TSTP Solution File: SET601+3 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET601+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n014.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 09:14:25 EDT 2024
% Result : Theorem 7.30s 1.42s
% Output : Refutation 7.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 213
% Syntax : Number of formulae : 763 ( 43 unt; 0 def)
% Number of atoms : 2361 ( 375 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 2865 (1267 ~;1358 |; 33 &)
% ( 203 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 200 ( 198 usr; 197 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 1536 (1524 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f22276,plain,
$false,
inference(avatar_sat_refutation,[],[f66,f70,f75,f83,f87,f91,f95,f102,f109,f113,f117,f121,f125,f129,f139,f155,f159,f165,f169,f173,f179,f234,f238,f242,f291,f298,f302,f306,f340,f344,f348,f398,f402,f440,f444,f449,f453,f457,f461,f465,f791,f795,f799,f804,f808,f812,f816,f820,f824,f953,f1046,f1050,f1054,f1058,f1062,f1066,f1133,f1597,f1601,f1676,f1680,f1684,f1879,f1883,f1887,f1891,f1895,f1899,f1903,f1907,f1911,f1915,f2539,f2543,f2547,f2850,f3000,f3004,f3008,f3012,f3016,f3062,f3275,f3279,f3283,f3287,f3291,f3295,f3299,f3303,f3307,f3311,f3315,f3876,f4572,f4576,f4580,f4584,f4588,f4592,f4596,f4600,f4604,f4951,f5027,f5032,f5036,f5040,f5044,f5048,f5052,f5056,f5060,f5064,f5068,f5072,f5076,f5080,f5084,f5088,f5092,f5096,f5100,f5104,f5108,f5112,f5116,f5120,f5124,f5128,f5132,f5136,f7580,f10197,f10981,f10985,f10989,f10993,f10997,f11001,f11005,f11009,f11013,f11017,f11021,f11025,f11029,f11033,f11037,f11041,f11045,f11049,f11115,f11119,f11123,f11127,f11131,f13661,f13665,f13670,f13803,f13808,f13812,f13817,f13821,f13825,f13829,f13833,f13837,f13841,f14049,f14053,f14058,f14063,f14067,f14071,f14075,f14079,f14083,f14087,f14305,f14309,f14313,f14317,f14321,f14325,f14329,f14334,f14338,f14342,f14511,f14515,f15161,f15539,f16453,f19622,f22208,f22216]) ).
fof(f22216,plain,
( spl5_4
| ~ spl5_5
| ~ spl5_6
| ~ spl5_54
| ~ spl5_118
| ~ spl5_130
| ~ spl5_132
| ~ spl5_134
| ~ spl5_185 ),
inference(avatar_contradiction_clause,[],[f22215]) ).
fof(f22215,plain,
( $false
| spl5_4
| ~ spl5_5
| ~ spl5_6
| ~ spl5_54
| ~ spl5_118
| ~ spl5_130
| ~ spl5_132
| ~ spl5_134
| ~ spl5_185 ),
inference(trivial_inequality_removal,[],[f22214]) ).
fof(f22214,plain,
( union(intersection(sK0,sK2),intersection(sK1,union(sK0,sK2))) != union(intersection(sK0,sK2),intersection(sK1,union(sK0,sK2)))
| spl5_4
| ~ spl5_5
| ~ spl5_6
| ~ spl5_54
| ~ spl5_118
| ~ spl5_130
| ~ spl5_132
| ~ spl5_134
| ~ spl5_185 ),
inference(forward_demodulation,[],[f22213,f86]) ).
fof(f86,plain,
( ! [X0,X1] : union(X0,X1) = union(X1,X0)
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f85,plain,
( spl5_5
<=> ! [X0,X1] : union(X0,X1) = union(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_5])]) ).
fof(f22213,plain,
( union(intersection(sK0,sK2),intersection(sK1,union(sK0,sK2))) != union(intersection(sK0,sK2),intersection(sK1,union(sK2,sK0)))
| spl5_4
| ~ spl5_6
| ~ spl5_54
| ~ spl5_118
| ~ spl5_130
| ~ spl5_132
| ~ spl5_134
| ~ spl5_185 ),
inference(forward_demodulation,[],[f22212,f14259]) ).
fof(f14259,plain,
( ! [X2,X0,X1] : union(intersection(X0,X1),intersection(X1,X2)) = intersection(X1,union(X2,X0))
| ~ spl5_54
| ~ spl5_132
| ~ spl5_134 ),
inference(forward_demodulation,[],[f14157,f10806]) ).
fof(f10806,plain,
( ! [X2,X0,X1] : intersection(X2,union(X0,X1)) = intersection(X2,union(X0,intersection(X1,X2)))
| ~ spl5_54
| ~ spl5_132 ),
inference(superposition,[],[f5135,f1057]) ).
fof(f1057,plain,
( ! [X2,X0,X1] : union(X0,intersection(X2,X1)) = intersection(union(X0,X2),union(X1,X0))
| ~ spl5_54 ),
inference(avatar_component_clause,[],[f1056]) ).
fof(f1056,plain,
( spl5_54
<=> ! [X2,X0,X1] : union(X0,intersection(X2,X1)) = intersection(union(X0,X2),union(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_54])]) ).
fof(f5135,plain,
( ! [X2,X3,X0] : intersection(X0,X3) = intersection(X0,intersection(X3,union(X0,X2)))
| ~ spl5_132 ),
inference(avatar_component_clause,[],[f5134]) ).
fof(f5134,plain,
( spl5_132
<=> ! [X2,X0,X3] : intersection(X0,X3) = intersection(X0,intersection(X3,union(X0,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_132])]) ).
fof(f14157,plain,
( ! [X2,X0,X1] : union(intersection(X0,X1),intersection(X1,X2)) = intersection(X1,union(X2,intersection(X0,X1)))
| ~ spl5_54
| ~ spl5_134 ),
inference(superposition,[],[f1057,f10196]) ).
fof(f10196,plain,
( ! [X0,X1] : union(intersection(X1,X0),X0) = X0
| ~ spl5_134 ),
inference(avatar_component_clause,[],[f10195]) ).
fof(f10195,plain,
( spl5_134
<=> ! [X0,X1] : union(intersection(X1,X0),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_134])]) ).
fof(f22212,plain,
( union(intersection(sK0,sK2),union(intersection(sK0,sK1),intersection(sK1,sK2))) != union(intersection(sK0,sK2),intersection(sK1,union(sK0,sK2)))
| spl5_4
| ~ spl5_6
| ~ spl5_54
| ~ spl5_118
| ~ spl5_130
| ~ spl5_185 ),
inference(forward_demodulation,[],[f22211,f90]) ).
fof(f90,plain,
( ! [X0,X1] : intersection(X0,X1) = intersection(X1,X0)
| ~ spl5_6 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f89,plain,
( spl5_6
<=> ! [X0,X1] : intersection(X0,X1) = intersection(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_6])]) ).
fof(f22211,plain,
( union(intersection(sK0,sK2),union(intersection(sK0,sK1),intersection(sK1,sK2))) != union(intersection(sK2,sK0),intersection(sK1,union(sK0,sK2)))
| spl5_4
| ~ spl5_6
| ~ spl5_54
| ~ spl5_118
| ~ spl5_130
| ~ spl5_185 ),
inference(forward_demodulation,[],[f22210,f5127]) ).
fof(f5127,plain,
( ! [X2,X0,X1] : union(X0,intersection(X1,X2)) = union(X0,intersection(X2,X1))
| ~ spl5_130 ),
inference(avatar_component_clause,[],[f5126]) ).
fof(f5126,plain,
( spl5_130
<=> ! [X2,X0,X1] : union(X0,intersection(X1,X2)) = union(X0,intersection(X2,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_130])]) ).
fof(f22210,plain,
( union(intersection(sK0,sK2),union(intersection(sK0,sK1),intersection(sK1,sK2))) != union(intersection(sK2,sK0),intersection(union(sK0,sK2),sK1))
| spl5_4
| ~ spl5_6
| ~ spl5_54
| ~ spl5_118
| ~ spl5_185 ),
inference(forward_demodulation,[],[f22209,f7496]) ).
fof(f7496,plain,
( ! [X2,X3,X0,X1] : union(intersection(X0,X1),intersection(union(X1,X2),X3)) = intersection(union(X1,X2),union(X3,intersection(X0,X1)))
| ~ spl5_54
| ~ spl5_118 ),
inference(superposition,[],[f1057,f5079]) ).
fof(f5079,plain,
( ! [X2,X0,X1] : union(X0,X2) = union(intersection(X1,X0),union(X0,X2))
| ~ spl5_118 ),
inference(avatar_component_clause,[],[f5078]) ).
fof(f5078,plain,
( spl5_118
<=> ! [X2,X0,X1] : union(X0,X2) = union(intersection(X1,X0),union(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_118])]) ).
fof(f22209,plain,
( union(intersection(sK0,sK2),union(intersection(sK0,sK1),intersection(sK1,sK2))) != intersection(union(sK0,sK2),union(sK1,intersection(sK2,sK0)))
| spl5_4
| ~ spl5_6
| ~ spl5_185 ),
inference(forward_demodulation,[],[f21896,f90]) ).
fof(f21896,plain,
( union(intersection(sK0,sK2),union(intersection(sK0,sK1),intersection(sK1,sK2))) != intersection(union(sK1,intersection(sK2,sK0)),union(sK0,sK2))
| spl5_4
| ~ spl5_185 ),
inference(superposition,[],[f82,f14320]) ).
fof(f14320,plain,
( ! [X2,X0,X1] : union(X0,intersection(X1,X2)) = intersection(union(X2,X0),union(X0,X1))
| ~ spl5_185 ),
inference(avatar_component_clause,[],[f14319]) ).
fof(f14319,plain,
( spl5_185
<=> ! [X2,X0,X1] : union(X0,intersection(X1,X2)) = intersection(union(X2,X0),union(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_185])]) ).
fof(f82,plain,
( intersection(intersection(union(sK0,sK1),union(sK1,sK2)),union(sK0,sK2)) != union(intersection(sK0,sK2),union(intersection(sK0,sK1),intersection(sK1,sK2)))
| spl5_4 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f80,plain,
( spl5_4
<=> intersection(intersection(union(sK0,sK1),union(sK1,sK2)),union(sK0,sK2)) = union(intersection(sK0,sK2),union(intersection(sK0,sK1),intersection(sK1,sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).
fof(f22208,plain,
( ~ spl5_5
| ~ spl5_6
| spl5_8
| ~ spl5_54
| ~ spl5_118
| ~ spl5_130
| ~ spl5_132
| ~ spl5_134
| ~ spl5_185 ),
inference(avatar_contradiction_clause,[],[f22207]) ).
fof(f22207,plain,
( $false
| ~ spl5_5
| ~ spl5_6
| spl5_8
| ~ spl5_54
| ~ spl5_118
| ~ spl5_130
| ~ spl5_132
| ~ spl5_134
| ~ spl5_185 ),
inference(trivial_inequality_removal,[],[f22206]) ).
fof(f22206,plain,
( union(intersection(sK0,sK2),intersection(sK1,union(sK0,sK2))) != union(intersection(sK0,sK2),intersection(sK1,union(sK0,sK2)))
| ~ spl5_5
| ~ spl5_6
| spl5_8
| ~ spl5_54
| ~ spl5_118
| ~ spl5_130
| ~ spl5_132
| ~ spl5_134
| ~ spl5_185 ),
inference(forward_demodulation,[],[f22205,f86]) ).
fof(f22205,plain,
( union(intersection(sK0,sK2),intersection(sK1,union(sK0,sK2))) != union(intersection(sK0,sK2),intersection(sK1,union(sK2,sK0)))
| ~ spl5_6
| spl5_8
| ~ spl5_54
| ~ spl5_118
| ~ spl5_130
| ~ spl5_132
| ~ spl5_134
| ~ spl5_185 ),
inference(forward_demodulation,[],[f22204,f14259]) ).
fof(f22204,plain,
( union(intersection(sK0,sK2),union(intersection(sK0,sK1),intersection(sK1,sK2))) != union(intersection(sK0,sK2),intersection(sK1,union(sK0,sK2)))
| ~ spl5_6
| spl5_8
| ~ spl5_54
| ~ spl5_118
| ~ spl5_130
| ~ spl5_185 ),
inference(forward_demodulation,[],[f22203,f90]) ).
fof(f22203,plain,
( union(intersection(sK0,sK2),union(intersection(sK0,sK1),intersection(sK1,sK2))) != union(intersection(sK2,sK0),intersection(sK1,union(sK0,sK2)))
| spl5_8
| ~ spl5_54
| ~ spl5_118
| ~ spl5_130
| ~ spl5_185 ),
inference(forward_demodulation,[],[f22202,f5127]) ).
fof(f22202,plain,
( union(intersection(sK0,sK2),union(intersection(sK0,sK1),intersection(sK1,sK2))) != union(intersection(sK2,sK0),intersection(union(sK0,sK2),sK1))
| spl5_8
| ~ spl5_54
| ~ spl5_118
| ~ spl5_185 ),
inference(forward_demodulation,[],[f21895,f7496]) ).
fof(f21895,plain,
( union(intersection(sK0,sK2),union(intersection(sK0,sK1),intersection(sK1,sK2))) != intersection(union(sK0,sK2),union(sK1,intersection(sK2,sK0)))
| spl5_8
| ~ spl5_185 ),
inference(superposition,[],[f101,f14320]) ).
fof(f101,plain,
( intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))) != union(intersection(sK0,sK2),union(intersection(sK0,sK1),intersection(sK1,sK2)))
| spl5_8 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f99,plain,
( spl5_8
<=> intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))) = union(intersection(sK0,sK2),union(intersection(sK0,sK1),intersection(sK1,sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_8])]) ).
fof(f19622,plain,
( spl5_196
| ~ spl5_18
| ~ spl5_50 ),
inference(avatar_split_clause,[],[f2333,f951,f163,f19620]) ).
fof(f19620,plain,
( spl5_196
<=> ! [X2,X0,X1] : subset(intersection(X0,intersection(X1,X2)),intersection(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_196])]) ).
fof(f163,plain,
( spl5_18
<=> ! [X2,X0,X1] : intersection(intersection(X0,X1),X2) = intersection(X0,intersection(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_18])]) ).
fof(f951,plain,
( spl5_50
<=> ! [X0,X1] : subset(intersection(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_50])]) ).
fof(f2333,plain,
( ! [X2,X0,X1] : subset(intersection(X0,intersection(X1,X2)),intersection(X0,X1))
| ~ spl5_18
| ~ spl5_50 ),
inference(superposition,[],[f952,f164]) ).
fof(f164,plain,
( ! [X2,X0,X1] : intersection(intersection(X0,X1),X2) = intersection(X0,intersection(X1,X2))
| ~ spl5_18 ),
inference(avatar_component_clause,[],[f163]) ).
fof(f952,plain,
( ! [X0,X1] : subset(intersection(X0,X1),X0)
| ~ spl5_50 ),
inference(avatar_component_clause,[],[f951]) ).
fof(f16453,plain,
( spl5_195
| ~ spl5_34
| ~ spl5_50 ),
inference(avatar_split_clause,[],[f2332,f951,f438,f16451]) ).
fof(f16451,plain,
( spl5_195
<=> ! [X2,X0,X1] : subset(intersection(X1,intersection(X0,X2)),intersection(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_195])]) ).
fof(f438,plain,
( spl5_34
<=> ! [X2,X0,X1] : intersection(X0,intersection(X1,X2)) = intersection(intersection(X1,X0),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_34])]) ).
fof(f2332,plain,
( ! [X2,X0,X1] : subset(intersection(X1,intersection(X0,X2)),intersection(X0,X1))
| ~ spl5_34
| ~ spl5_50 ),
inference(superposition,[],[f952,f439]) ).
fof(f439,plain,
( ! [X2,X0,X1] : intersection(X0,intersection(X1,X2)) = intersection(intersection(X1,X0),X2)
| ~ spl5_34 ),
inference(avatar_component_clause,[],[f438]) ).
fof(f15539,plain,
( spl5_194
| ~ spl5_7
| ~ spl5_53
| ~ spl5_163 ),
inference(avatar_split_clause,[],[f13813,f13810,f1052,f93,f15537]) ).
fof(f15537,plain,
( spl5_194
<=> ! [X2,X0,X1] : intersection(X0,X1) = intersection(X1,union(intersection(X0,X1),intersection(X0,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_194])]) ).
fof(f93,plain,
( spl5_7
<=> ! [X0,X1] : union(X0,intersection(X0,X1)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_7])]) ).
fof(f1052,plain,
( spl5_53
<=> ! [X2,X0,X1] : union(X0,intersection(X1,X2)) = intersection(union(X1,X0),union(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_53])]) ).
fof(f13810,plain,
( spl5_163
<=> ! [X2,X0,X1] : intersection(X0,X1) = intersection(X1,intersection(X0,union(intersection(X0,X1),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_163])]) ).
fof(f13813,plain,
( ! [X2,X0,X1] : intersection(X0,X1) = intersection(X1,union(intersection(X0,X1),intersection(X0,X2)))
| ~ spl5_7
| ~ spl5_53
| ~ spl5_163 ),
inference(forward_demodulation,[],[f13811,f1211]) ).
fof(f1211,plain,
( ! [X2,X0,X1] : intersection(X0,union(intersection(X0,X1),X2)) = union(intersection(X0,X1),intersection(X0,X2))
| ~ spl5_7
| ~ spl5_53 ),
inference(superposition,[],[f1053,f94]) ).
fof(f94,plain,
( ! [X0,X1] : union(X0,intersection(X0,X1)) = X0
| ~ spl5_7 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f1053,plain,
( ! [X2,X0,X1] : union(X0,intersection(X1,X2)) = intersection(union(X1,X0),union(X0,X2))
| ~ spl5_53 ),
inference(avatar_component_clause,[],[f1052]) ).
fof(f13811,plain,
( ! [X2,X0,X1] : intersection(X0,X1) = intersection(X1,intersection(X0,union(intersection(X0,X1),X2)))
| ~ spl5_163 ),
inference(avatar_component_clause,[],[f13810]) ).
fof(f15161,plain,
( spl5_193
| ~ spl5_27
| ~ spl5_53
| ~ spl5_161 ),
inference(avatar_split_clause,[],[f13804,f13801,f1052,f300,f15159]) ).
fof(f15159,plain,
( spl5_193
<=> ! [X2,X0,X1] : intersection(X0,X1) = intersection(X0,union(intersection(X0,X1),intersection(X1,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_193])]) ).
fof(f300,plain,
( spl5_27
<=> ! [X0,X1] : union(X0,intersection(X1,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_27])]) ).
fof(f13801,plain,
( spl5_161
<=> ! [X2,X0,X1] : intersection(X0,X1) = intersection(X0,intersection(X1,union(intersection(X0,X1),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_161])]) ).
fof(f13804,plain,
( ! [X2,X0,X1] : intersection(X0,X1) = intersection(X0,union(intersection(X0,X1),intersection(X1,X2)))
| ~ spl5_27
| ~ spl5_53
| ~ spl5_161 ),
inference(forward_demodulation,[],[f13802,f1212]) ).
fof(f1212,plain,
( ! [X2,X0,X1] : union(intersection(X1,X0),intersection(X0,X2)) = intersection(X0,union(intersection(X1,X0),X2))
| ~ spl5_27
| ~ spl5_53 ),
inference(superposition,[],[f1053,f301]) ).
fof(f301,plain,
( ! [X0,X1] : union(X0,intersection(X1,X0)) = X0
| ~ spl5_27 ),
inference(avatar_component_clause,[],[f300]) ).
fof(f13802,plain,
( ! [X2,X0,X1] : intersection(X0,X1) = intersection(X0,intersection(X1,union(intersection(X0,X1),X2)))
| ~ spl5_161 ),
inference(avatar_component_clause,[],[f13801]) ).
fof(f14515,plain,
( spl5_192
| ~ spl5_15
| ~ spl5_19
| ~ spl5_24
| ~ spl5_37
| ~ spl5_39
| ~ spl5_40
| ~ spl5_53
| ~ spl5_72 ),
inference(avatar_split_clause,[],[f2517,f1913,f1052,f463,f459,f451,f240,f167,f137,f14513]) ).
fof(f14513,plain,
( spl5_192
<=> ! [X2,X0,X1] : union(X1,X0) = union(union(X0,X1),union(X0,intersection(X1,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_192])]) ).
fof(f137,plain,
( spl5_15
<=> ! [X0] : union(X0,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_15])]) ).
fof(f167,plain,
( spl5_19
<=> ! [X2,X0,X1] : union(union(X0,X1),X2) = union(X0,union(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_19])]) ).
fof(f240,plain,
( spl5_24
<=> ! [X2,X0,X1] : union(X0,intersection(X1,X2)) = intersection(union(X0,X1),union(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_24])]) ).
fof(f451,plain,
( spl5_37
<=> ! [X2,X0,X1] : union(X0,union(X1,X2)) = union(union(X1,X0),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_37])]) ).
fof(f459,plain,
( spl5_39
<=> ! [X2,X0,X1] : union(X0,X2) = union(X0,union(intersection(X0,X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_39])]) ).
fof(f463,plain,
( spl5_40
<=> ! [X2,X0,X1] : union(X0,union(X1,X2)) = union(X2,union(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_40])]) ).
fof(f1913,plain,
( spl5_72
<=> ! [X0,X3,X2,X1] : intersection(union(X0,union(X1,X2)),union(X0,union(X1,X3))) = union(X0,union(X1,intersection(X2,X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_72])]) ).
fof(f2517,plain,
( ! [X2,X0,X1] : union(X1,X0) = union(union(X0,X1),union(X0,intersection(X1,X2)))
| ~ spl5_15
| ~ spl5_19
| ~ spl5_24
| ~ spl5_37
| ~ spl5_39
| ~ spl5_40
| ~ spl5_53
| ~ spl5_72 ),
inference(forward_demodulation,[],[f2516,f241]) ).
fof(f241,plain,
( ! [X2,X0,X1] : union(X0,intersection(X1,X2)) = intersection(union(X0,X1),union(X0,X2))
| ~ spl5_24 ),
inference(avatar_component_clause,[],[f240]) ).
fof(f2516,plain,
( ! [X2,X0,X1] : union(X1,X0) = union(union(X0,X1),intersection(union(X0,X1),union(X0,X2)))
| ~ spl5_15
| ~ spl5_19
| ~ spl5_37
| ~ spl5_39
| ~ spl5_40
| ~ spl5_53
| ~ spl5_72 ),
inference(forward_demodulation,[],[f2515,f641]) ).
fof(f641,plain,
( ! [X0,X1] : union(X0,X1) = union(X1,union(X0,X1))
| ~ spl5_15
| ~ spl5_19
| ~ spl5_37 ),
inference(forward_demodulation,[],[f622,f200]) ).
fof(f200,plain,
( ! [X0,X1] : union(X0,X1) = union(X0,union(X0,X1))
| ~ spl5_15
| ~ spl5_19 ),
inference(superposition,[],[f168,f138]) ).
fof(f138,plain,
( ! [X0] : union(X0,X0) = X0
| ~ spl5_15 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f168,plain,
( ! [X2,X0,X1] : union(union(X0,X1),X2) = union(X0,union(X1,X2))
| ~ spl5_19 ),
inference(avatar_component_clause,[],[f167]) ).
fof(f622,plain,
( ! [X0,X1] : union(X0,X1) = union(X1,union(X0,union(X0,X1)))
| ~ spl5_15
| ~ spl5_37 ),
inference(superposition,[],[f452,f138]) ).
fof(f452,plain,
( ! [X2,X0,X1] : union(X0,union(X1,X2)) = union(union(X1,X0),X2)
| ~ spl5_37 ),
inference(avatar_component_clause,[],[f451]) ).
fof(f2515,plain,
( ! [X2,X0,X1] : union(union(X0,X1),intersection(union(X0,X1),union(X0,X2))) = union(X0,union(X1,X0))
| ~ spl5_19
| ~ spl5_39
| ~ spl5_40
| ~ spl5_53
| ~ spl5_72 ),
inference(forward_demodulation,[],[f2514,f460]) ).
fof(f460,plain,
( ! [X2,X0,X1] : union(X0,X2) = union(X0,union(intersection(X0,X1),X2))
| ~ spl5_39 ),
inference(avatar_component_clause,[],[f459]) ).
fof(f2514,plain,
( ! [X2,X0,X1] : union(union(X0,X1),intersection(union(X0,X1),union(X0,X2))) = union(X0,union(X1,union(intersection(X1,X2),X0)))
| ~ spl5_19
| ~ spl5_40
| ~ spl5_53
| ~ spl5_72 ),
inference(forward_demodulation,[],[f2513,f773]) ).
fof(f773,plain,
( ! [X2,X3,X0,X1] : union(X0,union(X1,union(X2,X3))) = union(X3,union(X2,union(X0,X1)))
| ~ spl5_19
| ~ spl5_40 ),
inference(forward_demodulation,[],[f720,f168]) ).
fof(f720,plain,
( ! [X2,X3,X0,X1] : union(X0,union(union(X1,X2),X3)) = union(X3,union(X2,union(X0,X1)))
| ~ spl5_40 ),
inference(superposition,[],[f464,f464]) ).
fof(f464,plain,
( ! [X2,X0,X1] : union(X0,union(X1,X2)) = union(X2,union(X0,X1))
| ~ spl5_40 ),
inference(avatar_component_clause,[],[f463]) ).
fof(f2513,plain,
( ! [X2,X0,X1] : union(union(X0,X1),intersection(union(X0,X1),union(X0,X2))) = union(X0,union(intersection(X1,X2),union(X0,X1)))
| ~ spl5_40
| ~ spl5_53
| ~ spl5_72 ),
inference(forward_demodulation,[],[f2389,f464]) ).
fof(f2389,plain,
( ! [X2,X0,X1] : union(union(X0,X1),intersection(union(X0,X1),union(X0,X2))) = union(union(X0,X1),union(X0,intersection(X1,X2)))
| ~ spl5_53
| ~ spl5_72 ),
inference(superposition,[],[f1914,f1053]) ).
fof(f1914,plain,
( ! [X2,X3,X0,X1] : intersection(union(X0,union(X1,X2)),union(X0,union(X1,X3))) = union(X0,union(X1,intersection(X2,X3)))
| ~ spl5_72 ),
inference(avatar_component_clause,[],[f1913]) ).
fof(f14511,plain,
( spl5_191
| ~ spl5_15
| ~ spl5_27
| ~ spl5_72 ),
inference(avatar_split_clause,[],[f2475,f1913,f300,f137,f14509]) ).
fof(f14509,plain,
( spl5_191
<=> ! [X2,X0,X1] : union(X1,X0) = intersection(union(X1,union(X0,X2)),union(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_191])]) ).
fof(f2475,plain,
( ! [X2,X0,X1] : union(X1,X0) = intersection(union(X1,union(X0,X2)),union(X1,X0))
| ~ spl5_15
| ~ spl5_27
| ~ spl5_72 ),
inference(forward_demodulation,[],[f2363,f301]) ).
fof(f2363,plain,
( ! [X2,X0,X1] : union(X1,union(X0,intersection(X2,X0))) = intersection(union(X1,union(X0,X2)),union(X1,X0))
| ~ spl5_15
| ~ spl5_72 ),
inference(superposition,[],[f1914,f138]) ).
fof(f14342,plain,
( spl5_190
| ~ spl5_14
| ~ spl5_59 ),
inference(avatar_split_clause,[],[f1640,f1599,f127,f14340]) ).
fof(f14340,plain,
( spl5_190
<=> ! [X0,X3,X2,X1] :
( member(X0,union(X1,X2))
| member(X0,X3)
| ~ member(X0,union(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_190])]) ).
fof(f127,plain,
( spl5_14
<=> ! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_14])]) ).
fof(f1599,plain,
( spl5_59
<=> ! [X0,X3,X2,X1] :
( ~ member(X3,union(X0,union(X1,X2)))
| member(X3,union(X0,X1))
| member(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_59])]) ).
fof(f1640,plain,
( ! [X2,X3,X0,X1] :
( member(X0,union(X1,X2))
| member(X0,X3)
| ~ member(X0,union(X2,X3)) )
| ~ spl5_14
| ~ spl5_59 ),
inference(resolution,[],[f1600,f128]) ).
fof(f128,plain,
( ! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X1) )
| ~ spl5_14 ),
inference(avatar_component_clause,[],[f127]) ).
fof(f1600,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X3,union(X0,union(X1,X2)))
| member(X3,union(X0,X1))
| member(X3,X2) )
| ~ spl5_59 ),
inference(avatar_component_clause,[],[f1599]) ).
fof(f14338,plain,
( spl5_189
| ~ spl5_12
| ~ spl5_58 ),
inference(avatar_split_clause,[],[f1607,f1595,f119,f14336]) ).
fof(f14336,plain,
( spl5_189
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,X1)
| ~ member(X0,intersection(X2,X3))
| member(X0,intersection(X3,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_189])]) ).
fof(f119,plain,
( spl5_12
<=> ! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_12])]) ).
fof(f1595,plain,
( spl5_58
<=> ! [X0,X3,X2,X1] :
( member(X3,intersection(X0,intersection(X1,X2)))
| ~ member(X3,X2)
| ~ member(X3,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_58])]) ).
fof(f1607,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,intersection(X2,X3))
| member(X0,intersection(X3,X1)) )
| ~ spl5_12
| ~ spl5_58 ),
inference(resolution,[],[f1596,f120]) ).
fof(f120,plain,
( ! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X1) )
| ~ spl5_12 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f1596,plain,
( ! [X2,X3,X0,X1] :
( member(X3,intersection(X0,intersection(X1,X2)))
| ~ member(X3,X2)
| ~ member(X3,intersection(X0,X1)) )
| ~ spl5_58 ),
inference(avatar_component_clause,[],[f1595]) ).
fof(f14334,plain,
( spl5_188
| ~ spl5_5
| ~ spl5_56 ),
inference(avatar_split_clause,[],[f1505,f1064,f85,f14332]) ).
fof(f14332,plain,
( spl5_188
<=> ! [X2,X0,X1] : union(X0,X1) = union(union(X0,X1),union(intersection(X1,X2),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_188])]) ).
fof(f1064,plain,
( spl5_56
<=> ! [X2,X0,X1] : union(X0,X1) = union(union(X0,X1),union(X0,intersection(X1,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_56])]) ).
fof(f1505,plain,
( ! [X2,X0,X1] : union(X0,X1) = union(union(X0,X1),union(intersection(X1,X2),X0))
| ~ spl5_5
| ~ spl5_56 ),
inference(superposition,[],[f1065,f86]) ).
fof(f1065,plain,
( ! [X2,X0,X1] : union(X0,X1) = union(union(X0,X1),union(X0,intersection(X1,X2)))
| ~ spl5_56 ),
inference(avatar_component_clause,[],[f1064]) ).
fof(f14329,plain,
( spl5_187
| ~ spl5_52
| ~ spl5_55 ),
inference(avatar_split_clause,[],[f1416,f1060,f1048,f14327]) ).
fof(f14327,plain,
( spl5_187
<=> ! [X2,X0,X1] : union(X0,X1) = union(X0,union(X1,union(X0,intersection(X2,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_187])]) ).
fof(f1048,plain,
( spl5_52
<=> ! [X2,X0,X1] : union(X0,X1) = union(X0,union(X1,intersection(union(X0,X1),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_52])]) ).
fof(f1060,plain,
( spl5_55
<=> ! [X2,X0,X1] : union(X0,intersection(X1,X2)) = intersection(union(X0,X2),union(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_55])]) ).
fof(f1416,plain,
( ! [X2,X0,X1] : union(X0,X1) = union(X0,union(X1,union(X0,intersection(X2,X1))))
| ~ spl5_52
| ~ spl5_55 ),
inference(superposition,[],[f1049,f1061]) ).
fof(f1061,plain,
( ! [X2,X0,X1] : union(X0,intersection(X1,X2)) = intersection(union(X0,X2),union(X0,X1))
| ~ spl5_55 ),
inference(avatar_component_clause,[],[f1060]) ).
fof(f1049,plain,
( ! [X2,X0,X1] : union(X0,X1) = union(X0,union(X1,intersection(union(X0,X1),X2)))
| ~ spl5_52 ),
inference(avatar_component_clause,[],[f1048]) ).
fof(f14325,plain,
( spl5_186
| ~ spl5_27
| ~ spl5_54 ),
inference(avatar_split_clause,[],[f1332,f1056,f300,f14323]) ).
fof(f14323,plain,
( spl5_186
<=> ! [X2,X0,X1] : union(X2,X0) = union(union(X2,X0),union(X0,intersection(X1,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_186])]) ).
fof(f1332,plain,
( ! [X2,X0,X1] : union(X2,X0) = union(union(X2,X0),union(X0,intersection(X1,X2)))
| ~ spl5_27
| ~ spl5_54 ),
inference(superposition,[],[f301,f1057]) ).
fof(f14321,plain,
( spl5_185
| ~ spl5_6
| ~ spl5_54 ),
inference(avatar_split_clause,[],[f1319,f1056,f89,f14319]) ).
fof(f1319,plain,
( ! [X2,X0,X1] : union(X0,intersection(X1,X2)) = intersection(union(X2,X0),union(X0,X1))
| ~ spl5_6
| ~ spl5_54 ),
inference(superposition,[],[f1057,f90]) ).
fof(f14317,plain,
( spl5_184
| ~ spl5_7
| ~ spl5_53 ),
inference(avatar_split_clause,[],[f1239,f1052,f93,f14315]) ).
fof(f14315,plain,
( spl5_184
<=> ! [X2,X0,X1] : union(X0,X1) = union(union(X0,X1),union(X1,intersection(X0,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_184])]) ).
fof(f1239,plain,
( ! [X2,X0,X1] : union(X0,X1) = union(union(X0,X1),union(X1,intersection(X0,X2)))
| ~ spl5_7
| ~ spl5_53 ),
inference(superposition,[],[f94,f1053]) ).
fof(f14313,plain,
( spl5_183
| ~ spl5_6
| ~ spl5_53 ),
inference(avatar_split_clause,[],[f1231,f1052,f89,f14311]) ).
fof(f14311,plain,
( spl5_183
<=> ! [X2,X0,X1] : union(X1,intersection(X0,X2)) = intersection(union(X1,X2),union(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_183])]) ).
fof(f1231,plain,
( ! [X2,X0,X1] : union(X1,intersection(X0,X2)) = intersection(union(X1,X2),union(X0,X1))
| ~ spl5_6
| ~ spl5_53 ),
inference(superposition,[],[f1053,f90]) ).
fof(f14309,plain,
( spl5_182
| ~ spl5_5
| ~ spl5_53 ),
inference(avatar_split_clause,[],[f1218,f1052,f85,f14307]) ).
fof(f14307,plain,
( spl5_182
<=> ! [X2,X0,X1] : union(X0,intersection(X2,X1)) = intersection(union(X2,X0),union(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_182])]) ).
fof(f1218,plain,
( ! [X2,X0,X1] : union(X0,intersection(X2,X1)) = intersection(union(X2,X0),union(X1,X0))
| ~ spl5_5
| ~ spl5_53 ),
inference(superposition,[],[f1053,f86]) ).
fof(f14305,plain,
( spl5_181
| ~ spl5_30
| ~ spl5_52 ),
inference(avatar_split_clause,[],[f1143,f1048,f342,f14303]) ).
fof(f14303,plain,
( spl5_181
<=> ! [X0,X3,X2,X1] : union(X0,union(intersection(X1,intersection(X0,X2)),intersection(X0,X3))) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_181])]) ).
fof(f342,plain,
( spl5_30
<=> ! [X2,X0,X1] : union(X0,intersection(X2,intersection(X0,X1))) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_30])]) ).
fof(f1143,plain,
( ! [X2,X3,X0,X1] : union(X0,union(intersection(X1,intersection(X0,X2)),intersection(X0,X3))) = X0
| ~ spl5_30
| ~ spl5_52 ),
inference(superposition,[],[f1049,f343]) ).
fof(f343,plain,
( ! [X2,X0,X1] : union(X0,intersection(X2,intersection(X0,X1))) = X0
| ~ spl5_30 ),
inference(avatar_component_clause,[],[f342]) ).
fof(f14087,plain,
( spl5_180
| ~ spl5_6
| ~ spl5_51 ),
inference(avatar_split_clause,[],[f1078,f1044,f89,f14085]) ).
fof(f14085,plain,
( spl5_180
<=> ! [X2,X0,X1] : intersection(X2,X0) = union(intersection(X2,X0),intersection(X2,intersection(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_180])]) ).
fof(f1044,plain,
( spl5_51
<=> ! [X2,X0,X1] : intersection(X0,X1) = union(intersection(X0,X1),intersection(X0,intersection(X1,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_51])]) ).
fof(f1078,plain,
( ! [X2,X0,X1] : intersection(X2,X0) = union(intersection(X2,X0),intersection(X2,intersection(X1,X0)))
| ~ spl5_6
| ~ spl5_51 ),
inference(superposition,[],[f1045,f90]) ).
fof(f1045,plain,
( ! [X2,X0,X1] : intersection(X0,X1) = union(intersection(X0,X1),intersection(X0,intersection(X1,X2)))
| ~ spl5_51 ),
inference(avatar_component_clause,[],[f1044]) ).
fof(f14083,plain,
( spl5_179
| ~ spl5_21
| ~ spl5_47 ),
inference(avatar_split_clause,[],[f957,f814,f177,f14081]) ).
fof(f14081,plain,
( spl5_179
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,union(X1,X2))
| member(X0,X1)
| member(X0,union(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_179])]) ).
fof(f177,plain,
( spl5_21
<=> ! [X2,X0,X1] :
( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_21])]) ).
fof(f814,plain,
( spl5_47
<=> ! [X0,X3,X2,X1] :
( member(X3,union(X0,union(X1,X2)))
| ~ member(X3,union(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_47])]) ).
fof(f957,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,union(X1,X2))
| member(X0,X1)
| member(X0,union(X2,X3)) )
| ~ spl5_21
| ~ spl5_47 ),
inference(resolution,[],[f815,f178]) ).
fof(f178,plain,
( ! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X0)
| member(X2,X1) )
| ~ spl5_21 ),
inference(avatar_component_clause,[],[f177]) ).
fof(f815,plain,
( ! [X2,X3,X0,X1] :
( member(X3,union(X0,union(X1,X2)))
| ~ member(X3,union(X0,X1)) )
| ~ spl5_47 ),
inference(avatar_component_clause,[],[f814]) ).
fof(f14079,plain,
( spl5_178
| ~ spl5_20
| ~ spl5_46 ),
inference(avatar_split_clause,[],[f918,f810,f171,f14077]) ).
fof(f14077,plain,
( spl5_178
<=> ! [X0,X3,X2,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,intersection(X2,X3))
| ~ member(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_178])]) ).
fof(f171,plain,
( spl5_20
<=> ! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_20])]) ).
fof(f810,plain,
( spl5_46
<=> ! [X0,X3,X2,X1] :
( ~ member(X3,intersection(X0,intersection(X1,X2)))
| member(X3,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_46])]) ).
fof(f918,plain,
( ! [X2,X3,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,intersection(X2,X3))
| ~ member(X0,X1) )
| ~ spl5_20
| ~ spl5_46 ),
inference(resolution,[],[f811,f172]) ).
fof(f172,plain,
( ! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) )
| ~ spl5_20 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f811,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X3,intersection(X0,intersection(X1,X2)))
| member(X3,intersection(X0,X1)) )
| ~ spl5_46 ),
inference(avatar_component_clause,[],[f810]) ).
fof(f14075,plain,
( spl5_177
| ~ spl5_30
| ~ spl5_40 ),
inference(avatar_split_clause,[],[f723,f463,f342,f14073]) ).
fof(f14073,plain,
( spl5_177
<=> ! [X0,X3,X2,X1] : union(X3,X0) = union(X0,union(intersection(X1,intersection(X0,X2)),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_177])]) ).
fof(f723,plain,
( ! [X2,X3,X0,X1] : union(X3,X0) = union(X0,union(intersection(X1,intersection(X0,X2)),X3))
| ~ spl5_30
| ~ spl5_40 ),
inference(superposition,[],[f464,f343]) ).
fof(f14071,plain,
( spl5_176
| ~ spl5_30
| ~ spl5_40 ),
inference(avatar_split_clause,[],[f705,f463,f342,f14069]) ).
fof(f14069,plain,
( spl5_176
<=> ! [X0,X3,X2,X1] : union(X3,X0) = union(intersection(X1,intersection(X0,X2)),union(X3,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_176])]) ).
fof(f705,plain,
( ! [X2,X3,X0,X1] : union(X3,X0) = union(intersection(X1,intersection(X0,X2)),union(X3,X0))
| ~ spl5_30
| ~ spl5_40 ),
inference(superposition,[],[f464,f343]) ).
fof(f14067,plain,
( spl5_175
| ~ spl5_36
| ~ spl5_39 ),
inference(avatar_split_clause,[],[f654,f459,f447,f14065]) ).
fof(f14065,plain,
( spl5_175
<=> ! [X0,X3,X2,X1] : union(X0,X3) = union(X0,union(intersection(X1,intersection(X2,X0)),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_175])]) ).
fof(f447,plain,
( spl5_36
<=> ! [X2,X0,X1] : intersection(X0,intersection(X1,X2)) = intersection(X2,intersection(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_36])]) ).
fof(f654,plain,
( ! [X2,X3,X0,X1] : union(X0,X3) = union(X0,union(intersection(X1,intersection(X2,X0)),X3))
| ~ spl5_36
| ~ spl5_39 ),
inference(superposition,[],[f460,f448]) ).
fof(f448,plain,
( ! [X2,X0,X1] : intersection(X0,intersection(X1,X2)) = intersection(X2,intersection(X0,X1))
| ~ spl5_36 ),
inference(avatar_component_clause,[],[f447]) ).
fof(f14063,plain,
( spl5_174
| ~ spl5_28
| ~ spl5_37 ),
inference(avatar_split_clause,[],[f633,f451,f304,f14061]) ).
fof(f14061,plain,
( spl5_174
<=> ! [X2,X0,X1] : union(X0,X1) = intersection(union(X0,X1),union(X1,union(X0,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_174])]) ).
fof(f304,plain,
( spl5_28
<=> ! [X2,X0] : intersection(X0,union(X0,X2)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_28])]) ).
fof(f633,plain,
( ! [X2,X0,X1] : union(X0,X1) = intersection(union(X0,X1),union(X1,union(X0,X2)))
| ~ spl5_28
| ~ spl5_37 ),
inference(superposition,[],[f305,f452]) ).
fof(f305,plain,
( ! [X2,X0] : intersection(X0,union(X0,X2)) = X0
| ~ spl5_28 ),
inference(avatar_component_clause,[],[f304]) ).
fof(f14058,plain,
( spl5_173
| ~ spl5_27
| ~ spl5_37 ),
inference(avatar_split_clause,[],[f620,f451,f300,f14056]) ).
fof(f14056,plain,
( spl5_173
<=> ! [X2,X0,X1] : union(X0,X1) = union(X1,union(X0,intersection(X2,union(X0,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_173])]) ).
fof(f620,plain,
( ! [X2,X0,X1] : union(X0,X1) = union(X1,union(X0,intersection(X2,union(X0,X1))))
| ~ spl5_27
| ~ spl5_37 ),
inference(superposition,[],[f452,f301]) ).
fof(f14053,plain,
( spl5_172
| ~ spl5_7
| ~ spl5_37 ),
inference(avatar_split_clause,[],[f619,f451,f93,f14051]) ).
fof(f14051,plain,
( spl5_172
<=> ! [X2,X0,X1] : union(X0,X1) = union(X1,union(X0,intersection(union(X0,X1),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_172])]) ).
fof(f619,plain,
( ! [X2,X0,X1] : union(X0,X1) = union(X1,union(X0,intersection(union(X0,X1),X2)))
| ~ spl5_7
| ~ spl5_37 ),
inference(superposition,[],[f452,f94]) ).
fof(f14049,plain,
( spl5_171
| ~ spl5_30
| ~ spl5_37 ),
inference(avatar_split_clause,[],[f612,f451,f342,f14047]) ).
fof(f14047,plain,
( spl5_171
<=> ! [X0,X3,X2,X1] : union(X0,X3) = union(intersection(X1,intersection(X0,X2)),union(X0,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_171])]) ).
fof(f612,plain,
( ! [X2,X3,X0,X1] : union(X0,X3) = union(intersection(X1,intersection(X0,X2)),union(X0,X3))
| ~ spl5_30
| ~ spl5_37 ),
inference(superposition,[],[f452,f343]) ).
fof(f13841,plain,
( spl5_170
| ~ spl5_18
| ~ spl5_29
| ~ spl5_36 ),
inference(avatar_split_clause,[],[f586,f447,f338,f163,f13839]) ).
fof(f13839,plain,
( spl5_170
<=> ! [X2,X0,X1] : intersection(X2,intersection(X0,X1)) = intersection(X0,intersection(X0,intersection(X1,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_170])]) ).
fof(f338,plain,
( spl5_29
<=> ! [X0,X1] : intersection(X0,X1) = intersection(X0,intersection(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_29])]) ).
fof(f586,plain,
( ! [X2,X0,X1] : intersection(X2,intersection(X0,X1)) = intersection(X0,intersection(X0,intersection(X1,X2)))
| ~ spl5_18
| ~ spl5_29
| ~ spl5_36 ),
inference(forward_demodulation,[],[f531,f164]) ).
fof(f531,plain,
( ! [X2,X0,X1] : intersection(X2,intersection(X0,X1)) = intersection(X0,intersection(intersection(X0,X1),X2))
| ~ spl5_29
| ~ spl5_36 ),
inference(superposition,[],[f448,f339]) ).
fof(f339,plain,
( ! [X0,X1] : intersection(X0,X1) = intersection(X0,intersection(X0,X1))
| ~ spl5_29 ),
inference(avatar_component_clause,[],[f338]) ).
fof(f13837,plain,
( spl5_169
| ~ spl5_29
| ~ spl5_36 ),
inference(avatar_split_clause,[],[f574,f447,f338,f13835]) ).
fof(f13835,plain,
( spl5_169
<=> ! [X2,X0,X1] : intersection(X1,intersection(X2,X0)) = intersection(X0,intersection(X1,intersection(X2,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_169])]) ).
fof(f574,plain,
( ! [X2,X0,X1] : intersection(X1,intersection(X2,X0)) = intersection(X0,intersection(X1,intersection(X2,X0)))
| ~ spl5_29
| ~ spl5_36 ),
inference(superposition,[],[f339,f448]) ).
fof(f13833,plain,
( spl5_168
| ~ spl5_27
| ~ spl5_36 ),
inference(avatar_split_clause,[],[f555,f447,f300,f13831]) ).
fof(f13831,plain,
( spl5_168
<=> ! [X2,X0,X1] : intersection(X1,X2) = union(intersection(X1,X2),intersection(X2,intersection(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_168])]) ).
fof(f555,plain,
( ! [X2,X0,X1] : intersection(X1,X2) = union(intersection(X1,X2),intersection(X2,intersection(X0,X1)))
| ~ spl5_27
| ~ spl5_36 ),
inference(superposition,[],[f301,f448]) ).
fof(f13829,plain,
( spl5_167
| ~ spl5_29
| ~ spl5_36 ),
inference(avatar_split_clause,[],[f514,f447,f338,f13827]) ).
fof(f13827,plain,
( spl5_167
<=> ! [X2,X0,X1] : intersection(X2,intersection(X0,X1)) = intersection(intersection(X0,X1),intersection(X2,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_167])]) ).
fof(f514,plain,
( ! [X2,X0,X1] : intersection(X2,intersection(X0,X1)) = intersection(intersection(X0,X1),intersection(X2,X0))
| ~ spl5_29
| ~ spl5_36 ),
inference(superposition,[],[f448,f339]) ).
fof(f13825,plain,
( spl5_166
| ~ spl5_18
| ~ spl5_29
| ~ spl5_34 ),
inference(avatar_split_clause,[],[f503,f438,f338,f163,f13823]) ).
fof(f13823,plain,
( spl5_166
<=> ! [X2,X0,X1] : intersection(X0,intersection(X1,X2)) = intersection(X1,intersection(X0,intersection(X1,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_166])]) ).
fof(f503,plain,
( ! [X2,X0,X1] : intersection(X0,intersection(X1,X2)) = intersection(X1,intersection(X0,intersection(X1,X2)))
| ~ spl5_18
| ~ spl5_29
| ~ spl5_34 ),
inference(forward_demodulation,[],[f502,f339]) ).
fof(f502,plain,
( ! [X2,X0,X1] : intersection(X0,intersection(X1,X2)) = intersection(X1,intersection(X0,intersection(X0,intersection(X1,X2))))
| ~ spl5_18
| ~ spl5_29
| ~ spl5_34 ),
inference(forward_demodulation,[],[f479,f164]) ).
fof(f479,plain,
( ! [X2,X0,X1] : intersection(intersection(X0,X1),X2) = intersection(X1,intersection(X0,intersection(intersection(X0,X1),X2)))
| ~ spl5_29
| ~ spl5_34 ),
inference(superposition,[],[f439,f339]) ).
fof(f13821,plain,
( spl5_165
| ~ spl5_18
| ~ spl5_29
| ~ spl5_34 ),
inference(avatar_split_clause,[],[f498,f438,f338,f163,f13819]) ).
fof(f13819,plain,
( spl5_165
<=> ! [X2,X0,X1] : intersection(X0,intersection(X1,X2)) = intersection(intersection(X0,X1),intersection(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_165])]) ).
fof(f498,plain,
( ! [X2,X0,X1] : intersection(X0,intersection(X1,X2)) = intersection(intersection(X0,X1),intersection(X0,X2))
| ~ spl5_18
| ~ spl5_29
| ~ spl5_34 ),
inference(forward_demodulation,[],[f470,f164]) ).
fof(f470,plain,
( ! [X2,X0,X1] : intersection(intersection(X0,X1),X2) = intersection(intersection(X0,X1),intersection(X0,X2))
| ~ spl5_29
| ~ spl5_34 ),
inference(superposition,[],[f439,f339]) ).
fof(f13817,plain,
( spl5_164
| ~ spl5_7
| ~ spl5_34 ),
inference(avatar_split_clause,[],[f485,f438,f93,f13815]) ).
fof(f13815,plain,
( spl5_164
<=> ! [X2,X0,X1] : intersection(X0,X1) = union(intersection(X0,X1),intersection(X1,intersection(X0,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_164])]) ).
fof(f485,plain,
( ! [X2,X0,X1] : intersection(X0,X1) = union(intersection(X0,X1),intersection(X1,intersection(X0,X2)))
| ~ spl5_7
| ~ spl5_34 ),
inference(superposition,[],[f94,f439]) ).
fof(f13812,plain,
( spl5_163
| ~ spl5_28
| ~ spl5_34 ),
inference(avatar_split_clause,[],[f478,f438,f304,f13810]) ).
fof(f478,plain,
( ! [X2,X0,X1] : intersection(X0,X1) = intersection(X1,intersection(X0,union(intersection(X0,X1),X2)))
| ~ spl5_28
| ~ spl5_34 ),
inference(superposition,[],[f439,f305]) ).
fof(f13808,plain,
( spl5_162
| ~ spl5_19
| ~ spl5_30 ),
inference(avatar_split_clause,[],[f382,f342,f167,f13806]) ).
fof(f13806,plain,
( spl5_162
<=> ! [X0,X3,X2,X1] : union(X0,union(intersection(X1,intersection(X0,X2)),X3)) = union(X0,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_162])]) ).
fof(f382,plain,
( ! [X2,X3,X0,X1] : union(X0,union(intersection(X1,intersection(X0,X2)),X3)) = union(X0,X3)
| ~ spl5_19
| ~ spl5_30 ),
inference(superposition,[],[f168,f343]) ).
fof(f13803,plain,
( spl5_161
| ~ spl5_18
| ~ spl5_28 ),
inference(avatar_split_clause,[],[f329,f304,f163,f13801]) ).
fof(f329,plain,
( ! [X2,X0,X1] : intersection(X0,X1) = intersection(X0,intersection(X1,union(intersection(X0,X1),X2)))
| ~ spl5_18
| ~ spl5_28 ),
inference(superposition,[],[f305,f164]) ).
fof(f13670,plain,
( spl5_160
| ~ spl5_19
| ~ spl5_28 ),
inference(avatar_split_clause,[],[f328,f304,f167,f13668]) ).
fof(f13668,plain,
( spl5_160
<=> ! [X2,X0,X1] : union(X0,X1) = intersection(union(X0,X1),union(X0,union(X1,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_160])]) ).
fof(f328,plain,
( ! [X2,X0,X1] : union(X0,X1) = intersection(union(X0,X1),union(X0,union(X1,X2)))
| ~ spl5_19
| ~ spl5_28 ),
inference(superposition,[],[f305,f168]) ).
fof(f13665,plain,
( spl5_159
| ~ spl5_19
| ~ spl5_27 ),
inference(avatar_split_clause,[],[f312,f300,f167,f13663]) ).
fof(f13663,plain,
( spl5_159
<=> ! [X2,X0,X1] : union(X0,X1) = union(X0,union(X1,intersection(X2,union(X0,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_159])]) ).
fof(f312,plain,
( ! [X2,X0,X1] : union(X0,X1) = union(X0,union(X1,intersection(X2,union(X0,X1))))
| ~ spl5_19
| ~ spl5_27 ),
inference(superposition,[],[f301,f168]) ).
fof(f13661,plain,
( spl5_158
| ~ spl5_24
| ~ spl5_27 ),
inference(avatar_split_clause,[],[f311,f300,f240,f13659]) ).
fof(f13659,plain,
( spl5_158
<=> ! [X2,X0,X1] : union(X0,X2) = union(union(X0,X2),union(X0,intersection(X1,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_158])]) ).
fof(f311,plain,
( ! [X2,X0,X1] : union(X0,X2) = union(union(X0,X2),union(X0,intersection(X1,X2)))
| ~ spl5_24
| ~ spl5_27 ),
inference(superposition,[],[f301,f241]) ).
fof(f11131,plain,
( spl5_157
| ~ spl5_68 ),
inference(avatar_split_clause,[],[f2205,f1897,f11129]) ).
fof(f11129,plain,
( spl5_157
<=> ! [X0,X1] :
( member(sK3(intersection(X0,X1),X0),X0)
| intersection(X0,X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_157])]) ).
fof(f1897,plain,
( spl5_68
<=> ! [X2,X0,X1] :
( member(sK3(intersection(X0,X1),X2),X2)
| intersection(X0,X1) = X2
| member(sK3(intersection(X0,X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_68])]) ).
fof(f2205,plain,
( ! [X0,X1] :
( member(sK3(intersection(X0,X1),X0),X0)
| intersection(X0,X1) = X0 )
| ~ spl5_68 ),
inference(factoring,[],[f1898]) ).
fof(f1898,plain,
( ! [X2,X0,X1] :
( member(sK3(intersection(X0,X1),X2),X2)
| member(sK3(intersection(X0,X1),X2),X0)
| intersection(X0,X1) = X2 )
| ~ spl5_68 ),
inference(avatar_component_clause,[],[f1897]) ).
fof(f11127,plain,
( spl5_156
| ~ spl5_67 ),
inference(avatar_split_clause,[],[f2157,f1893,f11125]) ).
fof(f11125,plain,
( spl5_156
<=> ! [X0,X1] :
( member(sK3(intersection(X0,X1),X1),X1)
| intersection(X0,X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_156])]) ).
fof(f1893,plain,
( spl5_67
<=> ! [X2,X0,X1] :
( member(sK3(intersection(X0,X1),X2),X2)
| intersection(X0,X1) = X2
| member(sK3(intersection(X0,X1),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_67])]) ).
fof(f2157,plain,
( ! [X0,X1] :
( member(sK3(intersection(X0,X1),X1),X1)
| intersection(X0,X1) = X1 )
| ~ spl5_67 ),
inference(factoring,[],[f1894]) ).
fof(f1894,plain,
( ! [X2,X0,X1] :
( member(sK3(intersection(X0,X1),X2),X2)
| member(sK3(intersection(X0,X1),X2),X1)
| intersection(X0,X1) = X2 )
| ~ spl5_67 ),
inference(avatar_component_clause,[],[f1893]) ).
fof(f11123,plain,
( spl5_155
| ~ spl5_66 ),
inference(avatar_split_clause,[],[f2091,f1889,f11121]) ).
fof(f11121,plain,
( spl5_155
<=> ! [X0,X1] :
( member(sK3(X0,intersection(X0,X1)),X0)
| intersection(X0,X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_155])]) ).
fof(f1889,plain,
( spl5_66
<=> ! [X2,X0,X1] :
( member(sK3(X0,intersection(X1,X2)),X0)
| intersection(X1,X2) = X0
| member(sK3(X0,intersection(X1,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_66])]) ).
fof(f2091,plain,
( ! [X0,X1] :
( member(sK3(X0,intersection(X0,X1)),X0)
| intersection(X0,X1) = X0 )
| ~ spl5_66 ),
inference(factoring,[],[f1890]) ).
fof(f1890,plain,
( ! [X2,X0,X1] :
( member(sK3(X0,intersection(X1,X2)),X1)
| member(sK3(X0,intersection(X1,X2)),X0)
| intersection(X1,X2) = X0 )
| ~ spl5_66 ),
inference(avatar_component_clause,[],[f1889]) ).
fof(f11119,plain,
( spl5_154
| ~ spl5_65 ),
inference(avatar_split_clause,[],[f2044,f1885,f11117]) ).
fof(f11117,plain,
( spl5_154
<=> ! [X0,X1] :
( member(sK3(X0,intersection(X1,X0)),X0)
| intersection(X1,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_154])]) ).
fof(f1885,plain,
( spl5_65
<=> ! [X2,X0,X1] :
( member(sK3(X0,intersection(X1,X2)),X0)
| intersection(X1,X2) = X0
| member(sK3(X0,intersection(X1,X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_65])]) ).
fof(f2044,plain,
( ! [X0,X1] :
( member(sK3(X0,intersection(X1,X0)),X0)
| intersection(X1,X0) = X0 )
| ~ spl5_65 ),
inference(factoring,[],[f1886]) ).
fof(f1886,plain,
( ! [X2,X0,X1] :
( member(sK3(X0,intersection(X1,X2)),X2)
| member(sK3(X0,intersection(X1,X2)),X0)
| intersection(X1,X2) = X0 )
| ~ spl5_65 ),
inference(avatar_component_clause,[],[f1885]) ).
fof(f11115,plain,
( spl5_153
| ~ spl5_10
| ~ spl5_64 ),
inference(avatar_split_clause,[],[f2006,f1881,f111,f11113]) ).
fof(f11113,plain,
( spl5_153
<=> ! [X0,X1] :
( member(sK4(union(X0,X1),X1),X0)
| subset(union(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_153])]) ).
fof(f111,plain,
( spl5_10
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ member(sK4(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_10])]) ).
fof(f1881,plain,
( spl5_64
<=> ! [X2,X0,X1] :
( member(sK4(union(X0,X1),X2),X0)
| member(sK4(union(X0,X1),X2),X1)
| subset(union(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_64])]) ).
fof(f2006,plain,
( ! [X0,X1] :
( member(sK4(union(X0,X1),X1),X0)
| subset(union(X0,X1),X1) )
| ~ spl5_10
| ~ spl5_64 ),
inference(duplicate_literal_removal,[],[f1944]) ).
fof(f1944,plain,
( ! [X0,X1] :
( member(sK4(union(X0,X1),X1),X0)
| subset(union(X0,X1),X1)
| subset(union(X0,X1),X1) )
| ~ spl5_10
| ~ spl5_64 ),
inference(resolution,[],[f1882,f112]) ).
fof(f112,plain,
( ! [X0,X1] :
( ~ member(sK4(X0,X1),X1)
| subset(X0,X1) )
| ~ spl5_10 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f1882,plain,
( ! [X2,X0,X1] :
( member(sK4(union(X0,X1),X2),X1)
| member(sK4(union(X0,X1),X2),X0)
| subset(union(X0,X1),X2) )
| ~ spl5_64 ),
inference(avatar_component_clause,[],[f1881]) ).
fof(f11049,plain,
( spl5_152
| ~ spl5_10
| ~ spl5_64 ),
inference(avatar_split_clause,[],[f2002,f1881,f111,f11047]) ).
fof(f11047,plain,
( spl5_152
<=> ! [X0,X1] :
( member(sK4(union(X0,X1),X0),X1)
| subset(union(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_152])]) ).
fof(f2002,plain,
( ! [X0,X1] :
( member(sK4(union(X0,X1),X0),X1)
| subset(union(X0,X1),X0) )
| ~ spl5_10
| ~ spl5_64 ),
inference(duplicate_literal_removal,[],[f1956]) ).
fof(f1956,plain,
( ! [X0,X1] :
( member(sK4(union(X0,X1),X0),X1)
| subset(union(X0,X1),X0)
| subset(union(X0,X1),X0) )
| ~ spl5_10
| ~ spl5_64 ),
inference(resolution,[],[f1882,f112]) ).
fof(f11045,plain,
( spl5_151
| ~ spl5_9
| ~ spl5_63 ),
inference(avatar_split_clause,[],[f1943,f1877,f107,f11043]) ).
fof(f11043,plain,
( spl5_151
<=> ! [X0,X1] :
( ~ member(sK4(X0,intersection(X1,X0)),X1)
| subset(X0,intersection(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_151])]) ).
fof(f107,plain,
( spl5_9
<=> ! [X0,X1] :
( subset(X0,X1)
| member(sK4(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_9])]) ).
fof(f1877,plain,
( spl5_63
<=> ! [X2,X0,X1] :
( ~ member(sK4(X0,intersection(X1,X2)),X2)
| ~ member(sK4(X0,intersection(X1,X2)),X1)
| subset(X0,intersection(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_63])]) ).
fof(f1943,plain,
( ! [X0,X1] :
( ~ member(sK4(X0,intersection(X1,X0)),X1)
| subset(X0,intersection(X1,X0)) )
| ~ spl5_9
| ~ spl5_63 ),
inference(duplicate_literal_removal,[],[f1916]) ).
fof(f1916,plain,
( ! [X0,X1] :
( ~ member(sK4(X0,intersection(X1,X0)),X1)
| subset(X0,intersection(X1,X0))
| subset(X0,intersection(X1,X0)) )
| ~ spl5_9
| ~ spl5_63 ),
inference(resolution,[],[f1878,f108]) ).
fof(f108,plain,
( ! [X0,X1] :
( member(sK4(X0,X1),X0)
| subset(X0,X1) )
| ~ spl5_9 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f1878,plain,
( ! [X2,X0,X1] :
( ~ member(sK4(X0,intersection(X1,X2)),X2)
| ~ member(sK4(X0,intersection(X1,X2)),X1)
| subset(X0,intersection(X1,X2)) )
| ~ spl5_63 ),
inference(avatar_component_clause,[],[f1877]) ).
fof(f11041,plain,
( spl5_150
| ~ spl5_12
| ~ spl5_54 ),
inference(avatar_split_clause,[],[f1329,f1056,f119,f11039]) ).
fof(f11039,plain,
( spl5_150
<=> ! [X0,X3,X2,X1] :
( ~ member(X3,union(X0,intersection(X1,X2)))
| member(X3,union(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_150])]) ).
fof(f1329,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X3,union(X0,intersection(X1,X2)))
| member(X3,union(X2,X0)) )
| ~ spl5_12
| ~ spl5_54 ),
inference(superposition,[],[f120,f1057]) ).
fof(f11037,plain,
( spl5_149
| ~ spl5_11
| ~ spl5_53 ),
inference(avatar_split_clause,[],[f1240,f1052,f115,f11035]) ).
fof(f11035,plain,
( spl5_149
<=> ! [X0,X3,X2,X1] :
( ~ member(X3,union(X1,intersection(X0,X2)))
| member(X3,union(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_149])]) ).
fof(f115,plain,
( spl5_11
<=> ! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_11])]) ).
fof(f1240,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X3,union(X1,intersection(X0,X2)))
| member(X3,union(X0,X1)) )
| ~ spl5_11
| ~ spl5_53 ),
inference(superposition,[],[f116,f1053]) ).
fof(f116,plain,
( ! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X0) )
| ~ spl5_11 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f11033,plain,
( spl5_148
| ~ spl5_5
| ~ spl5_49 ),
inference(avatar_split_clause,[],[f1037,f822,f85,f11031]) ).
fof(f11031,plain,
( spl5_148
<=> ! [X0,X3,X2,X1] :
( ~ member(X3,union(intersection(X1,X2),X0))
| member(X3,union(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_148])]) ).
fof(f822,plain,
( spl5_49
<=> ! [X0,X3,X2,X1] :
( ~ member(X3,union(X0,intersection(X1,X2)))
| member(X3,union(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_49])]) ).
fof(f1037,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X3,union(intersection(X1,X2),X0))
| member(X3,union(X0,X2)) )
| ~ spl5_5
| ~ spl5_49 ),
inference(superposition,[],[f823,f86]) ).
fof(f823,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X3,union(X0,intersection(X1,X2)))
| member(X3,union(X0,X2)) )
| ~ spl5_49 ),
inference(avatar_component_clause,[],[f822]) ).
fof(f11029,plain,
( spl5_147
| ~ spl5_5
| ~ spl5_48 ),
inference(avatar_split_clause,[],[f1010,f818,f85,f11027]) ).
fof(f11027,plain,
( spl5_147
<=> ! [X0,X3,X2,X1] :
( ~ member(X3,union(intersection(X1,X2),X0))
| member(X3,union(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_147])]) ).
fof(f818,plain,
( spl5_48
<=> ! [X0,X3,X2,X1] :
( ~ member(X3,union(X0,intersection(X1,X2)))
| member(X3,union(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_48])]) ).
fof(f1010,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X3,union(intersection(X1,X2),X0))
| member(X3,union(X0,X1)) )
| ~ spl5_5
| ~ spl5_48 ),
inference(superposition,[],[f819,f86]) ).
fof(f819,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X3,union(X0,intersection(X1,X2)))
| member(X3,union(X0,X1)) )
| ~ spl5_48 ),
inference(avatar_component_clause,[],[f818]) ).
fof(f11025,plain,
( spl5_146
| ~ spl5_5
| ~ spl5_47 ),
inference(avatar_split_clause,[],[f960,f814,f85,f11023]) ).
fof(f11023,plain,
( spl5_146
<=> ! [X0,X3,X2,X1] :
( member(X2,union(X3,union(X1,X0)))
| ~ member(X2,union(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_146])]) ).
fof(f960,plain,
( ! [X2,X3,X0,X1] :
( member(X2,union(X3,union(X1,X0)))
| ~ member(X2,union(X3,X0)) )
| ~ spl5_5
| ~ spl5_47 ),
inference(superposition,[],[f815,f86]) ).
fof(f11021,plain,
( spl5_145
| ~ spl5_6
| ~ spl5_46 ),
inference(avatar_split_clause,[],[f922,f810,f89,f11019]) ).
fof(f11019,plain,
( spl5_145
<=> ! [X0,X3,X2,X1] :
( ~ member(X2,intersection(X3,intersection(X1,X0)))
| member(X2,intersection(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_145])]) ).
fof(f922,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X2,intersection(X3,intersection(X1,X0)))
| member(X2,intersection(X3,X0)) )
| ~ spl5_6
| ~ spl5_46 ),
inference(superposition,[],[f811,f90]) ).
fof(f11017,plain,
( spl5_144
| ~ spl5_30
| ~ spl5_45 ),
inference(avatar_split_clause,[],[f909,f806,f342,f11015]) ).
fof(f11015,plain,
( spl5_144
<=> ! [X0,X3,X2,X1] :
( ~ member(sK4(X3,X0),intersection(X1,intersection(X0,X2)))
| subset(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_144])]) ).
fof(f806,plain,
( spl5_45
<=> ! [X2,X0,X1] :
( ~ member(sK4(X0,union(X1,X2)),X2)
| subset(X0,union(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_45])]) ).
fof(f909,plain,
( ! [X2,X3,X0,X1] :
( ~ member(sK4(X3,X0),intersection(X1,intersection(X0,X2)))
| subset(X3,X0) )
| ~ spl5_30
| ~ spl5_45 ),
inference(superposition,[],[f807,f343]) ).
fof(f807,plain,
( ! [X2,X0,X1] :
( ~ member(sK4(X0,union(X1,X2)),X2)
| subset(X0,union(X1,X2)) )
| ~ spl5_45 ),
inference(avatar_component_clause,[],[f806]) ).
fof(f11013,plain,
( spl5_143
| ~ spl5_14
| ~ spl5_40 ),
inference(avatar_split_clause,[],[f738,f463,f127,f11011]) ).
fof(f11011,plain,
( spl5_143
<=> ! [X0,X3,X2,X1] :
( member(X3,union(X2,union(X0,X1)))
| ~ member(X3,union(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_143])]) ).
fof(f738,plain,
( ! [X2,X3,X0,X1] :
( member(X3,union(X2,union(X0,X1)))
| ~ member(X3,union(X1,X2)) )
| ~ spl5_14
| ~ spl5_40 ),
inference(superposition,[],[f128,f464]) ).
fof(f11009,plain,
( spl5_142
| ~ spl5_70
| ~ spl5_90 ),
inference(avatar_split_clause,[],[f4161,f3301,f1905,f11007]) ).
fof(f11007,plain,
( spl5_142
<=> ! [X0,X1] : subset(union(X0,X1),union(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_142])]) ).
fof(f1905,plain,
( spl5_70
<=> ! [X0,X1] : subset(X0,union(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_70])]) ).
fof(f3301,plain,
( spl5_90
<=> ! [X0,X1] : union(X1,X0) = union(X0,union(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_90])]) ).
fof(f4161,plain,
( ! [X0,X1] : subset(union(X0,X1),union(X1,X0))
| ~ spl5_70
| ~ spl5_90 ),
inference(superposition,[],[f1906,f3302]) ).
fof(f3302,plain,
( ! [X0,X1] : union(X1,X0) = union(X0,union(X0,X1))
| ~ spl5_90 ),
inference(avatar_component_clause,[],[f3301]) ).
fof(f1906,plain,
( ! [X0,X1] : subset(X0,union(X1,X0))
| ~ spl5_70 ),
inference(avatar_component_clause,[],[f1905]) ).
fof(f11005,plain,
( spl5_141
| ~ spl5_14
| ~ spl5_39 ),
inference(avatar_split_clause,[],[f669,f459,f127,f11003]) ).
fof(f11003,plain,
( spl5_141
<=> ! [X0,X3,X2,X1] :
( member(X3,union(X0,X2))
| ~ member(X3,union(intersection(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_141])]) ).
fof(f669,plain,
( ! [X2,X3,X0,X1] :
( member(X3,union(X0,X2))
| ~ member(X3,union(intersection(X0,X1),X2)) )
| ~ spl5_14
| ~ spl5_39 ),
inference(superposition,[],[f128,f460]) ).
fof(f11001,plain,
( spl5_140
| ~ spl5_13
| ~ spl5_37 ),
inference(avatar_split_clause,[],[f627,f451,f123,f10999]) ).
fof(f10999,plain,
( spl5_140
<=> ! [X0,X3,X2,X1] :
( member(X3,union(X1,union(X0,X2)))
| ~ member(X3,union(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_140])]) ).
fof(f123,plain,
( spl5_13
<=> ! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_13])]) ).
fof(f627,plain,
( ! [X2,X3,X0,X1] :
( member(X3,union(X1,union(X0,X2)))
| ~ member(X3,union(X0,X1)) )
| ~ spl5_13
| ~ spl5_37 ),
inference(superposition,[],[f124,f452]) ).
fof(f124,plain,
( ! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X0) )
| ~ spl5_13 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f10997,plain,
( spl5_139
| ~ spl5_12
| ~ spl5_36 ),
inference(avatar_split_clause,[],[f552,f447,f119,f10995]) ).
fof(f10995,plain,
( spl5_139
<=> ! [X0,X3,X2,X1] :
( ~ member(X3,intersection(X2,intersection(X0,X1)))
| member(X3,intersection(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_139])]) ).
fof(f552,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X3,intersection(X2,intersection(X0,X1)))
| member(X3,intersection(X1,X2)) )
| ~ spl5_12
| ~ spl5_36 ),
inference(superposition,[],[f120,f448]) ).
fof(f10993,plain,
( spl5_138
| ~ spl5_11
| ~ spl5_34 ),
inference(avatar_split_clause,[],[f486,f438,f115,f10991]) ).
fof(f10991,plain,
( spl5_138
<=> ! [X0,X3,X2,X1] :
( ~ member(X3,intersection(X1,intersection(X0,X2)))
| member(X3,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_138])]) ).
fof(f486,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X3,intersection(X1,intersection(X0,X2)))
| member(X3,intersection(X0,X1)) )
| ~ spl5_11
| ~ spl5_34 ),
inference(superposition,[],[f116,f439]) ).
fof(f10989,plain,
( spl5_137
| ~ spl5_19
| ~ spl5_33 ),
inference(avatar_split_clause,[],[f430,f400,f167,f10987]) ).
fof(f10987,plain,
( spl5_137
<=> ! [X4,X0,X3,X2,X1] :
( member(X3,union(X4,union(X0,union(X1,X2))))
| ~ member(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_137])]) ).
fof(f400,plain,
( spl5_33
<=> ! [X0,X3,X2,X1] :
( member(X3,union(X0,union(X1,X2)))
| ~ member(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_33])]) ).
fof(f430,plain,
( ! [X2,X3,X0,X1,X4] :
( member(X3,union(X4,union(X0,union(X1,X2))))
| ~ member(X3,X2) )
| ~ spl5_19
| ~ spl5_33 ),
inference(superposition,[],[f401,f168]) ).
fof(f401,plain,
( ! [X2,X3,X0,X1] :
( member(X3,union(X0,union(X1,X2)))
| ~ member(X3,X2) )
| ~ spl5_33 ),
inference(avatar_component_clause,[],[f400]) ).
fof(f10985,plain,
( spl5_136
| ~ spl5_30
| ~ spl5_33 ),
inference(avatar_split_clause,[],[f428,f400,f342,f10983]) ).
fof(f10983,plain,
( spl5_136
<=> ! [X4,X0,X3,X2,X1] :
( member(X3,union(X4,X0))
| ~ member(X3,intersection(X1,intersection(X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_136])]) ).
fof(f428,plain,
( ! [X2,X3,X0,X1,X4] :
( member(X3,union(X4,X0))
| ~ member(X3,intersection(X1,intersection(X0,X2))) )
| ~ spl5_30
| ~ spl5_33 ),
inference(superposition,[],[f401,f343]) ).
fof(f10981,plain,
( spl5_135
| ~ spl5_18
| ~ spl5_32 ),
inference(avatar_split_clause,[],[f412,f396,f163,f10979]) ).
fof(f10979,plain,
( spl5_135
<=> ! [X4,X0,X3,X2,X1] :
( ~ member(X3,intersection(X4,intersection(X0,intersection(X1,X2))))
| member(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_135])]) ).
fof(f396,plain,
( spl5_32
<=> ! [X0,X3,X2,X1] :
( ~ member(X3,intersection(X0,intersection(X1,X2)))
| member(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_32])]) ).
fof(f412,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ member(X3,intersection(X4,intersection(X0,intersection(X1,X2))))
| member(X3,X2) )
| ~ spl5_18
| ~ spl5_32 ),
inference(superposition,[],[f397,f164]) ).
fof(f397,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X3,intersection(X0,intersection(X1,X2)))
| member(X3,X2) )
| ~ spl5_32 ),
inference(avatar_component_clause,[],[f396]) ).
fof(f10197,plain,
( spl5_134
| ~ spl5_27
| ~ spl5_89 ),
inference(avatar_split_clause,[],[f4000,f3297,f300,f10195]) ).
fof(f3297,plain,
( spl5_89
<=> ! [X0,X1] : union(X0,X1) = union(X1,union(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_89])]) ).
fof(f4000,plain,
( ! [X0,X1] : union(intersection(X1,X0),X0) = X0
| ~ spl5_27
| ~ spl5_89 ),
inference(superposition,[],[f3298,f301]) ).
fof(f3298,plain,
( ! [X0,X1] : union(X0,X1) = union(X1,union(X0,X1))
| ~ spl5_89 ),
inference(avatar_component_clause,[],[f3297]) ).
fof(f7580,plain,
( spl5_133
| ~ spl5_7
| ~ spl5_89 ),
inference(avatar_split_clause,[],[f3999,f3297,f93,f7578]) ).
fof(f7578,plain,
( spl5_133
<=> ! [X0,X1] : union(intersection(X0,X1),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_133])]) ).
fof(f3999,plain,
( ! [X0,X1] : union(intersection(X0,X1),X0) = X0
| ~ spl5_7
| ~ spl5_89 ),
inference(superposition,[],[f3298,f94]) ).
fof(f5136,plain,
( spl5_132
| ~ spl5_7
| ~ spl5_30
| ~ spl5_36
| ~ spl5_60 ),
inference(avatar_split_clause,[],[f1791,f1674,f447,f342,f93,f5134]) ).
fof(f1674,plain,
( spl5_60
<=> ! [X0,X3,X2,X1] : intersection(union(X0,X1),intersection(union(X0,X2),X3)) = intersection(union(X0,intersection(X1,X2)),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_60])]) ).
fof(f1791,plain,
( ! [X2,X3,X0] : intersection(X0,X3) = intersection(X0,intersection(X3,union(X0,X2)))
| ~ spl5_7
| ~ spl5_30
| ~ spl5_36
| ~ spl5_60 ),
inference(forward_demodulation,[],[f1790,f343]) ).
fof(f1790,plain,
( ! [X2,X3,X0,X1] : intersection(union(X0,intersection(X2,intersection(X0,X1))),X3) = intersection(X0,intersection(X3,union(X0,X2)))
| ~ spl5_7
| ~ spl5_36
| ~ spl5_60 ),
inference(forward_demodulation,[],[f1706,f448]) ).
fof(f1706,plain,
( ! [X2,X3,X0,X1] : intersection(union(X0,intersection(X2,intersection(X0,X1))),X3) = intersection(union(X0,X2),intersection(X0,X3))
| ~ spl5_7
| ~ spl5_60 ),
inference(superposition,[],[f1675,f94]) ).
fof(f1675,plain,
( ! [X2,X3,X0,X1] : intersection(union(X0,X1),intersection(union(X0,X2),X3)) = intersection(union(X0,intersection(X1,X2)),X3)
| ~ spl5_60 ),
inference(avatar_component_clause,[],[f1674]) ).
fof(f5132,plain,
( spl5_131
| ~ spl5_15
| ~ spl5_19
| ~ spl5_37
| ~ spl5_56 ),
inference(avatar_split_clause,[],[f1559,f1064,f451,f167,f137,f5130]) ).
fof(f5130,plain,
( spl5_131
<=> ! [X2,X0,X1] : union(X0,X1) = union(X1,union(X0,intersection(X1,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_131])]) ).
fof(f1559,plain,
( ! [X2,X0,X1] : union(X0,X1) = union(X1,union(X0,intersection(X1,X2)))
| ~ spl5_15
| ~ spl5_19
| ~ spl5_37
| ~ spl5_56 ),
inference(forward_demodulation,[],[f1510,f200]) ).
fof(f1510,plain,
( ! [X2,X0,X1] : union(X0,X1) = union(X1,union(X0,union(X0,intersection(X1,X2))))
| ~ spl5_37
| ~ spl5_56 ),
inference(superposition,[],[f1065,f452]) ).
fof(f5128,plain,
( spl5_130
| ~ spl5_24
| ~ spl5_55 ),
inference(avatar_split_clause,[],[f1407,f1060,f240,f5126]) ).
fof(f1407,plain,
( ! [X2,X0,X1] : union(X0,intersection(X1,X2)) = union(X0,intersection(X2,X1))
| ~ spl5_24
| ~ spl5_55 ),
inference(superposition,[],[f1061,f241]) ).
fof(f5124,plain,
( spl5_129
| ~ spl5_27
| ~ spl5_52 ),
inference(avatar_split_clause,[],[f1142,f1048,f300,f5122]) ).
fof(f5122,plain,
( spl5_129
<=> ! [X2,X0,X1] : union(X0,union(intersection(X1,X0),intersection(X0,X2))) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_129])]) ).
fof(f1142,plain,
( ! [X2,X0,X1] : union(X0,union(intersection(X1,X0),intersection(X0,X2))) = X0
| ~ spl5_27
| ~ spl5_52 ),
inference(superposition,[],[f1049,f301]) ).
fof(f5120,plain,
( spl5_128
| ~ spl5_7
| ~ spl5_52 ),
inference(avatar_split_clause,[],[f1141,f1048,f93,f5118]) ).
fof(f5118,plain,
( spl5_128
<=> ! [X2,X0,X1] : union(X0,union(intersection(X0,X1),intersection(X0,X2))) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_128])]) ).
fof(f1141,plain,
( ! [X2,X0,X1] : union(X0,union(intersection(X0,X1),intersection(X0,X2))) = X0
| ~ spl5_7
| ~ spl5_52 ),
inference(superposition,[],[f1049,f94]) ).
fof(f5116,plain,
( spl5_127
| ~ spl5_27
| ~ spl5_40 ),
inference(avatar_split_clause,[],[f722,f463,f300,f5114]) ).
fof(f5114,plain,
( spl5_127
<=> ! [X2,X0,X1] : union(X2,X0) = union(X0,union(intersection(X1,X0),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_127])]) ).
fof(f722,plain,
( ! [X2,X0,X1] : union(X2,X0) = union(X0,union(intersection(X1,X0),X2))
| ~ spl5_27
| ~ spl5_40 ),
inference(superposition,[],[f464,f301]) ).
fof(f5112,plain,
( spl5_126
| ~ spl5_7
| ~ spl5_40 ),
inference(avatar_split_clause,[],[f721,f463,f93,f5110]) ).
fof(f5110,plain,
( spl5_126
<=> ! [X2,X0,X1] : union(X2,X0) = union(X0,union(intersection(X0,X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_126])]) ).
fof(f721,plain,
( ! [X2,X0,X1] : union(X2,X0) = union(X0,union(intersection(X0,X1),X2))
| ~ spl5_7
| ~ spl5_40 ),
inference(superposition,[],[f464,f94]) ).
fof(f5108,plain,
( spl5_125
| ~ spl5_5
| ~ spl5_40 ),
inference(avatar_split_clause,[],[f711,f463,f85,f5106]) ).
fof(f5106,plain,
( spl5_125
<=> ! [X2,X0,X1] : union(union(X1,X2),X0) = union(X2,union(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_125])]) ).
fof(f711,plain,
( ! [X2,X0,X1] : union(union(X1,X2),X0) = union(X2,union(X0,X1))
| ~ spl5_5
| ~ spl5_40 ),
inference(superposition,[],[f464,f86]) ).
fof(f5104,plain,
( spl5_124
| ~ spl5_57
| ~ spl5_87 ),
inference(avatar_split_clause,[],[f3821,f3289,f1131,f5102]) ).
fof(f5102,plain,
( spl5_124
<=> ! [X0,X1] : subset(intersection(X1,X0),intersection(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_124])]) ).
fof(f1131,plain,
( spl5_57
<=> ! [X0,X1] : subset(intersection(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_57])]) ).
fof(f3289,plain,
( spl5_87
<=> ! [X0,X1] : intersection(X1,X0) = intersection(X0,intersection(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_87])]) ).
fof(f3821,plain,
( ! [X0,X1] : subset(intersection(X1,X0),intersection(X0,X1))
| ~ spl5_57
| ~ spl5_87 ),
inference(superposition,[],[f1132,f3290]) ).
fof(f3290,plain,
( ! [X0,X1] : intersection(X1,X0) = intersection(X0,intersection(X0,X1))
| ~ spl5_87 ),
inference(avatar_component_clause,[],[f3289]) ).
fof(f1132,plain,
( ! [X0,X1] : subset(intersection(X0,X1),X1)
| ~ spl5_57 ),
inference(avatar_component_clause,[],[f1131]) ).
fof(f5100,plain,
( spl5_123
| ~ spl5_27
| ~ spl5_40 ),
inference(avatar_split_clause,[],[f704,f463,f300,f5098]) ).
fof(f5098,plain,
( spl5_123
<=> ! [X2,X0,X1] : union(X2,X0) = union(intersection(X1,X0),union(X2,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_123])]) ).
fof(f704,plain,
( ! [X2,X0,X1] : union(X2,X0) = union(intersection(X1,X0),union(X2,X0))
| ~ spl5_27
| ~ spl5_40 ),
inference(superposition,[],[f464,f301]) ).
fof(f5096,plain,
( spl5_122
| ~ spl5_7
| ~ spl5_40 ),
inference(avatar_split_clause,[],[f703,f463,f93,f5094]) ).
fof(f5094,plain,
( spl5_122
<=> ! [X2,X0,X1] : union(X2,X0) = union(intersection(X0,X1),union(X2,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_122])]) ).
fof(f703,plain,
( ! [X2,X0,X1] : union(X2,X0) = union(intersection(X0,X1),union(X2,X0))
| ~ spl5_7
| ~ spl5_40 ),
inference(superposition,[],[f464,f94]) ).
fof(f5092,plain,
( spl5_121
| ~ spl5_5
| ~ spl5_39 ),
inference(avatar_split_clause,[],[f659,f459,f85,f5090]) ).
fof(f5090,plain,
( spl5_121
<=> ! [X2,X0,X1] : union(X0,X2) = union(X0,union(X2,intersection(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_121])]) ).
fof(f659,plain,
( ! [X2,X0,X1] : union(X0,X2) = union(X0,union(X2,intersection(X0,X1)))
| ~ spl5_5
| ~ spl5_39 ),
inference(superposition,[],[f460,f86]) ).
fof(f5088,plain,
( spl5_120
| ~ spl5_5
| ~ spl5_37 ),
inference(avatar_split_clause,[],[f617,f451,f85,f5086]) ).
fof(f5086,plain,
( spl5_120
<=> ! [X2,X0,X1] : union(X2,union(X0,X1)) = union(X1,union(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_120])]) ).
fof(f617,plain,
( ! [X2,X0,X1] : union(X2,union(X0,X1)) = union(X1,union(X0,X2))
| ~ spl5_5
| ~ spl5_37 ),
inference(superposition,[],[f452,f86]) ).
fof(f5084,plain,
( spl5_119
| ~ spl5_19
| ~ spl5_37 ),
inference(avatar_split_clause,[],[f616,f451,f167,f5082]) ).
fof(f5082,plain,
( spl5_119
<=> ! [X2,X0,X1] : union(X0,union(X1,X2)) = union(X1,union(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_119])]) ).
fof(f616,plain,
( ! [X2,X0,X1] : union(X0,union(X1,X2)) = union(X1,union(X0,X2))
| ~ spl5_19
| ~ spl5_37 ),
inference(superposition,[],[f452,f168]) ).
fof(f5080,plain,
( spl5_118
| ~ spl5_27
| ~ spl5_37 ),
inference(avatar_split_clause,[],[f611,f451,f300,f5078]) ).
fof(f611,plain,
( ! [X2,X0,X1] : union(X0,X2) = union(intersection(X1,X0),union(X0,X2))
| ~ spl5_27
| ~ spl5_37 ),
inference(superposition,[],[f452,f301]) ).
fof(f5076,plain,
( spl5_117
| ~ spl5_7
| ~ spl5_37 ),
inference(avatar_split_clause,[],[f610,f451,f93,f5074]) ).
fof(f5074,plain,
( spl5_117
<=> ! [X2,X0,X1] : union(X0,X2) = union(intersection(X0,X1),union(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_117])]) ).
fof(f610,plain,
( ! [X2,X0,X1] : union(X0,X2) = union(intersection(X0,X1),union(X0,X2))
| ~ spl5_7
| ~ spl5_37 ),
inference(superposition,[],[f452,f94]) ).
fof(f5072,plain,
( spl5_116
| ~ spl5_30
| ~ spl5_36 ),
inference(avatar_split_clause,[],[f575,f447,f342,f5070]) ).
fof(f5070,plain,
( spl5_116
<=> ! [X0,X3,X2,X1] : union(X0,intersection(X3,intersection(X1,intersection(X2,X0)))) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_116])]) ).
fof(f575,plain,
( ! [X2,X3,X0,X1] : union(X0,intersection(X3,intersection(X1,intersection(X2,X0)))) = X0
| ~ spl5_30
| ~ spl5_36 ),
inference(superposition,[],[f343,f448]) ).
fof(f5068,plain,
( spl5_115
| ~ spl5_28
| ~ spl5_36 ),
inference(avatar_split_clause,[],[f530,f447,f304,f5066]) ).
fof(f5066,plain,
( spl5_115
<=> ! [X2,X0,X1] : intersection(X2,X0) = intersection(X0,intersection(union(X0,X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_115])]) ).
fof(f530,plain,
( ! [X2,X0,X1] : intersection(X2,X0) = intersection(X0,intersection(union(X0,X1),X2))
| ~ spl5_28
| ~ spl5_36 ),
inference(superposition,[],[f448,f305]) ).
fof(f5064,plain,
( spl5_114
| ~ spl5_6
| ~ spl5_36 ),
inference(avatar_split_clause,[],[f523,f447,f89,f5062]) ).
fof(f5062,plain,
( spl5_114
<=> ! [X2,X0,X1] : intersection(intersection(X1,X2),X0) = intersection(X2,intersection(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_114])]) ).
fof(f523,plain,
( ! [X2,X0,X1] : intersection(intersection(X1,X2),X0) = intersection(X2,intersection(X0,X1))
| ~ spl5_6
| ~ spl5_36 ),
inference(superposition,[],[f448,f90]) ).
fof(f5060,plain,
( spl5_113
| ~ spl5_40
| ~ spl5_61 ),
inference(avatar_split_clause,[],[f2821,f1678,f463,f5058]) ).
fof(f5058,plain,
( spl5_113
<=> ! [X2,X0,X1] : subset(X0,union(X2,union(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_113])]) ).
fof(f1678,plain,
( spl5_61
<=> ! [X0,X1] : subset(X0,union(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_61])]) ).
fof(f2821,plain,
( ! [X2,X0,X1] : subset(X0,union(X2,union(X0,X1)))
| ~ spl5_40
| ~ spl5_61 ),
inference(superposition,[],[f1679,f464]) ).
fof(f1679,plain,
( ! [X0,X1] : subset(X0,union(X0,X1))
| ~ spl5_61 ),
inference(avatar_component_clause,[],[f1678]) ).
fof(f5056,plain,
( spl5_112
| ~ spl5_28
| ~ spl5_36 ),
inference(avatar_split_clause,[],[f513,f447,f304,f5054]) ).
fof(f5054,plain,
( spl5_112
<=> ! [X2,X0,X1] : intersection(X2,X0) = intersection(union(X0,X1),intersection(X2,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_112])]) ).
fof(f513,plain,
( ! [X2,X0,X1] : intersection(X2,X0) = intersection(union(X0,X1),intersection(X2,X0))
| ~ spl5_28
| ~ spl5_36 ),
inference(superposition,[],[f448,f305]) ).
fof(f5052,plain,
( spl5_111
| ~ spl5_6
| ~ spl5_34 ),
inference(avatar_split_clause,[],[f476,f438,f89,f5050]) ).
fof(f5050,plain,
( spl5_111
<=> ! [X2,X0,X1] : intersection(X2,intersection(X0,X1)) = intersection(X1,intersection(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_111])]) ).
fof(f476,plain,
( ! [X2,X0,X1] : intersection(X2,intersection(X0,X1)) = intersection(X1,intersection(X0,X2))
| ~ spl5_6
| ~ spl5_34 ),
inference(superposition,[],[f439,f90]) ).
fof(f5048,plain,
( spl5_110
| ~ spl5_18
| ~ spl5_34 ),
inference(avatar_split_clause,[],[f474,f438,f163,f5046]) ).
fof(f5046,plain,
( spl5_110
<=> ! [X2,X0,X1] : intersection(X0,intersection(X1,X2)) = intersection(X1,intersection(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_110])]) ).
fof(f474,plain,
( ! [X2,X0,X1] : intersection(X0,intersection(X1,X2)) = intersection(X1,intersection(X0,X2))
| ~ spl5_18
| ~ spl5_34 ),
inference(superposition,[],[f439,f164]) ).
fof(f5044,plain,
( spl5_109
| ~ spl5_28
| ~ spl5_34 ),
inference(avatar_split_clause,[],[f469,f438,f304,f5042]) ).
fof(f5042,plain,
( spl5_109
<=> ! [X2,X0,X1] : intersection(X0,X2) = intersection(union(X0,X1),intersection(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_109])]) ).
fof(f469,plain,
( ! [X2,X0,X1] : intersection(X0,X2) = intersection(union(X0,X1),intersection(X0,X2))
| ~ spl5_28
| ~ spl5_34 ),
inference(superposition,[],[f439,f305]) ).
fof(f5040,plain,
( spl5_108
| ~ spl5_18
| ~ spl5_30 ),
inference(avatar_split_clause,[],[f378,f342,f163,f5038]) ).
fof(f5038,plain,
( spl5_108
<=> ! [X0,X3,X2,X1] : union(X2,intersection(X0,intersection(X1,intersection(X2,X3)))) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_108])]) ).
fof(f378,plain,
( ! [X2,X3,X0,X1] : union(X2,intersection(X0,intersection(X1,intersection(X2,X3)))) = X2
| ~ spl5_18
| ~ spl5_30 ),
inference(superposition,[],[f343,f164]) ).
fof(f5036,plain,
( spl5_107
| ~ spl5_18
| ~ spl5_28 ),
inference(avatar_split_clause,[],[f333,f304,f163,f5034]) ).
fof(f5034,plain,
( spl5_107
<=> ! [X2,X0,X1] : intersection(X0,X2) = intersection(X0,intersection(union(X0,X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_107])]) ).
fof(f333,plain,
( ! [X2,X0,X1] : intersection(X0,X2) = intersection(X0,intersection(union(X0,X1),X2))
| ~ spl5_18
| ~ spl5_28 ),
inference(superposition,[],[f164,f305]) ).
fof(f5032,plain,
( spl5_106
| ~ spl5_19
| ~ spl5_27 ),
inference(avatar_split_clause,[],[f315,f300,f167,f5030]) ).
fof(f5030,plain,
( spl5_106
<=> ! [X2,X0,X1] : union(X0,X2) = union(X0,union(intersection(X1,X0),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_106])]) ).
fof(f315,plain,
( ! [X2,X0,X1] : union(X0,X2) = union(X0,union(intersection(X1,X0),X2))
| ~ spl5_19
| ~ spl5_27 ),
inference(superposition,[],[f168,f301]) ).
fof(f5027,plain,
( spl5_105
| ~ spl5_15
| ~ spl5_19 ),
inference(avatar_split_clause,[],[f205,f167,f137,f5025]) ).
fof(f5025,plain,
( spl5_105
<=> ! [X0,X1] : union(X0,X1) = union(X0,union(X1,union(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_105])]) ).
fof(f205,plain,
( ! [X0,X1] : union(X0,X1) = union(X0,union(X1,union(X0,X1)))
| ~ spl5_15
| ~ spl5_19 ),
inference(superposition,[],[f168,f138]) ).
fof(f4951,plain,
( spl5_104
| ~ spl5_40
| ~ spl5_61 ),
inference(avatar_split_clause,[],[f2820,f1678,f463,f4949]) ).
fof(f4949,plain,
( spl5_104
<=> ! [X2,X0,X1] : subset(X0,union(X1,union(X2,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_104])]) ).
fof(f2820,plain,
( ! [X2,X0,X1] : subset(X0,union(X1,union(X2,X0)))
| ~ spl5_40
| ~ spl5_61 ),
inference(superposition,[],[f1679,f464]) ).
fof(f4604,plain,
( spl5_103
| ~ spl5_27
| ~ spl5_45 ),
inference(avatar_split_clause,[],[f908,f806,f300,f4602]) ).
fof(f4602,plain,
( spl5_103
<=> ! [X2,X0,X1] :
( ~ member(sK4(X2,X0),intersection(X1,X0))
| subset(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_103])]) ).
fof(f908,plain,
( ! [X2,X0,X1] :
( ~ member(sK4(X2,X0),intersection(X1,X0))
| subset(X2,X0) )
| ~ spl5_27
| ~ spl5_45 ),
inference(superposition,[],[f807,f301]) ).
fof(f4600,plain,
( spl5_102
| ~ spl5_7
| ~ spl5_45 ),
inference(avatar_split_clause,[],[f907,f806,f93,f4598]) ).
fof(f4598,plain,
( spl5_102
<=> ! [X2,X0,X1] :
( ~ member(sK4(X2,X0),intersection(X0,X1))
| subset(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_102])]) ).
fof(f907,plain,
( ! [X2,X0,X1] :
( ~ member(sK4(X2,X0),intersection(X0,X1))
| subset(X2,X0) )
| ~ spl5_7
| ~ spl5_45 ),
inference(superposition,[],[f807,f94]) ).
fof(f4596,plain,
( spl5_101
| ~ spl5_28
| ~ spl5_42 ),
inference(avatar_split_clause,[],[f857,f793,f304,f4594]) ).
fof(f4594,plain,
( spl5_101
<=> ! [X2,X0,X1] :
( member(sK4(X0,X2),union(X0,X1))
| subset(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_101])]) ).
fof(f793,plain,
( spl5_42
<=> ! [X2,X0,X1] :
( member(sK4(intersection(X0,X1),X2),X1)
| subset(intersection(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_42])]) ).
fof(f857,plain,
( ! [X2,X0,X1] :
( member(sK4(X0,X2),union(X0,X1))
| subset(X0,X2) )
| ~ spl5_28
| ~ spl5_42 ),
inference(superposition,[],[f794,f305]) ).
fof(f794,plain,
( ! [X2,X0,X1] :
( member(sK4(intersection(X0,X1),X2),X1)
| subset(intersection(X0,X1),X2) )
| ~ spl5_42 ),
inference(avatar_component_clause,[],[f793]) ).
fof(f4592,plain,
( spl5_100
| ~ spl5_27
| ~ spl5_33 ),
inference(avatar_split_clause,[],[f427,f400,f300,f4590]) ).
fof(f4590,plain,
( spl5_100
<=> ! [X0,X3,X2,X1] :
( member(X2,union(X3,X0))
| ~ member(X2,intersection(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_100])]) ).
fof(f427,plain,
( ! [X2,X3,X0,X1] :
( member(X2,union(X3,X0))
| ~ member(X2,intersection(X1,X0)) )
| ~ spl5_27
| ~ spl5_33 ),
inference(superposition,[],[f401,f301]) ).
fof(f4588,plain,
( spl5_99
| ~ spl5_36
| ~ spl5_50 ),
inference(avatar_split_clause,[],[f2331,f951,f447,f4586]) ).
fof(f4586,plain,
( spl5_99
<=> ! [X2,X0,X1] : subset(intersection(X2,intersection(X0,X1)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_99])]) ).
fof(f2331,plain,
( ! [X2,X0,X1] : subset(intersection(X2,intersection(X0,X1)),X0)
| ~ spl5_36
| ~ spl5_50 ),
inference(superposition,[],[f952,f448]) ).
fof(f4584,plain,
( spl5_98
| ~ spl5_7
| ~ spl5_33 ),
inference(avatar_split_clause,[],[f426,f400,f93,f4582]) ).
fof(f4582,plain,
( spl5_98
<=> ! [X0,X3,X2,X1] :
( member(X2,union(X3,X0))
| ~ member(X2,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_98])]) ).
fof(f426,plain,
( ! [X2,X3,X0,X1] :
( member(X2,union(X3,X0))
| ~ member(X2,intersection(X0,X1)) )
| ~ spl5_7
| ~ spl5_33 ),
inference(superposition,[],[f401,f94]) ).
fof(f4580,plain,
( spl5_97
| ~ spl5_5
| ~ spl5_33 ),
inference(avatar_split_clause,[],[f424,f400,f85,f4578]) ).
fof(f4578,plain,
( spl5_97
<=> ! [X0,X3,X2,X1] :
( member(X2,union(X3,union(X1,X0)))
| ~ member(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_97])]) ).
fof(f424,plain,
( ! [X2,X3,X0,X1] :
( member(X2,union(X3,union(X1,X0)))
| ~ member(X2,X1) )
| ~ spl5_5
| ~ spl5_33 ),
inference(superposition,[],[f401,f86]) ).
fof(f4576,plain,
( spl5_96
| ~ spl5_28
| ~ spl5_32 ),
inference(avatar_split_clause,[],[f410,f396,f304,f4574]) ).
fof(f4574,plain,
( spl5_96
<=> ! [X0,X3,X2,X1] :
( ~ member(X2,intersection(X3,X0))
| member(X2,union(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_96])]) ).
fof(f410,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X2,intersection(X3,X0))
| member(X2,union(X0,X1)) )
| ~ spl5_28
| ~ spl5_32 ),
inference(superposition,[],[f397,f305]) ).
fof(f4572,plain,
( spl5_95
| ~ spl5_14
| ~ spl5_30 ),
inference(avatar_split_clause,[],[f381,f342,f127,f4570]) ).
fof(f4570,plain,
( spl5_95
<=> ! [X0,X3,X2,X1] :
( member(X3,X0)
| ~ member(X3,intersection(X1,intersection(X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_95])]) ).
fof(f381,plain,
( ! [X2,X3,X0,X1] :
( member(X3,X0)
| ~ member(X3,intersection(X1,intersection(X0,X2))) )
| ~ spl5_14
| ~ spl5_30 ),
inference(superposition,[],[f128,f343]) ).
fof(f3876,plain,
( spl5_94
| ~ spl5_36
| ~ spl5_50 ),
inference(avatar_split_clause,[],[f2330,f951,f447,f3874]) ).
fof(f3874,plain,
( spl5_94
<=> ! [X2,X0,X1] : subset(intersection(X1,intersection(X2,X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_94])]) ).
fof(f2330,plain,
( ! [X2,X0,X1] : subset(intersection(X1,intersection(X2,X0)),X0)
| ~ spl5_36
| ~ spl5_50 ),
inference(superposition,[],[f952,f448]) ).
fof(f3315,plain,
( spl5_93
| ~ spl5_5
| ~ spl5_24
| ~ spl5_39
| ~ spl5_52 ),
inference(avatar_split_clause,[],[f1188,f1048,f459,f240,f85,f3313]) ).
fof(f3313,plain,
( spl5_93
<=> ! [X0,X1] : union(X0,X1) = union(X0,union(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_93])]) ).
fof(f1188,plain,
( ! [X0,X1] : union(X0,X1) = union(X0,union(X1,X0))
| ~ spl5_5
| ~ spl5_24
| ~ spl5_39
| ~ spl5_52 ),
inference(forward_demodulation,[],[f1147,f659]) ).
fof(f1147,plain,
( ! [X2,X0,X1] : union(X0,X1) = union(X0,union(X1,union(X0,intersection(X1,X2))))
| ~ spl5_24
| ~ spl5_52 ),
inference(superposition,[],[f1049,f241]) ).
fof(f3311,plain,
( spl5_92
| ~ spl5_28
| ~ spl5_40 ),
inference(avatar_split_clause,[],[f759,f463,f304,f3309]) ).
fof(f3309,plain,
( spl5_92
<=> ! [X2,X0,X1] : intersection(X0,union(X1,union(X2,X0))) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_92])]) ).
fof(f759,plain,
( ! [X2,X0,X1] : intersection(X0,union(X1,union(X2,X0))) = X0
| ~ spl5_28
| ~ spl5_40 ),
inference(superposition,[],[f305,f464]) ).
fof(f3307,plain,
( spl5_91
| ~ spl5_28
| ~ spl5_40 ),
inference(avatar_split_clause,[],[f743,f463,f304,f3305]) ).
fof(f3305,plain,
( spl5_91
<=> ! [X2,X0,X1] : intersection(X0,union(X2,union(X0,X1))) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_91])]) ).
fof(f743,plain,
( ! [X2,X0,X1] : intersection(X0,union(X2,union(X0,X1))) = X0
| ~ spl5_28
| ~ spl5_40 ),
inference(superposition,[],[f305,f464]) ).
fof(f3303,plain,
( spl5_90
| ~ spl5_15
| ~ spl5_40 ),
inference(avatar_split_clause,[],[f715,f463,f137,f3301]) ).
fof(f715,plain,
( ! [X0,X1] : union(X1,X0) = union(X0,union(X0,X1))
| ~ spl5_15
| ~ spl5_40 ),
inference(superposition,[],[f464,f138]) ).
fof(f3299,plain,
( spl5_89
| ~ spl5_15
| ~ spl5_19
| ~ spl5_37 ),
inference(avatar_split_clause,[],[f641,f451,f167,f137,f3297]) ).
fof(f3295,plain,
( spl5_88
| ~ spl5_29
| ~ spl5_36 ),
inference(avatar_split_clause,[],[f537,f447,f338,f3293]) ).
fof(f3293,plain,
( spl5_88
<=> ! [X0,X1] : intersection(X0,X1) = intersection(X0,intersection(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_88])]) ).
fof(f537,plain,
( ! [X0,X1] : intersection(X0,X1) = intersection(X0,intersection(X1,X0))
| ~ spl5_29
| ~ spl5_36 ),
inference(superposition,[],[f448,f339]) ).
fof(f3291,plain,
( spl5_87
| ~ spl5_2
| ~ spl5_36 ),
inference(avatar_split_clause,[],[f527,f447,f68,f3289]) ).
fof(f68,plain,
( spl5_2
<=> ! [X0] : intersection(X0,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).
fof(f527,plain,
( ! [X0,X1] : intersection(X1,X0) = intersection(X0,intersection(X0,X1))
| ~ spl5_2
| ~ spl5_36 ),
inference(superposition,[],[f448,f69]) ).
fof(f69,plain,
( ! [X0] : intersection(X0,X0) = X0
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f3287,plain,
( spl5_86
| ~ spl5_6
| ~ spl5_29 ),
inference(avatar_split_clause,[],[f350,f338,f89,f3285]) ).
fof(f3285,plain,
( spl5_86
<=> ! [X0,X1] : intersection(X1,X0) = intersection(X0,intersection(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_86])]) ).
fof(f350,plain,
( ! [X0,X1] : intersection(X1,X0) = intersection(X0,intersection(X1,X0))
| ~ spl5_6
| ~ spl5_29 ),
inference(superposition,[],[f339,f90]) ).
fof(f3283,plain,
( spl5_85
| ~ spl5_27
| ~ spl5_28 ),
inference(avatar_split_clause,[],[f335,f304,f300,f3281]) ).
fof(f3281,plain,
( spl5_85
<=> ! [X0,X1] : union(X0,X1) = union(union(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_85])]) ).
fof(f335,plain,
( ! [X0,X1] : union(X0,X1) = union(union(X0,X1),X0)
| ~ spl5_27
| ~ spl5_28 ),
inference(superposition,[],[f301,f305]) ).
fof(f3279,plain,
( spl5_84
| ~ spl5_18
| ~ spl5_27 ),
inference(avatar_split_clause,[],[f310,f300,f163,f3277]) ).
fof(f3277,plain,
( spl5_84
<=> ! [X2,X0,X1] : union(X2,intersection(X0,intersection(X1,X2))) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_84])]) ).
fof(f310,plain,
( ! [X2,X0,X1] : union(X2,intersection(X0,intersection(X1,X2))) = X2
| ~ spl5_18
| ~ spl5_27 ),
inference(superposition,[],[f301,f164]) ).
fof(f3275,plain,
( spl5_83
| ~ spl5_15
| ~ spl5_19 ),
inference(avatar_split_clause,[],[f200,f167,f137,f3273]) ).
fof(f3273,plain,
( spl5_83
<=> ! [X0,X1] : union(X0,X1) = union(X0,union(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_83])]) ).
fof(f3062,plain,
( ~ spl5_82
| ~ spl5_5
| ~ spl5_40
| spl5_76 ),
inference(avatar_split_clause,[],[f2852,f2847,f463,f85,f3059]) ).
fof(f3059,plain,
( spl5_82
<=> union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))) = intersection(union(sK0,sK2),union(sK1,intersection(sK0,sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_82])]) ).
fof(f2847,plain,
( spl5_76
<=> union(intersection(sK0,sK2),union(intersection(sK0,sK1),intersection(sK1,sK2))) = intersection(union(sK0,sK2),union(sK1,intersection(sK0,sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_76])]) ).
fof(f2852,plain,
( union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))) != intersection(union(sK0,sK2),union(sK1,intersection(sK0,sK2)))
| ~ spl5_5
| ~ spl5_40
| spl5_76 ),
inference(forward_demodulation,[],[f2851,f86]) ).
fof(f2851,plain,
( union(intersection(sK0,sK1),union(intersection(sK1,sK2),intersection(sK0,sK2))) != intersection(union(sK0,sK2),union(sK1,intersection(sK0,sK2)))
| ~ spl5_40
| spl5_76 ),
inference(superposition,[],[f2849,f464]) ).
fof(f2849,plain,
( union(intersection(sK0,sK2),union(intersection(sK0,sK1),intersection(sK1,sK2))) != intersection(union(sK0,sK2),union(sK1,intersection(sK0,sK2)))
| spl5_76 ),
inference(avatar_component_clause,[],[f2847]) ).
fof(f3016,plain,
( spl5_81
| ~ spl5_15
| ~ spl5_27
| ~ spl5_53 ),
inference(avatar_split_clause,[],[f1270,f1052,f300,f137,f3014]) ).
fof(f3014,plain,
( spl5_81
<=> ! [X0,X1] : intersection(union(X1,X0),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_81])]) ).
fof(f1270,plain,
( ! [X0,X1] : intersection(union(X1,X0),X0) = X0
| ~ spl5_15
| ~ spl5_27
| ~ spl5_53 ),
inference(forward_demodulation,[],[f1217,f301]) ).
fof(f1217,plain,
( ! [X0,X1] : union(X0,intersection(X1,X0)) = intersection(union(X1,X0),X0)
| ~ spl5_15
| ~ spl5_53 ),
inference(superposition,[],[f1053,f138]) ).
fof(f3012,plain,
( spl5_80
| ~ spl5_41
| ~ spl5_45 ),
inference(avatar_split_clause,[],[f913,f806,f789,f3010]) ).
fof(f3010,plain,
( spl5_80
<=> ! [X2,X0,X1] : subset(intersection(X0,X1),union(X2,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_80])]) ).
fof(f789,plain,
( spl5_41
<=> ! [X2,X0,X1] :
( member(sK4(intersection(X0,X1),X2),X0)
| subset(intersection(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_41])]) ).
fof(f913,plain,
( ! [X2,X0,X1] : subset(intersection(X0,X1),union(X2,X0))
| ~ spl5_41
| ~ spl5_45 ),
inference(duplicate_literal_removal,[],[f895]) ).
fof(f895,plain,
( ! [X2,X0,X1] :
( subset(intersection(X0,X1),union(X2,X0))
| subset(intersection(X0,X1),union(X2,X0)) )
| ~ spl5_41
| ~ spl5_45 ),
inference(resolution,[],[f807,f790]) ).
fof(f790,plain,
( ! [X2,X0,X1] :
( member(sK4(intersection(X0,X1),X2),X0)
| subset(intersection(X0,X1),X2) )
| ~ spl5_41 ),
inference(avatar_component_clause,[],[f789]) ).
fof(f3008,plain,
( spl5_79
| ~ spl5_42
| ~ spl5_45 ),
inference(avatar_split_clause,[],[f912,f806,f793,f3006]) ).
fof(f3006,plain,
( spl5_79
<=> ! [X2,X0,X1] : subset(intersection(X0,X1),union(X2,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_79])]) ).
fof(f912,plain,
( ! [X2,X0,X1] : subset(intersection(X0,X1),union(X2,X1))
| ~ spl5_42
| ~ spl5_45 ),
inference(duplicate_literal_removal,[],[f896]) ).
fof(f896,plain,
( ! [X2,X0,X1] :
( subset(intersection(X0,X1),union(X2,X1))
| subset(intersection(X0,X1),union(X2,X1)) )
| ~ spl5_42
| ~ spl5_45 ),
inference(resolution,[],[f807,f794]) ).
fof(f3004,plain,
( spl5_78
| ~ spl5_41
| ~ spl5_43 ),
inference(avatar_split_clause,[],[f884,f797,f789,f3002]) ).
fof(f3002,plain,
( spl5_78
<=> ! [X2,X0,X1] : subset(intersection(X0,X1),union(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_78])]) ).
fof(f797,plain,
( spl5_43
<=> ! [X2,X0,X1] :
( ~ member(sK4(X0,union(X1,X2)),X1)
| subset(X0,union(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_43])]) ).
fof(f884,plain,
( ! [X2,X0,X1] : subset(intersection(X0,X1),union(X0,X2))
| ~ spl5_41
| ~ spl5_43 ),
inference(duplicate_literal_removal,[],[f866]) ).
fof(f866,plain,
( ! [X2,X0,X1] :
( subset(intersection(X0,X1),union(X0,X2))
| subset(intersection(X0,X1),union(X0,X2)) )
| ~ spl5_41
| ~ spl5_43 ),
inference(resolution,[],[f798,f790]) ).
fof(f798,plain,
( ! [X2,X0,X1] :
( ~ member(sK4(X0,union(X1,X2)),X1)
| subset(X0,union(X1,X2)) )
| ~ spl5_43 ),
inference(avatar_component_clause,[],[f797]) ).
fof(f3000,plain,
( spl5_77
| ~ spl5_42
| ~ spl5_43 ),
inference(avatar_split_clause,[],[f883,f797,f793,f2998]) ).
fof(f2998,plain,
( spl5_77
<=> ! [X2,X0,X1] : subset(intersection(X0,X1),union(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_77])]) ).
fof(f883,plain,
( ! [X2,X0,X1] : subset(intersection(X0,X1),union(X1,X2))
| ~ spl5_42
| ~ spl5_43 ),
inference(duplicate_literal_removal,[],[f867]) ).
fof(f867,plain,
( ! [X2,X0,X1] :
( subset(intersection(X0,X1),union(X1,X2))
| subset(intersection(X0,X1),union(X1,X2)) )
| ~ spl5_42
| ~ spl5_43 ),
inference(resolution,[],[f798,f794]) ).
fof(f2850,plain,
( ~ spl5_76
| spl5_8
| ~ spl5_53 ),
inference(avatar_split_clause,[],[f1233,f1052,f99,f2847]) ).
fof(f1233,plain,
( union(intersection(sK0,sK2),union(intersection(sK0,sK1),intersection(sK1,sK2))) != intersection(union(sK0,sK2),union(sK1,intersection(sK0,sK2)))
| spl5_8
| ~ spl5_53 ),
inference(superposition,[],[f101,f1053]) ).
fof(f2547,plain,
( spl5_75
| ~ spl5_20
| ~ spl5_23 ),
inference(avatar_split_clause,[],[f254,f236,f171,f2545]) ).
fof(f2545,plain,
( spl5_75
<=> ! [X2,X0,X1] :
( intersection(X1,X2) = X0
| ~ member(sK3(X0,intersection(X1,X2)),X0)
| ~ member(sK3(X0,intersection(X1,X2)),X2)
| ~ member(sK3(X0,intersection(X1,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_75])]) ).
fof(f236,plain,
( spl5_23
<=> ! [X0,X1] :
( X0 = X1
| ~ member(sK3(X0,X1),X1)
| ~ member(sK3(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_23])]) ).
fof(f254,plain,
( ! [X2,X0,X1] :
( intersection(X1,X2) = X0
| ~ member(sK3(X0,intersection(X1,X2)),X0)
| ~ member(sK3(X0,intersection(X1,X2)),X2)
| ~ member(sK3(X0,intersection(X1,X2)),X1) )
| ~ spl5_20
| ~ spl5_23 ),
inference(resolution,[],[f237,f172]) ).
fof(f237,plain,
( ! [X0,X1] :
( ~ member(sK3(X0,X1),X1)
| X0 = X1
| ~ member(sK3(X0,X1),X0) )
| ~ spl5_23 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f2543,plain,
( spl5_74
| ~ spl5_21
| ~ spl5_22 ),
inference(avatar_split_clause,[],[f248,f232,f177,f2541]) ).
fof(f2541,plain,
( spl5_74
<=> ! [X2,X0,X1] :
( member(sK3(union(X0,X1),X2),X2)
| union(X0,X1) = X2
| member(sK3(union(X0,X1),X2),X0)
| member(sK3(union(X0,X1),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_74])]) ).
fof(f232,plain,
( spl5_22
<=> ! [X0,X1] :
( X0 = X1
| member(sK3(X0,X1),X1)
| member(sK3(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_22])]) ).
fof(f248,plain,
( ! [X2,X0,X1] :
( member(sK3(union(X0,X1),X2),X2)
| union(X0,X1) = X2
| member(sK3(union(X0,X1),X2),X0)
| member(sK3(union(X0,X1),X2),X1) )
| ~ spl5_21
| ~ spl5_22 ),
inference(resolution,[],[f233,f178]) ).
fof(f233,plain,
( ! [X0,X1] :
( member(sK3(X0,X1),X1)
| member(sK3(X0,X1),X0)
| X0 = X1 )
| ~ spl5_22 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f2539,plain,
( spl5_73
| ~ spl5_21
| ~ spl5_22 ),
inference(avatar_split_clause,[],[f245,f232,f177,f2537]) ).
fof(f2537,plain,
( spl5_73
<=> ! [X2,X0,X1] :
( member(sK3(X0,union(X1,X2)),X0)
| union(X1,X2) = X0
| member(sK3(X0,union(X1,X2)),X1)
| member(sK3(X0,union(X1,X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_73])]) ).
fof(f245,plain,
( ! [X2,X0,X1] :
( member(sK3(X0,union(X1,X2)),X0)
| union(X1,X2) = X0
| member(sK3(X0,union(X1,X2)),X1)
| member(sK3(X0,union(X1,X2)),X2) )
| ~ spl5_21
| ~ spl5_22 ),
inference(resolution,[],[f233,f178]) ).
fof(f1915,plain,
( spl5_72
| ~ spl5_19
| ~ spl5_24 ),
inference(avatar_split_clause,[],[f281,f240,f167,f1913]) ).
fof(f281,plain,
( ! [X2,X3,X0,X1] : intersection(union(X0,union(X1,X2)),union(X0,union(X1,X3))) = union(X0,union(X1,intersection(X2,X3)))
| ~ spl5_19
| ~ spl5_24 ),
inference(forward_demodulation,[],[f280,f168]) ).
fof(f280,plain,
( ! [X2,X3,X0,X1] : union(union(X0,X1),intersection(X2,X3)) = intersection(union(X0,union(X1,X2)),union(X0,union(X1,X3)))
| ~ spl5_19
| ~ spl5_24 ),
inference(forward_demodulation,[],[f260,f168]) ).
fof(f260,plain,
( ! [X2,X3,X0,X1] : union(union(X0,X1),intersection(X2,X3)) = intersection(union(X0,union(X1,X2)),union(union(X0,X1),X3))
| ~ spl5_19
| ~ spl5_24 ),
inference(superposition,[],[f241,f168]) ).
fof(f1911,plain,
( spl5_71
| ~ spl5_13
| ~ spl5_23 ),
inference(avatar_split_clause,[],[f253,f236,f123,f1909]) ).
fof(f1909,plain,
( spl5_71
<=> ! [X2,X0,X1] :
( union(X1,X2) = X0
| ~ member(sK3(X0,union(X1,X2)),X0)
| ~ member(sK3(X0,union(X1,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_71])]) ).
fof(f253,plain,
( ! [X2,X0,X1] :
( union(X1,X2) = X0
| ~ member(sK3(X0,union(X1,X2)),X0)
| ~ member(sK3(X0,union(X1,X2)),X1) )
| ~ spl5_13
| ~ spl5_23 ),
inference(resolution,[],[f237,f124]) ).
fof(f1907,plain,
( spl5_70
| ~ spl5_9
| ~ spl5_45 ),
inference(avatar_split_clause,[],[f914,f806,f107,f1905]) ).
fof(f914,plain,
( ! [X0,X1] : subset(X0,union(X1,X0))
| ~ spl5_9
| ~ spl5_45 ),
inference(duplicate_literal_removal,[],[f894]) ).
fof(f894,plain,
( ! [X0,X1] :
( subset(X0,union(X1,X0))
| subset(X0,union(X1,X0)) )
| ~ spl5_9
| ~ spl5_45 ),
inference(resolution,[],[f807,f108]) ).
fof(f1903,plain,
( spl5_69
| ~ spl5_14
| ~ spl5_23 ),
inference(avatar_split_clause,[],[f252,f236,f127,f1901]) ).
fof(f1901,plain,
( spl5_69
<=> ! [X2,X0,X1] :
( union(X1,X2) = X0
| ~ member(sK3(X0,union(X1,X2)),X0)
| ~ member(sK3(X0,union(X1,X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_69])]) ).
fof(f252,plain,
( ! [X2,X0,X1] :
( union(X1,X2) = X0
| ~ member(sK3(X0,union(X1,X2)),X0)
| ~ member(sK3(X0,union(X1,X2)),X2) )
| ~ spl5_14
| ~ spl5_23 ),
inference(resolution,[],[f237,f128]) ).
fof(f1899,plain,
( spl5_68
| ~ spl5_11
| ~ spl5_22 ),
inference(avatar_split_clause,[],[f247,f232,f115,f1897]) ).
fof(f247,plain,
( ! [X2,X0,X1] :
( member(sK3(intersection(X0,X1),X2),X2)
| intersection(X0,X1) = X2
| member(sK3(intersection(X0,X1),X2),X0) )
| ~ spl5_11
| ~ spl5_22 ),
inference(resolution,[],[f233,f116]) ).
fof(f1895,plain,
( spl5_67
| ~ spl5_12
| ~ spl5_22 ),
inference(avatar_split_clause,[],[f246,f232,f119,f1893]) ).
fof(f246,plain,
( ! [X2,X0,X1] :
( member(sK3(intersection(X0,X1),X2),X2)
| intersection(X0,X1) = X2
| member(sK3(intersection(X0,X1),X2),X1) )
| ~ spl5_12
| ~ spl5_22 ),
inference(resolution,[],[f233,f120]) ).
fof(f1891,plain,
( spl5_66
| ~ spl5_11
| ~ spl5_22 ),
inference(avatar_split_clause,[],[f244,f232,f115,f1889]) ).
fof(f244,plain,
( ! [X2,X0,X1] :
( member(sK3(X0,intersection(X1,X2)),X0)
| intersection(X1,X2) = X0
| member(sK3(X0,intersection(X1,X2)),X1) )
| ~ spl5_11
| ~ spl5_22 ),
inference(resolution,[],[f233,f116]) ).
fof(f1887,plain,
( spl5_65
| ~ spl5_12
| ~ spl5_22 ),
inference(avatar_split_clause,[],[f243,f232,f119,f1885]) ).
fof(f243,plain,
( ! [X2,X0,X1] :
( member(sK3(X0,intersection(X1,X2)),X0)
| intersection(X1,X2) = X0
| member(sK3(X0,intersection(X1,X2)),X2) )
| ~ spl5_12
| ~ spl5_22 ),
inference(resolution,[],[f233,f120]) ).
fof(f1883,plain,
( spl5_64
| ~ spl5_9
| ~ spl5_21 ),
inference(avatar_split_clause,[],[f222,f177,f107,f1881]) ).
fof(f222,plain,
( ! [X2,X0,X1] :
( member(sK4(union(X0,X1),X2),X0)
| member(sK4(union(X0,X1),X2),X1)
| subset(union(X0,X1),X2) )
| ~ spl5_9
| ~ spl5_21 ),
inference(resolution,[],[f178,f108]) ).
fof(f1879,plain,
( spl5_63
| ~ spl5_10
| ~ spl5_20 ),
inference(avatar_split_clause,[],[f214,f171,f111,f1877]) ).
fof(f214,plain,
( ! [X2,X0,X1] :
( ~ member(sK4(X0,intersection(X1,X2)),X2)
| ~ member(sK4(X0,intersection(X1,X2)),X1)
| subset(X0,intersection(X1,X2)) )
| ~ spl5_10
| ~ spl5_20 ),
inference(resolution,[],[f172,f112]) ).
fof(f1684,plain,
( spl5_62
| ~ spl5_20
| ~ spl5_24 ),
inference(avatar_split_clause,[],[f276,f240,f171,f1682]) ).
fof(f1682,plain,
( spl5_62
<=> ! [X0,X3,X2,X1] :
( member(X3,union(X0,intersection(X1,X2)))
| ~ member(X3,union(X0,X2))
| ~ member(X3,union(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_62])]) ).
fof(f276,plain,
( ! [X2,X3,X0,X1] :
( member(X3,union(X0,intersection(X1,X2)))
| ~ member(X3,union(X0,X2))
| ~ member(X3,union(X0,X1)) )
| ~ spl5_20
| ~ spl5_24 ),
inference(superposition,[],[f172,f241]) ).
fof(f1680,plain,
( spl5_61
| ~ spl5_9
| ~ spl5_43 ),
inference(avatar_split_clause,[],[f885,f797,f107,f1678]) ).
fof(f885,plain,
( ! [X0,X1] : subset(X0,union(X0,X1))
| ~ spl5_9
| ~ spl5_43 ),
inference(duplicate_literal_removal,[],[f865]) ).
fof(f865,plain,
( ! [X0,X1] :
( subset(X0,union(X0,X1))
| subset(X0,union(X0,X1)) )
| ~ spl5_9
| ~ spl5_43 ),
inference(resolution,[],[f798,f108]) ).
fof(f1676,plain,
( spl5_60
| ~ spl5_18
| ~ spl5_24 ),
inference(avatar_split_clause,[],[f275,f240,f163,f1674]) ).
fof(f275,plain,
( ! [X2,X3,X0,X1] : intersection(union(X0,X1),intersection(union(X0,X2),X3)) = intersection(union(X0,intersection(X1,X2)),X3)
| ~ spl5_18
| ~ spl5_24 ),
inference(superposition,[],[f164,f241]) ).
fof(f1601,plain,
( spl5_59
| ~ spl5_19
| ~ spl5_21 ),
inference(avatar_split_clause,[],[f229,f177,f167,f1599]) ).
fof(f229,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X3,union(X0,union(X1,X2)))
| member(X3,union(X0,X1))
| member(X3,X2) )
| ~ spl5_19
| ~ spl5_21 ),
inference(superposition,[],[f178,f168]) ).
fof(f1597,plain,
( spl5_58
| ~ spl5_18
| ~ spl5_20 ),
inference(avatar_split_clause,[],[f220,f171,f163,f1595]) ).
fof(f220,plain,
( ! [X2,X3,X0,X1] :
( member(X3,intersection(X0,intersection(X1,X2)))
| ~ member(X3,X2)
| ~ member(X3,intersection(X0,X1)) )
| ~ spl5_18
| ~ spl5_20 ),
inference(superposition,[],[f172,f164]) ).
fof(f1133,plain,
( spl5_57
| ~ spl5_10
| ~ spl5_42 ),
inference(avatar_split_clause,[],[f864,f793,f111,f1131]) ).
fof(f864,plain,
( ! [X0,X1] : subset(intersection(X0,X1),X1)
| ~ spl5_10
| ~ spl5_42 ),
inference(duplicate_literal_removal,[],[f849]) ).
fof(f849,plain,
( ! [X0,X1] :
( subset(intersection(X0,X1),X1)
| subset(intersection(X0,X1),X1) )
| ~ spl5_10
| ~ spl5_42 ),
inference(resolution,[],[f794,f112]) ).
fof(f1066,plain,
( spl5_56
| ~ spl5_7
| ~ spl5_24 ),
inference(avatar_split_clause,[],[f272,f240,f93,f1064]) ).
fof(f272,plain,
( ! [X2,X0,X1] : union(X0,X1) = union(union(X0,X1),union(X0,intersection(X1,X2)))
| ~ spl5_7
| ~ spl5_24 ),
inference(superposition,[],[f94,f241]) ).
fof(f1062,plain,
( spl5_55
| ~ spl5_6
| ~ spl5_24 ),
inference(avatar_split_clause,[],[f267,f240,f89,f1060]) ).
fof(f267,plain,
( ! [X2,X0,X1] : union(X0,intersection(X1,X2)) = intersection(union(X0,X2),union(X0,X1))
| ~ spl5_6
| ~ spl5_24 ),
inference(superposition,[],[f241,f90]) ).
fof(f1058,plain,
( spl5_54
| ~ spl5_5
| ~ spl5_24 ),
inference(avatar_split_clause,[],[f261,f240,f85,f1056]) ).
fof(f261,plain,
( ! [X2,X0,X1] : union(X0,intersection(X2,X1)) = intersection(union(X0,X2),union(X1,X0))
| ~ spl5_5
| ~ spl5_24 ),
inference(superposition,[],[f241,f86]) ).
fof(f1054,plain,
( spl5_53
| ~ spl5_5
| ~ spl5_24 ),
inference(avatar_split_clause,[],[f256,f240,f85,f1052]) ).
fof(f256,plain,
( ! [X2,X0,X1] : union(X0,intersection(X1,X2)) = intersection(union(X1,X0),union(X0,X2))
| ~ spl5_5
| ~ spl5_24 ),
inference(superposition,[],[f241,f86]) ).
fof(f1050,plain,
( spl5_52
| ~ spl5_7
| ~ spl5_19 ),
inference(avatar_split_clause,[],[f204,f167,f93,f1048]) ).
fof(f204,plain,
( ! [X2,X0,X1] : union(X0,X1) = union(X0,union(X1,intersection(union(X0,X1),X2)))
| ~ spl5_7
| ~ spl5_19 ),
inference(superposition,[],[f168,f94]) ).
fof(f1046,plain,
( spl5_51
| ~ spl5_7
| ~ spl5_18 ),
inference(avatar_split_clause,[],[f191,f163,f93,f1044]) ).
fof(f191,plain,
( ! [X2,X0,X1] : intersection(X0,X1) = union(intersection(X0,X1),intersection(X0,intersection(X1,X2)))
| ~ spl5_7
| ~ spl5_18 ),
inference(superposition,[],[f94,f164]) ).
fof(f953,plain,
( spl5_50
| ~ spl5_10
| ~ spl5_41 ),
inference(avatar_split_clause,[],[f840,f789,f111,f951]) ).
fof(f840,plain,
( ! [X0,X1] : subset(intersection(X0,X1),X0)
| ~ spl5_10
| ~ spl5_41 ),
inference(duplicate_literal_removal,[],[f825]) ).
fof(f825,plain,
( ! [X0,X1] :
( subset(intersection(X0,X1),X0)
| subset(intersection(X0,X1),X0) )
| ~ spl5_10
| ~ spl5_41 ),
inference(resolution,[],[f790,f112]) ).
fof(f824,plain,
( spl5_49
| ~ spl5_12
| ~ spl5_24 ),
inference(avatar_split_clause,[],[f274,f240,f119,f822]) ).
fof(f274,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X3,union(X0,intersection(X1,X2)))
| member(X3,union(X0,X2)) )
| ~ spl5_12
| ~ spl5_24 ),
inference(superposition,[],[f120,f241]) ).
fof(f820,plain,
( spl5_48
| ~ spl5_11
| ~ spl5_24 ),
inference(avatar_split_clause,[],[f273,f240,f115,f818]) ).
fof(f273,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X3,union(X0,intersection(X1,X2)))
| member(X3,union(X0,X1)) )
| ~ spl5_11
| ~ spl5_24 ),
inference(superposition,[],[f116,f241]) ).
fof(f816,plain,
( spl5_47
| ~ spl5_13
| ~ spl5_19 ),
inference(avatar_split_clause,[],[f207,f167,f123,f814]) ).
fof(f207,plain,
( ! [X2,X3,X0,X1] :
( member(X3,union(X0,union(X1,X2)))
| ~ member(X3,union(X0,X1)) )
| ~ spl5_13
| ~ spl5_19 ),
inference(superposition,[],[f124,f168]) ).
fof(f812,plain,
( spl5_46
| ~ spl5_11
| ~ spl5_18 ),
inference(avatar_split_clause,[],[f190,f163,f115,f810]) ).
fof(f190,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X3,intersection(X0,intersection(X1,X2)))
| member(X3,intersection(X0,X1)) )
| ~ spl5_11
| ~ spl5_18 ),
inference(superposition,[],[f116,f164]) ).
fof(f808,plain,
( spl5_45
| ~ spl5_10
| ~ spl5_14 ),
inference(avatar_split_clause,[],[f148,f127,f111,f806]) ).
fof(f148,plain,
( ! [X2,X0,X1] :
( ~ member(sK4(X0,union(X1,X2)),X2)
| subset(X0,union(X1,X2)) )
| ~ spl5_10
| ~ spl5_14 ),
inference(resolution,[],[f128,f112]) ).
fof(f804,plain,
( ~ spl5_44
| ~ spl5_5
| ~ spl5_6
| spl5_8
| ~ spl5_24
| ~ spl5_36
| ~ spl5_40 ),
inference(avatar_split_clause,[],[f607,f463,f447,f240,f99,f89,f85,f801]) ).
fof(f801,plain,
( spl5_44
<=> intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2))) = union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_44])]) ).
fof(f607,plain,
( intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2))) != union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2)))
| ~ spl5_5
| ~ spl5_6
| spl5_8
| ~ spl5_24
| ~ spl5_36
| ~ spl5_40 ),
inference(forward_demodulation,[],[f606,f90]) ).
fof(f606,plain,
( union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))) != intersection(union(sK1,sK2),union(sK0,intersection(sK2,sK1)))
| ~ spl5_5
| spl5_8
| ~ spl5_24
| ~ spl5_36
| ~ spl5_40 ),
inference(forward_demodulation,[],[f605,f519]) ).
fof(f519,plain,
( ! [X2,X3,X0,X1] : intersection(X3,union(X0,intersection(X1,X2))) = intersection(union(X0,X2),intersection(X3,union(X0,X1)))
| ~ spl5_24
| ~ spl5_36 ),
inference(superposition,[],[f448,f241]) ).
fof(f605,plain,
( intersection(union(sK0,sK1),intersection(union(sK1,sK2),union(sK0,sK2))) != union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2)))
| ~ spl5_5
| spl5_8
| ~ spl5_36
| ~ spl5_40 ),
inference(forward_demodulation,[],[f604,f86]) ).
fof(f604,plain,
( intersection(union(sK0,sK1),intersection(union(sK1,sK2),union(sK0,sK2))) != union(intersection(sK0,sK1),union(intersection(sK1,sK2),intersection(sK0,sK2)))
| spl5_8
| ~ spl5_36
| ~ spl5_40 ),
inference(forward_demodulation,[],[f578,f464]) ).
fof(f578,plain,
( intersection(union(sK0,sK1),intersection(union(sK1,sK2),union(sK0,sK2))) != union(intersection(sK0,sK2),union(intersection(sK0,sK1),intersection(sK1,sK2)))
| spl5_8
| ~ spl5_36 ),
inference(superposition,[],[f101,f448]) ).
fof(f799,plain,
( spl5_43
| ~ spl5_10
| ~ spl5_13 ),
inference(avatar_split_clause,[],[f144,f123,f111,f797]) ).
fof(f144,plain,
( ! [X2,X0,X1] :
( ~ member(sK4(X0,union(X1,X2)),X1)
| subset(X0,union(X1,X2)) )
| ~ spl5_10
| ~ spl5_13 ),
inference(resolution,[],[f124,f112]) ).
fof(f795,plain,
( spl5_42
| ~ spl5_9
| ~ spl5_12 ),
inference(avatar_split_clause,[],[f140,f119,f107,f793]) ).
fof(f140,plain,
( ! [X2,X0,X1] :
( member(sK4(intersection(X0,X1),X2),X1)
| subset(intersection(X0,X1),X2) )
| ~ spl5_9
| ~ spl5_12 ),
inference(resolution,[],[f120,f108]) ).
fof(f791,plain,
( spl5_41
| ~ spl5_9
| ~ spl5_11 ),
inference(avatar_split_clause,[],[f132,f115,f107,f789]) ).
fof(f132,plain,
( ! [X2,X0,X1] :
( member(sK4(intersection(X0,X1),X2),X0)
| subset(intersection(X0,X1),X2) )
| ~ spl5_9
| ~ spl5_11 ),
inference(resolution,[],[f116,f108]) ).
fof(f465,plain,
( spl5_40
| ~ spl5_5
| ~ spl5_19 ),
inference(avatar_split_clause,[],[f202,f167,f85,f463]) ).
fof(f202,plain,
( ! [X2,X0,X1] : union(X0,union(X1,X2)) = union(X2,union(X0,X1))
| ~ spl5_5
| ~ spl5_19 ),
inference(superposition,[],[f168,f86]) ).
fof(f461,plain,
( spl5_39
| ~ spl5_7
| ~ spl5_19 ),
inference(avatar_split_clause,[],[f199,f167,f93,f459]) ).
fof(f199,plain,
( ! [X2,X0,X1] : union(X0,X2) = union(X0,union(intersection(X0,X1),X2))
| ~ spl5_7
| ~ spl5_19 ),
inference(superposition,[],[f168,f94]) ).
fof(f457,plain,
( spl5_38
| ~ spl5_5
| ~ spl5_28 ),
inference(avatar_split_clause,[],[f323,f304,f85,f455]) ).
fof(f455,plain,
( spl5_38
<=> ! [X0,X1] : intersection(X0,union(X1,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_38])]) ).
fof(f323,plain,
( ! [X0,X1] : intersection(X0,union(X1,X0)) = X0
| ~ spl5_5
| ~ spl5_28 ),
inference(superposition,[],[f305,f86]) ).
fof(f453,plain,
( spl5_37
| ~ spl5_5
| ~ spl5_19 ),
inference(avatar_split_clause,[],[f197,f167,f85,f451]) ).
fof(f197,plain,
( ! [X2,X0,X1] : union(X0,union(X1,X2)) = union(union(X1,X0),X2)
| ~ spl5_5
| ~ spl5_19 ),
inference(superposition,[],[f168,f86]) ).
fof(f449,plain,
( spl5_36
| ~ spl5_6
| ~ spl5_18 ),
inference(avatar_split_clause,[],[f185,f163,f89,f447]) ).
fof(f185,plain,
( ! [X2,X0,X1] : intersection(X0,intersection(X1,X2)) = intersection(X2,intersection(X0,X1))
| ~ spl5_6
| ~ spl5_18 ),
inference(superposition,[],[f164,f90]) ).
fof(f444,plain,
( spl5_35
| ~ spl5_2
| ~ spl5_18 ),
inference(avatar_split_clause,[],[f184,f163,f68,f442]) ).
fof(f442,plain,
( spl5_35
<=> ! [X0,X1] : intersection(X0,X1) = intersection(X0,intersection(X1,intersection(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_35])]) ).
fof(f184,plain,
( ! [X0,X1] : intersection(X0,X1) = intersection(X0,intersection(X1,intersection(X0,X1)))
| ~ spl5_2
| ~ spl5_18 ),
inference(superposition,[],[f164,f69]) ).
fof(f440,plain,
( spl5_34
| ~ spl5_6
| ~ spl5_18 ),
inference(avatar_split_clause,[],[f181,f163,f89,f438]) ).
fof(f181,plain,
( ! [X2,X0,X1] : intersection(X0,intersection(X1,X2)) = intersection(intersection(X1,X0),X2)
| ~ spl5_6
| ~ spl5_18 ),
inference(superposition,[],[f164,f90]) ).
fof(f402,plain,
( spl5_33
| ~ spl5_14
| ~ spl5_19 ),
inference(avatar_split_clause,[],[f206,f167,f127,f400]) ).
fof(f206,plain,
( ! [X2,X3,X0,X1] :
( member(X3,union(X0,union(X1,X2)))
| ~ member(X3,X2) )
| ~ spl5_14
| ~ spl5_19 ),
inference(superposition,[],[f128,f168]) ).
fof(f398,plain,
( spl5_32
| ~ spl5_12
| ~ spl5_18 ),
inference(avatar_split_clause,[],[f189,f163,f119,f396]) ).
fof(f189,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X3,intersection(X0,intersection(X1,X2)))
| member(X3,X2) )
| ~ spl5_12
| ~ spl5_18 ),
inference(superposition,[],[f120,f164]) ).
fof(f348,plain,
( spl5_31
| ~ spl5_6
| ~ spl5_7
| ~ spl5_15
| ~ spl5_24 ),
inference(avatar_split_clause,[],[f284,f240,f137,f93,f89,f346]) ).
fof(f346,plain,
( spl5_31
<=> ! [X0,X1] : intersection(union(X0,X1),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_31])]) ).
fof(f284,plain,
( ! [X0,X1] : intersection(union(X0,X1),X0) = X0
| ~ spl5_6
| ~ spl5_7
| ~ spl5_15
| ~ spl5_24 ),
inference(forward_demodulation,[],[f264,f104]) ).
fof(f104,plain,
( ! [X0,X1] : union(X0,intersection(X1,X0)) = X0
| ~ spl5_6
| ~ spl5_7 ),
inference(superposition,[],[f94,f90]) ).
fof(f264,plain,
( ! [X0,X1] : union(X0,intersection(X1,X0)) = intersection(union(X0,X1),X0)
| ~ spl5_15
| ~ spl5_24 ),
inference(superposition,[],[f241,f138]) ).
fof(f344,plain,
( spl5_30
| ~ spl5_6
| ~ spl5_7
| ~ spl5_18
| ~ spl5_24 ),
inference(avatar_split_clause,[],[f283,f240,f163,f93,f89,f342]) ).
fof(f283,plain,
( ! [X2,X0,X1] : union(X0,intersection(X2,intersection(X0,X1))) = X0
| ~ spl5_6
| ~ spl5_7
| ~ spl5_18
| ~ spl5_24 ),
inference(forward_demodulation,[],[f282,f278]) ).
fof(f278,plain,
( ! [X2,X0] : intersection(X0,union(X0,X2)) = X0
| ~ spl5_7
| ~ spl5_18
| ~ spl5_24 ),
inference(forward_demodulation,[],[f277,f94]) ).
fof(f277,plain,
( ! [X2,X0,X1] : intersection(X0,union(X0,X2)) = union(X0,intersection(X0,intersection(X1,X2)))
| ~ spl5_7
| ~ spl5_18
| ~ spl5_24 ),
inference(forward_demodulation,[],[f258,f164]) ).
fof(f258,plain,
( ! [X2,X0,X1] : union(X0,intersection(intersection(X0,X1),X2)) = intersection(X0,union(X0,X2))
| ~ spl5_7
| ~ spl5_24 ),
inference(superposition,[],[f241,f94]) ).
fof(f282,plain,
( ! [X2,X0,X1] : intersection(X0,union(X0,X2)) = union(X0,intersection(X2,intersection(X0,X1)))
| ~ spl5_6
| ~ spl5_7
| ~ spl5_24 ),
inference(forward_demodulation,[],[f263,f90]) ).
fof(f263,plain,
( ! [X2,X0,X1] : union(X0,intersection(X2,intersection(X0,X1))) = intersection(union(X0,X2),X0)
| ~ spl5_7
| ~ spl5_24 ),
inference(superposition,[],[f241,f94]) ).
fof(f340,plain,
( spl5_29
| ~ spl5_2
| ~ spl5_18 ),
inference(avatar_split_clause,[],[f180,f163,f68,f338]) ).
fof(f180,plain,
( ! [X0,X1] : intersection(X0,X1) = intersection(X0,intersection(X0,X1))
| ~ spl5_2
| ~ spl5_18 ),
inference(superposition,[],[f164,f69]) ).
fof(f306,plain,
( spl5_28
| ~ spl5_7
| ~ spl5_18
| ~ spl5_24 ),
inference(avatar_split_clause,[],[f278,f240,f163,f93,f304]) ).
fof(f302,plain,
( spl5_27
| ~ spl5_6
| ~ spl5_7 ),
inference(avatar_split_clause,[],[f104,f93,f89,f300]) ).
fof(f298,plain,
( ~ spl5_26
| ~ spl5_6
| ~ spl5_18
| ~ spl5_24
| spl5_25 ),
inference(avatar_split_clause,[],[f293,f288,f240,f163,f89,f295]) ).
fof(f295,plain,
( spl5_26
<=> union(intersection(sK0,sK2),union(intersection(sK0,sK1),intersection(sK1,sK2))) = intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_26])]) ).
fof(f288,plain,
( spl5_25
<=> union(intersection(sK0,sK2),union(intersection(sK0,sK1),intersection(sK1,sK2))) = intersection(union(sK0,sK1),intersection(union(sK0,sK2),union(sK1,sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_25])]) ).
fof(f293,plain,
( union(intersection(sK0,sK2),union(intersection(sK0,sK1),intersection(sK1,sK2))) != intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))
| ~ spl5_6
| ~ spl5_18
| ~ spl5_24
| spl5_25 ),
inference(forward_demodulation,[],[f292,f90]) ).
fof(f292,plain,
( union(intersection(sK0,sK2),union(intersection(sK0,sK1),intersection(sK1,sK2))) != intersection(union(sK0,intersection(sK1,sK2)),union(sK1,sK2))
| ~ spl5_18
| ~ spl5_24
| spl5_25 ),
inference(forward_demodulation,[],[f290,f275]) ).
fof(f290,plain,
( union(intersection(sK0,sK2),union(intersection(sK0,sK1),intersection(sK1,sK2))) != intersection(union(sK0,sK1),intersection(union(sK0,sK2),union(sK1,sK2)))
| spl5_25 ),
inference(avatar_component_clause,[],[f288]) ).
fof(f291,plain,
( ~ spl5_25
| spl5_4
| ~ spl5_6
| ~ spl5_18 ),
inference(avatar_split_clause,[],[f196,f163,f89,f80,f288]) ).
fof(f196,plain,
( union(intersection(sK0,sK2),union(intersection(sK0,sK1),intersection(sK1,sK2))) != intersection(union(sK0,sK1),intersection(union(sK0,sK2),union(sK1,sK2)))
| spl5_4
| ~ spl5_6
| ~ spl5_18 ),
inference(forward_demodulation,[],[f187,f90]) ).
fof(f187,plain,
( intersection(union(sK0,sK1),intersection(union(sK1,sK2),union(sK0,sK2))) != union(intersection(sK0,sK2),union(intersection(sK0,sK1),intersection(sK1,sK2)))
| spl5_4
| ~ spl5_18 ),
inference(superposition,[],[f82,f164]) ).
fof(f242,plain,
spl5_24,
inference(avatar_split_clause,[],[f52,f240]) ).
fof(f52,plain,
! [X2,X0,X1] : union(X0,intersection(X1,X2)) = intersection(union(X0,X1),union(X0,X2)),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1,X2] : union(X0,intersection(X1,X2)) = intersection(union(X0,X1),union(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_distributes_over_intersection) ).
fof(f238,plain,
spl5_23,
inference(avatar_split_clause,[],[f46,f236]) ).
fof(f46,plain,
! [X0,X1] :
( X0 = X1
| ~ member(sK3(X0,X1),X1)
| ~ member(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1] :
( ( X0 = X1
| ( ( ~ member(sK3(X0,X1),X1)
| ~ member(sK3(X0,X1),X0) )
& ( member(sK3(X0,X1),X1)
| member(sK3(X0,X1),X0) ) ) )
& ( ! [X3] :
( ( member(X3,X0)
| ~ member(X3,X1) )
& ( member(X3,X1)
| ~ member(X3,X0) ) )
| X0 != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f23,f24]) ).
fof(f24,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) )
=> ( ( ~ member(sK3(X0,X1),X1)
| ~ member(sK3(X0,X1),X0) )
& ( member(sK3(X0,X1),X1)
| member(sK3(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
! [X0,X1] :
( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) ) )
& ( ! [X3] :
( ( member(X3,X0)
| ~ member(X3,X1) )
& ( member(X3,X1)
| ~ member(X3,X0) ) )
| X0 != X1 ) ),
inference(rectify,[],[f22]) ).
fof(f22,plain,
! [X0,X1] :
( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) ) )
& ( ! [X2] :
( ( member(X2,X0)
| ~ member(X2,X1) )
& ( member(X2,X1)
| ~ member(X2,X0) ) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0,X1] :
( X0 = X1
<=> ! [X2] :
( member(X2,X0)
<=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f234,plain,
spl5_22,
inference(avatar_split_clause,[],[f45,f232]) ).
fof(f45,plain,
! [X0,X1] :
( X0 = X1
| member(sK3(X0,X1),X1)
| member(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f179,plain,
spl5_21,
inference(avatar_split_clause,[],[f56,f177]) ).
fof(f56,plain,
! [X2,X0,X1] :
( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X1)
& ~ member(X2,X0) ) )
& ( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ) ),
inference(flattening,[],[f32]) ).
fof(f32,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X1)
& ~ member(X2,X0) ) )
& ( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
fof(f173,plain,
spl5_20,
inference(avatar_split_clause,[],[f55,f171]) ).
fof(f55,plain,
! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) )
& ( ( member(X2,X1)
& member(X2,X0) )
| ~ member(X2,intersection(X0,X1)) ) ),
inference(flattening,[],[f30]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) )
& ( ( member(X2,X1)
& member(X2,X0) )
| ~ member(X2,intersection(X0,X1)) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
fof(f169,plain,
spl5_19,
inference(avatar_split_clause,[],[f51,f167]) ).
fof(f51,plain,
! [X2,X0,X1] : union(union(X0,X1),X2) = union(X0,union(X1,X2)),
inference(cnf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1,X2] : union(union(X0,X1),X2) = union(X0,union(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_union) ).
fof(f165,plain,
spl5_18,
inference(avatar_split_clause,[],[f50,f163]) ).
fof(f50,plain,
! [X2,X0,X1] : intersection(intersection(X0,X1),X2) = intersection(X0,intersection(X1,X2)),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1,X2] : intersection(intersection(X0,X1),X2) = intersection(X0,intersection(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_intersection) ).
fof(f159,plain,
spl5_17,
inference(avatar_split_clause,[],[f47,f157]) ).
fof(f157,plain,
( spl5_17
<=> ! [X0,X1,X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_17])]) ).
fof(f47,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK4(X0,X1),X1)
& member(sK4(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f27,f28]) ).
fof(f28,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK4(X0,X1),X1)
& member(sK4(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f26]) ).
fof(f26,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f17,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f155,plain,
spl5_16,
inference(avatar_split_clause,[],[f42,f153]) ).
fof(f153,plain,
( spl5_16
<=> ! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_16])]) ).
fof(f42,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f21,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(f139,plain,
( spl5_15
| ~ spl5_2
| ~ spl5_7 ),
inference(avatar_split_clause,[],[f103,f93,f68,f137]) ).
fof(f103,plain,
( ! [X0] : union(X0,X0) = X0
| ~ spl5_2
| ~ spl5_7 ),
inference(superposition,[],[f94,f69]) ).
fof(f129,plain,
spl5_14,
inference(avatar_split_clause,[],[f58,f127]) ).
fof(f58,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f125,plain,
spl5_13,
inference(avatar_split_clause,[],[f57,f123]) ).
fof(f57,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f121,plain,
spl5_12,
inference(avatar_split_clause,[],[f54,f119]) ).
fof(f54,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f31]) ).
fof(f117,plain,
spl5_11,
inference(avatar_split_clause,[],[f53,f115]) ).
fof(f53,plain,
! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f31]) ).
fof(f113,plain,
spl5_10,
inference(avatar_split_clause,[],[f49,f111]) ).
fof(f49,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK4(X0,X1),X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f109,plain,
spl5_9,
inference(avatar_split_clause,[],[f48,f107]) ).
fof(f48,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK4(X0,X1),X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f102,plain,
( ~ spl5_8
| spl5_4
| ~ spl5_6 ),
inference(avatar_split_clause,[],[f96,f89,f80,f99]) ).
fof(f96,plain,
( intersection(union(sK0,sK2),intersection(union(sK0,sK1),union(sK1,sK2))) != union(intersection(sK0,sK2),union(intersection(sK0,sK1),intersection(sK1,sK2)))
| spl5_4
| ~ spl5_6 ),
inference(superposition,[],[f82,f90]) ).
fof(f95,plain,
spl5_7,
inference(avatar_split_clause,[],[f39,f93]) ).
fof(f39,plain,
! [X0,X1] : union(X0,intersection(X0,X1)) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] : union(X0,intersection(X0,X1)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_intersection) ).
fof(f91,plain,
spl5_6,
inference(avatar_split_clause,[],[f38,f89]) ).
fof(f38,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f87,plain,
spl5_5,
inference(avatar_split_clause,[],[f37,f85]) ).
fof(f37,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(f83,plain,
( ~ spl5_4
| spl5_3 ),
inference(avatar_split_clause,[],[f78,f72,f80]) ).
fof(f72,plain,
( spl5_3
<=> union(union(intersection(sK0,sK1),intersection(sK1,sK2)),intersection(sK2,sK0)) = intersection(intersection(union(sK0,sK1),union(sK1,sK2)),union(sK2,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).
fof(f78,plain,
( intersection(intersection(union(sK0,sK1),union(sK1,sK2)),union(sK0,sK2)) != union(intersection(sK0,sK2),union(intersection(sK0,sK1),intersection(sK1,sK2)))
| spl5_3 ),
inference(forward_demodulation,[],[f77,f38]) ).
fof(f77,plain,
( intersection(intersection(union(sK0,sK1),union(sK1,sK2)),union(sK0,sK2)) != union(intersection(sK2,sK0),union(intersection(sK0,sK1),intersection(sK1,sK2)))
| spl5_3 ),
inference(forward_demodulation,[],[f76,f37]) ).
fof(f76,plain,
( union(union(intersection(sK0,sK1),intersection(sK1,sK2)),intersection(sK2,sK0)) != intersection(intersection(union(sK0,sK1),union(sK1,sK2)),union(sK0,sK2))
| spl5_3 ),
inference(forward_demodulation,[],[f74,f37]) ).
fof(f74,plain,
( union(union(intersection(sK0,sK1),intersection(sK1,sK2)),intersection(sK2,sK0)) != intersection(intersection(union(sK0,sK1),union(sK1,sK2)),union(sK2,sK0))
| spl5_3 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f75,plain,
~ spl5_3,
inference(avatar_split_clause,[],[f34,f72]) ).
fof(f34,plain,
union(union(intersection(sK0,sK1),intersection(sK1,sK2)),intersection(sK2,sK0)) != intersection(intersection(union(sK0,sK1),union(sK1,sK2)),union(sK2,sK0)),
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
union(union(intersection(sK0,sK1),intersection(sK1,sK2)),intersection(sK2,sK0)) != intersection(intersection(union(sK0,sK1),union(sK1,sK2)),union(sK2,sK0)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f16,f18]) ).
fof(f18,plain,
( ? [X0,X1,X2] : union(union(intersection(X0,X1),intersection(X1,X2)),intersection(X2,X0)) != intersection(intersection(union(X0,X1),union(X1,X2)),union(X2,X0))
=> union(union(intersection(sK0,sK1),intersection(sK1,sK2)),intersection(sK2,sK0)) != intersection(intersection(union(sK0,sK1),union(sK1,sK2)),union(sK2,sK0)) ),
introduced(choice_axiom,[]) ).
fof(f16,plain,
? [X0,X1,X2] : union(union(intersection(X0,X1),intersection(X1,X2)),intersection(X2,X0)) != intersection(intersection(union(X0,X1),union(X1,X2)),union(X2,X0)),
inference(ennf_transformation,[],[f15]) ).
fof(f15,negated_conjecture,
~ ! [X0,X1,X2] : union(union(intersection(X0,X1),intersection(X1,X2)),intersection(X2,X0)) = intersection(intersection(union(X0,X1),union(X1,X2)),union(X2,X0)),
inference(negated_conjecture,[],[f14]) ).
fof(f14,conjecture,
! [X0,X1,X2] : union(union(intersection(X0,X1),intersection(X1,X2)),intersection(X2,X0)) = intersection(intersection(union(X0,X1),union(X1,X2)),union(X2,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th72) ).
fof(f70,plain,
spl5_2,
inference(avatar_split_clause,[],[f36,f68]) ).
fof(f36,plain,
! [X0] : intersection(X0,X0) = X0,
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] : intersection(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotency_of_intersection) ).
fof(f66,plain,
spl5_1,
inference(avatar_split_clause,[],[f35,f64]) ).
fof(f64,plain,
( spl5_1
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).
fof(f35,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SET601+3 : TPTP v8.1.2. Released v2.2.0.
% 0.02/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.32 % Computer : n014.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri May 3 16:52:53 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.33 % (1262)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.34 % (1265)WARNING: value z3 for option sas not known
% 0.11/0.34 % (1268)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)
% 0.11/0.34 % (1267)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)
% 0.11/0.34 % (1263)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.11/0.34 % (1269)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)
% 0.11/0.34 % (1265)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)
% 0.11/0.34 % (1266)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.11/0.34 % (1264)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.11/0.34 TRYING [1]
% 0.11/0.35 TRYING [2]
% 0.11/0.35 TRYING [3]
% 0.11/0.35 TRYING [1]
% 0.11/0.35 TRYING [2]
% 0.16/0.36 TRYING [4]
% 0.16/0.36 TRYING [3]
% 0.16/0.39 TRYING [5]
% 0.16/0.40 TRYING [4]
% 0.16/0.47 TRYING [6]
% 0.16/0.51 TRYING [5]
% 2.34/0.72 TRYING [7]
% 3.89/0.90 TRYING [6]
% 6.46/1.26 TRYING [8]
% 7.30/1.40 % (1267)First to succeed.
% 7.30/1.41 % (1267)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1262"
% 7.30/1.42 % (1267)Refutation found. Thanks to Tanya!
% 7.30/1.42 % SZS status Theorem for theBenchmark
% 7.30/1.42 % SZS output start Proof for theBenchmark
% See solution above
% 7.30/1.42 % (1267)------------------------------
% 7.30/1.42 % (1267)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 7.30/1.42 % (1267)Termination reason: Refutation
% 7.30/1.42
% 7.30/1.42 % (1267)Memory used [KB]: 13157
% 7.30/1.42 % (1267)Time elapsed: 1.071 s
% 7.30/1.42 % (1267)Instructions burned: 2199 (million)
% 7.30/1.42 % (1262)Success in time 1.079 s
%------------------------------------------------------------------------------