TSTP Solution File: SET619+3 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET619+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 : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 15:08:53 EDT 2024
% Result : Theorem 0.17s 0.39s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 83
% Syntax : Number of formulae : 282 ( 40 unt; 0 def)
% Number of atoms : 839 ( 123 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 946 ( 389 ~; 446 |; 33 &)
% ( 74 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 71 ( 69 usr; 68 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 519 ( 509 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1499,plain,
$false,
inference(avatar_sat_refutation,[],[f68,f73,f77,f81,f85,f93,f97,f102,f106,f110,f114,f118,f138,f142,f146,f160,f164,f168,f189,f206,f210,f227,f239,f246,f250,f270,f290,f294,f298,f334,f449,f453,f457,f461,f465,f572,f576,f580,f700,f744,f748,f752,f756,f760,f764,f768,f772,f776,f995,f999,f1003,f1092,f1199,f1203,f1207,f1251,f1255,f1259,f1263,f1267,f1343,f1347,f1351,f1357,f1361,f1365,f1369,f1490]) ).
fof(f1490,plain,
( spl4_40
| ~ spl4_63 ),
inference(avatar_contradiction_clause,[],[f1489]) ).
fof(f1489,plain,
( $false
| spl4_40
| ~ spl4_63 ),
inference(trivial_inequality_removal,[],[f1488]) ).
fof(f1488,plain,
( union(sK0,sK1) != union(sK0,sK1)
| spl4_40
| ~ spl4_63 ),
inference(superposition,[],[f743,f1350]) ).
fof(f1350,plain,
( ! [X0,X1] : union(X0,X1) = union(X0,difference(X1,X0))
| ~ spl4_63 ),
inference(avatar_component_clause,[],[f1349]) ).
fof(f1349,plain,
( spl4_63
<=> ! [X0,X1] : union(X0,X1) = union(X0,difference(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_63])]) ).
fof(f743,plain,
( union(sK0,sK1) != union(sK0,difference(sK1,sK0))
| spl4_40 ),
inference(avatar_component_clause,[],[f741]) ).
fof(f741,plain,
( spl4_40
<=> union(sK0,sK1) = union(sK0,difference(sK1,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_40])]) ).
fof(f1369,plain,
( spl4_67
| ~ spl4_13
| ~ spl4_22
| ~ spl4_36 ),
inference(avatar_split_clause,[],[f611,f570,f225,f136,f1367]) ).
fof(f1367,plain,
( spl4_67
<=> ! [X2,X0,X1] : union(X0,intersection(X2,difference(X0,X1))) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_67])]) ).
fof(f136,plain,
( spl4_13
<=> ! [X0,X1] : union(intersection(X0,X1),difference(X0,X1)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_13])]) ).
fof(f225,plain,
( spl4_22
<=> ! [X0,X1] : union(X0,intersection(X1,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_22])]) ).
fof(f570,plain,
( spl4_36
<=> ! [X2,X0,X1] : union(X0,X2) = union(intersection(X0,X1),union(difference(X0,X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_36])]) ).
fof(f611,plain,
( ! [X2,X0,X1] : union(X0,intersection(X2,difference(X0,X1))) = X0
| ~ spl4_13
| ~ spl4_22
| ~ spl4_36 ),
inference(forward_demodulation,[],[f587,f137]) ).
fof(f137,plain,
( ! [X0,X1] : union(intersection(X0,X1),difference(X0,X1)) = X0
| ~ spl4_13 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f587,plain,
( ! [X2,X0,X1] : union(intersection(X0,X1),difference(X0,X1)) = union(X0,intersection(X2,difference(X0,X1)))
| ~ spl4_22
| ~ spl4_36 ),
inference(superposition,[],[f571,f226]) ).
fof(f226,plain,
( ! [X0,X1] : union(X0,intersection(X1,X0)) = X0
| ~ spl4_22 ),
inference(avatar_component_clause,[],[f225]) ).
fof(f571,plain,
( ! [X2,X0,X1] : union(X0,X2) = union(intersection(X0,X1),union(difference(X0,X1),X2))
| ~ spl4_36 ),
inference(avatar_component_clause,[],[f570]) ).
fof(f1365,plain,
( spl4_66
| ~ spl4_5
| ~ spl4_13
| ~ spl4_36 ),
inference(avatar_split_clause,[],[f610,f570,f136,f83,f1363]) ).
fof(f1363,plain,
( spl4_66
<=> ! [X2,X0,X1] : union(X0,intersection(difference(X0,X1),X2)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_66])]) ).
fof(f83,plain,
( spl4_5
<=> ! [X0,X1] : union(X0,intersection(X0,X1)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_5])]) ).
fof(f610,plain,
( ! [X2,X0,X1] : union(X0,intersection(difference(X0,X1),X2)) = X0
| ~ spl4_5
| ~ spl4_13
| ~ spl4_36 ),
inference(forward_demodulation,[],[f586,f137]) ).
fof(f586,plain,
( ! [X2,X0,X1] : union(intersection(X0,X1),difference(X0,X1)) = union(X0,intersection(difference(X0,X1),X2))
| ~ spl4_5
| ~ spl4_36 ),
inference(superposition,[],[f571,f84]) ).
fof(f84,plain,
( ! [X0,X1] : union(X0,intersection(X0,X1)) = X0
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f1361,plain,
( spl4_65
| ~ spl4_5
| ~ spl4_22
| ~ spl4_28 ),
inference(avatar_split_clause,[],[f356,f292,f225,f83,f1359]) ).
fof(f1359,plain,
( spl4_65
<=> ! [X2,X0,X1] : union(X0,intersection(X2,intersection(X0,X1))) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_65])]) ).
fof(f292,plain,
( spl4_28
<=> ! [X2,X0,X1] : union(X0,union(intersection(X0,X1),X2)) = union(X0,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_28])]) ).
fof(f356,plain,
( ! [X2,X0,X1] : union(X0,intersection(X2,intersection(X0,X1))) = X0
| ~ spl4_5
| ~ spl4_22
| ~ spl4_28 ),
inference(forward_demodulation,[],[f342,f84]) ).
fof(f342,plain,
( ! [X2,X0,X1] : union(X0,intersection(X0,X1)) = union(X0,intersection(X2,intersection(X0,X1)))
| ~ spl4_22
| ~ spl4_28 ),
inference(superposition,[],[f293,f226]) ).
fof(f293,plain,
( ! [X2,X0,X1] : union(X0,union(intersection(X0,X1),X2)) = union(X0,X2)
| ~ spl4_28 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f1357,plain,
( spl4_64
| ~ spl4_5
| ~ spl4_28 ),
inference(avatar_split_clause,[],[f355,f292,f83,f1355]) ).
fof(f1355,plain,
( spl4_64
<=> ! [X2,X0,X1] : union(X0,intersection(intersection(X0,X1),X2)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_64])]) ).
fof(f355,plain,
( ! [X2,X0,X1] : union(X0,intersection(intersection(X0,X1),X2)) = X0
| ~ spl4_5
| ~ spl4_28 ),
inference(forward_demodulation,[],[f341,f84]) ).
fof(f341,plain,
( ! [X2,X0,X1] : union(X0,intersection(X0,X1)) = union(X0,intersection(intersection(X0,X1),X2))
| ~ spl4_5
| ~ spl4_28 ),
inference(superposition,[],[f293,f84]) ).
fof(f1351,plain,
( spl4_63
| ~ spl4_24
| ~ spl4_28 ),
inference(avatar_split_clause,[],[f338,f292,f244,f1349]) ).
fof(f244,plain,
( spl4_24
<=> ! [X0,X1] : union(intersection(X1,X0),difference(X0,X1)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_24])]) ).
fof(f338,plain,
( ! [X0,X1] : union(X0,X1) = union(X0,difference(X1,X0))
| ~ spl4_24
| ~ spl4_28 ),
inference(superposition,[],[f293,f245]) ).
fof(f245,plain,
( ! [X0,X1] : union(intersection(X1,X0),difference(X0,X1)) = X0
| ~ spl4_24 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f1347,plain,
( spl4_62
| ~ spl4_13
| ~ spl4_28 ),
inference(avatar_split_clause,[],[f337,f292,f136,f1345]) ).
fof(f1345,plain,
( spl4_62
<=> ! [X0,X1] : union(X0,difference(X0,X1)) = union(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_62])]) ).
fof(f337,plain,
( ! [X0,X1] : union(X0,difference(X0,X1)) = union(X0,X0)
| ~ spl4_13
| ~ spl4_28 ),
inference(superposition,[],[f293,f137]) ).
fof(f1343,plain,
( spl4_61
| ~ spl4_4
| ~ spl4_24 ),
inference(avatar_split_clause,[],[f253,f244,f79,f1341]) ).
fof(f1341,plain,
( spl4_61
<=> ! [X0,X1] : union(difference(X1,X0),intersection(X0,X1)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_61])]) ).
fof(f79,plain,
( spl4_4
<=> ! [X0,X1] : union(X0,X1) = union(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_4])]) ).
fof(f253,plain,
( ! [X0,X1] : union(difference(X1,X0),intersection(X0,X1)) = X1
| ~ spl4_4
| ~ spl4_24 ),
inference(superposition,[],[f245,f80]) ).
fof(f80,plain,
( ! [X0,X1] : union(X0,X1) = union(X1,X0)
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f1267,plain,
( spl4_60
| ~ spl4_31
| ~ spl4_34 ),
inference(avatar_split_clause,[],[f534,f459,f447,f1265]) ).
fof(f1265,plain,
( spl4_60
<=> ! [X2,X0,X1] : subset(intersection(X0,X1),union(X2,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_60])]) ).
fof(f447,plain,
( spl4_31
<=> ! [X2,X0,X1] :
( member(sK3(intersection(X0,X1),X2),X0)
| subset(intersection(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_31])]) ).
fof(f459,plain,
( spl4_34
<=> ! [X2,X0,X1] :
( ~ member(sK3(X0,union(X1,X2)),X2)
| subset(X0,union(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_34])]) ).
fof(f534,plain,
( ! [X2,X0,X1] : subset(intersection(X0,X1),union(X2,X0))
| ~ spl4_31
| ~ spl4_34 ),
inference(duplicate_literal_removal,[],[f515]) ).
fof(f515,plain,
( ! [X2,X0,X1] :
( subset(intersection(X0,X1),union(X2,X0))
| subset(intersection(X0,X1),union(X2,X0)) )
| ~ spl4_31
| ~ spl4_34 ),
inference(resolution,[],[f460,f448]) ).
fof(f448,plain,
( ! [X2,X0,X1] :
( member(sK3(intersection(X0,X1),X2),X0)
| subset(intersection(X0,X1),X2) )
| ~ spl4_31 ),
inference(avatar_component_clause,[],[f447]) ).
fof(f460,plain,
( ! [X2,X0,X1] :
( ~ member(sK3(X0,union(X1,X2)),X2)
| subset(X0,union(X1,X2)) )
| ~ spl4_34 ),
inference(avatar_component_clause,[],[f459]) ).
fof(f1263,plain,
( spl4_59
| ~ spl4_32
| ~ spl4_34 ),
inference(avatar_split_clause,[],[f533,f459,f451,f1261]) ).
fof(f1261,plain,
( spl4_59
<=> ! [X2,X0,X1] : subset(intersection(X0,X1),union(X2,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_59])]) ).
fof(f451,plain,
( spl4_32
<=> ! [X2,X0,X1] :
( member(sK3(intersection(X0,X1),X2),X1)
| subset(intersection(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_32])]) ).
fof(f533,plain,
( ! [X2,X0,X1] : subset(intersection(X0,X1),union(X2,X1))
| ~ spl4_32
| ~ spl4_34 ),
inference(duplicate_literal_removal,[],[f516]) ).
fof(f516,plain,
( ! [X2,X0,X1] :
( subset(intersection(X0,X1),union(X2,X1))
| subset(intersection(X0,X1),union(X2,X1)) )
| ~ spl4_32
| ~ spl4_34 ),
inference(resolution,[],[f460,f452]) ).
fof(f452,plain,
( ! [X2,X0,X1] :
( member(sK3(intersection(X0,X1),X2),X1)
| subset(intersection(X0,X1),X2) )
| ~ spl4_32 ),
inference(avatar_component_clause,[],[f451]) ).
fof(f1259,plain,
( spl4_58
| ~ spl4_31
| ~ spl4_33 ),
inference(avatar_split_clause,[],[f502,f455,f447,f1257]) ).
fof(f1257,plain,
( spl4_58
<=> ! [X2,X0,X1] : subset(intersection(X0,X1),union(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_58])]) ).
fof(f455,plain,
( spl4_33
<=> ! [X2,X0,X1] :
( ~ member(sK3(X0,union(X1,X2)),X1)
| subset(X0,union(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_33])]) ).
fof(f502,plain,
( ! [X2,X0,X1] : subset(intersection(X0,X1),union(X0,X2))
| ~ spl4_31
| ~ spl4_33 ),
inference(duplicate_literal_removal,[],[f483]) ).
fof(f483,plain,
( ! [X2,X0,X1] :
( subset(intersection(X0,X1),union(X0,X2))
| subset(intersection(X0,X1),union(X0,X2)) )
| ~ spl4_31
| ~ spl4_33 ),
inference(resolution,[],[f456,f448]) ).
fof(f456,plain,
( ! [X2,X0,X1] :
( ~ member(sK3(X0,union(X1,X2)),X1)
| subset(X0,union(X1,X2)) )
| ~ spl4_33 ),
inference(avatar_component_clause,[],[f455]) ).
fof(f1255,plain,
( spl4_57
| ~ spl4_25
| ~ spl4_54 ),
inference(avatar_split_clause,[],[f1226,f1201,f248,f1253]) ).
fof(f1253,plain,
( spl4_57
<=> ! [X0,X1] : subset(difference(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_57])]) ).
fof(f248,plain,
( spl4_25
<=> ! [X0,X1] : union(difference(X0,X1),intersection(X0,X1)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_25])]) ).
fof(f1201,plain,
( spl4_54
<=> ! [X0,X1] : subset(X0,union(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_54])]) ).
fof(f1226,plain,
( ! [X0,X1] : subset(difference(X0,X1),X0)
| ~ spl4_25
| ~ spl4_54 ),
inference(superposition,[],[f1202,f249]) ).
fof(f249,plain,
( ! [X0,X1] : union(difference(X0,X1),intersection(X0,X1)) = X0
| ~ spl4_25 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f1202,plain,
( ! [X0,X1] : subset(X0,union(X0,X1))
| ~ spl4_54 ),
inference(avatar_component_clause,[],[f1201]) ).
fof(f1251,plain,
( spl4_56
| ~ spl4_32
| ~ spl4_33 ),
inference(avatar_split_clause,[],[f501,f455,f451,f1249]) ).
fof(f1249,plain,
( spl4_56
<=> ! [X2,X0,X1] : subset(intersection(X0,X1),union(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_56])]) ).
fof(f501,plain,
( ! [X2,X0,X1] : subset(intersection(X0,X1),union(X1,X2))
| ~ spl4_32
| ~ spl4_33 ),
inference(duplicate_literal_removal,[],[f484]) ).
fof(f484,plain,
( ! [X2,X0,X1] :
( subset(intersection(X0,X1),union(X1,X2))
| subset(intersection(X0,X1),union(X1,X2)) )
| ~ spl4_32
| ~ spl4_33 ),
inference(resolution,[],[f456,f452]) ).
fof(f1207,plain,
( spl4_55
| ~ spl4_6
| ~ spl4_34 ),
inference(avatar_split_clause,[],[f535,f459,f91,f1205]) ).
fof(f1205,plain,
( spl4_55
<=> ! [X0,X1] : subset(X0,union(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_55])]) ).
fof(f91,plain,
( spl4_6
<=> ! [X0,X1] :
( subset(X0,X1)
| member(sK3(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_6])]) ).
fof(f535,plain,
( ! [X0,X1] : subset(X0,union(X1,X0))
| ~ spl4_6
| ~ spl4_34 ),
inference(duplicate_literal_removal,[],[f514]) ).
fof(f514,plain,
( ! [X0,X1] :
( subset(X0,union(X1,X0))
| subset(X0,union(X1,X0)) )
| ~ spl4_6
| ~ spl4_34 ),
inference(resolution,[],[f460,f92]) ).
fof(f92,plain,
( ! [X0,X1] :
( member(sK3(X0,X1),X0)
| subset(X0,X1) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f1203,plain,
( spl4_54
| ~ spl4_6
| ~ spl4_33 ),
inference(avatar_split_clause,[],[f503,f455,f91,f1201]) ).
fof(f503,plain,
( ! [X0,X1] : subset(X0,union(X0,X1))
| ~ spl4_6
| ~ spl4_33 ),
inference(duplicate_literal_removal,[],[f482]) ).
fof(f482,plain,
( ! [X0,X1] :
( subset(X0,union(X0,X1))
| subset(X0,union(X0,X1)) )
| ~ spl4_6
| ~ spl4_33 ),
inference(resolution,[],[f456,f92]) ).
fof(f1199,plain,
( spl4_53
| ~ spl4_7
| ~ spl4_32 ),
inference(avatar_split_clause,[],[f481,f451,f95,f1197]) ).
fof(f1197,plain,
( spl4_53
<=> ! [X0,X1] : subset(intersection(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_53])]) ).
fof(f95,plain,
( spl4_7
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ member(sK3(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_7])]) ).
fof(f481,plain,
( ! [X0,X1] : subset(intersection(X0,X1),X1)
| ~ spl4_7
| ~ spl4_32 ),
inference(duplicate_literal_removal,[],[f474]) ).
fof(f474,plain,
( ! [X0,X1] :
( subset(intersection(X0,X1),X1)
| subset(intersection(X0,X1),X1) )
| ~ spl4_7
| ~ spl4_32 ),
inference(resolution,[],[f452,f96]) ).
fof(f96,plain,
( ! [X0,X1] :
( ~ member(sK3(X0,X1),X1)
| subset(X0,X1) )
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f1092,plain,
( spl4_52
| ~ spl4_7
| ~ spl4_31 ),
inference(avatar_split_clause,[],[f473,f447,f95,f1090]) ).
fof(f1090,plain,
( spl4_52
<=> ! [X0,X1] : subset(intersection(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_52])]) ).
fof(f473,plain,
( ! [X0,X1] : subset(intersection(X0,X1),X0)
| ~ spl4_7
| ~ spl4_31 ),
inference(duplicate_literal_removal,[],[f466]) ).
fof(f466,plain,
( ! [X0,X1] :
( subset(intersection(X0,X1),X0)
| subset(intersection(X0,X1),X0) )
| ~ spl4_7
| ~ spl4_31 ),
inference(resolution,[],[f448,f96]) ).
fof(f1003,plain,
( spl4_51
| ~ spl4_17
| ~ spl4_21 ),
inference(avatar_split_clause,[],[f222,f208,f162,f1001]) ).
fof(f1001,plain,
( spl4_51
<=> ! [X2,X0,X1] :
( intersection(X1,X2) = X0
| ~ member(sK2(X0,intersection(X1,X2)),X0)
| ~ member(sK2(X0,intersection(X1,X2)),X2)
| ~ member(sK2(X0,intersection(X1,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_51])]) ).
fof(f162,plain,
( spl4_17
<=> ! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_17])]) ).
fof(f208,plain,
( spl4_21
<=> ! [X0,X1] :
( X0 = X1
| ~ member(sK2(X0,X1),X1)
| ~ member(sK2(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_21])]) ).
fof(f222,plain,
( ! [X2,X0,X1] :
( intersection(X1,X2) = X0
| ~ member(sK2(X0,intersection(X1,X2)),X0)
| ~ member(sK2(X0,intersection(X1,X2)),X2)
| ~ member(sK2(X0,intersection(X1,X2)),X1) )
| ~ spl4_17
| ~ spl4_21 ),
inference(resolution,[],[f209,f163]) ).
fof(f163,plain,
( ! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) )
| ~ spl4_17 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f209,plain,
( ! [X0,X1] :
( ~ member(sK2(X0,X1),X1)
| X0 = X1
| ~ member(sK2(X0,X1),X0) )
| ~ spl4_21 ),
inference(avatar_component_clause,[],[f208]) ).
fof(f999,plain,
( spl4_50
| ~ spl4_18
| ~ spl4_20 ),
inference(avatar_split_clause,[],[f216,f204,f166,f997]) ).
fof(f997,plain,
( spl4_50
<=> ! [X2,X0,X1] :
( member(sK2(union(X0,X1),X2),X2)
| union(X0,X1) = X2
| member(sK2(union(X0,X1),X2),X0)
| member(sK2(union(X0,X1),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_50])]) ).
fof(f166,plain,
( spl4_18
<=> ! [X2,X0,X1] :
( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_18])]) ).
fof(f204,plain,
( spl4_20
<=> ! [X0,X1] :
( X0 = X1
| member(sK2(X0,X1),X1)
| member(sK2(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_20])]) ).
fof(f216,plain,
( ! [X2,X0,X1] :
( member(sK2(union(X0,X1),X2),X2)
| union(X0,X1) = X2
| member(sK2(union(X0,X1),X2),X0)
| member(sK2(union(X0,X1),X2),X1) )
| ~ spl4_18
| ~ spl4_20 ),
inference(resolution,[],[f205,f167]) ).
fof(f167,plain,
( ! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X0)
| member(X2,X1) )
| ~ spl4_18 ),
inference(avatar_component_clause,[],[f166]) ).
fof(f205,plain,
( ! [X0,X1] :
( member(sK2(X0,X1),X1)
| member(sK2(X0,X1),X0)
| X0 = X1 )
| ~ spl4_20 ),
inference(avatar_component_clause,[],[f204]) ).
fof(f995,plain,
( spl4_49
| ~ spl4_18
| ~ spl4_20 ),
inference(avatar_split_clause,[],[f213,f204,f166,f993]) ).
fof(f993,plain,
( spl4_49
<=> ! [X2,X0,X1] :
( member(sK2(X0,union(X1,X2)),X0)
| union(X1,X2) = X0
| member(sK2(X0,union(X1,X2)),X1)
| member(sK2(X0,union(X1,X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_49])]) ).
fof(f213,plain,
( ! [X2,X0,X1] :
( member(sK2(X0,union(X1,X2)),X0)
| union(X1,X2) = X0
| member(sK2(X0,union(X1,X2)),X1)
| member(sK2(X0,union(X1,X2)),X2) )
| ~ spl4_18
| ~ spl4_20 ),
inference(resolution,[],[f205,f167]) ).
fof(f776,plain,
( spl4_48
| ~ spl4_11
| ~ spl4_21 ),
inference(avatar_split_clause,[],[f221,f208,f112,f774]) ).
fof(f774,plain,
( spl4_48
<=> ! [X2,X0,X1] :
( union(X1,X2) = X0
| ~ member(sK2(X0,union(X1,X2)),X0)
| ~ member(sK2(X0,union(X1,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_48])]) ).
fof(f112,plain,
( spl4_11
<=> ! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_11])]) ).
fof(f221,plain,
( ! [X2,X0,X1] :
( union(X1,X2) = X0
| ~ member(sK2(X0,union(X1,X2)),X0)
| ~ member(sK2(X0,union(X1,X2)),X1) )
| ~ spl4_11
| ~ spl4_21 ),
inference(resolution,[],[f209,f113]) ).
fof(f113,plain,
( ! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X0) )
| ~ spl4_11 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f772,plain,
( spl4_47
| ~ spl4_12
| ~ spl4_21 ),
inference(avatar_split_clause,[],[f220,f208,f116,f770]) ).
fof(f770,plain,
( spl4_47
<=> ! [X2,X0,X1] :
( union(X1,X2) = X0
| ~ member(sK2(X0,union(X1,X2)),X0)
| ~ member(sK2(X0,union(X1,X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_47])]) ).
fof(f116,plain,
( spl4_12
<=> ! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_12])]) ).
fof(f220,plain,
( ! [X2,X0,X1] :
( union(X1,X2) = X0
| ~ member(sK2(X0,union(X1,X2)),X0)
| ~ member(sK2(X0,union(X1,X2)),X2) )
| ~ spl4_12
| ~ spl4_21 ),
inference(resolution,[],[f209,f117]) ).
fof(f117,plain,
( ! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X1) )
| ~ spl4_12 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f768,plain,
( spl4_46
| ~ spl4_9
| ~ spl4_20 ),
inference(avatar_split_clause,[],[f215,f204,f104,f766]) ).
fof(f766,plain,
( spl4_46
<=> ! [X2,X0,X1] :
( member(sK2(intersection(X0,X1),X2),X2)
| intersection(X0,X1) = X2
| member(sK2(intersection(X0,X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_46])]) ).
fof(f104,plain,
( spl4_9
<=> ! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_9])]) ).
fof(f215,plain,
( ! [X2,X0,X1] :
( member(sK2(intersection(X0,X1),X2),X2)
| intersection(X0,X1) = X2
| member(sK2(intersection(X0,X1),X2),X0) )
| ~ spl4_9
| ~ spl4_20 ),
inference(resolution,[],[f205,f105]) ).
fof(f105,plain,
( ! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X0) )
| ~ spl4_9 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f764,plain,
( spl4_45
| ~ spl4_10
| ~ spl4_20 ),
inference(avatar_split_clause,[],[f214,f204,f108,f762]) ).
fof(f762,plain,
( spl4_45
<=> ! [X2,X0,X1] :
( member(sK2(intersection(X0,X1),X2),X2)
| intersection(X0,X1) = X2
| member(sK2(intersection(X0,X1),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_45])]) ).
fof(f108,plain,
( spl4_10
<=> ! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_10])]) ).
fof(f214,plain,
( ! [X2,X0,X1] :
( member(sK2(intersection(X0,X1),X2),X2)
| intersection(X0,X1) = X2
| member(sK2(intersection(X0,X1),X2),X1) )
| ~ spl4_10
| ~ spl4_20 ),
inference(resolution,[],[f205,f109]) ).
fof(f109,plain,
( ! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X1) )
| ~ spl4_10 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f760,plain,
( spl4_44
| ~ spl4_9
| ~ spl4_20 ),
inference(avatar_split_clause,[],[f212,f204,f104,f758]) ).
fof(f758,plain,
( spl4_44
<=> ! [X2,X0,X1] :
( member(sK2(X0,intersection(X1,X2)),X0)
| intersection(X1,X2) = X0
| member(sK2(X0,intersection(X1,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_44])]) ).
fof(f212,plain,
( ! [X2,X0,X1] :
( member(sK2(X0,intersection(X1,X2)),X0)
| intersection(X1,X2) = X0
| member(sK2(X0,intersection(X1,X2)),X1) )
| ~ spl4_9
| ~ spl4_20 ),
inference(resolution,[],[f205,f105]) ).
fof(f756,plain,
( spl4_43
| ~ spl4_10
| ~ spl4_20 ),
inference(avatar_split_clause,[],[f211,f204,f108,f754]) ).
fof(f754,plain,
( spl4_43
<=> ! [X2,X0,X1] :
( member(sK2(X0,intersection(X1,X2)),X0)
| intersection(X1,X2) = X0
| member(sK2(X0,intersection(X1,X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_43])]) ).
fof(f211,plain,
( ! [X2,X0,X1] :
( member(sK2(X0,intersection(X1,X2)),X0)
| intersection(X1,X2) = X0
| member(sK2(X0,intersection(X1,X2)),X2) )
| ~ spl4_10
| ~ spl4_20 ),
inference(resolution,[],[f205,f109]) ).
fof(f752,plain,
( spl4_42
| ~ spl4_6
| ~ spl4_18 ),
inference(avatar_split_clause,[],[f195,f166,f91,f750]) ).
fof(f750,plain,
( spl4_42
<=> ! [X2,X0,X1] :
( member(sK3(union(X0,X1),X2),X0)
| member(sK3(union(X0,X1),X2),X1)
| subset(union(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_42])]) ).
fof(f195,plain,
( ! [X2,X0,X1] :
( member(sK3(union(X0,X1),X2),X0)
| member(sK3(union(X0,X1),X2),X1)
| subset(union(X0,X1),X2) )
| ~ spl4_6
| ~ spl4_18 ),
inference(resolution,[],[f167,f92]) ).
fof(f748,plain,
( spl4_41
| ~ spl4_7
| ~ spl4_17 ),
inference(avatar_split_clause,[],[f190,f162,f95,f746]) ).
fof(f746,plain,
( spl4_41
<=> ! [X2,X0,X1] :
( ~ member(sK3(X0,intersection(X1,X2)),X2)
| ~ member(sK3(X0,intersection(X1,X2)),X1)
| subset(X0,intersection(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_41])]) ).
fof(f190,plain,
( ! [X2,X0,X1] :
( ~ member(sK3(X0,intersection(X1,X2)),X2)
| ~ member(sK3(X0,intersection(X1,X2)),X1)
| subset(X0,intersection(X1,X2)) )
| ~ spl4_7
| ~ spl4_17 ),
inference(resolution,[],[f163,f96]) ).
fof(f744,plain,
( ~ spl4_40
| ~ spl4_4
| spl4_30 ),
inference(avatar_split_clause,[],[f512,f331,f79,f741]) ).
fof(f331,plain,
( spl4_30
<=> union(sK0,sK1) = union(difference(sK1,sK0),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_30])]) ).
fof(f512,plain,
( union(sK0,sK1) != union(sK0,difference(sK1,sK0))
| ~ spl4_4
| spl4_30 ),
inference(superposition,[],[f333,f80]) ).
fof(f333,plain,
( union(sK0,sK1) != union(difference(sK1,sK0),sK0)
| spl4_30 ),
inference(avatar_component_clause,[],[f331]) ).
fof(f700,plain,
( spl4_39
| ~ spl4_16
| ~ spl4_18 ),
inference(avatar_split_clause,[],[f202,f166,f158,f698]) ).
fof(f698,plain,
( spl4_39
<=> ! [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,[spl4_39])]) ).
fof(f158,plain,
( spl4_16
<=> ! [X2,X0,X1] : union(union(X0,X1),X2) = union(X0,union(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_16])]) ).
fof(f202,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X3,union(X0,union(X1,X2)))
| member(X3,union(X0,X1))
| member(X3,X2) )
| ~ spl4_16
| ~ spl4_18 ),
inference(superposition,[],[f167,f159]) ).
fof(f159,plain,
( ! [X2,X0,X1] : union(union(X0,X1),X2) = union(X0,union(X1,X2))
| ~ spl4_16 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f580,plain,
( spl4_38
| ~ spl4_13
| ~ spl4_18 ),
inference(avatar_split_clause,[],[f201,f166,f136,f578]) ).
fof(f578,plain,
( spl4_38
<=> ! [X2,X0,X1] :
( ~ member(X2,X0)
| member(X2,intersection(X0,X1))
| member(X2,difference(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_38])]) ).
fof(f201,plain,
( ! [X2,X0,X1] :
( ~ member(X2,X0)
| member(X2,intersection(X0,X1))
| member(X2,difference(X0,X1)) )
| ~ spl4_13
| ~ spl4_18 ),
inference(superposition,[],[f167,f137]) ).
fof(f576,plain,
( spl4_37
| ~ spl4_5
| ~ spl4_16 ),
inference(avatar_split_clause,[],[f176,f158,f83,f574]) ).
fof(f574,plain,
( spl4_37
<=> ! [X2,X0,X1] : union(X0,X1) = union(X0,union(X1,intersection(union(X0,X1),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_37])]) ).
fof(f176,plain,
( ! [X2,X0,X1] : union(X0,X1) = union(X0,union(X1,intersection(union(X0,X1),X2)))
| ~ spl4_5
| ~ spl4_16 ),
inference(superposition,[],[f159,f84]) ).
fof(f572,plain,
( spl4_36
| ~ spl4_13
| ~ spl4_16 ),
inference(avatar_split_clause,[],[f172,f158,f136,f570]) ).
fof(f172,plain,
( ! [X2,X0,X1] : union(X0,X2) = union(intersection(X0,X1),union(difference(X0,X1),X2))
| ~ spl4_13
| ~ spl4_16 ),
inference(superposition,[],[f159,f137]) ).
fof(f465,plain,
( spl4_35
| ~ spl4_11
| ~ spl4_16 ),
inference(avatar_split_clause,[],[f179,f158,f112,f463]) ).
fof(f463,plain,
( spl4_35
<=> ! [X0,X3,X2,X1] :
( member(X3,union(X0,union(X1,X2)))
| ~ member(X3,union(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_35])]) ).
fof(f179,plain,
( ! [X2,X3,X0,X1] :
( member(X3,union(X0,union(X1,X2)))
| ~ member(X3,union(X0,X1)) )
| ~ spl4_11
| ~ spl4_16 ),
inference(superposition,[],[f113,f159]) ).
fof(f461,plain,
( spl4_34
| ~ spl4_7
| ~ spl4_12 ),
inference(avatar_split_clause,[],[f131,f116,f95,f459]) ).
fof(f131,plain,
( ! [X2,X0,X1] :
( ~ member(sK3(X0,union(X1,X2)),X2)
| subset(X0,union(X1,X2)) )
| ~ spl4_7
| ~ spl4_12 ),
inference(resolution,[],[f117,f96]) ).
fof(f457,plain,
( spl4_33
| ~ spl4_7
| ~ spl4_11 ),
inference(avatar_split_clause,[],[f127,f112,f95,f455]) ).
fof(f127,plain,
( ! [X2,X0,X1] :
( ~ member(sK3(X0,union(X1,X2)),X1)
| subset(X0,union(X1,X2)) )
| ~ spl4_7
| ~ spl4_11 ),
inference(resolution,[],[f113,f96]) ).
fof(f453,plain,
( spl4_32
| ~ spl4_6
| ~ spl4_10 ),
inference(avatar_split_clause,[],[f124,f108,f91,f451]) ).
fof(f124,plain,
( ! [X2,X0,X1] :
( member(sK3(intersection(X0,X1),X2),X1)
| subset(intersection(X0,X1),X2) )
| ~ spl4_6
| ~ spl4_10 ),
inference(resolution,[],[f109,f92]) ).
fof(f449,plain,
( spl4_31
| ~ spl4_6
| ~ spl4_9 ),
inference(avatar_split_clause,[],[f121,f104,f91,f447]) ).
fof(f121,plain,
( ! [X2,X0,X1] :
( member(sK3(intersection(X0,X1),X2),X0)
| subset(intersection(X0,X1),X2) )
| ~ spl4_6
| ~ spl4_9 ),
inference(resolution,[],[f105,f92]) ).
fof(f334,plain,
( ~ spl4_30
| spl4_2
| ~ spl4_25
| ~ spl4_27 ),
inference(avatar_split_clause,[],[f327,f288,f248,f70,f331]) ).
fof(f70,plain,
( spl4_2
<=> union(sK0,sK1) = union(union(difference(sK0,sK1),difference(sK1,sK0)),intersection(sK0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).
fof(f288,plain,
( spl4_27
<=> ! [X2,X0,X1] : union(X0,union(X1,X2)) = union(union(X1,X0),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_27])]) ).
fof(f327,plain,
( union(sK0,sK1) != union(difference(sK1,sK0),sK0)
| spl4_2
| ~ spl4_25
| ~ spl4_27 ),
inference(forward_demodulation,[],[f313,f249]) ).
fof(f313,plain,
( union(sK0,sK1) != union(difference(sK1,sK0),union(difference(sK0,sK1),intersection(sK0,sK1)))
| spl4_2
| ~ spl4_27 ),
inference(superposition,[],[f72,f289]) ).
fof(f289,plain,
( ! [X2,X0,X1] : union(X0,union(X1,X2)) = union(union(X1,X0),X2)
| ~ spl4_27 ),
inference(avatar_component_clause,[],[f288]) ).
fof(f72,plain,
( union(sK0,sK1) != union(union(difference(sK0,sK1),difference(sK1,sK0)),intersection(sK0,sK1))
| spl4_2 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f298,plain,
( spl4_29
| ~ spl4_4
| ~ spl4_16 ),
inference(avatar_split_clause,[],[f174,f158,f79,f296]) ).
fof(f296,plain,
( spl4_29
<=> ! [X2,X0,X1] : union(X0,union(X1,X2)) = union(X2,union(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_29])]) ).
fof(f174,plain,
( ! [X2,X0,X1] : union(X0,union(X1,X2)) = union(X2,union(X0,X1))
| ~ spl4_4
| ~ spl4_16 ),
inference(superposition,[],[f159,f80]) ).
fof(f294,plain,
( spl4_28
| ~ spl4_5
| ~ spl4_16 ),
inference(avatar_split_clause,[],[f171,f158,f83,f292]) ).
fof(f171,plain,
( ! [X2,X0,X1] : union(X0,union(intersection(X0,X1),X2)) = union(X0,X2)
| ~ spl4_5
| ~ spl4_16 ),
inference(superposition,[],[f159,f84]) ).
fof(f290,plain,
( spl4_27
| ~ spl4_4
| ~ spl4_16 ),
inference(avatar_split_clause,[],[f169,f158,f79,f288]) ).
fof(f169,plain,
( ! [X2,X0,X1] : union(X0,union(X1,X2)) = union(union(X1,X0),X2)
| ~ spl4_4
| ~ spl4_16 ),
inference(superposition,[],[f159,f80]) ).
fof(f270,plain,
( spl4_26
| ~ spl4_12
| ~ spl4_16 ),
inference(avatar_split_clause,[],[f178,f158,f116,f268]) ).
fof(f268,plain,
( spl4_26
<=> ! [X0,X3,X2,X1] :
( member(X3,union(X0,union(X1,X2)))
| ~ member(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_26])]) ).
fof(f178,plain,
( ! [X2,X3,X0,X1] :
( member(X3,union(X0,union(X1,X2)))
| ~ member(X3,X2) )
| ~ spl4_12
| ~ spl4_16 ),
inference(superposition,[],[f117,f159]) ).
fof(f250,plain,
( spl4_25
| ~ spl4_4
| ~ spl4_13 ),
inference(avatar_split_clause,[],[f149,f136,f79,f248]) ).
fof(f149,plain,
( ! [X0,X1] : union(difference(X0,X1),intersection(X0,X1)) = X0
| ~ spl4_4
| ~ spl4_13 ),
inference(superposition,[],[f137,f80]) ).
fof(f246,plain,
( spl4_24
| ~ spl4_3
| ~ spl4_13 ),
inference(avatar_split_clause,[],[f147,f136,f75,f244]) ).
fof(f75,plain,
( spl4_3
<=> ! [X0,X1] : intersection(X0,X1) = intersection(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_3])]) ).
fof(f147,plain,
( ! [X0,X1] : union(intersection(X1,X0),difference(X0,X1)) = X0
| ~ spl4_3
| ~ spl4_13 ),
inference(superposition,[],[f137,f76]) ).
fof(f76,plain,
( ! [X0,X1] : intersection(X0,X1) = intersection(X1,X0)
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f239,plain,
( spl4_23
| ~ spl4_12
| ~ spl4_13 ),
inference(avatar_split_clause,[],[f151,f136,f116,f237]) ).
fof(f237,plain,
( spl4_23
<=> ! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,difference(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_23])]) ).
fof(f151,plain,
( ! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,difference(X0,X1)) )
| ~ spl4_12
| ~ spl4_13 ),
inference(superposition,[],[f117,f137]) ).
fof(f227,plain,
( spl4_22
| ~ spl4_3
| ~ spl4_5 ),
inference(avatar_split_clause,[],[f88,f83,f75,f225]) ).
fof(f88,plain,
( ! [X0,X1] : union(X0,intersection(X1,X0)) = X0
| ~ spl4_3
| ~ spl4_5 ),
inference(superposition,[],[f84,f76]) ).
fof(f210,plain,
spl4_21,
inference(avatar_split_clause,[],[f48,f208]) ).
fof(f48,plain,
! [X0,X1] :
( X0 = X1
| ~ member(sK2(X0,X1),X1)
| ~ member(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1] :
( ( X0 = X1
| ( ( ~ member(sK2(X0,X1),X1)
| ~ member(sK2(X0,X1),X0) )
& ( member(sK2(X0,X1),X1)
| member(sK2(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,[sK2])],[f23,f24]) ).
fof(f24,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) )
=> ( ( ~ member(sK2(X0,X1),X1)
| ~ member(sK2(X0,X1),X0) )
& ( member(sK2(X0,X1),X1)
| member(sK2(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,[],[f11]) ).
fof(f11,axiom,
! [X0,X1] :
( X0 = X1
<=> ! [X2] :
( member(X2,X0)
<=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f206,plain,
spl4_20,
inference(avatar_split_clause,[],[f47,f204]) ).
fof(f47,plain,
! [X0,X1] :
( X0 = X1
| member(sK2(X0,X1),X1)
| member(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f189,plain,
( ~ spl4_19
| spl4_2
| ~ spl4_16 ),
inference(avatar_split_clause,[],[f177,f158,f70,f186]) ).
fof(f186,plain,
( spl4_19
<=> union(sK0,sK1) = union(difference(sK0,sK1),union(difference(sK1,sK0),intersection(sK0,sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_19])]) ).
fof(f177,plain,
( union(sK0,sK1) != union(difference(sK0,sK1),union(difference(sK1,sK0),intersection(sK0,sK1)))
| spl4_2
| ~ spl4_16 ),
inference(superposition,[],[f72,f159]) ).
fof(f168,plain,
spl4_18,
inference(avatar_split_clause,[],[f56,f166]) ).
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,[],[f5]) ).
fof(f5,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(f164,plain,
spl4_17,
inference(avatar_split_clause,[],[f55,f162]) ).
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,[],[f6]) ).
fof(f6,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
fof(f160,plain,
spl4_16,
inference(avatar_split_clause,[],[f52,f158]) ).
fof(f52,plain,
! [X2,X0,X1] : union(union(X0,X1),X2) = union(X0,union(X1,X2)),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1,X2] : union(union(X0,X1),X2) = union(X0,union(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_union) ).
fof(f146,plain,
spl4_15,
inference(avatar_split_clause,[],[f49,f144]) ).
fof(f144,plain,
( spl4_15
<=> ! [X0,X1,X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_15])]) ).
fof(f49,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(sK3(X0,X1),X1)
& member(sK3(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f27,f28]) ).
fof(f28,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK3(X0,X1),X1)
& member(sK3(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,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f142,plain,
spl4_14,
inference(avatar_split_clause,[],[f44,f140]) ).
fof(f140,plain,
( spl4_14
<=> ! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_14])]) ).
fof(f44,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,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(f138,plain,
spl4_13,
inference(avatar_split_clause,[],[f40,f136]) ).
fof(f40,plain,
! [X0,X1] : union(intersection(X0,X1),difference(X0,X1)) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] : union(intersection(X0,X1),difference(X0,X1)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_intersection_difference) ).
fof(f118,plain,
spl4_12,
inference(avatar_split_clause,[],[f58,f116]) ).
fof(f58,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f114,plain,
spl4_11,
inference(avatar_split_clause,[],[f57,f112]) ).
fof(f57,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f110,plain,
spl4_10,
inference(avatar_split_clause,[],[f54,f108]) ).
fof(f54,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f31]) ).
fof(f106,plain,
spl4_9,
inference(avatar_split_clause,[],[f53,f104]) ).
fof(f53,plain,
! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f31]) ).
fof(f102,plain,
( ~ spl4_8
| spl4_2
| ~ spl4_4 ),
inference(avatar_split_clause,[],[f86,f79,f70,f99]) ).
fof(f99,plain,
( spl4_8
<=> union(sK0,sK1) = union(intersection(sK0,sK1),union(difference(sK0,sK1),difference(sK1,sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_8])]) ).
fof(f86,plain,
( union(sK0,sK1) != union(intersection(sK0,sK1),union(difference(sK0,sK1),difference(sK1,sK0)))
| spl4_2
| ~ spl4_4 ),
inference(superposition,[],[f72,f80]) ).
fof(f97,plain,
spl4_7,
inference(avatar_split_clause,[],[f51,f95]) ).
fof(f51,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f93,plain,
spl4_6,
inference(avatar_split_clause,[],[f50,f91]) ).
fof(f50,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f85,plain,
spl4_5,
inference(avatar_split_clause,[],[f39,f83]) ).
fof(f39,plain,
! [X0,X1] : union(X0,intersection(X0,X1)) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] : union(X0,intersection(X0,X1)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_intersection) ).
fof(f81,plain,
spl4_4,
inference(avatar_split_clause,[],[f38,f79]) ).
fof(f38,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(f77,plain,
spl4_3,
inference(avatar_split_clause,[],[f37,f75]) ).
fof(f37,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f73,plain,
~ spl4_2,
inference(avatar_split_clause,[],[f59,f70]) ).
fof(f59,plain,
union(sK0,sK1) != union(union(difference(sK0,sK1),difference(sK1,sK0)),intersection(sK0,sK1)),
inference(definition_unfolding,[],[f34,f41]) ).
fof(f41,plain,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(cnf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_difference_defn) ).
fof(f34,plain,
union(sK0,sK1) != union(symmetric_difference(sK0,sK1),intersection(sK0,sK1)),
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
union(sK0,sK1) != union(symmetric_difference(sK0,sK1),intersection(sK0,sK1)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f16,f18]) ).
fof(f18,plain,
( ? [X0,X1] : union(X0,X1) != union(symmetric_difference(X0,X1),intersection(X0,X1))
=> union(sK0,sK1) != union(symmetric_difference(sK0,sK1),intersection(sK0,sK1)) ),
introduced(choice_axiom,[]) ).
fof(f16,plain,
? [X0,X1] : union(X0,X1) != union(symmetric_difference(X0,X1),intersection(X0,X1)),
inference(ennf_transformation,[],[f15]) ).
fof(f15,negated_conjecture,
~ ! [X0,X1] : union(X0,X1) = union(symmetric_difference(X0,X1),intersection(X0,X1)),
inference(negated_conjecture,[],[f14]) ).
fof(f14,conjecture,
! [X0,X1] : union(X0,X1) = union(symmetric_difference(X0,X1),intersection(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th95) ).
fof(f68,plain,
spl4_1,
inference(avatar_split_clause,[],[f35,f66]) ).
fof(f66,plain,
( spl4_1
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).
fof(f35,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : SET619+3 : TPTP v8.1.2. Released v2.2.0.
% 0.02/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.32 % Computer : n002.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 : Tue Apr 30 01:49:24 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.32 % (12339)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.34 % (12342)WARNING: value z3 for option sas not known
% 0.11/0.34 % (12342)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 % (12340)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.11/0.34 % (12346)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 % (12341)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 % (12344)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 % (12345)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 % (12343)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.11/0.34 TRYING [1]
% 0.11/0.34 TRYING [2]
% 0.11/0.34 TRYING [3]
% 0.11/0.34 TRYING [1]
% 0.11/0.34 TRYING [2]
% 0.17/0.35 TRYING [4]
% 0.17/0.35 TRYING [3]
% 0.17/0.37 TRYING [5]
% 0.17/0.38 TRYING [4]
% 0.17/0.39 % (12344)First to succeed.
% 0.17/0.39 % (12344)Refutation found. Thanks to Tanya!
% 0.17/0.39 % SZS status Theorem for theBenchmark
% 0.17/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.39 % (12344)------------------------------
% 0.17/0.39 % (12344)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.17/0.39 % (12344)Termination reason: Refutation
% 0.17/0.39
% 0.17/0.39 % (12344)Memory used [KB]: 1670
% 0.17/0.39 % (12344)Time elapsed: 0.055 s
% 0.17/0.39 % (12344)Instructions burned: 107 (million)
% 0.17/0.39 % (12344)------------------------------
% 0.17/0.39 % (12344)------------------------------
% 0.17/0.39 % (12339)Success in time 0.064 s
%------------------------------------------------------------------------------