TSTP Solution File: CAT003-3 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : CAT003-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n017.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 04:43:42 EDT 2024
% Result : Unsatisfiable 0.21s 0.45s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 139
% Syntax : Number of formulae : 419 ( 28 unt; 0 def)
% Number of atoms : 1206 ( 257 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 1398 ( 611 ~; 668 |; 0 &)
% ( 119 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 123 ( 121 usr; 120 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 329 ( 329 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2278,plain,
$false,
inference(avatar_sat_refutation,[],[f32,f37,f42,f46,f50,f54,f58,f62,f68,f72,f76,f82,f86,f90,f94,f106,f114,f131,f136,f140,f152,f162,f167,f174,f179,f186,f190,f197,f201,f208,f217,f222,f226,f248,f252,f256,f263,f313,f328,f332,f374,f422,f446,f457,f473,f483,f488,f493,f498,f534,f548,f552,f556,f609,f615,f621,f627,f632,f636,f641,f680,f688,f724,f729,f734,f739,f744,f809,f813,f817,f821,f825,f829,f860,f979,f983,f1003,f1016,f1131,f1143,f1171,f1178,f1182,f1218,f1228,f1250,f1255,f1260,f1295,f1299,f1303,f1307,f1311,f1315,f1321,f1325,f1329,f1333,f1337,f1341,f1345,f1349,f1353,f1357,f1687,f1911,f1915,f1919,f1923,f1937,f1946,f2030,f2048,f2052,f2191,f2195,f2276,f2277]) ).
fof(f2277,plain,
( spl0_1
| ~ spl0_117 ),
inference(avatar_split_clause,[],[f2202,f2189,f29]) ).
fof(f29,plain,
( spl0_1
<=> h = g ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f2189,plain,
( spl0_117
<=> ! [X0] :
( compose(X0,compose(a,b)) != compose(g,compose(a,b))
| h = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f2202,plain,
( h = g
| ~ spl0_117 ),
inference(equality_resolution,[],[f2190]) ).
fof(f2190,plain,
( ! [X0] :
( compose(X0,compose(a,b)) != compose(g,compose(a,b))
| h = X0 )
| ~ spl0_117 ),
inference(avatar_component_clause,[],[f2189]) ).
fof(f2276,plain,
( spl0_119
| ~ spl0_34
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f292,f254,f224,f2274]) ).
fof(f2274,plain,
( spl0_119
<=> ! [X0,X1] :
( X0 = X1
| f1(X0,X1) = X1
| codomain(X0) = domain(codomain(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f224,plain,
( spl0_34
<=> ! [X0] :
( ~ there_exists(X0)
| codomain(X0) = domain(codomain(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f254,plain,
( spl0_37
<=> ! [X0,X1] :
( there_exists(X0)
| X0 = X1
| f1(X0,X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f292,plain,
( ! [X0,X1] :
( X0 = X1
| f1(X0,X1) = X1
| codomain(X0) = domain(codomain(X0)) )
| ~ spl0_34
| ~ spl0_37 ),
inference(resolution,[],[f255,f225]) ).
fof(f225,plain,
( ! [X0] :
( ~ there_exists(X0)
| codomain(X0) = domain(codomain(X0)) )
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f224]) ).
fof(f255,plain,
( ! [X0,X1] :
( there_exists(X0)
| X0 = X1
| f1(X0,X1) = X1 )
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f2195,plain,
( spl0_118
| ~ spl0_36
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f318,f311,f250,f2193]) ).
fof(f2193,plain,
( spl0_118
<=> ! [X0] : compose(g,compose(a,X0)) = compose(codomain(h),compose(g,compose(a,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f250,plain,
( spl0_36
<=> ! [X0,X1] : compose(X0,X1) = compose(codomain(X0),compose(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f311,plain,
( spl0_39
<=> ! [X0] : compose(h,compose(a,X0)) = compose(g,compose(a,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f318,plain,
( ! [X0] : compose(g,compose(a,X0)) = compose(codomain(h),compose(g,compose(a,X0)))
| ~ spl0_36
| ~ spl0_39 ),
inference(superposition,[],[f251,f312]) ).
fof(f312,plain,
( ! [X0] : compose(h,compose(a,X0)) = compose(g,compose(a,X0))
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f311]) ).
fof(f251,plain,
( ! [X0,X1] : compose(X0,X1) = compose(codomain(X0),compose(X0,X1))
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f2191,plain,
( spl0_117
| ~ spl0_21
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f316,f311,f150,f2189]) ).
fof(f150,plain,
( spl0_21
<=> ! [X2,X0] :
( X0 = X2
| compose(X0,compose(a,b)) != compose(X2,compose(a,b)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f316,plain,
( ! [X0] :
( compose(X0,compose(a,b)) != compose(g,compose(a,b))
| h = X0 )
| ~ spl0_21
| ~ spl0_39 ),
inference(superposition,[],[f151,f312]) ).
fof(f151,plain,
( ! [X2,X0] :
( compose(X0,compose(a,b)) != compose(X2,compose(a,b))
| X0 = X2 )
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f2052,plain,
( spl0_116
| ~ spl0_35
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f415,f372,f246,f2050]) ).
fof(f2050,plain,
( spl0_116
<=> ! [X0,X1] : compose(X0,X1) = compose(X0,compose(X1,domain(compose(domain(X0),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f246,plain,
( spl0_35
<=> ! [X0,X1] : compose(X0,X1) = compose(X0,compose(domain(X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f372,plain,
( spl0_42
<=> ! [X0,X1] : compose(X0,X1) = compose(X0,compose(X1,domain(compose(X0,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f415,plain,
( ! [X0,X1] : compose(X0,X1) = compose(X0,compose(X1,domain(compose(domain(X0),X1))))
| ~ spl0_35
| ~ spl0_42 ),
inference(forward_demodulation,[],[f398,f247]) ).
fof(f247,plain,
( ! [X0,X1] : compose(X0,X1) = compose(X0,compose(domain(X0),X1))
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f398,plain,
( ! [X0,X1] : compose(X0,compose(domain(X0),X1)) = compose(X0,compose(X1,domain(compose(domain(X0),X1))))
| ~ spl0_35
| ~ spl0_42 ),
inference(superposition,[],[f247,f373]) ).
fof(f373,plain,
( ! [X0,X1] : compose(X0,X1) = compose(X0,compose(X1,domain(compose(X0,X1))))
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f372]) ).
fof(f2048,plain,
( spl0_115
| ~ spl0_15
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f243,f224,f92,f2046]) ).
fof(f2046,plain,
( spl0_115
<=> ! [X0,X1] :
( codomain(f1(X0,X1)) = domain(codomain(f1(X0,X1)))
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f92,plain,
( spl0_15
<=> ! [X0,X1] :
( X0 = X1
| there_exists(f1(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f243,plain,
( ! [X0,X1] :
( codomain(f1(X0,X1)) = domain(codomain(f1(X0,X1)))
| X0 = X1 )
| ~ spl0_15
| ~ spl0_34 ),
inference(resolution,[],[f225,f93]) ).
fof(f93,plain,
( ! [X0,X1] :
( there_exists(f1(X0,X1))
| X0 = X1 )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f2030,plain,
( spl0_114
| ~ spl0_15
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f234,f220,f92,f2028]) ).
fof(f2028,plain,
( spl0_114
<=> ! [X0,X1] :
( domain(f1(X0,X1)) = codomain(domain(f1(X0,X1)))
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f220,plain,
( spl0_33
<=> ! [X0] :
( ~ there_exists(X0)
| domain(X0) = codomain(domain(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f234,plain,
( ! [X0,X1] :
( domain(f1(X0,X1)) = codomain(domain(f1(X0,X1)))
| X0 = X1 )
| ~ spl0_15
| ~ spl0_33 ),
inference(resolution,[],[f221,f93]) ).
fof(f221,plain,
( ! [X0] :
( ~ there_exists(X0)
| domain(X0) = codomain(domain(X0)) )
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f220]) ).
fof(f1946,plain,
( ~ spl0_112
| spl0_113
| ~ spl0_36
| ~ spl0_39
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f453,f444,f311,f250,f1943,f1939]) ).
fof(f1939,plain,
( spl0_112
<=> compose(a,b) = compose(g,compose(a,b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f1943,plain,
( spl0_113
<=> h = codomain(a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f444,plain,
( spl0_44
<=> ! [X0] :
( compose(a,b) != compose(X0,compose(a,b))
| codomain(compose(a,b)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f453,plain,
( h = codomain(a)
| compose(a,b) != compose(g,compose(a,b))
| ~ spl0_36
| ~ spl0_39
| ~ spl0_44 ),
inference(forward_demodulation,[],[f450,f451]) ).
fof(f451,plain,
( codomain(a) = codomain(compose(a,b))
| ~ spl0_36
| ~ spl0_44 ),
inference(trivial_inequality_removal,[],[f447]) ).
fof(f447,plain,
( compose(a,b) != compose(a,b)
| codomain(a) = codomain(compose(a,b))
| ~ spl0_36
| ~ spl0_44 ),
inference(superposition,[],[f445,f251]) ).
fof(f445,plain,
( ! [X0] :
( compose(a,b) != compose(X0,compose(a,b))
| codomain(compose(a,b)) = X0 )
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f444]) ).
fof(f450,plain,
( compose(a,b) != compose(g,compose(a,b))
| h = codomain(compose(a,b))
| ~ spl0_39
| ~ spl0_44 ),
inference(superposition,[],[f445,f312]) ).
fof(f1937,plain,
( spl0_111
| ~ spl0_12
| ~ spl0_43 ),
inference(avatar_split_clause,[],[f431,f420,f79,f1935]) ).
fof(f1935,plain,
( spl0_111
<=> ! [X0] :
( ~ there_exists(compose(X0,compose(g,a)))
| codomain(a) = domain(compose(X0,h)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f79,plain,
( spl0_12
<=> compose(h,a) = compose(g,a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f420,plain,
( spl0_43
<=> ! [X2,X0,X1] :
( ~ there_exists(compose(X0,compose(X1,X2)))
| domain(compose(X0,X1)) = codomain(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f431,plain,
( ! [X0] :
( ~ there_exists(compose(X0,compose(g,a)))
| codomain(a) = domain(compose(X0,h)) )
| ~ spl0_12
| ~ spl0_43 ),
inference(superposition,[],[f421,f81]) ).
fof(f81,plain,
( compose(h,a) = compose(g,a)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f421,plain,
( ! [X2,X0,X1] :
( ~ there_exists(compose(X0,compose(X1,X2)))
| domain(compose(X0,X1)) = codomain(X2) )
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f420]) ).
fof(f1923,plain,
( spl0_110
| ~ spl0_39
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f361,f330,f311,f1921]) ).
fof(f1921,plain,
( spl0_110
<=> ! [X0,X1] :
( ~ there_exists(compose(X1,compose(g,compose(a,X0))))
| there_exists(domain(compose(X1,h))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f330,plain,
( spl0_41
<=> ! [X2,X0,X1] :
( ~ there_exists(compose(X0,compose(X1,X2)))
| there_exists(domain(compose(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f361,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X1,compose(g,compose(a,X0))))
| there_exists(domain(compose(X1,h))) )
| ~ spl0_39
| ~ spl0_41 ),
inference(superposition,[],[f331,f312]) ).
fof(f331,plain,
( ! [X2,X0,X1] :
( ~ there_exists(compose(X0,compose(X1,X2)))
| there_exists(domain(compose(X0,X1))) )
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f330]) ).
fof(f1919,plain,
( spl0_109
| ~ spl0_39
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f341,f326,f311,f1917]) ).
fof(f1917,plain,
( spl0_109
<=> ! [X0,X1] :
( ~ there_exists(compose(X1,compose(g,compose(a,X0))))
| there_exists(codomain(compose(X1,h))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f326,plain,
( spl0_40
<=> ! [X2,X0,X1] :
( ~ there_exists(compose(X0,compose(X1,X2)))
| there_exists(codomain(compose(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f341,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X1,compose(g,compose(a,X0))))
| there_exists(codomain(compose(X1,h))) )
| ~ spl0_39
| ~ spl0_40 ),
inference(superposition,[],[f327,f312]) ).
fof(f327,plain,
( ! [X2,X0,X1] :
( ~ there_exists(compose(X0,compose(X1,X2)))
| there_exists(codomain(compose(X0,X1))) )
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f326]) ).
fof(f1915,plain,
( spl0_108
| ~ spl0_16
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f320,f311,f104,f1913]) ).
fof(f1913,plain,
( spl0_108
<=> ! [X0] :
( ~ there_exists(compose(g,compose(a,X0)))
| domain(h) = codomain(compose(a,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f104,plain,
( spl0_16
<=> ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| domain(X0) = codomain(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f320,plain,
( ! [X0] :
( ~ there_exists(compose(g,compose(a,X0)))
| domain(h) = codomain(compose(a,X0)) )
| ~ spl0_16
| ~ spl0_39 ),
inference(superposition,[],[f105,f312]) ).
fof(f105,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| domain(X0) = codomain(X1) )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f1911,plain,
( spl0_107
| ~ spl0_21
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f285,f250,f150,f1909]) ).
fof(f1909,plain,
( spl0_107
<=> ! [X0] :
( compose(a,b) != compose(X0,compose(a,b))
| codomain(a) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f285,plain,
( ! [X0] :
( compose(a,b) != compose(X0,compose(a,b))
| codomain(a) = X0 )
| ~ spl0_21
| ~ spl0_36 ),
inference(superposition,[],[f151,f251]) ).
fof(f1687,plain,
( spl0_106
| ~ spl0_33
| ~ spl0_48
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f684,f674,f490,f220,f1684]) ).
fof(f1684,plain,
( spl0_106
<=> codomain(h) = codomain(codomain(h)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f490,plain,
( spl0_48
<=> codomain(h) = domain(codomain(h)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f674,plain,
( spl0_61
<=> there_exists(codomain(h)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f684,plain,
( codomain(h) = codomain(codomain(h))
| ~ spl0_33
| ~ spl0_48
| ~ spl0_61 ),
inference(forward_demodulation,[],[f683,f492]) ).
fof(f492,plain,
( codomain(h) = domain(codomain(h))
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f490]) ).
fof(f683,plain,
( domain(codomain(h)) = codomain(domain(codomain(h)))
| ~ spl0_33
| ~ spl0_61 ),
inference(resolution,[],[f676,f221]) ).
fof(f676,plain,
( there_exists(codomain(h))
| ~ spl0_61 ),
inference(avatar_component_clause,[],[f674]) ).
fof(f1357,plain,
( spl0_105
| ~ spl0_11
| ~ spl0_43 ),
inference(avatar_split_clause,[],[f428,f420,f74,f1355]) ).
fof(f1355,plain,
( spl0_105
<=> ! [X0,X1] :
( ~ there_exists(compose(X1,X0))
| codomain(X0) = domain(compose(X1,codomain(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f74,plain,
( spl0_11
<=> ! [X0] : compose(codomain(X0),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f428,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X1,X0))
| codomain(X0) = domain(compose(X1,codomain(X0))) )
| ~ spl0_11
| ~ spl0_43 ),
inference(superposition,[],[f421,f75]) ).
fof(f75,plain,
( ! [X0] : compose(codomain(X0),X0) = X0
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f1353,plain,
( spl0_104
| ~ spl0_10
| ~ spl0_43 ),
inference(avatar_split_clause,[],[f425,f420,f70,f1351]) ).
fof(f1351,plain,
( spl0_104
<=> ! [X0,X1] :
( ~ there_exists(compose(X1,X0))
| codomain(domain(X0)) = domain(compose(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f70,plain,
( spl0_10
<=> ! [X0] : compose(X0,domain(X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f425,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X1,X0))
| codomain(domain(X0)) = domain(compose(X1,X0)) )
| ~ spl0_10
| ~ spl0_43 ),
inference(superposition,[],[f421,f71]) ).
fof(f71,plain,
( ! [X0] : compose(X0,domain(X0)) = X0
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f1349,plain,
( spl0_103
| ~ spl0_11
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f364,f330,f74,f1347]) ).
fof(f1347,plain,
( spl0_103
<=> ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| there_exists(domain(compose(codomain(compose(X0,X1)),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f364,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| there_exists(domain(compose(codomain(compose(X0,X1)),X0))) )
| ~ spl0_11
| ~ spl0_41 ),
inference(superposition,[],[f331,f75]) ).
fof(f1345,plain,
( spl0_102
| ~ spl0_36
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f358,f330,f250,f1343]) ).
fof(f1343,plain,
( spl0_102
<=> ! [X2,X0,X1] :
( ~ there_exists(compose(X2,compose(X0,X1)))
| there_exists(domain(compose(X2,codomain(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f358,plain,
( ! [X2,X0,X1] :
( ~ there_exists(compose(X2,compose(X0,X1)))
| there_exists(domain(compose(X2,codomain(X0)))) )
| ~ spl0_36
| ~ spl0_41 ),
inference(superposition,[],[f331,f251]) ).
fof(f1341,plain,
( spl0_101
| ~ spl0_11
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f344,f326,f74,f1339]) ).
fof(f1339,plain,
( spl0_101
<=> ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| there_exists(codomain(compose(codomain(compose(X0,X1)),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f344,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| there_exists(codomain(compose(codomain(compose(X0,X1)),X0))) )
| ~ spl0_11
| ~ spl0_40 ),
inference(superposition,[],[f327,f75]) ).
fof(f1337,plain,
( spl0_100
| ~ spl0_36
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f338,f326,f250,f1335]) ).
fof(f1335,plain,
( spl0_100
<=> ! [X2,X0,X1] :
( ~ there_exists(compose(X2,compose(X0,X1)))
| there_exists(codomain(compose(X2,codomain(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f338,plain,
( ! [X2,X0,X1] :
( ~ there_exists(compose(X2,compose(X0,X1)))
| there_exists(codomain(compose(X2,codomain(X0)))) )
| ~ spl0_36
| ~ spl0_40 ),
inference(superposition,[],[f327,f251]) ).
fof(f1333,plain,
( spl0_99
| ~ spl0_6
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f305,f261,f52,f1331]) ).
fof(f1331,plain,
( spl0_99
<=> ! [X0,X1] :
( codomain(X1) = X0
| f1(X0,codomain(X1)) = X0
| there_exists(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f52,plain,
( spl0_6
<=> ! [X0] :
( there_exists(X0)
| ~ there_exists(codomain(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f261,plain,
( spl0_38
<=> ! [X0,X1] :
( there_exists(X1)
| X0 = X1
| f1(X0,X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f305,plain,
( ! [X0,X1] :
( codomain(X1) = X0
| f1(X0,codomain(X1)) = X0
| there_exists(X1) )
| ~ spl0_6
| ~ spl0_38 ),
inference(resolution,[],[f262,f53]) ).
fof(f53,plain,
( ! [X0] :
( ~ there_exists(codomain(X0))
| there_exists(X0) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f262,plain,
( ! [X0,X1] :
( there_exists(X1)
| X0 = X1
| f1(X0,X1) = X0 )
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f261]) ).
fof(f1329,plain,
( spl0_98
| ~ spl0_5
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f303,f261,f48,f1327]) ).
fof(f1327,plain,
( spl0_98
<=> ! [X0,X1] :
( domain(X1) = X0
| f1(X0,domain(X1)) = X0
| there_exists(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f48,plain,
( spl0_5
<=> ! [X0] :
( there_exists(X0)
| ~ there_exists(domain(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f303,plain,
( ! [X0,X1] :
( domain(X1) = X0
| f1(X0,domain(X1)) = X0
| there_exists(X1) )
| ~ spl0_5
| ~ spl0_38 ),
inference(resolution,[],[f262,f49]) ).
fof(f49,plain,
( ! [X0] :
( ~ there_exists(domain(X0))
| there_exists(X0) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f1325,plain,
( spl0_97
| ~ spl0_6
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f296,f254,f52,f1323]) ).
fof(f1323,plain,
( spl0_97
<=> ! [X0,X1] :
( codomain(X0) = X1
| f1(codomain(X0),X1) = X1
| there_exists(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f296,plain,
( ! [X0,X1] :
( codomain(X0) = X1
| f1(codomain(X0),X1) = X1
| there_exists(X0) )
| ~ spl0_6
| ~ spl0_37 ),
inference(resolution,[],[f255,f53]) ).
fof(f1321,plain,
( spl0_96
| ~ spl0_5
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f294,f254,f48,f1319]) ).
fof(f1319,plain,
( spl0_96
<=> ! [X0,X1] :
( domain(X0) = X1
| f1(domain(X0),X1) = X1
| there_exists(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f294,plain,
( ! [X0,X1] :
( domain(X0) = X1
| f1(domain(X0),X1) = X1
| there_exists(X0) )
| ~ spl0_5
| ~ spl0_37 ),
inference(resolution,[],[f255,f49]) ).
fof(f1315,plain,
( spl0_95
| ~ spl0_16
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f288,f250,f104,f1313]) ).
fof(f1313,plain,
( spl0_95
<=> ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| domain(codomain(X0)) = codomain(compose(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f288,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| domain(codomain(X0)) = codomain(compose(X0,X1)) )
| ~ spl0_16
| ~ spl0_36 ),
inference(superposition,[],[f105,f251]) ).
fof(f1311,plain,
( spl0_94
| ~ spl0_16
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f269,f246,f104,f1309]) ).
fof(f1309,plain,
( spl0_94
<=> ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| domain(X0) = codomain(compose(domain(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f269,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| domain(X0) = codomain(compose(domain(X0),X1)) )
| ~ spl0_16
| ~ spl0_35 ),
inference(superposition,[],[f105,f247]) ).
fof(f1307,plain,
( spl0_93
| ~ spl0_29
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f239,f224,f199,f1305]) ).
fof(f1305,plain,
( spl0_93
<=> ! [X0] :
( codomain(codomain(codomain(X0))) = domain(codomain(codomain(codomain(X0))))
| ~ there_exists(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f199,plain,
( spl0_29
<=> ! [X0] :
( ~ there_exists(X0)
| there_exists(codomain(codomain(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f239,plain,
( ! [X0] :
( codomain(codomain(codomain(X0))) = domain(codomain(codomain(codomain(X0))))
| ~ there_exists(X0) )
| ~ spl0_29
| ~ spl0_34 ),
inference(resolution,[],[f225,f200]) ).
fof(f200,plain,
( ! [X0] :
( there_exists(codomain(codomain(X0)))
| ~ there_exists(X0) )
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f199]) ).
fof(f1303,plain,
( spl0_92
| ~ spl0_28
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f237,f224,f195,f1301]) ).
fof(f1301,plain,
( spl0_92
<=> ! [X0] :
( codomain(domain(codomain(X0))) = domain(codomain(domain(codomain(X0))))
| ~ there_exists(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f195,plain,
( spl0_28
<=> ! [X0] :
( ~ there_exists(X0)
| there_exists(domain(codomain(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f237,plain,
( ! [X0] :
( codomain(domain(codomain(X0))) = domain(codomain(domain(codomain(X0))))
| ~ there_exists(X0) )
| ~ spl0_28
| ~ spl0_34 ),
inference(resolution,[],[f225,f196]) ).
fof(f196,plain,
( ! [X0] :
( there_exists(domain(codomain(X0)))
| ~ there_exists(X0) )
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f195]) ).
fof(f1299,plain,
( spl0_91
| ~ spl0_29
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f230,f220,f199,f1297]) ).
fof(f1297,plain,
( spl0_91
<=> ! [X0] :
( domain(codomain(codomain(X0))) = codomain(domain(codomain(codomain(X0))))
| ~ there_exists(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f230,plain,
( ! [X0] :
( domain(codomain(codomain(X0))) = codomain(domain(codomain(codomain(X0))))
| ~ there_exists(X0) )
| ~ spl0_29
| ~ spl0_33 ),
inference(resolution,[],[f221,f200]) ).
fof(f1295,plain,
( spl0_90
| ~ spl0_28
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f228,f220,f195,f1293]) ).
fof(f1293,plain,
( spl0_90
<=> ! [X0] :
( domain(domain(codomain(X0))) = codomain(domain(domain(codomain(X0))))
| ~ there_exists(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f228,plain,
( ! [X0] :
( domain(domain(codomain(X0))) = codomain(domain(domain(codomain(X0))))
| ~ there_exists(X0) )
| ~ spl0_28
| ~ spl0_33 ),
inference(resolution,[],[f221,f196]) ).
fof(f1260,plain,
( spl0_89
| ~ spl0_12
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f381,f372,f79,f1257]) ).
fof(f1257,plain,
( spl0_89
<=> compose(g,a) = compose(h,compose(a,domain(compose(g,a)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f381,plain,
( compose(g,a) = compose(h,compose(a,domain(compose(g,a))))
| ~ spl0_12
| ~ spl0_42 ),
inference(superposition,[],[f373,f81]) ).
fof(f1255,plain,
( ~ spl0_88
| ~ spl0_27
| spl0_85 ),
inference(avatar_split_clause,[],[f1221,f1215,f188,f1252]) ).
fof(f1252,plain,
( spl0_88
<=> there_exists(g) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f188,plain,
( spl0_27
<=> ! [X0] :
( ~ there_exists(X0)
| there_exists(codomain(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f1215,plain,
( spl0_85
<=> there_exists(codomain(g)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f1221,plain,
( ~ there_exists(g)
| ~ spl0_27
| spl0_85 ),
inference(resolution,[],[f1216,f189]) ).
fof(f189,plain,
( ! [X0] :
( there_exists(codomain(X0))
| ~ there_exists(X0) )
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f188]) ).
fof(f1216,plain,
( ~ there_exists(codomain(g))
| spl0_85 ),
inference(avatar_component_clause,[],[f1215]) ).
fof(f1250,plain,
( spl0_87
| ~ spl0_35
| ~ spl0_82 ),
inference(avatar_split_clause,[],[f1207,f1168,f246,f1248]) ).
fof(f1248,plain,
( spl0_87
<=> ! [X0] : compose(h,X0) = compose(h,compose(codomain(a),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f1168,plain,
( spl0_82
<=> domain(h) = codomain(a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f1207,plain,
( ! [X0] : compose(h,X0) = compose(h,compose(codomain(a),X0))
| ~ spl0_35
| ~ spl0_82 ),
inference(superposition,[],[f247,f1170]) ).
fof(f1170,plain,
( domain(h) = codomain(a)
| ~ spl0_82 ),
inference(avatar_component_clause,[],[f1168]) ).
fof(f1228,plain,
( spl0_86
| ~ spl0_10
| ~ spl0_82 ),
inference(avatar_split_clause,[],[f1204,f1168,f70,f1225]) ).
fof(f1225,plain,
( spl0_86
<=> h = compose(h,codomain(a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f1204,plain,
( h = compose(h,codomain(a))
| ~ spl0_10
| ~ spl0_82 ),
inference(superposition,[],[f71,f1170]) ).
fof(f1218,plain,
( spl0_85
| ~ spl0_14
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f1158,f214,f88,f1215]) ).
fof(f88,plain,
( spl0_14
<=> ! [X0,X1] :
( there_exists(codomain(X0))
| ~ there_exists(compose(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f214,plain,
( spl0_32
<=> there_exists(compose(g,a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f1158,plain,
( there_exists(codomain(g))
| ~ spl0_14
| ~ spl0_32 ),
inference(resolution,[],[f215,f89]) ).
fof(f89,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| there_exists(codomain(X0)) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f215,plain,
( there_exists(compose(g,a))
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f1182,plain,
( spl0_84
| spl0_32
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f309,f261,f214,f1180]) ).
fof(f1180,plain,
( spl0_84
<=> ! [X0] :
( compose(g,a) = X0
| f1(X0,compose(g,a)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f309,plain,
( ! [X0] :
( compose(g,a) = X0
| f1(X0,compose(g,a)) = X0 )
| spl0_32
| ~ spl0_38 ),
inference(resolution,[],[f262,f216]) ).
fof(f216,plain,
( ~ there_exists(compose(g,a))
| spl0_32 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f1178,plain,
( spl0_83
| ~ spl0_44
| ~ spl0_50
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f600,f554,f531,f444,f1175]) ).
fof(f1175,plain,
( spl0_83
<=> codomain(a) = codomain(codomain(a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f531,plain,
( spl0_50
<=> codomain(a) = codomain(compose(a,b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f554,plain,
( spl0_53
<=> ! [X0] : compose(codomain(codomain(X0)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f600,plain,
( codomain(a) = codomain(codomain(a))
| ~ spl0_44
| ~ spl0_50
| ~ spl0_53 ),
inference(forward_demodulation,[],[f596,f533]) ).
fof(f533,plain,
( codomain(a) = codomain(compose(a,b))
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f531]) ).
fof(f596,plain,
( codomain(compose(a,b)) = codomain(codomain(compose(a,b)))
| ~ spl0_44
| ~ spl0_53 ),
inference(trivial_inequality_removal,[],[f589]) ).
fof(f589,plain,
( compose(a,b) != compose(a,b)
| codomain(compose(a,b)) = codomain(codomain(compose(a,b)))
| ~ spl0_44
| ~ spl0_53 ),
inference(superposition,[],[f445,f555]) ).
fof(f555,plain,
( ! [X0] : compose(codomain(codomain(X0)),X0) = X0
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f554]) ).
fof(f1171,plain,
( spl0_82
| ~ spl0_32
| ~ spl0_12
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f110,f104,f79,f214,f1168]) ).
fof(f110,plain,
( ~ there_exists(compose(g,a))
| domain(h) = codomain(a)
| ~ spl0_12
| ~ spl0_16 ),
inference(superposition,[],[f105,f81]) ).
fof(f1143,plain,
( spl0_81
| spl0_32
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f300,f254,f214,f1141]) ).
fof(f1141,plain,
( spl0_81
<=> ! [X0] :
( compose(g,a) = X0
| f1(compose(g,a),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f300,plain,
( ! [X0] :
( compose(g,a) = X0
| f1(compose(g,a),X0) = X0 )
| spl0_32
| ~ spl0_37 ),
inference(resolution,[],[f255,f216]) ).
fof(f1131,plain,
( ~ spl0_23
| spl0_80
| ~ spl0_19
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f180,f176,f134,f1129,f164]) ).
fof(f164,plain,
( spl0_23
<=> there_exists(codomain(b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f1129,plain,
( spl0_80
<=> ! [X0] :
( codomain(X0) != codomain(b)
| there_exists(compose(a,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f134,plain,
( spl0_19
<=> ! [X0,X1] :
( ~ there_exists(domain(X0))
| there_exists(compose(X0,X1))
| domain(X0) != codomain(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f176,plain,
( spl0_25
<=> domain(a) = codomain(b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f180,plain,
( ! [X0] :
( codomain(X0) != codomain(b)
| there_exists(compose(a,X0))
| ~ there_exists(codomain(b)) )
| ~ spl0_19
| ~ spl0_25 ),
inference(superposition,[],[f135,f178]) ).
fof(f178,plain,
( domain(a) = codomain(b)
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f176]) ).
fof(f135,plain,
( ! [X0,X1] :
( domain(X0) != codomain(X1)
| there_exists(compose(X0,X1))
| ~ there_exists(domain(X0)) )
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f1016,plain,
( spl0_79
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f282,f250,f1014]) ).
fof(f1014,plain,
( spl0_79
<=> ! [X0,X1] : compose(X0,X1) = compose(codomain(codomain(X0)),compose(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f282,plain,
( ! [X0,X1] : compose(X0,X1) = compose(codomain(codomain(X0)),compose(X0,X1))
| ~ spl0_36 ),
inference(superposition,[],[f251,f251]) ).
fof(f1003,plain,
( spl0_78
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f274,f246,f1001]) ).
fof(f1001,plain,
( spl0_78
<=> ! [X0,X1] : compose(X0,X1) = compose(X0,compose(domain(domain(X0)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f274,plain,
( ! [X0,X1] : compose(X0,X1) = compose(X0,compose(domain(domain(X0)),X1))
| ~ spl0_35 ),
inference(forward_demodulation,[],[f266,f247]) ).
fof(f266,plain,
( ! [X0,X1] : compose(X0,compose(domain(X0),X1)) = compose(X0,compose(domain(domain(X0)),X1))
| ~ spl0_35 ),
inference(superposition,[],[f247,f247]) ).
fof(f983,plain,
( spl0_77
| ~ spl0_12
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f360,f330,f79,f981]) ).
fof(f981,plain,
( spl0_77
<=> ! [X0] :
( ~ there_exists(compose(X0,compose(g,a)))
| there_exists(domain(compose(X0,h))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f360,plain,
( ! [X0] :
( ~ there_exists(compose(X0,compose(g,a)))
| there_exists(domain(compose(X0,h))) )
| ~ spl0_12
| ~ spl0_41 ),
inference(superposition,[],[f331,f81]) ).
fof(f979,plain,
( spl0_76
| ~ spl0_12
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f340,f326,f79,f977]) ).
fof(f977,plain,
( spl0_76
<=> ! [X0] :
( ~ there_exists(compose(X0,compose(g,a)))
| there_exists(codomain(compose(X0,h))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f340,plain,
( ! [X0] :
( ~ there_exists(compose(X0,compose(g,a)))
| there_exists(codomain(compose(X0,h))) )
| ~ spl0_12
| ~ spl0_40 ),
inference(superposition,[],[f327,f81]) ).
fof(f860,plain,
( spl0_75
| ~ spl0_30
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f352,f220,f205,f857]) ).
fof(f857,plain,
( spl0_75
<=> domain(b) = codomain(domain(b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f205,plain,
( spl0_30
<=> there_exists(b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f352,plain,
( domain(b) = codomain(domain(b))
| ~ spl0_30
| ~ spl0_33 ),
inference(resolution,[],[f207,f221]) ).
fof(f207,plain,
( there_exists(b)
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f205]) ).
fof(f829,plain,
( spl0_74
| ~ spl0_11
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f357,f330,f74,f827]) ).
fof(f827,plain,
( spl0_74
<=> ! [X0,X1] :
( ~ there_exists(compose(X1,X0))
| there_exists(domain(compose(X1,codomain(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f357,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X1,X0))
| there_exists(domain(compose(X1,codomain(X0)))) )
| ~ spl0_11
| ~ spl0_41 ),
inference(superposition,[],[f331,f75]) ).
fof(f825,plain,
( spl0_73
| ~ spl0_11
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f337,f326,f74,f823]) ).
fof(f823,plain,
( spl0_73
<=> ! [X0,X1] :
( ~ there_exists(compose(X1,X0))
| there_exists(codomain(compose(X1,codomain(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f337,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X1,X0))
| there_exists(codomain(compose(X1,codomain(X0)))) )
| ~ spl0_11
| ~ spl0_40 ),
inference(superposition,[],[f327,f75]) ).
fof(f821,plain,
( spl0_72
| ~ spl0_27
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f238,f224,f188,f819]) ).
fof(f819,plain,
( spl0_72
<=> ! [X0] :
( codomain(codomain(X0)) = domain(codomain(codomain(X0)))
| ~ there_exists(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f238,plain,
( ! [X0] :
( codomain(codomain(X0)) = domain(codomain(codomain(X0)))
| ~ there_exists(X0) )
| ~ spl0_27
| ~ spl0_34 ),
inference(resolution,[],[f225,f189]) ).
fof(f817,plain,
( spl0_71
| ~ spl0_26
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f236,f224,f184,f815]) ).
fof(f815,plain,
( spl0_71
<=> ! [X0] :
( codomain(domain(X0)) = domain(codomain(domain(X0)))
| ~ there_exists(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f184,plain,
( spl0_26
<=> ! [X0] :
( ~ there_exists(X0)
| there_exists(domain(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f236,plain,
( ! [X0] :
( codomain(domain(X0)) = domain(codomain(domain(X0)))
| ~ there_exists(X0) )
| ~ spl0_26
| ~ spl0_34 ),
inference(resolution,[],[f225,f185]) ).
fof(f185,plain,
( ! [X0] :
( there_exists(domain(X0))
| ~ there_exists(X0) )
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f813,plain,
( spl0_70
| ~ spl0_27
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f229,f220,f188,f811]) ).
fof(f811,plain,
( spl0_70
<=> ! [X0] :
( domain(codomain(X0)) = codomain(domain(codomain(X0)))
| ~ there_exists(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f229,plain,
( ! [X0] :
( domain(codomain(X0)) = codomain(domain(codomain(X0)))
| ~ there_exists(X0) )
| ~ spl0_27
| ~ spl0_33 ),
inference(resolution,[],[f221,f189]) ).
fof(f809,plain,
( spl0_69
| ~ spl0_26
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f227,f220,f184,f807]) ).
fof(f807,plain,
( spl0_69
<=> ! [X0] :
( domain(domain(X0)) = codomain(domain(domain(X0)))
| ~ there_exists(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f227,plain,
( ! [X0] :
( domain(domain(X0)) = codomain(domain(domain(X0)))
| ~ there_exists(X0) )
| ~ spl0_26
| ~ spl0_33 ),
inference(resolution,[],[f221,f185]) ).
fof(f744,plain,
( spl0_68
| ~ spl0_30
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f351,f224,f205,f741]) ).
fof(f741,plain,
( spl0_68
<=> codomain(b) = domain(codomain(b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f351,plain,
( codomain(b) = domain(codomain(b))
| ~ spl0_30
| ~ spl0_34 ),
inference(resolution,[],[f207,f225]) ).
fof(f739,plain,
( spl0_67
| ~ spl0_12
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f284,f250,f79,f736]) ).
fof(f736,plain,
( spl0_67
<=> compose(g,a) = compose(codomain(h),compose(g,a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f284,plain,
( compose(g,a) = compose(codomain(h),compose(g,a))
| ~ spl0_12
| ~ spl0_36 ),
inference(superposition,[],[f251,f81]) ).
fof(f734,plain,
( spl0_66
| ~ spl0_25
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f264,f246,f176,f732]) ).
fof(f732,plain,
( spl0_66
<=> ! [X0] : compose(a,X0) = compose(a,compose(codomain(b),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f264,plain,
( ! [X0] : compose(a,X0) = compose(a,compose(codomain(b),X0))
| ~ spl0_25
| ~ spl0_35 ),
inference(superposition,[],[f247,f178]) ).
fof(f729,plain,
( spl0_65
| ~ spl0_3
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f242,f224,f39,f726]) ).
fof(f726,plain,
( spl0_65
<=> codomain(compose(a,b)) = domain(codomain(compose(a,b))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f39,plain,
( spl0_3
<=> there_exists(compose(a,b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f242,plain,
( codomain(compose(a,b)) = domain(codomain(compose(a,b)))
| ~ spl0_3
| ~ spl0_34 ),
inference(resolution,[],[f225,f41]) ).
fof(f41,plain,
( there_exists(compose(a,b))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f724,plain,
( spl0_64
| ~ spl0_3
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f233,f220,f39,f721]) ).
fof(f721,plain,
( spl0_64
<=> domain(compose(a,b)) = codomain(domain(compose(a,b))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f233,plain,
( domain(compose(a,b)) = codomain(domain(compose(a,b)))
| ~ spl0_3
| ~ spl0_33 ),
inference(resolution,[],[f221,f41]) ).
fof(f688,plain,
( spl0_63
| ~ spl0_10
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f375,f372,f70,f686]) ).
fof(f686,plain,
( spl0_63
<=> ! [X0] : compose(X0,compose(domain(X0),domain(X0))) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f375,plain,
( ! [X0] : compose(X0,compose(domain(X0),domain(X0))) = X0
| ~ spl0_10
| ~ spl0_42 ),
inference(superposition,[],[f373,f71]) ).
fof(f680,plain,
( spl0_61
| spl0_62
| ~ spl0_14
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f321,f311,f88,f678,f674]) ).
fof(f678,plain,
( spl0_62
<=> ! [X0] : ~ there_exists(compose(g,compose(a,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f321,plain,
( ! [X0] :
( ~ there_exists(compose(g,compose(a,X0)))
| there_exists(codomain(h)) )
| ~ spl0_14
| ~ spl0_39 ),
inference(superposition,[],[f89,f312]) ).
fof(f641,plain,
( spl0_60
| ~ spl0_24
| ~ spl0_25
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f259,f220,f176,f171,f638]) ).
fof(f638,plain,
( spl0_60
<=> codomain(b) = codomain(codomain(b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f171,plain,
( spl0_24
<=> there_exists(a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f259,plain,
( codomain(b) = codomain(codomain(b))
| ~ spl0_24
| ~ spl0_25
| ~ spl0_33 ),
inference(forward_demodulation,[],[f258,f178]) ).
fof(f258,plain,
( domain(a) = codomain(domain(a))
| ~ spl0_24
| ~ spl0_33 ),
inference(resolution,[],[f173,f221]) ).
fof(f173,plain,
( there_exists(a)
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f636,plain,
( spl0_59
| ~ spl0_13
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f290,f250,f84,f634]) ).
fof(f634,plain,
( spl0_59
<=> ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| there_exists(domain(codomain(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f84,plain,
( spl0_13
<=> ! [X0,X1] :
( there_exists(domain(X0))
| ~ there_exists(compose(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f290,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| there_exists(domain(codomain(X0))) )
| ~ spl0_13
| ~ spl0_36 ),
inference(superposition,[],[f85,f251]) ).
fof(f85,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| there_exists(domain(X0)) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f632,plain,
( spl0_58
| ~ spl0_14
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f289,f250,f88,f630]) ).
fof(f630,plain,
( spl0_58
<=> ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| there_exists(codomain(codomain(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f289,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| there_exists(codomain(codomain(X0))) )
| ~ spl0_14
| ~ spl0_36 ),
inference(superposition,[],[f89,f251]) ).
fof(f627,plain,
( spl0_57
| ~ spl0_23
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f241,f224,f164,f624]) ).
fof(f624,plain,
( spl0_57
<=> codomain(codomain(b)) = domain(codomain(codomain(b))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f241,plain,
( codomain(codomain(b)) = domain(codomain(codomain(b)))
| ~ spl0_23
| ~ spl0_34 ),
inference(resolution,[],[f225,f166]) ).
fof(f166,plain,
( there_exists(codomain(b))
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f621,plain,
( spl0_56
| ~ spl0_22
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f240,f224,f159,f618]) ).
fof(f618,plain,
( spl0_56
<=> codomain(codomain(a)) = domain(codomain(codomain(a))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f159,plain,
( spl0_22
<=> there_exists(codomain(a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f240,plain,
( codomain(codomain(a)) = domain(codomain(codomain(a)))
| ~ spl0_22
| ~ spl0_34 ),
inference(resolution,[],[f225,f161]) ).
fof(f161,plain,
( there_exists(codomain(a))
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f615,plain,
( spl0_55
| ~ spl0_23
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f232,f220,f164,f612]) ).
fof(f612,plain,
( spl0_55
<=> domain(codomain(b)) = codomain(domain(codomain(b))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f232,plain,
( domain(codomain(b)) = codomain(domain(codomain(b)))
| ~ spl0_23
| ~ spl0_33 ),
inference(resolution,[],[f221,f166]) ).
fof(f609,plain,
( spl0_54
| ~ spl0_22
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f231,f220,f159,f606]) ).
fof(f606,plain,
( spl0_54
<=> domain(codomain(a)) = codomain(domain(codomain(a))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f231,plain,
( domain(codomain(a)) = codomain(domain(codomain(a)))
| ~ spl0_22
| ~ spl0_33 ),
inference(resolution,[],[f221,f161]) ).
fof(f556,plain,
( spl0_53
| ~ spl0_11
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f281,f250,f74,f554]) ).
fof(f281,plain,
( ! [X0] : compose(codomain(codomain(X0)),X0) = X0
| ~ spl0_11
| ~ spl0_36 ),
inference(superposition,[],[f251,f75]) ).
fof(f552,plain,
( spl0_52
| ~ spl0_10
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f273,f246,f70,f550]) ).
fof(f550,plain,
( spl0_52
<=> ! [X0] : compose(X0,domain(domain(X0))) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f273,plain,
( ! [X0] : compose(X0,domain(domain(X0))) = X0
| ~ spl0_10
| ~ spl0_35 ),
inference(forward_demodulation,[],[f265,f71]) ).
fof(f265,plain,
( ! [X0] : compose(X0,domain(X0)) = compose(X0,domain(domain(X0)))
| ~ spl0_10
| ~ spl0_35 ),
inference(superposition,[],[f247,f71]) ).
fof(f548,plain,
( spl0_51
| ~ spl0_24
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f257,f224,f171,f545]) ).
fof(f545,plain,
( spl0_51
<=> codomain(a) = domain(codomain(a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f257,plain,
( codomain(a) = domain(codomain(a))
| ~ spl0_24
| ~ spl0_34 ),
inference(resolution,[],[f173,f225]) ).
fof(f534,plain,
( spl0_50
| ~ spl0_36
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f451,f444,f250,f531]) ).
fof(f498,plain,
( spl0_49
| ~ spl0_2
| ~ spl0_31
| ~ spl0_33
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f477,f224,f220,f210,f34,f495]) ).
fof(f495,plain,
( spl0_49
<=> domain(h) = domain(domain(h)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f34,plain,
( spl0_2
<=> there_exists(h) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f210,plain,
( spl0_31
<=> there_exists(domain(h)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f477,plain,
( domain(h) = domain(domain(h))
| ~ spl0_2
| ~ spl0_31
| ~ spl0_33
| ~ spl0_34 ),
inference(forward_demodulation,[],[f475,f235]) ).
fof(f235,plain,
( domain(h) = codomain(domain(h))
| ~ spl0_2
| ~ spl0_33 ),
inference(resolution,[],[f221,f36]) ).
fof(f36,plain,
( there_exists(h)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f34]) ).
fof(f475,plain,
( codomain(domain(h)) = domain(codomain(domain(h)))
| ~ spl0_31
| ~ spl0_34 ),
inference(resolution,[],[f212,f225]) ).
fof(f212,plain,
( there_exists(domain(h))
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f210]) ).
fof(f493,plain,
( spl0_48
| ~ spl0_2
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f244,f224,f34,f490]) ).
fof(f244,plain,
( codomain(h) = domain(codomain(h))
| ~ spl0_2
| ~ spl0_34 ),
inference(resolution,[],[f225,f36]) ).
fof(f488,plain,
( spl0_47
| ~ spl0_2
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f235,f220,f34,f485]) ).
fof(f485,plain,
( spl0_47
<=> domain(h) = codomain(domain(h)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f483,plain,
( spl0_46
| ~ spl0_10
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f181,f176,f70,f480]) ).
fof(f480,plain,
( spl0_46
<=> a = compose(a,codomain(b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f181,plain,
( a = compose(a,codomain(b))
| ~ spl0_10
| ~ spl0_25 ),
inference(superposition,[],[f71,f178]) ).
fof(f473,plain,
( ~ spl0_2
| ~ spl0_26
| spl0_31 ),
inference(avatar_split_clause,[],[f218,f210,f184,f34]) ).
fof(f218,plain,
( ~ there_exists(h)
| ~ spl0_26
| spl0_31 ),
inference(resolution,[],[f211,f185]) ).
fof(f211,plain,
( ~ there_exists(domain(h))
| spl0_31 ),
inference(avatar_component_clause,[],[f210]) ).
fof(f457,plain,
( spl0_45
| ~ spl0_17
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f154,f150,f112,f455]) ).
fof(f455,plain,
( spl0_45
<=> ! [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_45])]) ).
fof(f112,plain,
( spl0_17
<=> ! [X2,X0,X1] : compose(X0,compose(X1,X2)) = compose(compose(X0,X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f154,plain,
( ! [X2,X0,X1] :
( compose(X2,compose(a,b)) != compose(X0,compose(X1,compose(a,b)))
| compose(X0,X1) = X2 )
| ~ spl0_17
| ~ spl0_21 ),
inference(superposition,[],[f151,f113]) ).
fof(f113,plain,
( ! [X2,X0,X1] : compose(X0,compose(X1,X2)) = compose(compose(X0,X1),X2)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f446,plain,
( spl0_44
| ~ spl0_11
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f153,f150,f74,f444]) ).
fof(f153,plain,
( ! [X0] :
( compose(a,b) != compose(X0,compose(a,b))
| codomain(compose(a,b)) = X0 )
| ~ spl0_11
| ~ spl0_21 ),
inference(superposition,[],[f151,f75]) ).
fof(f422,plain,
( spl0_43
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f121,f112,f104,f420]) ).
fof(f121,plain,
( ! [X2,X0,X1] :
( ~ there_exists(compose(X0,compose(X1,X2)))
| domain(compose(X0,X1)) = codomain(X2) )
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f105,f113]) ).
fof(f374,plain,
( spl0_42
| ~ spl0_10
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f119,f112,f70,f372]) ).
fof(f119,plain,
( ! [X0,X1] : compose(X0,X1) = compose(X0,compose(X1,domain(compose(X0,X1))))
| ~ spl0_10
| ~ spl0_17 ),
inference(superposition,[],[f113,f71]) ).
fof(f332,plain,
( spl0_41
| ~ spl0_13
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f123,f112,f84,f330]) ).
fof(f123,plain,
( ! [X2,X0,X1] :
( ~ there_exists(compose(X0,compose(X1,X2)))
| there_exists(domain(compose(X0,X1))) )
| ~ spl0_13
| ~ spl0_17 ),
inference(superposition,[],[f85,f113]) ).
fof(f328,plain,
( spl0_40
| ~ spl0_14
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f122,f112,f88,f326]) ).
fof(f122,plain,
( ! [X2,X0,X1] :
( ~ there_exists(compose(X0,compose(X1,X2)))
| there_exists(codomain(compose(X0,X1))) )
| ~ spl0_14
| ~ spl0_17 ),
inference(superposition,[],[f89,f113]) ).
fof(f313,plain,
( spl0_39
| ~ spl0_12
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f126,f112,f79,f311]) ).
fof(f126,plain,
( ! [X0] : compose(h,compose(a,X0)) = compose(g,compose(a,X0))
| ~ spl0_12
| ~ spl0_17 ),
inference(forward_demodulation,[],[f118,f113]) ).
fof(f118,plain,
( ! [X0] : compose(h,compose(a,X0)) = compose(compose(g,a),X0)
| ~ spl0_12
| ~ spl0_17 ),
inference(superposition,[],[f113,f81]) ).
fof(f263,plain,
( spl0_38
| ~ spl0_15
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f148,f138,f92,f261]) ).
fof(f138,plain,
( spl0_20
<=> ! [X0,X1] :
( X0 = X1
| f1(X0,X1) = X1
| f1(X0,X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f148,plain,
( ! [X0,X1] :
( there_exists(X1)
| X0 = X1
| f1(X0,X1) = X0 )
| ~ spl0_15
| ~ spl0_20 ),
inference(duplicate_literal_removal,[],[f143]) ).
fof(f143,plain,
( ! [X0,X1] :
( there_exists(X1)
| X0 = X1
| f1(X0,X1) = X0
| X0 = X1 )
| ~ spl0_15
| ~ spl0_20 ),
inference(superposition,[],[f93,f139]) ).
fof(f139,plain,
( ! [X0,X1] :
( f1(X0,X1) = X1
| f1(X0,X1) = X0
| X0 = X1 )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f138]) ).
fof(f256,plain,
( spl0_37
| ~ spl0_15
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f147,f138,f92,f254]) ).
fof(f147,plain,
( ! [X0,X1] :
( there_exists(X0)
| X0 = X1
| f1(X0,X1) = X1 )
| ~ spl0_15
| ~ spl0_20 ),
inference(duplicate_literal_removal,[],[f144]) ).
fof(f144,plain,
( ! [X0,X1] :
( there_exists(X0)
| X0 = X1
| f1(X0,X1) = X1
| X0 = X1 )
| ~ spl0_15
| ~ spl0_20 ),
inference(superposition,[],[f93,f139]) ).
fof(f252,plain,
( spl0_36
| ~ spl0_11
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f116,f112,f74,f250]) ).
fof(f116,plain,
( ! [X0,X1] : compose(X0,X1) = compose(codomain(X0),compose(X0,X1))
| ~ spl0_11
| ~ spl0_17 ),
inference(superposition,[],[f113,f75]) ).
fof(f248,plain,
( spl0_35
| ~ spl0_10
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f115,f112,f70,f246]) ).
fof(f115,plain,
( ! [X0,X1] : compose(X0,X1) = compose(X0,compose(domain(X0),X1))
| ~ spl0_10
| ~ spl0_17 ),
inference(superposition,[],[f113,f71]) ).
fof(f226,plain,
( spl0_34
| ~ spl0_11
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f109,f104,f74,f224]) ).
fof(f109,plain,
( ! [X0] :
( ~ there_exists(X0)
| codomain(X0) = domain(codomain(X0)) )
| ~ spl0_11
| ~ spl0_16 ),
inference(superposition,[],[f105,f75]) ).
fof(f222,plain,
( spl0_33
| ~ spl0_10
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f108,f104,f70,f220]) ).
fof(f108,plain,
( ! [X0] :
( ~ there_exists(X0)
| domain(X0) = codomain(domain(X0)) )
| ~ spl0_10
| ~ spl0_16 ),
inference(superposition,[],[f105,f71]) ).
fof(f217,plain,
( spl0_31
| ~ spl0_32
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f98,f84,f79,f214,f210]) ).
fof(f98,plain,
( ~ there_exists(compose(g,a))
| there_exists(domain(h))
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f85,f81]) ).
fof(f208,plain,
( spl0_30
| ~ spl0_6
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f169,f164,f52,f205]) ).
fof(f169,plain,
( there_exists(b)
| ~ spl0_6
| ~ spl0_23 ),
inference(resolution,[],[f166,f53]) ).
fof(f201,plain,
( spl0_29
| ~ spl0_11
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f101,f88,f74,f199]) ).
fof(f101,plain,
( ! [X0] :
( ~ there_exists(X0)
| there_exists(codomain(codomain(X0))) )
| ~ spl0_11
| ~ spl0_14 ),
inference(superposition,[],[f89,f75]) ).
fof(f197,plain,
( spl0_28
| ~ spl0_11
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f97,f84,f74,f195]) ).
fof(f97,plain,
( ! [X0] :
( ~ there_exists(X0)
| there_exists(domain(codomain(X0))) )
| ~ spl0_11
| ~ spl0_13 ),
inference(superposition,[],[f85,f75]) ).
fof(f190,plain,
( spl0_27
| ~ spl0_10
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f100,f88,f70,f188]) ).
fof(f100,plain,
( ! [X0] :
( ~ there_exists(X0)
| there_exists(codomain(X0)) )
| ~ spl0_10
| ~ spl0_14 ),
inference(superposition,[],[f89,f71]) ).
fof(f186,plain,
( spl0_26
| ~ spl0_10
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f96,f84,f70,f184]) ).
fof(f96,plain,
( ! [X0] :
( ~ there_exists(X0)
| there_exists(domain(X0)) )
| ~ spl0_10
| ~ spl0_13 ),
inference(superposition,[],[f85,f71]) ).
fof(f179,plain,
( spl0_25
| ~ spl0_3
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f107,f104,f39,f176]) ).
fof(f107,plain,
( domain(a) = codomain(b)
| ~ spl0_3
| ~ spl0_16 ),
inference(resolution,[],[f105,f41]) ).
fof(f174,plain,
( spl0_24
| ~ spl0_6
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f168,f159,f52,f171]) ).
fof(f168,plain,
( there_exists(a)
| ~ spl0_6
| ~ spl0_22 ),
inference(resolution,[],[f161,f53]) ).
fof(f167,plain,
( spl0_23
| ~ spl0_3
| ~ spl0_16
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f132,f128,f104,f39,f164]) ).
fof(f128,plain,
( spl0_18
<=> there_exists(domain(a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f132,plain,
( there_exists(codomain(b))
| ~ spl0_3
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f130,f107]) ).
fof(f130,plain,
( there_exists(domain(a))
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f162,plain,
( spl0_22
| ~ spl0_3
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f99,f88,f39,f159]) ).
fof(f99,plain,
( there_exists(codomain(a))
| ~ spl0_3
| ~ spl0_14 ),
inference(resolution,[],[f89,f41]) ).
fof(f152,plain,
spl0_21,
inference(avatar_split_clause,[],[f23,f150]) ).
fof(f23,plain,
! [X2,X0] :
( X0 = X2
| compose(X0,compose(a,b)) != compose(X2,compose(a,b)) ),
inference(equality_resolution,[],[f19]) ).
fof(f19,axiom,
! [X2,X0,X1] :
( X0 = X2
| compose(X2,compose(a,b)) != X1
| compose(X0,compose(a,b)) != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',epimorphism) ).
fof(f140,plain,
spl0_20,
inference(avatar_split_clause,[],[f16,f138]) ).
fof(f16,axiom,
! [X0,X1] :
( X0 = X1
| f1(X0,X1) = X1
| f1(X0,X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',indiscernibles2) ).
fof(f136,plain,
spl0_19,
inference(avatar_split_clause,[],[f8,f134]) ).
fof(f8,axiom,
! [X0,X1] :
( ~ there_exists(domain(X0))
| there_exists(compose(X0,X1))
| domain(X0) != codomain(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_codomain_composition2) ).
fof(f131,plain,
( spl0_18
| ~ spl0_3
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f95,f84,f39,f128]) ).
fof(f95,plain,
( there_exists(domain(a))
| ~ spl0_3
| ~ spl0_13 ),
inference(resolution,[],[f85,f41]) ).
fof(f114,plain,
spl0_17,
inference(avatar_split_clause,[],[f9,f112]) ).
fof(f9,axiom,
! [X2,X0,X1] : compose(X0,compose(X1,X2)) = compose(compose(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_compose) ).
fof(f106,plain,
spl0_16,
inference(avatar_split_clause,[],[f7,f104]) ).
fof(f7,axiom,
! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| domain(X0) = codomain(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_codomain_composition1) ).
fof(f94,plain,
spl0_15,
inference(avatar_split_clause,[],[f15,f92]) ).
fof(f15,axiom,
! [X0,X1] :
( X0 = X1
| there_exists(f1(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',indiscernibles1) ).
fof(f90,plain,
spl0_14,
inference(avatar_split_clause,[],[f14,f88]) ).
fof(f14,axiom,
! [X0,X1] :
( there_exists(codomain(X0))
| ~ there_exists(compose(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_implies_codomain) ).
fof(f86,plain,
spl0_13,
inference(avatar_split_clause,[],[f6,f84]) ).
fof(f6,axiom,
! [X0,X1] :
( there_exists(domain(X0))
| ~ there_exists(compose(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_implies_domain) ).
fof(f82,plain,
spl0_12,
inference(avatar_split_clause,[],[f21,f79]) ).
fof(f21,axiom,
compose(h,a) = compose(g,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ha_equals_ga) ).
fof(f76,plain,
spl0_11,
inference(avatar_split_clause,[],[f11,f74]) ).
fof(f11,axiom,
! [X0] : compose(codomain(X0),X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_codomain) ).
fof(f72,plain,
spl0_10,
inference(avatar_split_clause,[],[f10,f70]) ).
fof(f10,axiom,
! [X0] : compose(X0,domain(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_domain) ).
fof(f68,plain,
spl0_9,
inference(avatar_split_clause,[],[f2,f66]) ).
fof(f66,plain,
( spl0_9
<=> ! [X0,X1] :
( ~ equivalent(X0,X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f2,axiom,
! [X0,X1] :
( ~ equivalent(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_implies_existence2) ).
fof(f62,plain,
spl0_8,
inference(avatar_split_clause,[],[f24,f60]) ).
fof(f60,plain,
( spl0_8
<=> ! [X1] :
( ~ there_exists(X1)
| equivalent(X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f24,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/sandbox2/benchmark/theBenchmark.p',existence_and_equality_implies_equivalence1) ).
fof(f58,plain,
spl0_7,
inference(avatar_split_clause,[],[f12,f56]) ).
fof(f56,plain,
( spl0_7
<=> ! [X0,X1] :
( there_exists(X1)
| ~ equivalent(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f12,axiom,
! [X0,X1] :
( there_exists(X1)
| ~ equivalent(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_implies_existence3) ).
fof(f54,plain,
spl0_6,
inference(avatar_split_clause,[],[f5,f52]) ).
fof(f5,axiom,
! [X0] :
( there_exists(X0)
| ~ there_exists(codomain(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain_has_elements) ).
fof(f50,plain,
spl0_5,
inference(avatar_split_clause,[],[f4,f48]) ).
fof(f4,axiom,
! [X0] :
( there_exists(X0)
| ~ there_exists(domain(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_has_elements) ).
fof(f46,plain,
spl0_4,
inference(avatar_split_clause,[],[f1,f44]) ).
fof(f44,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/sandbox2/benchmark/theBenchmark.p',equivalence_implies_existence1) ).
fof(f42,plain,
spl0_3,
inference(avatar_split_clause,[],[f18,f39]) ).
fof(f18,axiom,
there_exists(compose(a,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assume_ab_exists) ).
fof(f37,plain,
spl0_2,
inference(avatar_split_clause,[],[f20,f34]) ).
fof(f20,axiom,
there_exists(h),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assume_h_exists) ).
fof(f32,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f22,f29]) ).
fof(f22,axiom,
h != g,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_g_equals_h) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : CAT003-3 : TPTP v8.1.2. Released v1.0.0.
% 0.03/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n017.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 3 18:10:08 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.35 % (29421)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37 % (29426)WARNING: value z3 for option sas not known
% 0.15/0.37 % (29424)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.37 % (29425)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.37 % (29427)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.37 % (29428)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)
% 0.15/0.37 % (29429)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)
% 0.15/0.37 % (29426)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)
% 0.15/0.37 % (29430)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)
% 0.21/0.37 TRYING [1]
% 0.21/0.37 TRYING [2]
% 0.21/0.38 TRYING [3]
% 0.21/0.38 TRYING [1]
% 0.21/0.38 TRYING [2]
% 0.21/0.38 TRYING [4]
% 0.21/0.38 TRYING [3]
% 0.21/0.40 TRYING [5]
% 0.21/0.41 TRYING [4]
% 0.21/0.44 % (29428)First to succeed.
% 0.21/0.45 % (29428)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-29421"
% 0.21/0.45 TRYING [6]
% 0.21/0.45 % (29428)Refutation found. Thanks to Tanya!
% 0.21/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.21/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.45 % (29428)------------------------------
% 0.21/0.45 % (29428)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.45 % (29428)Termination reason: Refutation
% 0.21/0.45
% 0.21/0.45 % (29428)Memory used [KB]: 1771
% 0.21/0.45 % (29428)Time elapsed: 0.077 s
% 0.21/0.45 % (29428)Instructions burned: 124 (million)
% 0.21/0.45 % (29421)Success in time 0.092 s
%------------------------------------------------------------------------------