clause,[],[f56,f267]) ).
fof(f56,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(f265,plain,
spl0_33,
inference(avatar_split_clause,[],[f53,f263]) ).
fof(f53,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(f253,plain,
spl0_32,
inference(avatar_split_clause,[],[f49,f251]) ).
fof(f49,axiom,
! [X3,X10,X5] :
( X3 = X5
| ~ between(X10,X5,X3)
| ~ between(X10,X3,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b3) ).
fof(f249,plain,
spl0_31,
inference(avatar_split_clause,[],[f48,f247]) ).
fof(f48,axiom,
! [X3,X10,X5] :
( X3 = X10
| ~ between(X3,X10,X5)
| ~ between(X10,X3,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b2) ).
fof(f214,plain,
spl0_30,
inference(avatar_split_clause,[],[f68,f212]) ).
fof(f68,plain,
! [X3,X10] :
( X3 = X10
| extension(X10,X3,X10,X3) != X3 ),
inference(definition_unfolding,[],[f35,f19]) ).
fof(f35,axiom,
! [X3,X10] :
( X3 = X10
| reflection(X10,X3) != X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r4) ).
fof(f210,plain,
spl0_29,
inference(avatar_split_clause,[],[f27,f208]) ).
fof(f27,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(f206,plain,
spl0_28,
inference(avatar_split_clause,[],[f26,f204]) ).
fof(f26,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(f202,plain,
( spl0_27
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f170,f155,f151,f200]) ).
fof(f200,plain,
( spl0_27
<=> ! [X0,X3,X2,X1] : between(extension(X0,X1,X2,X3),X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f170,plain,
( ! [X2,X3,X0,X1] : between(extension(X0,X1,X2,X3),X1,X0)
| ~ spl0_18
| ~ spl0_19 ),
inference(resolution,[],[f156,f152]) ).
fof(f198,plain,
spl0_26,
inference(avatar_split_clause,[],[f25,f196]) ).
fof(f25,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(f194,plain,
spl0_25,
inference(avatar_split_clause,[],[f24,f192]) ).
fof(f24,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(f190,plain,
spl0_24,
inference(avatar_split_clause,[],[f23,f188]) ).
fof(f23,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(f186,plain,
spl0_23,
inference(avatar_split_clause,[],[f22,f184]) ).
fof(f22,axiom,
! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X3,X10,X5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3) ).
fof(f182,plain,
spl0_22,
inference(avatar_split_clause,[],[f21,f180]) ).
fof(f21,axiom,
! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X5,X0,X10,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2) ).
fof(f176,plain,
spl0_21,
inference(avatar_split_clause,[],[f5,f174]) ).
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(f167,plain,
( spl0_13
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f165]) ).
fof(f165,plain,
( $false
| spl0_13
| ~ spl0_18 ),
inference(resolution,[],[f152,f130]) ).
fof(f130,plain,
( ~ between(u,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2))
| spl0_13 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f128,plain,
( spl0_13
<=> between(u,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f161,plain,
spl0_20,
inference(avatar_split_clause,[],[f71,f159]) ).
fof(f71,plain,
! [X3,X10,X5] :
( ~ between(X10,X5,X10)
| between(X3,X5,X10) ),
inference(equality_resolution,[],[f45]) ).
fof(f45,axiom,
! [X3,X10,X0,X5] :
( X0 != X10
| ~ between(X10,X5,X0)
| between(X3,X5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b1) ).
fof(f157,plain,
spl0_19,
inference(avatar_split_clause,[],[f46,f155]) ).
fof(f46,axiom,
! [X3,X10,X5] :
( ~ between(X10,X3,X5)
| between(X5,X3,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1) ).
fof(f153,plain,
spl0_18,
inference(avatar_split_clause,[],[f4,f151]) ).
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(f149,plain,
spl0_17,
inference(avatar_split_clause,[],[f3,f147]) ).
fof(f3,axiom,
! [X2,X0,X1] :
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_equidistance) ).
fof(f143,plain,
spl0_16,
inference(avatar_split_clause,[],[f29,f141]) ).
fof(f29,axiom,
! [X3,X10,X5] : extension(X10,X3,X5,X5) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e1) ).
fof(f139,plain,
spl0_15,
inference(avatar_split_clause,[],[f7,f137]) ).
fof(f7,axiom,
! [X0,X1] :
( X0 = X1
| ~ between(X0,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_betweeness) ).
fof(f135,plain,
( ~ spl0_12
| ~ spl0_13
| spl0_14 ),
inference(avatar_split_clause,[],[f61,f132,f128,f124]) ).
fof(f61,axiom,
( v = extension(u,v,lower_dimension_point_1,lower_dimension_point_2)
| ~ between(u,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2))
| ~ equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_lengthen) ).
fof(f122,plain,
spl0_11,
inference(avatar_split_clause,[],[f36,f120]) ).
fof(f36,axiom,
! [X3,X10] : equidistant(X10,X10,X3,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7) ).
fof(f118,plain,
spl0_10,
inference(avatar_split_clause,[],[f20,f116]) ).
fof(f20,axiom,
! [X3,X10] : equidistant(X10,X3,X10,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1) ).
fof(f114,plain,
spl0_9,
inference(avatar_split_clause,[],[f1,f112]) ).
fof(f1,axiom,
! [X0,X1] : equidistant(X0,X1,X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).
fof(f110,plain,
spl0_8,
inference(avatar_split_clause,[],[f47,f108]) ).
fof(f47,axiom,
! [X3,X10] : between(X10,X10,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2) ).
fof(f106,plain,
spl0_7,
inference(avatar_split_clause,[],[f44,f104]) ).
fof(f104,plain,
( spl0_7
<=> ! [X3,X10] : between(X10,X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f44,axiom,
! [X3,X10] : between(X10,X3,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3) ).
fof(f102,plain,
~ spl0_6,
inference(avatar_split_clause,[],[f12,f99]) ).
fof(f99,plain,
( spl0_6
<=> between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
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(f97,plain,
~ spl0_5,
inference(avatar_split_clause,[],[f11,f94]) ).
fof(f94,plain,
( spl0_5
<=> between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
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(f92,plain,
~ spl0_4,
inference(avatar_split_clause,[],[f10,f89]) ).
fof(f89,plain,
( spl0_4
<=> between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
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(f87,plain,
~ spl0_3,
inference(avatar_split_clause,[],[f60,f84]) ).
fof(f84,plain,
( spl0_3
<=> lower_dimension_point_1 = lower_dimension_point_3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f60,axiom,
lower_dimension_point_1 != lower_dimension_point_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e2_3) ).
fof(f82,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f59,f79]) ).
fof(f79,plain,
( spl0_2
<=> lower_dimension_point_2 = lower_dimension_point_3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f59,axiom,
lower_dimension_point_2 != lower_dimension_point_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e2_2) ).
fof(f77,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f58,f74]) ).
fof(f58,axiom,
lower_dimension_point_1 != lower_dimension_point_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e2_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : GEO037-3 : TPTP v8.1.2. Released v1.0.0.
% 0.09/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri May 3 22:00:23 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.33 % (2153)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.35 % (2156)WARNING: value z3 for option sas not known
% 0.12/0.35 % (2159)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.12/0.35 % (2157)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.35 % (2155)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.35 % (2154)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.35 % (2156)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.12/0.35 % (2158)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.12/0.35 % (2160)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.12/0.35 Detected minimum model sizes of [3]
% 0.12/0.35 Detected maximum model sizes of [max]
% 0.12/0.35 TRYING [3]
% 0.12/0.37 Detected minimum model sizes of [3]
% 0.12/0.37 Detected maximum model sizes of [max]
% 0.12/0.39 TRYING [3]
% 0.17/0.40 Detected minimum model sizes of [3]
% 0.17/0.40 Detected maximum model sizes of [max]
% 0.17/0.40 TRYING [3]
% 0.17/0.42 % (2158)First to succeed.
% 0.17/0.42 TRYING [4]
% 0.17/0.42 % (2158)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2153"
% 0.17/0.42 % (2158)Refutation found. Thanks to Tanya!
% 0.17/0.42 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.43 % (2158)------------------------------
% 0.17/0.43 % (2158)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.17/0.43 % (2158)Termination reason: Refutation
% 0.17/0.43
% 0.17/0.43 % (2158)Memory used [KB]: 1835
% 0.17/0.43 % (2158)Time elapsed: 0.076 s
% 0.17/0.43 % (2158)Instructions burned: 136 (million)
% 0.17/0.43 % (2153)Success in time 0.093 s
%------------------------------------------------------------------------------