TSTP Solution File: CAT003-4 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : CAT003-4 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 04:43:43 EDT 2024
% Result : Unsatisfiable 0.22s 0.43s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 98
% Syntax : Number of formulae : 290 ( 24 unt; 0 def)
% Number of atoms : 801 ( 161 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 942 ( 431 ~; 429 |; 0 &)
% ( 82 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 86 ( 84 usr; 83 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 215 ( 215 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1320,plain,
$false,
inference(avatar_sat_refutation,[],[f23,f28,f33,f37,f41,f45,f49,f54,f58,f62,f68,f72,f80,f88,f103,f107,f117,f123,f129,f136,f142,f152,f157,f162,f166,f180,f184,f214,f228,f229,f254,f299,f321,f332,f354,f361,f369,f374,f379,f384,f417,f429,f433,f481,f487,f492,f497,f515,f546,f551,f556,f561,f616,f620,f624,f628,f681,f691,f695,f805,f818,f838,f842,f846,f850,f855,f859,f863,f867,f871,f1042,f1090,f1094,f1098,f1102,f1111,f1126,f1161,f1249,f1253,f1318,f1319]) ).
fof(f1319,plain,
( spl0_1
| ~ spl0_80 ),
inference(avatar_split_clause,[],[f1260,f1247,f20]) ).
fof(f20,plain,
( spl0_1
<=> h = g ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f1247,plain,
( spl0_80
<=> ! [X0] :
( compose(X0,compose(a,b)) != compose(g,compose(a,b))
| h = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f1260,plain,
( h = g
| ~ spl0_80 ),
inference(equality_resolution,[],[f1248]) ).
fof(f1248,plain,
( ! [X0] :
( compose(X0,compose(a,b)) != compose(g,compose(a,b))
| h = X0 )
| ~ spl0_80 ),
inference(avatar_component_clause,[],[f1247]) ).
fof(f1318,plain,
( spl0_82
| ~ spl0_13
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f273,f252,f78,f1316]) ).
fof(f1316,plain,
( spl0_82
<=> ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| domain(X0) = codomain(compose(X1,domain(compose(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f78,plain,
( spl0_13
<=> ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| domain(X0) = codomain(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f252,plain,
( spl0_31
<=> ! [X0,X1] : compose(X0,X1) = compose(X0,compose(X1,domain(compose(X0,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f273,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| domain(X0) = codomain(compose(X1,domain(compose(X0,X1)))) )
| ~ spl0_13
| ~ spl0_31 ),
inference(superposition,[],[f79,f253]) ).
fof(f253,plain,
( ! [X0,X1] : compose(X0,X1) = compose(X0,compose(X1,domain(compose(X0,X1))))
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f252]) ).
fof(f79,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| domain(X0) = codomain(X1) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f1253,plain,
( spl0_81
| ~ spl0_28
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f219,f212,f182,f1251]) ).
fof(f1251,plain,
( spl0_81
<=> ! [X0] : compose(g,compose(a,X0)) = compose(codomain(h),compose(g,compose(a,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f182,plain,
( spl0_28
<=> ! [X0,X1] : compose(X0,X1) = compose(codomain(X0),compose(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f212,plain,
( spl0_29
<=> ! [X0] : compose(h,compose(a,X0)) = compose(g,compose(a,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f219,plain,
( ! [X0] : compose(g,compose(a,X0)) = compose(codomain(h),compose(g,compose(a,X0)))
| ~ spl0_28
| ~ spl0_29 ),
inference(superposition,[],[f183,f213]) ).
fof(f213,plain,
( ! [X0] : compose(h,compose(a,X0)) = compose(g,compose(a,X0))
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f212]) ).
fof(f183,plain,
( ! [X0,X1] : compose(X0,X1) = compose(codomain(X0),compose(X0,X1))
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f182]) ).
fof(f1249,plain,
( spl0_80
| ~ spl0_16
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f217,f212,f105,f1247]) ).
fof(f105,plain,
( spl0_16
<=> ! [X2,X0] :
( X0 = X2
| compose(X0,compose(a,b)) != compose(X2,compose(a,b)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f217,plain,
( ! [X0] :
( compose(X0,compose(a,b)) != compose(g,compose(a,b))
| h = X0 )
| ~ spl0_16
| ~ spl0_29 ),
inference(superposition,[],[f106,f213]) ).
fof(f106,plain,
( ! [X2,X0] :
( compose(X0,compose(a,b)) != compose(X2,compose(a,b))
| X0 = X2 )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f1161,plain,
( spl0_79
| ~ spl0_27
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f292,f252,f178,f1159]) ).
fof(f1159,plain,
( spl0_79
<=> ! [X0,X1] : compose(X0,X1) = compose(X0,compose(X1,domain(compose(domain(X0),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f178,plain,
( spl0_27
<=> ! [X0,X1] : compose(X0,X1) = compose(X0,compose(domain(X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f292,plain,
( ! [X0,X1] : compose(X0,X1) = compose(X0,compose(X1,domain(compose(domain(X0),X1))))
| ~ spl0_27
| ~ spl0_31 ),
inference(forward_demodulation,[],[f275,f179]) ).
fof(f179,plain,
( ! [X0,X1] : compose(X0,X1) = compose(X0,compose(domain(X0),X1))
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f178]) ).
fof(f275,plain,
( ! [X0,X1] : compose(X0,compose(domain(X0),X1)) = compose(X0,compose(X1,domain(compose(domain(X0),X1))))
| ~ spl0_27
| ~ spl0_31 ),
inference(superposition,[],[f179,f253]) ).
fof(f1126,plain,
( spl0_78
| ~ spl0_19
| ~ spl0_24
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f357,f351,f155,f126,f1123]) ).
fof(f1123,plain,
( spl0_78
<=> codomain(b) = codomain(codomain(b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f126,plain,
( spl0_19
<=> domain(a) = codomain(b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f155,plain,
( spl0_24
<=> ! [X0] :
( ~ there_exists(X0)
| domain(X0) = codomain(domain(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f351,plain,
( spl0_35
<=> there_exists(a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f357,plain,
( codomain(b) = codomain(codomain(b))
| ~ spl0_19
| ~ spl0_24
| ~ spl0_35 ),
inference(forward_demodulation,[],[f356,f128]) ).
fof(f128,plain,
( domain(a) = codomain(b)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f356,plain,
( domain(a) = codomain(domain(a))
| ~ spl0_24
| ~ spl0_35 ),
inference(resolution,[],[f353,f156]) ).
fof(f156,plain,
( ! [X0] :
( ~ there_exists(X0)
| domain(X0) = codomain(domain(X0)) )
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f353,plain,
( there_exists(a)
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f351]) ).
fof(f1111,plain,
( ~ spl0_76
| spl0_77
| ~ spl0_28
| ~ spl0_29
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f328,f319,f212,f182,f1108,f1104]) ).
fof(f1104,plain,
( spl0_76
<=> compose(a,b) = compose(g,compose(a,b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f1108,plain,
( spl0_77
<=> h = codomain(a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f319,plain,
( spl0_33
<=> ! [X0] :
( compose(a,b) != compose(X0,compose(a,b))
| codomain(compose(a,b)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f328,plain,
( h = codomain(a)
| compose(a,b) != compose(g,compose(a,b))
| ~ spl0_28
| ~ spl0_29
| ~ spl0_33 ),
inference(forward_demodulation,[],[f325,f326]) ).
fof(f326,plain,
( codomain(a) = codomain(compose(a,b))
| ~ spl0_28
| ~ spl0_33 ),
inference(trivial_inequality_removal,[],[f322]) ).
fof(f322,plain,
( compose(a,b) != compose(a,b)
| codomain(a) = codomain(compose(a,b))
| ~ spl0_28
| ~ spl0_33 ),
inference(superposition,[],[f320,f183]) ).
fof(f320,plain,
( ! [X0] :
( compose(a,b) != compose(X0,compose(a,b))
| codomain(compose(a,b)) = X0 )
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f319]) ).
fof(f325,plain,
( compose(a,b) != compose(g,compose(a,b))
| h = codomain(compose(a,b))
| ~ spl0_29
| ~ spl0_33 ),
inference(superposition,[],[f320,f213]) ).
fof(f1102,plain,
( spl0_75
| ~ spl0_11
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f306,f297,f65,f1100]) ).
fof(f1100,plain,
( spl0_75
<=> ! [X0] :
( ~ there_exists(compose(X0,compose(g,a)))
| codomain(a) = domain(compose(X0,h)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f65,plain,
( spl0_11
<=> compose(h,a) = compose(g,a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f297,plain,
( spl0_32
<=> ! [X2,X0,X1] :
( ~ there_exists(compose(X0,compose(X1,X2)))
| domain(compose(X0,X1)) = codomain(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f306,plain,
( ! [X0] :
( ~ there_exists(compose(X0,compose(g,a)))
| codomain(a) = domain(compose(X0,h)) )
| ~ spl0_11
| ~ spl0_32 ),
inference(superposition,[],[f298,f67]) ).
fof(f67,plain,
( compose(h,a) = compose(g,a)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f65]) ).
fof(f298,plain,
( ! [X2,X0,X1] :
( ~ there_exists(compose(X0,compose(X1,X2)))
| domain(compose(X0,X1)) = codomain(X2) )
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f297]) ).
fof(f1098,plain,
( spl0_74
| ~ spl0_29
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f241,f226,f212,f1096]) ).
fof(f1096,plain,
( spl0_74
<=> ! [X0,X1] :
( ~ there_exists(compose(X1,compose(g,compose(a,X0))))
| there_exists(domain(compose(X1,h))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f226,plain,
( spl0_30
<=> ! [X2,X0,X1] :
( ~ there_exists(compose(X0,compose(X1,X2)))
| there_exists(domain(compose(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f241,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X1,compose(g,compose(a,X0))))
| there_exists(domain(compose(X1,h))) )
| ~ spl0_29
| ~ spl0_30 ),
inference(superposition,[],[f227,f213]) ).
fof(f227,plain,
( ! [X2,X0,X1] :
( ~ there_exists(compose(X0,compose(X1,X2)))
| there_exists(domain(compose(X0,X1))) )
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f226]) ).
fof(f1094,plain,
( spl0_73
| ~ spl0_13
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f221,f212,f78,f1092]) ).
fof(f1092,plain,
( spl0_73
<=> ! [X0] :
( ~ there_exists(compose(g,compose(a,X0)))
| domain(h) = codomain(compose(a,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f221,plain,
( ! [X0] :
( ~ there_exists(compose(g,compose(a,X0)))
| domain(h) = codomain(compose(a,X0)) )
| ~ spl0_13
| ~ spl0_29 ),
inference(superposition,[],[f79,f213]) ).
fof(f1090,plain,
( spl0_72
| ~ spl0_16
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f205,f182,f105,f1088]) ).
fof(f1088,plain,
( spl0_72
<=> ! [X0] :
( compose(a,b) != compose(X0,compose(a,b))
| codomain(a) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f205,plain,
( ! [X0] :
( compose(a,b) != compose(X0,compose(a,b))
| codomain(a) = X0 )
| ~ spl0_16
| ~ spl0_28 ),
inference(superposition,[],[f106,f183]) ).
fof(f1042,plain,
( spl0_71
| ~ spl0_26
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f355,f351,f164,f1039]) ).
fof(f1039,plain,
( spl0_71
<=> codomain(a) = domain(codomain(a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f164,plain,
( spl0_26
<=> ! [X0] :
( ~ there_exists(X0)
| codomain(X0) = domain(codomain(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f355,plain,
( codomain(a) = domain(codomain(a))
| ~ spl0_26
| ~ spl0_35 ),
inference(resolution,[],[f353,f165]) ).
fof(f165,plain,
( ! [X0] :
( ~ there_exists(X0)
| codomain(X0) = domain(codomain(X0)) )
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f871,plain,
( spl0_70
| ~ spl0_10
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f303,f297,f60,f869]) ).
fof(f869,plain,
( spl0_70
<=> ! [X0,X1] :
( ~ there_exists(compose(X1,X0))
| codomain(X0) = domain(compose(X1,codomain(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f60,plain,
( spl0_10
<=> ! [X0] : compose(codomain(X0),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f303,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X1,X0))
| codomain(X0) = domain(compose(X1,codomain(X0))) )
| ~ spl0_10
| ~ spl0_32 ),
inference(superposition,[],[f298,f61]) ).
fof(f61,plain,
( ! [X0] : compose(codomain(X0),X0) = X0
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f867,plain,
( spl0_69
| ~ spl0_9
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f300,f297,f56,f865]) ).
fof(f865,plain,
( spl0_69
<=> ! [X0,X1] :
( ~ there_exists(compose(X1,X0))
| codomain(domain(X0)) = domain(compose(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f56,plain,
( spl0_9
<=> ! [X0] : compose(X0,domain(X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f300,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X1,X0))
| codomain(domain(X0)) = domain(compose(X1,X0)) )
| ~ spl0_9
| ~ spl0_32 ),
inference(superposition,[],[f298,f57]) ).
fof(f57,plain,
( ! [X0] : compose(X0,domain(X0)) = X0
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f863,plain,
( spl0_68
| ~ spl0_10
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f244,f226,f60,f861]) ).
fof(f861,plain,
( spl0_68
<=> ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| there_exists(domain(compose(codomain(compose(X0,X1)),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f244,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| there_exists(domain(compose(codomain(compose(X0,X1)),X0))) )
| ~ spl0_10
| ~ spl0_30 ),
inference(superposition,[],[f227,f61]) ).
fof(f859,plain,
( spl0_67
| ~ spl0_28
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f238,f226,f182,f857]) ).
fof(f857,plain,
( spl0_67
<=> ! [X2,X0,X1] :
( ~ there_exists(compose(X2,compose(X0,X1)))
| there_exists(domain(compose(X2,codomain(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f238,plain,
( ! [X2,X0,X1] :
( ~ there_exists(compose(X2,compose(X0,X1)))
| there_exists(domain(compose(X2,codomain(X0)))) )
| ~ spl0_28
| ~ spl0_30 ),
inference(superposition,[],[f227,f183]) ).
fof(f855,plain,
( spl0_66
| ~ spl0_24
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f349,f159,f155,f852]) ).
fof(f852,plain,
( spl0_66
<=> domain(b) = codomain(domain(b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f159,plain,
( spl0_25
<=> there_exists(b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f349,plain,
( domain(b) = codomain(domain(b))
| ~ spl0_24
| ~ spl0_25 ),
inference(resolution,[],[f161,f156]) ).
fof(f161,plain,
( there_exists(b)
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f850,plain,
( spl0_65
| ~ spl0_13
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f208,f182,f78,f848]) ).
fof(f848,plain,
( spl0_65
<=> ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| domain(codomain(X0)) = codomain(compose(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f208,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| domain(codomain(X0)) = codomain(compose(X0,X1)) )
| ~ spl0_13
| ~ spl0_28 ),
inference(superposition,[],[f79,f183]) ).
fof(f846,plain,
( spl0_64
| ~ spl0_13
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f190,f178,f78,f844]) ).
fof(f844,plain,
( spl0_64
<=> ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| domain(X0) = codomain(compose(domain(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f190,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| domain(X0) = codomain(compose(domain(X0),X1)) )
| ~ spl0_13
| ~ spl0_27 ),
inference(superposition,[],[f79,f179]) ).
fof(f842,plain,
( spl0_63
| ~ spl0_21
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f173,f164,f140,f840]) ).
fof(f840,plain,
( spl0_63
<=> ! [X0] :
( codomain(domain(codomain(X0))) = domain(codomain(domain(codomain(X0))))
| ~ there_exists(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f140,plain,
( spl0_21
<=> ! [X0] :
( ~ there_exists(X0)
| there_exists(domain(codomain(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f173,plain,
( ! [X0] :
( codomain(domain(codomain(X0))) = domain(codomain(domain(codomain(X0))))
| ~ there_exists(X0) )
| ~ spl0_21
| ~ spl0_26 ),
inference(resolution,[],[f165,f141]) ).
fof(f141,plain,
( ! [X0] :
( there_exists(domain(codomain(X0)))
| ~ there_exists(X0) )
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f838,plain,
( spl0_62
| ~ spl0_21
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f168,f155,f140,f836]) ).
fof(f836,plain,
( spl0_62
<=> ! [X0] :
( domain(domain(codomain(X0))) = codomain(domain(domain(codomain(X0))))
| ~ there_exists(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f168,plain,
( ! [X0] :
( domain(domain(codomain(X0))) = codomain(domain(domain(codomain(X0))))
| ~ there_exists(X0) )
| ~ spl0_21
| ~ spl0_24 ),
inference(resolution,[],[f156,f141]) ).
fof(f818,plain,
( spl0_61
| ~ spl0_11
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f261,f252,f65,f815]) ).
fof(f815,plain,
( spl0_61
<=> compose(g,a) = compose(h,compose(a,domain(compose(g,a)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f261,plain,
( compose(g,a) = compose(h,compose(a,domain(compose(g,a))))
| ~ spl0_11
| ~ spl0_31 ),
inference(superposition,[],[f253,f67]) ).
fof(f805,plain,
( ~ spl0_18
| spl0_60
| ~ spl0_15
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f130,f126,f101,f803,f120]) ).
fof(f120,plain,
( spl0_18
<=> there_exists(codomain(b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f803,plain,
( spl0_60
<=> ! [X0] :
( codomain(X0) != codomain(b)
| there_exists(compose(a,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f101,plain,
( spl0_15
<=> ! [X0,X1] :
( ~ there_exists(domain(X0))
| there_exists(compose(X0,X1))
| domain(X0) != codomain(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f130,plain,
( ! [X0] :
( codomain(X0) != codomain(b)
| there_exists(compose(a,X0))
| ~ there_exists(codomain(b)) )
| ~ spl0_15
| ~ spl0_19 ),
inference(superposition,[],[f102,f128]) ).
fof(f102,plain,
( ! [X0,X1] :
( domain(X0) != codomain(X1)
| there_exists(compose(X0,X1))
| ~ there_exists(domain(X0)) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f695,plain,
( spl0_59
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f202,f182,f693]) ).
fof(f693,plain,
( spl0_59
<=> ! [X0,X1] : compose(X0,X1) = compose(codomain(codomain(X0)),compose(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f202,plain,
( ! [X0,X1] : compose(X0,X1) = compose(codomain(codomain(X0)),compose(X0,X1))
| ~ spl0_28 ),
inference(superposition,[],[f183,f183]) ).
fof(f691,plain,
( spl0_58
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f194,f178,f689]) ).
fof(f689,plain,
( spl0_58
<=> ! [X0,X1] : compose(X0,X1) = compose(X0,compose(domain(domain(X0)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f194,plain,
( ! [X0,X1] : compose(X0,X1) = compose(X0,compose(domain(domain(X0)),X1))
| ~ spl0_27 ),
inference(forward_demodulation,[],[f187,f179]) ).
fof(f187,plain,
( ! [X0,X1] : compose(X0,compose(domain(X0),X1)) = compose(X0,compose(domain(domain(X0)),X1))
| ~ spl0_27 ),
inference(superposition,[],[f179,f179]) ).
fof(f681,plain,
( spl0_57
| ~ spl0_11
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f240,f226,f65,f679]) ).
fof(f679,plain,
( spl0_57
<=> ! [X0] :
( ~ there_exists(compose(X0,compose(g,a)))
| there_exists(domain(compose(X0,h))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f240,plain,
( ! [X0] :
( ~ there_exists(compose(X0,compose(g,a)))
| there_exists(domain(compose(X0,h))) )
| ~ spl0_11
| ~ spl0_30 ),
inference(superposition,[],[f227,f67]) ).
fof(f628,plain,
( spl0_56
| ~ spl0_10
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f237,f226,f60,f626]) ).
fof(f626,plain,
( spl0_56
<=> ! [X0,X1] :
( ~ there_exists(compose(X1,X0))
| there_exists(domain(compose(X1,codomain(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f237,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X1,X0))
| there_exists(domain(compose(X1,codomain(X0)))) )
| ~ spl0_10
| ~ spl0_30 ),
inference(superposition,[],[f227,f61]) ).
fof(f624,plain,
( spl0_55
| ~ spl0_20
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f172,f164,f134,f622]) ).
fof(f622,plain,
( spl0_55
<=> ! [X0] :
( codomain(domain(X0)) = domain(codomain(domain(X0)))
| ~ there_exists(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f134,plain,
( spl0_20
<=> ! [X0] :
( ~ there_exists(X0)
| there_exists(domain(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f172,plain,
( ! [X0] :
( codomain(domain(X0)) = domain(codomain(domain(X0)))
| ~ there_exists(X0) )
| ~ spl0_20
| ~ spl0_26 ),
inference(resolution,[],[f165,f135]) ).
fof(f135,plain,
( ! [X0] :
( there_exists(domain(X0))
| ~ there_exists(X0) )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f620,plain,
( spl0_54
| ~ spl0_20
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f167,f155,f134,f618]) ).
fof(f618,plain,
( spl0_54
<=> ! [X0] :
( domain(domain(X0)) = codomain(domain(domain(X0)))
| ~ there_exists(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f167,plain,
( ! [X0] :
( domain(domain(X0)) = codomain(domain(domain(X0)))
| ~ there_exists(X0) )
| ~ spl0_20
| ~ spl0_24 ),
inference(resolution,[],[f156,f135]) ).
fof(f616,plain,
( spl0_53
| ~ spl0_3
| ~ spl0_26
| ~ spl0_35
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f510,f490,f351,f164,f30,f613]) ).
fof(f613,plain,
( spl0_53
<=> there_exists(codomain(a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f30,plain,
( spl0_3
<=> there_exists(compose(a,b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f490,plain,
( spl0_46
<=> ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| there_exists(domain(codomain(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f510,plain,
( there_exists(codomain(a))
| ~ spl0_3
| ~ spl0_26
| ~ spl0_35
| ~ spl0_46 ),
inference(forward_demodulation,[],[f498,f355]) ).
fof(f498,plain,
( there_exists(domain(codomain(a)))
| ~ spl0_3
| ~ spl0_46 ),
inference(resolution,[],[f491,f32]) ).
fof(f32,plain,
( there_exists(compose(a,b))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f30]) ).
fof(f491,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| there_exists(domain(codomain(X0))) )
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f490]) ).
fof(f561,plain,
( spl0_52
| ~ spl0_11
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f204,f182,f65,f558]) ).
fof(f558,plain,
( spl0_52
<=> compose(g,a) = compose(codomain(h),compose(g,a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f204,plain,
( compose(g,a) = compose(codomain(h),compose(g,a))
| ~ spl0_11
| ~ spl0_28 ),
inference(superposition,[],[f183,f67]) ).
fof(f556,plain,
( spl0_51
| ~ spl0_19
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f185,f178,f126,f554]) ).
fof(f554,plain,
( spl0_51
<=> ! [X0] : compose(a,X0) = compose(a,compose(codomain(b),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f185,plain,
( ! [X0] : compose(a,X0) = compose(a,compose(codomain(b),X0))
| ~ spl0_19
| ~ spl0_27 ),
inference(superposition,[],[f179,f128]) ).
fof(f551,plain,
( spl0_50
| ~ spl0_3
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f175,f164,f30,f548]) ).
fof(f548,plain,
( spl0_50
<=> codomain(compose(a,b)) = domain(codomain(compose(a,b))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f175,plain,
( codomain(compose(a,b)) = domain(codomain(compose(a,b)))
| ~ spl0_3
| ~ spl0_26 ),
inference(resolution,[],[f165,f32]) ).
fof(f546,plain,
( spl0_49
| ~ spl0_3
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f170,f155,f30,f543]) ).
fof(f543,plain,
( spl0_49
<=> domain(compose(a,b)) = codomain(domain(compose(a,b))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f170,plain,
( domain(compose(a,b)) = codomain(domain(compose(a,b)))
| ~ spl0_3
| ~ spl0_24 ),
inference(resolution,[],[f156,f32]) ).
fof(f515,plain,
( spl0_48
| ~ spl0_9
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f255,f252,f56,f513]) ).
fof(f513,plain,
( spl0_48
<=> ! [X0] : compose(X0,compose(domain(X0),domain(X0))) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f255,plain,
( ! [X0] : compose(X0,compose(domain(X0),domain(X0))) = X0
| ~ spl0_9
| ~ spl0_31 ),
inference(superposition,[],[f253,f57]) ).
fof(f497,plain,
( spl0_47
| ~ spl0_25
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f348,f164,f159,f494]) ).
fof(f494,plain,
( spl0_47
<=> codomain(b) = domain(codomain(b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f348,plain,
( codomain(b) = domain(codomain(b))
| ~ spl0_25
| ~ spl0_26 ),
inference(resolution,[],[f161,f165]) ).
fof(f492,plain,
( spl0_46
| ~ spl0_12
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f209,f182,f70,f490]) ).
fof(f70,plain,
( spl0_12
<=> ! [X0,X1] :
( there_exists(domain(X0))
| ~ there_exists(compose(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f209,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| there_exists(domain(codomain(X0))) )
| ~ spl0_12
| ~ spl0_28 ),
inference(superposition,[],[f71,f183]) ).
fof(f71,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| there_exists(domain(X0)) )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f487,plain,
( spl0_45
| ~ spl0_18
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f174,f164,f120,f484]) ).
fof(f484,plain,
( spl0_45
<=> codomain(codomain(b)) = domain(codomain(codomain(b))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f174,plain,
( codomain(codomain(b)) = domain(codomain(codomain(b)))
| ~ spl0_18
| ~ spl0_26 ),
inference(resolution,[],[f165,f122]) ).
fof(f122,plain,
( there_exists(codomain(b))
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f481,plain,
( spl0_44
| ~ spl0_18
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f169,f155,f120,f478]) ).
fof(f478,plain,
( spl0_44
<=> domain(codomain(b)) = codomain(domain(codomain(b))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f169,plain,
( domain(codomain(b)) = codomain(domain(codomain(b)))
| ~ spl0_18
| ~ spl0_24 ),
inference(resolution,[],[f156,f122]) ).
fof(f433,plain,
( spl0_43
| ~ spl0_10
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f201,f182,f60,f431]) ).
fof(f431,plain,
( spl0_43
<=> ! [X0] : compose(codomain(codomain(X0)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f201,plain,
( ! [X0] : compose(codomain(codomain(X0)),X0) = X0
| ~ spl0_10
| ~ spl0_28 ),
inference(superposition,[],[f183,f61]) ).
fof(f429,plain,
( spl0_42
| ~ spl0_9
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f193,f178,f56,f427]) ).
fof(f427,plain,
( spl0_42
<=> ! [X0] : compose(X0,domain(domain(X0))) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f193,plain,
( ! [X0] : compose(X0,domain(domain(X0))) = X0
| ~ spl0_9
| ~ spl0_27 ),
inference(forward_demodulation,[],[f186,f57]) ).
fof(f186,plain,
( ! [X0] : compose(X0,domain(X0)) = compose(X0,domain(domain(X0)))
| ~ spl0_9
| ~ spl0_27 ),
inference(superposition,[],[f179,f57]) ).
fof(f417,plain,
( spl0_41
| ~ spl0_28
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f326,f319,f182,f414]) ).
fof(f414,plain,
( spl0_41
<=> codomain(a) = codomain(compose(a,b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f384,plain,
( spl0_40
| ~ spl0_2
| ~ spl0_22
| ~ spl0_24
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f233,f164,f155,f145,f25,f381]) ).
fof(f381,plain,
( spl0_40
<=> domain(h) = domain(domain(h)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f25,plain,
( spl0_2
<=> there_exists(h) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f145,plain,
( spl0_22
<=> there_exists(domain(h)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f233,plain,
( domain(h) = domain(domain(h))
| ~ spl0_2
| ~ spl0_22
| ~ spl0_24
| ~ spl0_26 ),
inference(forward_demodulation,[],[f231,f171]) ).
fof(f171,plain,
( domain(h) = codomain(domain(h))
| ~ spl0_2
| ~ spl0_24 ),
inference(resolution,[],[f156,f27]) ).
fof(f27,plain,
( there_exists(h)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f25]) ).
fof(f231,plain,
( codomain(domain(h)) = domain(codomain(domain(h)))
| ~ spl0_22
| ~ spl0_26 ),
inference(resolution,[],[f147,f165]) ).
fof(f147,plain,
( there_exists(domain(h))
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f379,plain,
( spl0_39
| ~ spl0_2
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f176,f164,f25,f376]) ).
fof(f376,plain,
( spl0_39
<=> codomain(h) = domain(codomain(h)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f176,plain,
( codomain(h) = domain(codomain(h))
| ~ spl0_2
| ~ spl0_26 ),
inference(resolution,[],[f165,f27]) ).
fof(f374,plain,
( spl0_38
| ~ spl0_2
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f171,f155,f25,f371]) ).
fof(f371,plain,
( spl0_38
<=> domain(h) = codomain(domain(h)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f369,plain,
( spl0_37
| ~ spl0_9
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f131,f126,f56,f366]) ).
fof(f366,plain,
( spl0_37
<=> a = compose(a,codomain(b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f131,plain,
( a = compose(a,codomain(b))
| ~ spl0_9
| ~ spl0_19 ),
inference(superposition,[],[f57,f128]) ).
fof(f361,plain,
( spl0_36
| ~ spl0_5
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f143,f140,f39,f359]) ).
fof(f359,plain,
( spl0_36
<=> ! [X0] :
( ~ there_exists(X0)
| there_exists(codomain(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f39,plain,
( spl0_5
<=> ! [X0] :
( there_exists(X0)
| ~ there_exists(domain(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f143,plain,
( ! [X0] :
( ~ there_exists(X0)
| there_exists(codomain(X0)) )
| ~ spl0_5
| ~ spl0_21 ),
inference(resolution,[],[f141,f40]) ).
fof(f40,plain,
( ! [X0] :
( ~ there_exists(domain(X0))
| there_exists(X0) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f354,plain,
( spl0_35
| ~ spl0_18
| ~ spl0_5
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f132,f126,f39,f120,f351]) ).
fof(f132,plain,
( ~ there_exists(codomain(b))
| there_exists(a)
| ~ spl0_5
| ~ spl0_19 ),
inference(superposition,[],[f40,f128]) ).
fof(f332,plain,
( spl0_34
| ~ spl0_14
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f109,f105,f86,f330]) ).
fof(f330,plain,
( spl0_34
<=> ! [X2,X0,X1] :
( compose(X2,compose(a,b)) != compose(X0,compose(X1,compose(a,b)))
| compose(X0,X1) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f86,plain,
( spl0_14
<=> ! [X2,X0,X1] : compose(X0,compose(X1,X2)) = compose(compose(X0,X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f109,plain,
( ! [X2,X0,X1] :
( compose(X2,compose(a,b)) != compose(X0,compose(X1,compose(a,b)))
| compose(X0,X1) = X2 )
| ~ spl0_14
| ~ spl0_16 ),
inference(superposition,[],[f106,f87]) ).
fof(f87,plain,
( ! [X2,X0,X1] : compose(X0,compose(X1,X2)) = compose(compose(X0,X1),X2)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f321,plain,
( spl0_33
| ~ spl0_10
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f108,f105,f60,f319]) ).
fof(f108,plain,
( ! [X0] :
( compose(a,b) != compose(X0,compose(a,b))
| codomain(compose(a,b)) = X0 )
| ~ spl0_10
| ~ spl0_16 ),
inference(superposition,[],[f106,f61]) ).
fof(f299,plain,
( spl0_32
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f95,f86,f78,f297]) ).
fof(f95,plain,
( ! [X2,X0,X1] :
( ~ there_exists(compose(X0,compose(X1,X2)))
| domain(compose(X0,X1)) = codomain(X2) )
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f79,f87]) ).
fof(f254,plain,
( spl0_31
| ~ spl0_9
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f93,f86,f56,f252]) ).
fof(f93,plain,
( ! [X0,X1] : compose(X0,X1) = compose(X0,compose(X1,domain(compose(X0,X1))))
| ~ spl0_9
| ~ spl0_14 ),
inference(superposition,[],[f87,f57]) ).
fof(f229,plain,
( ~ spl0_2
| ~ spl0_20
| spl0_22 ),
inference(avatar_split_clause,[],[f153,f145,f134,f25]) ).
fof(f153,plain,
( ~ there_exists(h)
| ~ spl0_20
| spl0_22 ),
inference(resolution,[],[f146,f135]) ).
fof(f146,plain,
( ~ there_exists(domain(h))
| spl0_22 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f228,plain,
( spl0_30
| ~ spl0_12
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f96,f86,f70,f226]) ).
fof(f96,plain,
( ! [X2,X0,X1] :
( ~ there_exists(compose(X0,compose(X1,X2)))
| there_exists(domain(compose(X0,X1))) )
| ~ spl0_12
| ~ spl0_14 ),
inference(superposition,[],[f71,f87]) ).
fof(f214,plain,
( spl0_29
| ~ spl0_11
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f99,f86,f65,f212]) ).
fof(f99,plain,
( ! [X0] : compose(h,compose(a,X0)) = compose(g,compose(a,X0))
| ~ spl0_11
| ~ spl0_14 ),
inference(forward_demodulation,[],[f92,f87]) ).
fof(f92,plain,
( ! [X0] : compose(h,compose(a,X0)) = compose(compose(g,a),X0)
| ~ spl0_11
| ~ spl0_14 ),
inference(superposition,[],[f87,f67]) ).
fof(f184,plain,
( spl0_28
| ~ spl0_10
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f90,f86,f60,f182]) ).
fof(f90,plain,
( ! [X0,X1] : compose(X0,X1) = compose(codomain(X0),compose(X0,X1))
| ~ spl0_10
| ~ spl0_14 ),
inference(superposition,[],[f87,f61]) ).
fof(f180,plain,
( spl0_27
| ~ spl0_9
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f89,f86,f56,f178]) ).
fof(f89,plain,
( ! [X0,X1] : compose(X0,X1) = compose(X0,compose(domain(X0),X1))
| ~ spl0_9
| ~ spl0_14 ),
inference(superposition,[],[f87,f57]) ).
fof(f166,plain,
( spl0_26
| ~ spl0_10
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f83,f78,f60,f164]) ).
fof(f83,plain,
( ! [X0] :
( ~ there_exists(X0)
| codomain(X0) = domain(codomain(X0)) )
| ~ spl0_10
| ~ spl0_13 ),
inference(superposition,[],[f79,f61]) ).
fof(f162,plain,
( spl0_25
| ~ spl0_6
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f124,f120,f43,f159]) ).
fof(f43,plain,
( spl0_6
<=> ! [X0] :
( there_exists(X0)
| ~ there_exists(codomain(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f124,plain,
( there_exists(b)
| ~ spl0_6
| ~ spl0_18 ),
inference(resolution,[],[f122,f44]) ).
fof(f44,plain,
( ! [X0] :
( ~ there_exists(codomain(X0))
| there_exists(X0) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f157,plain,
( spl0_24
| ~ spl0_9
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f82,f78,f56,f155]) ).
fof(f82,plain,
( ! [X0] :
( ~ there_exists(X0)
| domain(X0) = codomain(domain(X0)) )
| ~ spl0_9
| ~ spl0_13 ),
inference(superposition,[],[f79,f57]) ).
fof(f152,plain,
( spl0_22
| ~ spl0_23
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f76,f70,f65,f149,f145]) ).
fof(f149,plain,
( spl0_23
<=> there_exists(compose(g,a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f76,plain,
( ~ there_exists(compose(g,a))
| there_exists(domain(h))
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f71,f67]) ).
fof(f142,plain,
( spl0_21
| ~ spl0_10
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f75,f70,f60,f140]) ).
fof(f75,plain,
( ! [X0] :
( ~ there_exists(X0)
| there_exists(domain(codomain(X0))) )
| ~ spl0_10
| ~ spl0_12 ),
inference(superposition,[],[f71,f61]) ).
fof(f136,plain,
( spl0_20
| ~ spl0_9
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f74,f70,f56,f134]) ).
fof(f74,plain,
( ! [X0] :
( ~ there_exists(X0)
| there_exists(domain(X0)) )
| ~ spl0_9
| ~ spl0_12 ),
inference(superposition,[],[f71,f57]) ).
fof(f129,plain,
( spl0_19
| ~ spl0_3
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f81,f78,f30,f126]) ).
fof(f81,plain,
( domain(a) = codomain(b)
| ~ spl0_3
| ~ spl0_13 ),
inference(resolution,[],[f79,f32]) ).
fof(f123,plain,
( spl0_18
| ~ spl0_3
| ~ spl0_13
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f118,f114,f78,f30,f120]) ).
fof(f114,plain,
( spl0_17
<=> there_exists(domain(a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f118,plain,
( there_exists(codomain(b))
| ~ spl0_3
| ~ spl0_13
| ~ spl0_17 ),
inference(forward_demodulation,[],[f116,f81]) ).
fof(f116,plain,
( there_exists(domain(a))
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f117,plain,
( spl0_17
| ~ spl0_3
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f73,f70,f30,f114]) ).
fof(f73,plain,
( there_exists(domain(a))
| ~ spl0_3
| ~ spl0_12 ),
inference(resolution,[],[f71,f32]) ).
fof(f107,plain,
spl0_16,
inference(avatar_split_clause,[],[f17,f105]) ).
fof(f17,plain,
! [X2,X0] :
( X0 = X2
| compose(X0,compose(a,b)) != compose(X2,compose(a,b)) ),
inference(equality_resolution,[],[f13]) ).
fof(f13,axiom,
! [X2,X0,X1] :
( X0 = X2
| compose(X2,compose(a,b)) != X1
| compose(X0,compose(a,b)) != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',epimorphism) ).
fof(f103,plain,
spl0_15,
inference(avatar_split_clause,[],[f8,f101]) ).
fof(f8,axiom,
! [X0,X1] :
( ~ there_exists(domain(X0))
| there_exists(compose(X0,X1))
| domain(X0) != codomain(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_codomain_composition2) ).
fof(f88,plain,
spl0_14,
inference(avatar_split_clause,[],[f9,f86]) ).
fof(f9,axiom,
! [X2,X0,X1] : compose(X0,compose(X1,X2)) = compose(compose(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_compose) ).
fof(f80,plain,
spl0_13,
inference(avatar_split_clause,[],[f7,f78]) ).
fof(f7,axiom,
! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| domain(X0) = codomain(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_codomain_composition1) ).
fof(f72,plain,
spl0_12,
inference(avatar_split_clause,[],[f6,f70]) ).
fof(f6,axiom,
! [X0,X1] :
( there_exists(domain(X0))
| ~ there_exists(compose(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_implies_domain) ).
fof(f68,plain,
spl0_11,
inference(avatar_split_clause,[],[f15,f65]) ).
fof(f15,axiom,
compose(h,a) = compose(g,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ha_equals_ga) ).
fof(f62,plain,
spl0_10,
inference(avatar_split_clause,[],[f11,f60]) ).
fof(f11,axiom,
! [X0] : compose(codomain(X0),X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_codomain) ).
fof(f58,plain,
spl0_9,
inference(avatar_split_clause,[],[f10,f56]) ).
fof(f10,axiom,
! [X0] : compose(X0,domain(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_domain) ).
fof(f54,plain,
spl0_8,
inference(avatar_split_clause,[],[f2,f52]) ).
fof(f52,plain,
( spl0_8
<=> ! [X0,X1] :
( ~ equivalent(X0,X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f2,axiom,
! [X0,X1] :
( ~ equivalent(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_implies_existence2) ).
fof(f49,plain,
spl0_7,
inference(avatar_split_clause,[],[f18,f47]) ).
fof(f47,plain,
( spl0_7
<=> ! [X1] :
( ~ there_exists(X1)
| equivalent(X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f18,plain,
! [X1] :
( ~ there_exists(X1)
| equivalent(X1,X1) ),
inference(equality_resolution,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] :
( ~ there_exists(X0)
| X0 != X1
| equivalent(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_and_equality_implies_equivalence1) ).
fof(f45,plain,
spl0_6,
inference(avatar_split_clause,[],[f5,f43]) ).
fof(f5,axiom,
! [X0] :
( there_exists(X0)
| ~ there_exists(codomain(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_has_elements) ).
fof(f41,plain,
spl0_5,
inference(avatar_split_clause,[],[f4,f39]) ).
fof(f4,axiom,
! [X0] :
( there_exists(X0)
| ~ there_exists(domain(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_has_elements) ).
fof(f37,plain,
spl0_4,
inference(avatar_split_clause,[],[f1,f35]) ).
fof(f35,plain,
( spl0_4
<=> ! [X0,X1] :
( there_exists(X0)
| ~ equivalent(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f1,axiom,
! [X0,X1] :
( there_exists(X0)
| ~ equivalent(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_implies_existence1) ).
fof(f33,plain,
spl0_3,
inference(avatar_split_clause,[],[f12,f30]) ).
fof(f12,axiom,
there_exists(compose(a,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assume_ab_exists) ).
fof(f28,plain,
spl0_2,
inference(avatar_split_clause,[],[f14,f25]) ).
fof(f14,axiom,
there_exists(h),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assume_h_exists) ).
fof(f23,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f16,f20]) ).
fof(f16,axiom,
h != g,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_g_equals_h) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : CAT003-4 : TPTP v8.1.2. Released v1.0.0.
% 0.08/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.36 % Computer : n026.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Fri May 3 18:12:38 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.16/0.36 % (19577)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.38 % (19581)WARNING: value z3 for option sas not known
% 0.16/0.38 % (19580)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.38 % (19579)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.38 % (19582)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.38 % (19581)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)
% 0.16/0.38 % (19585)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)
% 0.16/0.38 % (19586)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)
% 0.16/0.38 % (19583)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)
% 0.16/0.38 TRYING [1]
% 0.16/0.38 TRYING [2]
% 0.16/0.39 TRYING [3]
% 0.16/0.39 TRYING [1]
% 0.16/0.39 TRYING [2]
% 0.16/0.39 TRYING [4]
% 0.16/0.39 TRYING [3]
% 0.22/0.41 TRYING [5]
% 0.22/0.41 TRYING [4]
% 0.22/0.42 % (19583)First to succeed.
% 0.22/0.42 % (19583)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-19577"
% 0.22/0.43 % (19583)Refutation found. Thanks to Tanya!
% 0.22/0.43 % SZS status Unsatisfiable for theBenchmark
% 0.22/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.43 % (19583)------------------------------
% 0.22/0.43 % (19583)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.43 % (19583)Termination reason: Refutation
% 0.22/0.43
% 0.22/0.43 % (19583)Memory used [KB]: 1344
% 0.22/0.43 % (19583)Time elapsed: 0.044 s
% 0.22/0.43 % (19583)Instructions burned: 61 (million)
% 0.22/0.43 % (19577)Success in time 0.06 s
%------------------------------------------------------------------------------