TSTP Solution File: CAT009-4 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : CAT009-4 : 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 : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 04:43:46 EDT 2024
% Result : Unsatisfiable 0.22s 0.45s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 86
% Syntax : Number of formulae : 262 ( 19 unt; 0 def)
% Number of atoms : 735 ( 134 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 875 ( 402 ~; 400 |; 0 &)
% ( 73 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 77 ( 75 usr; 74 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 258 ( 258 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2197,plain,
$false,
inference(avatar_sat_refutation,[],[f19,f24,f28,f32,f36,f40,f45,f49,f53,f58,f65,f72,f77,f91,f96,f102,f109,f115,f120,f125,f129,f141,f145,f172,f190,f227,f246,f253,f261,f275,f279,f307,f313,f318,f333,f359,f364,f369,f373,f421,f425,f429,f481,f485,f563,f571,f575,f580,f584,f588,f592,f596,f600,f604,f685,f776,f854,f858,f914,f918,f922,f1063,f1067,f1071,f1075,f1350,f1436,f1440,f1637,f1641,f1645,f1841,f2195,f2196]) ).
fof(f2196,plain,
( spl0_1
| ~ spl0_2
| ~ spl0_53
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f751,f682,f598,f21,f16]) ).
fof(f16,plain,
( spl0_1
<=> domain(compose(a,b)) = domain(b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f21,plain,
( spl0_2
<=> there_exists(compose(a,b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f598,plain,
( spl0_53
<=> ! [X0,X1] :
( ~ there_exists(compose(X1,X0))
| codomain(domain(X0)) = domain(compose(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f682,plain,
( spl0_55
<=> domain(b) = codomain(domain(b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f751,plain,
( domain(compose(a,b)) = domain(b)
| ~ spl0_2
| ~ spl0_53
| ~ spl0_55 ),
inference(forward_demodulation,[],[f737,f684]) ).
fof(f684,plain,
( domain(b) = codomain(domain(b))
| ~ spl0_55 ),
inference(avatar_component_clause,[],[f682]) ).
fof(f737,plain,
( domain(compose(a,b)) = codomain(domain(b))
| ~ spl0_2
| ~ spl0_53 ),
inference(resolution,[],[f599,f23]) ).
fof(f23,plain,
( there_exists(compose(a,b))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f21]) ).
fof(f599,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X1,X0))
| codomain(domain(X0)) = domain(compose(X1,X0)) )
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f598]) ).
fof(f2195,plain,
( spl0_73
| ~ spl0_2
| ~ spl0_21
| ~ spl0_27
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f680,f586,f243,f127,f21,f2192]) ).
fof(f2192,plain,
( spl0_73
<=> codomain(compose(a,b)) = codomain(a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f127,plain,
( spl0_21
<=> ! [X0] :
( ~ there_exists(X0)
| codomain(X0) = domain(codomain(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f243,plain,
( spl0_27
<=> there_exists(a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f586,plain,
( spl0_50
<=> ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| domain(codomain(X0)) = codomain(compose(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f680,plain,
( codomain(compose(a,b)) = codomain(a)
| ~ spl0_2
| ~ spl0_21
| ~ spl0_27
| ~ spl0_50 ),
inference(forward_demodulation,[],[f666,f247]) ).
fof(f247,plain,
( codomain(a) = domain(codomain(a))
| ~ spl0_21
| ~ spl0_27 ),
inference(resolution,[],[f245,f128]) ).
fof(f128,plain,
( ! [X0] :
( ~ there_exists(X0)
| codomain(X0) = domain(codomain(X0)) )
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f127]) ).
fof(f245,plain,
( there_exists(a)
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f666,plain,
( codomain(compose(a,b)) = domain(codomain(a))
| ~ spl0_2
| ~ spl0_50 ),
inference(resolution,[],[f587,f23]) ).
fof(f587,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| domain(codomain(X0)) = codomain(compose(X0,X1)) )
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f586]) ).
fof(f1841,plain,
( spl0_72
| ~ spl0_19
| ~ spl0_20
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f464,f423,f123,f117,f1838]) ).
fof(f1838,plain,
( spl0_72
<=> domain(b) = domain(domain(b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f117,plain,
( spl0_19
<=> there_exists(b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f123,plain,
( spl0_20
<=> ! [X0] :
( ~ there_exists(X0)
| domain(X0) = codomain(domain(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f423,plain,
( spl0_41
<=> ! [X0] :
( codomain(domain(X0)) = domain(codomain(domain(X0)))
| ~ there_exists(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f464,plain,
( domain(b) = domain(domain(b))
| ~ spl0_19
| ~ spl0_20
| ~ spl0_41 ),
inference(forward_demodulation,[],[f456,f174]) ).
fof(f174,plain,
( domain(b) = codomain(domain(b))
| ~ spl0_19
| ~ spl0_20 ),
inference(resolution,[],[f119,f124]) ).
fof(f124,plain,
( ! [X0] :
( ~ there_exists(X0)
| domain(X0) = codomain(domain(X0)) )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f119,plain,
( there_exists(b)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f456,plain,
( codomain(domain(b)) = domain(codomain(domain(b)))
| ~ spl0_19
| ~ spl0_41 ),
inference(resolution,[],[f424,f119]) ).
fof(f424,plain,
( ! [X0] :
( ~ there_exists(X0)
| codomain(domain(X0)) = domain(codomain(domain(X0))) )
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f423]) ).
fof(f1645,plain,
( spl0_71
| ~ spl0_25
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f230,f225,f188,f1643]) ).
fof(f1643,plain,
( spl0_71
<=> ! [X2,X0,X1] :
( ~ there_exists(compose(X2,compose(X0,X1)))
| domain(compose(X2,X0)) = codomain(compose(X1,domain(compose(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f188,plain,
( spl0_25
<=> ! [X0,X1] : compose(X0,X1) = compose(X0,compose(X1,domain(compose(X0,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f225,plain,
( spl0_26
<=> ! [X2,X0,X1] :
( ~ there_exists(compose(X0,compose(X1,X2)))
| domain(compose(X0,X1)) = codomain(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f230,plain,
( ! [X2,X0,X1] :
( ~ there_exists(compose(X2,compose(X0,X1)))
| domain(compose(X2,X0)) = codomain(compose(X1,domain(compose(X0,X1)))) )
| ~ spl0_25
| ~ spl0_26 ),
inference(superposition,[],[f226,f189]) ).
fof(f189,plain,
( ! [X0,X1] : compose(X0,X1) = compose(X0,compose(X1,domain(compose(X0,X1))))
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f188]) ).
fof(f226,plain,
( ! [X2,X0,X1] :
( ~ there_exists(compose(X0,compose(X1,X2)))
| domain(compose(X0,X1)) = codomain(X2) )
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f225]) ).
fof(f1641,plain,
( spl0_70
| ~ spl0_12
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f197,f188,f70,f1639]) ).
fof(f1639,plain,
( spl0_70
<=> ! [X2,X0,X1] : compose(X2,compose(X0,X1)) = compose(X2,compose(X0,compose(X1,domain(compose(X2,compose(X0,X1)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f70,plain,
( spl0_12
<=> ! [X2,X0,X1] : compose(X0,compose(X1,X2)) = compose(compose(X0,X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f197,plain,
( ! [X2,X0,X1] : compose(X2,compose(X0,X1)) = compose(X2,compose(X0,compose(X1,domain(compose(X2,compose(X0,X1))))))
| ~ spl0_12
| ~ spl0_25 ),
inference(superposition,[],[f189,f71]) ).
fof(f71,plain,
( ! [X2,X0,X1] : compose(X0,compose(X1,X2)) = compose(compose(X0,X1),X2)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f1637,plain,
( spl0_69
| ~ spl0_12
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f196,f188,f70,f1635]) ).
fof(f1635,plain,
( spl0_69
<=> ! [X2,X0,X1] : compose(X0,compose(X1,X2)) = compose(compose(X0,X1),compose(X2,domain(compose(X0,compose(X1,X2))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f196,plain,
( ! [X2,X0,X1] : compose(X0,compose(X1,X2)) = compose(compose(X0,X1),compose(X2,domain(compose(X0,compose(X1,X2)))))
| ~ spl0_12
| ~ spl0_25 ),
inference(superposition,[],[f189,f71]) ).
fof(f1440,plain,
( spl0_68
| ~ spl0_12
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f233,f225,f70,f1438]) ).
fof(f1438,plain,
( spl0_68
<=> ! [X0,X3,X2,X1] :
( ~ there_exists(compose(X3,compose(X0,compose(X1,X2))))
| codomain(X2) = domain(compose(X3,compose(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f233,plain,
( ! [X2,X3,X0,X1] :
( ~ there_exists(compose(X3,compose(X0,compose(X1,X2))))
| codomain(X2) = domain(compose(X3,compose(X0,X1))) )
| ~ spl0_12
| ~ spl0_26 ),
inference(superposition,[],[f226,f71]) ).
fof(f1436,plain,
( spl0_67
| ~ spl0_12
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f212,f188,f70,f1434]) ).
fof(f1434,plain,
( spl0_67
<=> ! [X0,X1] : compose(X0,X1) = compose(X0,compose(X1,compose(domain(compose(X0,X1)),domain(compose(X0,X1))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f212,plain,
( ! [X0,X1] : compose(X0,X1) = compose(X0,compose(X1,compose(domain(compose(X0,X1)),domain(compose(X0,X1)))))
| ~ spl0_12
| ~ spl0_25 ),
inference(forward_demodulation,[],[f193,f71]) ).
fof(f193,plain,
( ! [X0,X1] : compose(X0,X1) = compose(X0,compose(compose(X1,domain(compose(X0,X1))),domain(compose(X0,X1))))
| ~ spl0_25 ),
inference(superposition,[],[f189,f189]) ).
fof(f1350,plain,
( spl0_66
| ~ spl0_16
| ~ spl0_20
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f249,f243,f123,f99,f1347]) ).
fof(f1347,plain,
( spl0_66
<=> codomain(b) = codomain(codomain(b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f99,plain,
( spl0_16
<=> domain(a) = codomain(b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f249,plain,
( codomain(b) = codomain(codomain(b))
| ~ spl0_16
| ~ spl0_20
| ~ spl0_27 ),
inference(forward_demodulation,[],[f248,f101]) ).
fof(f101,plain,
( domain(a) = codomain(b)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f248,plain,
( domain(a) = codomain(domain(a))
| ~ spl0_20
| ~ spl0_27 ),
inference(resolution,[],[f245,f124]) ).
fof(f1075,plain,
( spl0_65
| ~ spl0_23
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f232,f225,f143,f1073]) ).
fof(f1073,plain,
( spl0_65
<=> ! [X2,X0,X1] :
( ~ there_exists(compose(X2,compose(X0,X1)))
| codomain(compose(X0,X1)) = domain(compose(X2,codomain(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f143,plain,
( spl0_23
<=> ! [X0,X1] : compose(X0,X1) = compose(codomain(X0),compose(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f232,plain,
( ! [X2,X0,X1] :
( ~ there_exists(compose(X2,compose(X0,X1)))
| codomain(compose(X0,X1)) = domain(compose(X2,codomain(X0))) )
| ~ spl0_23
| ~ spl0_26 ),
inference(superposition,[],[f226,f144]) ).
fof(f144,plain,
( ! [X0,X1] : compose(X0,X1) = compose(codomain(X0),compose(X0,X1))
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f1071,plain,
( spl0_64
| ~ spl0_22
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f229,f225,f139,f1069]) ).
fof(f1069,plain,
( spl0_64
<=> ! [X2,X0,X1] :
( ~ there_exists(compose(X2,compose(X0,X1)))
| codomain(compose(domain(X0),X1)) = domain(compose(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f139,plain,
( spl0_22
<=> ! [X0,X1] : compose(X0,X1) = compose(X0,compose(domain(X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f229,plain,
( ! [X2,X0,X1] :
( ~ there_exists(compose(X2,compose(X0,X1)))
| codomain(compose(domain(X0),X1)) = domain(compose(X2,X0)) )
| ~ spl0_22
| ~ spl0_26 ),
inference(superposition,[],[f226,f140]) ).
fof(f140,plain,
( ! [X0,X1] : compose(X0,X1) = compose(X0,compose(domain(X0),X1))
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f1067,plain,
( spl0_63
| ~ spl0_12
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f164,f143,f70,f1065]) ).
fof(f1065,plain,
( spl0_63
<=> ! [X2,X0,X1] : compose(X0,compose(X1,X2)) = compose(codomain(compose(X0,X1)),compose(X0,compose(X1,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f164,plain,
( ! [X2,X0,X1] : compose(X0,compose(X1,X2)) = compose(codomain(compose(X0,X1)),compose(X0,compose(X1,X2)))
| ~ spl0_12
| ~ spl0_23 ),
inference(superposition,[],[f144,f71]) ).
fof(f1063,plain,
( spl0_62
| ~ spl0_12
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f156,f139,f70,f1061]) ).
fof(f1061,plain,
( spl0_62
<=> ! [X2,X0,X1] : compose(X0,compose(X1,X2)) = compose(X0,compose(X1,compose(domain(compose(X0,X1)),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f156,plain,
( ! [X2,X0,X1] : compose(X0,compose(X1,X2)) = compose(X0,compose(X1,compose(domain(compose(X0,X1)),X2)))
| ~ spl0_12
| ~ spl0_22 ),
inference(forward_demodulation,[],[f149,f71]) ).
fof(f149,plain,
( ! [X2,X0,X1] : compose(compose(X0,X1),X2) = compose(X0,compose(X1,compose(domain(compose(X0,X1)),X2)))
| ~ spl0_12
| ~ spl0_22 ),
inference(superposition,[],[f140,f71]) ).
fof(f922,plain,
( spl0_61
| ~ spl0_12
| ~ spl0_22
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f211,f188,f139,f70,f920]) ).
fof(f920,plain,
( spl0_61
<=> ! [X0,X1] : compose(X0,X1) = compose(X0,compose(domain(X0),compose(X1,domain(compose(X0,X1))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f211,plain,
( ! [X0,X1] : compose(X0,X1) = compose(X0,compose(domain(X0),compose(X1,domain(compose(X0,X1)))))
| ~ spl0_12
| ~ spl0_22
| ~ spl0_25 ),
inference(forward_demodulation,[],[f192,f71]) ).
fof(f192,plain,
( ! [X0,X1] : compose(X0,X1) = compose(X0,compose(compose(domain(X0),X1),domain(compose(X0,X1))))
| ~ spl0_22
| ~ spl0_25 ),
inference(superposition,[],[f189,f140]) ).
fof(f918,plain,
( spl0_60
| ~ spl0_12
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f179,f170,f70,f916]) ).
fof(f916,plain,
( spl0_60
<=> ! [X0,X3,X2,X1] :
( ~ there_exists(compose(X3,compose(X0,compose(X1,X2))))
| there_exists(domain(compose(X3,compose(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f170,plain,
( spl0_24
<=> ! [X2,X0,X1] :
( ~ there_exists(compose(X0,compose(X1,X2)))
| there_exists(domain(compose(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f179,plain,
( ! [X2,X3,X0,X1] :
( ~ there_exists(compose(X3,compose(X0,compose(X1,X2))))
| there_exists(domain(compose(X3,compose(X0,X1)))) )
| ~ spl0_12
| ~ spl0_24 ),
inference(superposition,[],[f171,f71]) ).
fof(f171,plain,
( ! [X2,X0,X1] :
( ~ there_exists(compose(X0,compose(X1,X2)))
| there_exists(domain(compose(X0,X1))) )
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f914,plain,
( spl0_59
| ~ spl0_21
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f247,f243,f127,f911]) ).
fof(f911,plain,
( spl0_59
<=> codomain(a) = domain(codomain(a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f858,plain,
( spl0_58
| ~ spl0_9
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f237,f225,f51,f856]) ).
fof(f856,plain,
( spl0_58
<=> ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| codomain(X1) = domain(compose(codomain(compose(X0,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f51,plain,
( spl0_9
<=> ! [X0] : compose(codomain(X0),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f237,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| codomain(X1) = domain(compose(codomain(compose(X0,X1)),X0)) )
| ~ spl0_9
| ~ spl0_26 ),
inference(superposition,[],[f226,f52]) ).
fof(f52,plain,
( ! [X0] : compose(codomain(X0),X0) = X0
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f854,plain,
( spl0_57
| ~ spl0_11
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f206,f188,f63,f852]) ).
fof(f852,plain,
( spl0_57
<=> ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| domain(X0) = codomain(compose(X1,domain(compose(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f63,plain,
( spl0_11
<=> ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| domain(X0) = codomain(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f206,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| domain(X0) = codomain(compose(X1,domain(compose(X0,X1)))) )
| ~ spl0_11
| ~ spl0_25 ),
inference(superposition,[],[f64,f189]) ).
fof(f64,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| domain(X0) = codomain(X1) )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f776,plain,
( spl0_56
| ~ spl0_22
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f221,f188,f139,f774]) ).
fof(f774,plain,
( spl0_56
<=> ! [X0,X1] : compose(X0,X1) = compose(X0,compose(X1,domain(compose(domain(X0),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f221,plain,
( ! [X0,X1] : compose(X0,X1) = compose(X0,compose(X1,domain(compose(domain(X0),X1))))
| ~ spl0_22
| ~ spl0_25 ),
inference(forward_demodulation,[],[f208,f140]) ).
fof(f208,plain,
( ! [X0,X1] : compose(X0,compose(domain(X0),X1)) = compose(X0,compose(X1,domain(compose(domain(X0),X1))))
| ~ spl0_22
| ~ spl0_25 ),
inference(superposition,[],[f140,f189]) ).
fof(f685,plain,
( spl0_55
| ~ spl0_19
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f174,f123,f117,f682]) ).
fof(f604,plain,
( spl0_54
| ~ spl0_9
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f231,f225,f51,f602]) ).
fof(f602,plain,
( spl0_54
<=> ! [X0,X1] :
( ~ there_exists(compose(X1,X0))
| codomain(X0) = domain(compose(X1,codomain(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f231,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X1,X0))
| codomain(X0) = domain(compose(X1,codomain(X0))) )
| ~ spl0_9
| ~ spl0_26 ),
inference(superposition,[],[f226,f52]) ).
fof(f600,plain,
( spl0_53
| ~ spl0_8
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f228,f225,f47,f598]) ).
fof(f47,plain,
( spl0_8
<=> ! [X0] : compose(X0,domain(X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f228,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X1,X0))
| codomain(domain(X0)) = domain(compose(X1,X0)) )
| ~ spl0_8
| ~ spl0_26 ),
inference(superposition,[],[f226,f48]) ).
fof(f48,plain,
( ! [X0] : compose(X0,domain(X0)) = X0
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f596,plain,
( spl0_52
| ~ spl0_9
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f182,f170,f51,f594]) ).
fof(f594,plain,
( spl0_52
<=> ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| there_exists(domain(compose(codomain(compose(X0,X1)),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f182,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| there_exists(domain(compose(codomain(compose(X0,X1)),X0))) )
| ~ spl0_9
| ~ spl0_24 ),
inference(superposition,[],[f171,f52]) ).
fof(f592,plain,
( spl0_51
| ~ spl0_23
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f178,f170,f143,f590]) ).
fof(f590,plain,
( spl0_51
<=> ! [X2,X0,X1] :
( ~ there_exists(compose(X2,compose(X0,X1)))
| there_exists(domain(compose(X2,codomain(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f178,plain,
( ! [X2,X0,X1] :
( ~ there_exists(compose(X2,compose(X0,X1)))
| there_exists(domain(compose(X2,codomain(X0)))) )
| ~ spl0_23
| ~ spl0_24 ),
inference(superposition,[],[f171,f144]) ).
fof(f588,plain,
( spl0_50
| ~ spl0_11
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f166,f143,f63,f586]) ).
fof(f166,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| domain(codomain(X0)) = codomain(compose(X0,X1)) )
| ~ spl0_11
| ~ spl0_23 ),
inference(superposition,[],[f64,f144]) ).
fof(f584,plain,
( spl0_49
| ~ spl0_11
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f151,f139,f63,f582]) ).
fof(f582,plain,
( spl0_49
<=> ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| domain(X0) = codomain(compose(domain(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f151,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| domain(X0) = codomain(compose(domain(X0),X1)) )
| ~ spl0_11
| ~ spl0_22 ),
inference(superposition,[],[f64,f140]) ).
fof(f580,plain,
( spl0_48
| ~ spl0_19
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f173,f127,f117,f577]) ).
fof(f577,plain,
( spl0_48
<=> codomain(b) = domain(codomain(b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f173,plain,
( codomain(b) = domain(codomain(b))
| ~ spl0_19
| ~ spl0_21 ),
inference(resolution,[],[f119,f128]) ).
fof(f575,plain,
( spl0_47
| ~ spl0_18
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f137,f127,f113,f573]) ).
fof(f573,plain,
( spl0_47
<=> ! [X0] :
( codomain(domain(codomain(X0))) = domain(codomain(domain(codomain(X0))))
| ~ there_exists(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f113,plain,
( spl0_18
<=> ! [X0] :
( ~ there_exists(X0)
| there_exists(domain(codomain(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f137,plain,
( ! [X0] :
( codomain(domain(codomain(X0))) = domain(codomain(domain(codomain(X0))))
| ~ there_exists(X0) )
| ~ spl0_18
| ~ spl0_21 ),
inference(resolution,[],[f128,f114]) ).
fof(f114,plain,
( ! [X0] :
( there_exists(domain(codomain(X0)))
| ~ there_exists(X0) )
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f571,plain,
( spl0_46
| ~ spl0_18
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f133,f123,f113,f569]) ).
fof(f569,plain,
( spl0_46
<=> ! [X0] :
( domain(domain(codomain(X0))) = codomain(domain(domain(codomain(X0))))
| ~ there_exists(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f133,plain,
( ! [X0] :
( domain(domain(codomain(X0))) = codomain(domain(domain(codomain(X0))))
| ~ there_exists(X0) )
| ~ spl0_18
| ~ spl0_20 ),
inference(resolution,[],[f124,f114]) ).
fof(f563,plain,
( ~ spl0_15
| spl0_45
| ~ spl0_14
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f103,f99,f89,f561,f93]) ).
fof(f93,plain,
( spl0_15
<=> there_exists(codomain(b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f561,plain,
( spl0_45
<=> ! [X0] :
( codomain(X0) != codomain(b)
| there_exists(compose(a,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f89,plain,
( spl0_14
<=> ! [X0,X1] :
( ~ there_exists(domain(X0))
| there_exists(compose(X0,X1))
| domain(X0) != codomain(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f103,plain,
( ! [X0] :
( codomain(X0) != codomain(b)
| there_exists(compose(a,X0))
| ~ there_exists(codomain(b)) )
| ~ spl0_14
| ~ spl0_16 ),
inference(superposition,[],[f90,f101]) ).
fof(f90,plain,
( ! [X0,X1] :
( domain(X0) != codomain(X1)
| there_exists(compose(X0,X1))
| ~ there_exists(domain(X0)) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f485,plain,
( spl0_44
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f163,f143,f483]) ).
fof(f483,plain,
( spl0_44
<=> ! [X0,X1] : compose(X0,X1) = compose(codomain(codomain(X0)),compose(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f163,plain,
( ! [X0,X1] : compose(X0,X1) = compose(codomain(codomain(X0)),compose(X0,X1))
| ~ spl0_23 ),
inference(superposition,[],[f144,f144]) ).
fof(f481,plain,
( spl0_43
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f155,f139,f479]) ).
fof(f479,plain,
( spl0_43
<=> ! [X0,X1] : compose(X0,X1) = compose(X0,compose(domain(domain(X0)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f155,plain,
( ! [X0,X1] : compose(X0,X1) = compose(X0,compose(domain(domain(X0)),X1))
| ~ spl0_22 ),
inference(forward_demodulation,[],[f148,f140]) ).
fof(f148,plain,
( ! [X0,X1] : compose(X0,compose(domain(X0),X1)) = compose(X0,compose(domain(domain(X0)),X1))
| ~ spl0_22 ),
inference(superposition,[],[f140,f140]) ).
fof(f429,plain,
( spl0_42
| ~ spl0_9
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f177,f170,f51,f427]) ).
fof(f427,plain,
( spl0_42
<=> ! [X0,X1] :
( ~ there_exists(compose(X1,X0))
| there_exists(domain(compose(X1,codomain(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f177,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X1,X0))
| there_exists(domain(compose(X1,codomain(X0)))) )
| ~ spl0_9
| ~ spl0_24 ),
inference(superposition,[],[f171,f52]) ).
fof(f425,plain,
( spl0_41
| ~ spl0_17
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f136,f127,f107,f423]) ).
fof(f107,plain,
( spl0_17
<=> ! [X0] :
( ~ there_exists(X0)
| there_exists(domain(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f136,plain,
( ! [X0] :
( codomain(domain(X0)) = domain(codomain(domain(X0)))
| ~ there_exists(X0) )
| ~ spl0_17
| ~ spl0_21 ),
inference(resolution,[],[f128,f108]) ).
fof(f108,plain,
( ! [X0] :
( there_exists(domain(X0))
| ~ there_exists(X0) )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f421,plain,
( spl0_40
| ~ spl0_17
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f132,f123,f107,f419]) ).
fof(f419,plain,
( spl0_40
<=> ! [X0] :
( domain(domain(X0)) = codomain(domain(domain(X0)))
| ~ there_exists(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f132,plain,
( ! [X0] :
( domain(domain(X0)) = codomain(domain(domain(X0)))
| ~ there_exists(X0) )
| ~ spl0_17
| ~ spl0_20 ),
inference(resolution,[],[f124,f108]) ).
fof(f373,plain,
( spl0_39
| ~ spl0_16
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f146,f139,f99,f371]) ).
fof(f371,plain,
( spl0_39
<=> ! [X0] : compose(a,X0) = compose(a,compose(codomain(b),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f146,plain,
( ! [X0] : compose(a,X0) = compose(a,compose(codomain(b),X0))
| ~ spl0_16
| ~ spl0_22 ),
inference(superposition,[],[f140,f101]) ).
fof(f369,plain,
( spl0_38
| ~ spl0_2
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f134,f127,f21,f366]) ).
fof(f366,plain,
( spl0_38
<=> codomain(compose(a,b)) = domain(codomain(compose(a,b))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f134,plain,
( codomain(compose(a,b)) = domain(codomain(compose(a,b)))
| ~ spl0_2
| ~ spl0_21 ),
inference(resolution,[],[f128,f23]) ).
fof(f364,plain,
( spl0_37
| ~ spl0_2
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f130,f123,f21,f361]) ).
fof(f361,plain,
( spl0_37
<=> domain(compose(a,b)) = codomain(domain(compose(a,b))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f130,plain,
( domain(compose(a,b)) = codomain(domain(compose(a,b)))
| ~ spl0_2
| ~ spl0_20 ),
inference(resolution,[],[f124,f23]) ).
fof(f359,plain,
( spl0_36
| ~ spl0_2
| ~ spl0_21
| ~ spl0_27
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f329,f316,f243,f127,f21,f356]) ).
fof(f356,plain,
( spl0_36
<=> there_exists(codomain(a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f316,plain,
( spl0_34
<=> ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| there_exists(domain(codomain(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f329,plain,
( there_exists(codomain(a))
| ~ spl0_2
| ~ spl0_21
| ~ spl0_27
| ~ spl0_34 ),
inference(forward_demodulation,[],[f319,f247]) ).
fof(f319,plain,
( there_exists(domain(codomain(a)))
| ~ spl0_2
| ~ spl0_34 ),
inference(resolution,[],[f317,f23]) ).
fof(f317,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| there_exists(domain(codomain(X0))) )
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f316]) ).
fof(f333,plain,
( spl0_35
| ~ spl0_8
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f191,f188,f47,f331]) ).
fof(f331,plain,
( spl0_35
<=> ! [X0] : compose(X0,compose(domain(X0),domain(X0))) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f191,plain,
( ! [X0] : compose(X0,compose(domain(X0),domain(X0))) = X0
| ~ spl0_8
| ~ spl0_25 ),
inference(superposition,[],[f189,f48]) ).
fof(f318,plain,
( spl0_34
| ~ spl0_10
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f167,f143,f56,f316]) ).
fof(f56,plain,
( spl0_10
<=> ! [X0,X1] :
( there_exists(domain(X0))
| ~ there_exists(compose(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f167,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| there_exists(domain(codomain(X0))) )
| ~ spl0_10
| ~ spl0_23 ),
inference(superposition,[],[f57,f144]) ).
fof(f57,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| there_exists(domain(X0)) )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f313,plain,
( spl0_33
| ~ spl0_15
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f135,f127,f93,f310]) ).
fof(f310,plain,
( spl0_33
<=> codomain(codomain(b)) = domain(codomain(codomain(b))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f135,plain,
( codomain(codomain(b)) = domain(codomain(codomain(b)))
| ~ spl0_15
| ~ spl0_21 ),
inference(resolution,[],[f128,f95]) ).
fof(f95,plain,
( there_exists(codomain(b))
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f307,plain,
( spl0_32
| ~ spl0_15
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f131,f123,f93,f304]) ).
fof(f304,plain,
( spl0_32
<=> domain(codomain(b)) = codomain(domain(codomain(b))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f131,plain,
( domain(codomain(b)) = codomain(domain(codomain(b)))
| ~ spl0_15
| ~ spl0_20 ),
inference(resolution,[],[f124,f95]) ).
fof(f279,plain,
( spl0_31
| ~ spl0_9
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f162,f143,f51,f277]) ).
fof(f277,plain,
( spl0_31
<=> ! [X0] : compose(codomain(codomain(X0)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f162,plain,
( ! [X0] : compose(codomain(codomain(X0)),X0) = X0
| ~ spl0_9
| ~ spl0_23 ),
inference(superposition,[],[f144,f52]) ).
fof(f275,plain,
( spl0_30
| ~ spl0_8
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f154,f139,f47,f273]) ).
fof(f273,plain,
( spl0_30
<=> ! [X0] : compose(X0,domain(domain(X0))) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f154,plain,
( ! [X0] : compose(X0,domain(domain(X0))) = X0
| ~ spl0_8
| ~ spl0_22 ),
inference(forward_demodulation,[],[f147,f48]) ).
fof(f147,plain,
( ! [X0] : compose(X0,domain(X0)) = compose(X0,domain(domain(X0)))
| ~ spl0_8
| ~ spl0_22 ),
inference(superposition,[],[f140,f48]) ).
fof(f261,plain,
( spl0_29
| ~ spl0_8
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f104,f99,f47,f258]) ).
fof(f258,plain,
( spl0_29
<=> a = compose(a,codomain(b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f104,plain,
( a = compose(a,codomain(b))
| ~ spl0_8
| ~ spl0_16 ),
inference(superposition,[],[f48,f101]) ).
fof(f253,plain,
( spl0_28
| ~ spl0_4
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f121,f113,f30,f251]) ).
fof(f251,plain,
( spl0_28
<=> ! [X0] :
( ~ there_exists(X0)
| there_exists(codomain(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f30,plain,
( spl0_4
<=> ! [X0] :
( there_exists(X0)
| ~ there_exists(domain(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f121,plain,
( ! [X0] :
( ~ there_exists(X0)
| there_exists(codomain(X0)) )
| ~ spl0_4
| ~ spl0_18 ),
inference(resolution,[],[f114,f31]) ).
fof(f31,plain,
( ! [X0] :
( ~ there_exists(domain(X0))
| there_exists(X0) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f30]) ).
fof(f246,plain,
( spl0_27
| ~ spl0_15
| ~ spl0_4
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f105,f99,f30,f93,f243]) ).
fof(f105,plain,
( ~ there_exists(codomain(b))
| there_exists(a)
| ~ spl0_4
| ~ spl0_16 ),
inference(superposition,[],[f31,f101]) ).
fof(f227,plain,
( spl0_26
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f84,f70,f63,f225]) ).
fof(f84,plain,
( ! [X2,X0,X1] :
( ~ there_exists(compose(X0,compose(X1,X2)))
| domain(compose(X0,X1)) = codomain(X2) )
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f64,f71]) ).
fof(f190,plain,
( spl0_25
| ~ spl0_8
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f82,f70,f47,f188]) ).
fof(f82,plain,
( ! [X0,X1] : compose(X0,X1) = compose(X0,compose(X1,domain(compose(X0,X1))))
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[],[f71,f48]) ).
fof(f172,plain,
( spl0_24
| ~ spl0_10
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f85,f70,f56,f170]) ).
fof(f85,plain,
( ! [X2,X0,X1] :
( ~ there_exists(compose(X0,compose(X1,X2)))
| there_exists(domain(compose(X0,X1))) )
| ~ spl0_10
| ~ spl0_12 ),
inference(superposition,[],[f57,f71]) ).
fof(f145,plain,
( spl0_23
| ~ spl0_9
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f80,f70,f51,f143]) ).
fof(f80,plain,
( ! [X0,X1] : compose(X0,X1) = compose(codomain(X0),compose(X0,X1))
| ~ spl0_9
| ~ spl0_12 ),
inference(superposition,[],[f71,f52]) ).
fof(f141,plain,
( spl0_22
| ~ spl0_8
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f79,f70,f47,f139]) ).
fof(f79,plain,
( ! [X0,X1] : compose(X0,X1) = compose(X0,compose(domain(X0),X1))
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[],[f71,f48]) ).
fof(f129,plain,
( spl0_21
| ~ spl0_9
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f68,f63,f51,f127]) ).
fof(f68,plain,
( ! [X0] :
( ~ there_exists(X0)
| codomain(X0) = domain(codomain(X0)) )
| ~ spl0_9
| ~ spl0_11 ),
inference(superposition,[],[f64,f52]) ).
fof(f125,plain,
( spl0_20
| ~ spl0_8
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f67,f63,f47,f123]) ).
fof(f67,plain,
( ! [X0] :
( ~ there_exists(X0)
| domain(X0) = codomain(domain(X0)) )
| ~ spl0_8
| ~ spl0_11 ),
inference(superposition,[],[f64,f48]) ).
fof(f120,plain,
( spl0_19
| ~ spl0_5
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f97,f93,f34,f117]) ).
fof(f34,plain,
( spl0_5
<=> ! [X0] :
( there_exists(X0)
| ~ there_exists(codomain(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f97,plain,
( there_exists(b)
| ~ spl0_5
| ~ spl0_15 ),
inference(resolution,[],[f95,f35]) ).
fof(f35,plain,
( ! [X0] :
( ~ there_exists(codomain(X0))
| there_exists(X0) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f34]) ).
fof(f115,plain,
( spl0_18
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f61,f56,f51,f113]) ).
fof(f61,plain,
( ! [X0] :
( ~ there_exists(X0)
| there_exists(domain(codomain(X0))) )
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f57,f52]) ).
fof(f109,plain,
( spl0_17
| ~ spl0_8
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f60,f56,f47,f107]) ).
fof(f60,plain,
( ! [X0] :
( ~ there_exists(X0)
| there_exists(domain(X0)) )
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f57,f48]) ).
fof(f102,plain,
( spl0_16
| ~ spl0_2
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f66,f63,f21,f99]) ).
fof(f66,plain,
( domain(a) = codomain(b)
| ~ spl0_2
| ~ spl0_11 ),
inference(resolution,[],[f64,f23]) ).
fof(f96,plain,
( spl0_15
| ~ spl0_2
| ~ spl0_11
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f78,f74,f63,f21,f93]) ).
fof(f74,plain,
( spl0_13
<=> there_exists(domain(a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f78,plain,
( there_exists(codomain(b))
| ~ spl0_2
| ~ spl0_11
| ~ spl0_13 ),
inference(forward_demodulation,[],[f76,f66]) ).
fof(f76,plain,
( there_exists(domain(a))
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f91,plain,
spl0_14,
inference(avatar_split_clause,[],[f8,f89]) ).
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(f77,plain,
( spl0_13
| ~ spl0_2
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f59,f56,f21,f74]) ).
fof(f59,plain,
( there_exists(domain(a))
| ~ spl0_2
| ~ spl0_10 ),
inference(resolution,[],[f57,f23]) ).
fof(f72,plain,
spl0_12,
inference(avatar_split_clause,[],[f9,f70]) ).
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(f65,plain,
spl0_11,
inference(avatar_split_clause,[],[f7,f63]) ).
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(f58,plain,
spl0_10,
inference(avatar_split_clause,[],[f6,f56]) ).
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(f53,plain,
spl0_9,
inference(avatar_split_clause,[],[f11,f51]) ).
fof(f11,axiom,
! [X0] : compose(codomain(X0),X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_codomain) ).
fof(f49,plain,
spl0_8,
inference(avatar_split_clause,[],[f10,f47]) ).
fof(f10,axiom,
! [X0] : compose(X0,domain(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_domain) ).
fof(f45,plain,
spl0_7,
inference(avatar_split_clause,[],[f2,f43]) ).
fof(f43,plain,
( spl0_7
<=> ! [X0,X1] :
( ~ equivalent(X0,X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f2,axiom,
! [X0,X1] :
( ~ equivalent(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_implies_existence2) ).
fof(f40,plain,
spl0_6,
inference(avatar_split_clause,[],[f14,f38]) ).
fof(f38,plain,
( spl0_6
<=> ! [X1] :
( ~ there_exists(X1)
| equivalent(X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f14,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(f36,plain,
spl0_5,
inference(avatar_split_clause,[],[f5,f34]) ).
fof(f5,axiom,
! [X0] :
( there_exists(X0)
| ~ there_exists(codomain(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_has_elements) ).
fof(f32,plain,
spl0_4,
inference(avatar_split_clause,[],[f4,f30]) ).
fof(f4,axiom,
! [X0] :
( there_exists(X0)
| ~ there_exists(domain(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_has_elements) ).
fof(f28,plain,
spl0_3,
inference(avatar_split_clause,[],[f1,f26]) ).
fof(f26,plain,
( spl0_3
<=> ! [X0,X1] :
( there_exists(X0)
| ~ equivalent(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f1,axiom,
! [X0,X1] :
( there_exists(X0)
| ~ equivalent(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_implies_existence1) ).
fof(f24,plain,
spl0_2,
inference(avatar_split_clause,[],[f12,f21]) ).
fof(f12,axiom,
there_exists(compose(a,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ab_exists) ).
fof(f19,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f13,f16]) ).
fof(f13,axiom,
domain(compose(a,b)) != domain(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_domain_of_ab_equals_domain_of_b) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : CAT009-4 : TPTP v8.1.2. Released v1.0.0.
% 0.03/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n014.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 3 18:11:23 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (19552)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.38 % (19557)WARNING: value z3 for option sas not known
% 0.22/0.38 % (19555)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.38 % (19558)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.38 % (19556)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.38 % (19557)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)
% 0.22/0.38 % (19559)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)
% 0.22/0.38 % (19561)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)
% 0.22/0.38 % (19560)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)
% 0.22/0.38 TRYING [1]
% 0.22/0.38 TRYING [2]
% 0.22/0.38 TRYING [1]
% 0.22/0.38 TRYING [3]
% 0.22/0.38 TRYING [2]
% 0.22/0.39 TRYING [4]
% 0.22/0.39 TRYING [3]
% 0.22/0.40 TRYING [5]
% 0.22/0.40 TRYING [4]
% 0.22/0.41 TRYING [1]
% 0.22/0.41 TRYING [2]
% 0.22/0.41 TRYING [3]
% 0.22/0.41 TRYING [4]
% 0.22/0.42 TRYING [5]
% 0.22/0.42 TRYING [5]
% 0.22/0.43 TRYING [6]
% 0.22/0.45 % (19559)First to succeed.
% 0.22/0.45 % (19559)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-19552"
% 0.22/0.45 % (19559)Refutation found. Thanks to Tanya!
% 0.22/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.22/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.45 % (19559)------------------------------
% 0.22/0.45 % (19559)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.45 % (19559)Termination reason: Refutation
% 0.22/0.45
% 0.22/0.45 % (19559)Memory used [KB]: 1795
% 0.22/0.45 % (19559)Time elapsed: 0.072 s
% 0.22/0.45 % (19559)Instructions burned: 119 (million)
% 0.22/0.45 % (19552)Success in time 0.089 s
%------------------------------------------------------------------------------