TSTP Solution File: CAT018-4 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : CAT018-4 : 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 : n018.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 04:43:50 EDT 2024
% Result : Unsatisfiable 0.22s 0.47s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 113
% Syntax : Number of formulae : 362 ( 21 unt; 0 def)
% Number of atoms : 1023 ( 189 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 1225 ( 564 ~; 562 |; 0 &)
% ( 99 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 103 ( 101 usr; 100 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 275 ( 275 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2922,plain,
$false,
inference(avatar_sat_refutation,[],[f20,f25,f30,f34,f38,f42,f46,f51,f55,f59,f64,f72,f77,f85,f98,f103,f110,f116,f121,f126,f137,f144,f149,f153,f165,f176,f180,f208,f224,f261,f285,f292,f300,f305,f329,f333,f337,f366,f372,f386,f391,f397,f406,f430,f448,f477,f482,f487,f492,f497,f501,f505,f599,f607,f611,f681,f685,f775,f780,f796,f815,f819,f823,f827,f831,f835,f839,f844,f848,f1075,f1080,f1172,f1176,f1248,f1252,f1415,f1420,f1424,f1428,f1432,f1829,f1833,f1979,f2054,f2058,f2062,f2647,f2653,f2658,f2663,f2668,f2759,f2763,f2785,f2790,f2795,f2912,f2916,f2920,f2921]) ).
fof(f2921,plain,
( spl0_1
| ~ spl0_58
| ~ spl0_89 ),
inference(avatar_split_clause,[],[f2701,f2655,f773,f17]) ).
fof(f17,plain,
( spl0_1
<=> there_exists(compose(a,compose(b,c))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f773,plain,
( spl0_58
<=> ! [X0] :
( codomain(X0) != codomain(b)
| there_exists(compose(a,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f2655,plain,
( spl0_89
<=> codomain(b) = codomain(compose(b,c)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f2701,plain,
( there_exists(compose(a,compose(b,c)))
| ~ spl0_58
| ~ spl0_89 ),
inference(trivial_inequality_removal,[],[f2699]) ).
fof(f2699,plain,
( codomain(b) != codomain(b)
| there_exists(compose(a,compose(b,c)))
| ~ spl0_58
| ~ spl0_89 ),
inference(superposition,[],[f774,f2657]) ).
fof(f2657,plain,
( codomain(b) = codomain(compose(b,c))
| ~ spl0_89 ),
inference(avatar_component_clause,[],[f2655]) ).
fof(f774,plain,
( ! [X0] :
( codomain(X0) != codomain(b)
| there_exists(compose(a,X0)) )
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f773]) ).
fof(f2920,plain,
( spl0_99
| ~ spl0_37
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f439,f428,f335,f2918]) ).
fof(f2918,plain,
( spl0_99
<=> ! [X0] :
( ~ there_exists(X0)
| there_exists(domain(codomain(codomain(codomain(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f335,plain,
( spl0_37
<=> ! [X0] : compose(codomain(codomain(X0)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f428,plain,
( spl0_44
<=> ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| there_exists(domain(codomain(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f439,plain,
( ! [X0] :
( ~ there_exists(X0)
| there_exists(domain(codomain(codomain(codomain(X0))))) )
| ~ spl0_37
| ~ spl0_44 ),
inference(superposition,[],[f429,f336]) ).
fof(f336,plain,
( ! [X0] : compose(codomain(codomain(X0)),X0) = X0
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f335]) ).
fof(f429,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| there_exists(domain(codomain(X0))) )
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f428]) ).
fof(f2916,plain,
( spl0_98
| ~ spl0_27
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f355,f335,f178,f2914]) ).
fof(f2914,plain,
( spl0_98
<=> ! [X0] : compose(codomain(codomain(codomain(X0))),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f178,plain,
( spl0_27
<=> ! [X0,X1] : compose(X0,X1) = compose(codomain(X0),compose(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f355,plain,
( ! [X0] : compose(codomain(codomain(codomain(X0))),X0) = X0
| ~ spl0_27
| ~ spl0_37 ),
inference(superposition,[],[f179,f336]) ).
fof(f179,plain,
( ! [X0,X1] : compose(X0,X1) = compose(codomain(X0),compose(X0,X1))
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f178]) ).
fof(f2912,plain,
( spl0_97
| ~ spl0_9
| ~ spl0_26
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f351,f331,f174,f53,f2910]) ).
fof(f2910,plain,
( spl0_97
<=> ! [X0] : compose(X0,domain(domain(domain(X0)))) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f53,plain,
( spl0_9
<=> ! [X0] : compose(X0,domain(X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f174,plain,
( spl0_26
<=> ! [X0,X1] : compose(X0,X1) = compose(X0,compose(domain(X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f331,plain,
( spl0_36
<=> ! [X0] : compose(X0,domain(domain(X0))) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f351,plain,
( ! [X0] : compose(X0,domain(domain(domain(X0)))) = X0
| ~ spl0_9
| ~ spl0_26
| ~ spl0_36 ),
inference(forward_demodulation,[],[f348,f54]) ).
fof(f54,plain,
( ! [X0] : compose(X0,domain(X0)) = X0
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f348,plain,
( ! [X0] : compose(X0,domain(X0)) = compose(X0,domain(domain(domain(X0))))
| ~ spl0_26
| ~ spl0_36 ),
inference(superposition,[],[f175,f332]) ).
fof(f332,plain,
( ! [X0] : compose(X0,domain(domain(X0))) = X0
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f331]) ).
fof(f175,plain,
( ! [X0,X1] : compose(X0,X1) = compose(X0,compose(domain(X0),X1))
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f2795,plain,
( spl0_96
| ~ spl0_25
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f623,f597,f162,f2792]) ).
fof(f2792,plain,
( spl0_96
<=> domain(domain(c)) = codomain(domain(domain(c))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f162,plain,
( spl0_25
<=> there_exists(c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f597,plain,
( spl0_53
<=> ! [X0] :
( domain(domain(X0)) = codomain(domain(domain(X0)))
| ~ there_exists(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f623,plain,
( domain(domain(c)) = codomain(domain(domain(c)))
| ~ spl0_25
| ~ spl0_53 ),
inference(resolution,[],[f598,f164]) ).
fof(f164,plain,
( there_exists(c)
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f598,plain,
( ! [X0] :
( ~ there_exists(X0)
| domain(domain(X0)) = codomain(domain(domain(X0))) )
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f597]) ).
fof(f2790,plain,
( spl0_95
| ~ spl0_9
| ~ spl0_43 ),
inference(avatar_split_clause,[],[f412,f403,f53,f2787]) ).
fof(f2787,plain,
( spl0_95
<=> codomain(b) = compose(codomain(b),codomain(b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f403,plain,
( spl0_43
<=> codomain(b) = domain(codomain(b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f412,plain,
( codomain(b) = compose(codomain(b),codomain(b))
| ~ spl0_9
| ~ spl0_43 ),
inference(superposition,[],[f54,f405]) ).
fof(f405,plain,
( codomain(b) = domain(codomain(b))
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f403]) ).
fof(f2785,plain,
( spl0_94
| ~ spl0_10
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f375,f369,f57,f2782]) ).
fof(f2782,plain,
( spl0_94
<=> codomain(c) = compose(codomain(c),codomain(c)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f57,plain,
( spl0_10
<=> ! [X0] : compose(codomain(X0),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f369,plain,
( spl0_39
<=> codomain(c) = codomain(codomain(c)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f375,plain,
( codomain(c) = compose(codomain(c),codomain(c))
| ~ spl0_10
| ~ spl0_39 ),
inference(superposition,[],[f58,f371]) ).
fof(f371,plain,
( codomain(c) = codomain(codomain(c))
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f369]) ).
fof(f58,plain,
( ! [X0] : compose(codomain(X0),X0) = X0
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f2763,plain,
( spl0_93
| ~ spl0_11
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f352,f335,f62,f2761]) ).
fof(f2761,plain,
( spl0_93
<=> ! [X0] :
( ~ there_exists(X0)
| there_exists(domain(codomain(codomain(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f62,plain,
( spl0_11
<=> ! [X0,X1] :
( there_exists(domain(X0))
| ~ there_exists(compose(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f352,plain,
( ! [X0] :
( ~ there_exists(X0)
| there_exists(domain(codomain(codomain(X0)))) )
| ~ spl0_11
| ~ spl0_37 ),
inference(superposition,[],[f63,f336]) ).
fof(f63,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| there_exists(domain(X0)) )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f2759,plain,
( spl0_92
| ~ spl0_19
| ~ spl0_23
| ~ spl0_24
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f603,f489,f151,f147,f118,f2756]) ).
fof(f2756,plain,
( spl0_92
<=> codomain(a) = codomain(codomain(a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f118,plain,
( spl0_19
<=> there_exists(a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f147,plain,
( spl0_23
<=> ! [X0] :
( ~ there_exists(X0)
| domain(X0) = codomain(domain(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f151,plain,
( spl0_24
<=> ! [X0] :
( ~ there_exists(X0)
| codomain(X0) = domain(codomain(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f489,plain,
( spl0_49
<=> there_exists(codomain(a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f603,plain,
( codomain(a) = codomain(codomain(a))
| ~ spl0_19
| ~ spl0_23
| ~ spl0_24
| ~ spl0_49 ),
inference(forward_demodulation,[],[f602,f262]) ).
fof(f262,plain,
( codomain(a) = domain(codomain(a))
| ~ spl0_19
| ~ spl0_24 ),
inference(resolution,[],[f120,f152]) ).
fof(f152,plain,
( ! [X0] :
( ~ there_exists(X0)
| codomain(X0) = domain(codomain(X0)) )
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f120,plain,
( there_exists(a)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f602,plain,
( domain(codomain(a)) = codomain(domain(codomain(a)))
| ~ spl0_23
| ~ spl0_49 ),
inference(resolution,[],[f491,f148]) ).
fof(f148,plain,
( ! [X0] :
( ~ there_exists(X0)
| domain(X0) = codomain(domain(X0)) )
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f147]) ).
fof(f491,plain,
( there_exists(codomain(a))
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f489]) ).
fof(f2668,plain,
( spl0_91
| ~ spl0_3
| ~ spl0_23
| ~ spl0_25
| ~ spl0_67 ),
inference(avatar_split_clause,[],[f1042,f837,f162,f147,f27,f2665]) ).
fof(f2665,plain,
( spl0_91
<=> domain(compose(b,c)) = domain(c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f27,plain,
( spl0_3
<=> there_exists(compose(b,c)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f837,plain,
( spl0_67
<=> ! [X0,X1] :
( ~ there_exists(compose(X1,X0))
| codomain(domain(X0)) = domain(compose(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f1042,plain,
( domain(compose(b,c)) = domain(c)
| ~ spl0_3
| ~ spl0_23
| ~ spl0_25
| ~ spl0_67 ),
inference(forward_demodulation,[],[f1024,f280]) ).
fof(f280,plain,
( domain(c) = codomain(domain(c))
| ~ spl0_23
| ~ spl0_25 ),
inference(resolution,[],[f164,f148]) ).
fof(f1024,plain,
( domain(compose(b,c)) = codomain(domain(c))
| ~ spl0_3
| ~ spl0_67 ),
inference(resolution,[],[f838,f29]) ).
fof(f29,plain,
( there_exists(compose(b,c))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f27]) ).
fof(f838,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X1,X0))
| codomain(domain(X0)) = domain(compose(X1,X0)) )
| ~ spl0_67 ),
inference(avatar_component_clause,[],[f837]) ).
fof(f2663,plain,
( spl0_90
| ~ spl0_2
| ~ spl0_20
| ~ spl0_39
| ~ spl0_67 ),
inference(avatar_split_clause,[],[f1041,f837,f369,f123,f22,f2660]) ).
fof(f2660,plain,
( spl0_90
<=> codomain(c) = domain(compose(a,b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f22,plain,
( spl0_2
<=> there_exists(compose(a,b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f123,plain,
( spl0_20
<=> domain(b) = codomain(c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f1041,plain,
( codomain(c) = domain(compose(a,b))
| ~ spl0_2
| ~ spl0_20
| ~ spl0_39
| ~ spl0_67 ),
inference(forward_demodulation,[],[f1040,f371]) ).
fof(f1040,plain,
( domain(compose(a,b)) = codomain(codomain(c))
| ~ spl0_2
| ~ spl0_20
| ~ spl0_67 ),
inference(forward_demodulation,[],[f1023,f125]) ).
fof(f125,plain,
( domain(b) = codomain(c)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f1023,plain,
( domain(compose(a,b)) = codomain(domain(b))
| ~ spl0_2
| ~ spl0_67 ),
inference(resolution,[],[f838,f24]) ).
fof(f24,plain,
( there_exists(compose(a,b))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f22]) ).
fof(f2658,plain,
( spl0_89
| ~ spl0_3
| ~ spl0_43
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f963,f825,f403,f27,f2655]) ).
fof(f825,plain,
( spl0_64
<=> ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| domain(codomain(X0)) = codomain(compose(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f963,plain,
( codomain(b) = codomain(compose(b,c))
| ~ spl0_3
| ~ spl0_43
| ~ spl0_64 ),
inference(forward_demodulation,[],[f946,f405]) ).
fof(f946,plain,
( domain(codomain(b)) = codomain(compose(b,c))
| ~ spl0_3
| ~ spl0_64 ),
inference(resolution,[],[f826,f29]) ).
fof(f826,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| domain(codomain(X0)) = codomain(compose(X0,X1)) )
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f825]) ).
fof(f2653,plain,
( spl0_88
| ~ spl0_2
| ~ spl0_59
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f962,f825,f777,f22,f2650]) ).
fof(f2650,plain,
( spl0_88
<=> codomain(compose(a,b)) = codomain(a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f777,plain,
( spl0_59
<=> codomain(a) = domain(codomain(a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f962,plain,
( codomain(compose(a,b)) = codomain(a)
| ~ spl0_2
| ~ spl0_59
| ~ spl0_64 ),
inference(forward_demodulation,[],[f945,f779]) ).
fof(f779,plain,
( codomain(a) = domain(codomain(a))
| ~ spl0_59 ),
inference(avatar_component_clause,[],[f777]) ).
fof(f945,plain,
( codomain(compose(a,b)) = domain(codomain(a))
| ~ spl0_2
| ~ spl0_64 ),
inference(resolution,[],[f826,f24]) ).
fof(f2647,plain,
( spl0_87
| ~ spl0_18
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f338,f331,f113,f2644]) ).
fof(f2644,plain,
( spl0_87
<=> a = compose(a,domain(codomain(b))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f113,plain,
( spl0_18
<=> domain(a) = codomain(b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f338,plain,
( a = compose(a,domain(codomain(b)))
| ~ spl0_18
| ~ spl0_36 ),
inference(superposition,[],[f332,f115]) ).
fof(f115,plain,
( domain(a) = codomain(b)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f2062,plain,
( spl0_86
| ~ spl0_29
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f267,f259,f222,f2060]) ).
fof(f2060,plain,
( spl0_86
<=> ! [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_86])]) ).
fof(f222,plain,
( spl0_29
<=> ! [X0,X1] : compose(X0,X1) = compose(X0,compose(X1,domain(compose(X0,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f259,plain,
( spl0_30
<=> ! [X2,X0,X1] :
( ~ there_exists(compose(X0,compose(X1,X2)))
| domain(compose(X0,X1)) = codomain(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f267,plain,
( ! [X2,X0,X1] :
( ~ there_exists(compose(X2,compose(X0,X1)))
| domain(compose(X2,X0)) = codomain(compose(X1,domain(compose(X0,X1)))) )
| ~ spl0_29
| ~ spl0_30 ),
inference(superposition,[],[f260,f223]) ).
fof(f223,plain,
( ! [X0,X1] : compose(X0,X1) = compose(X0,compose(X1,domain(compose(X0,X1))))
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f260,plain,
( ! [X2,X0,X1] :
( ~ there_exists(compose(X0,compose(X1,X2)))
| domain(compose(X0,X1)) = codomain(X2) )
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f2058,plain,
( spl0_85
| ~ spl0_14
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f231,f222,f83,f2056]) ).
fof(f2056,plain,
( spl0_85
<=> ! [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_85])]) ).
fof(f83,plain,
( spl0_14
<=> ! [X2,X0,X1] : compose(X0,compose(X1,X2)) = compose(compose(X0,X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f231,plain,
( ! [X2,X0,X1] : compose(X2,compose(X0,X1)) = compose(X2,compose(X0,compose(X1,domain(compose(X2,compose(X0,X1))))))
| ~ spl0_14
| ~ spl0_29 ),
inference(superposition,[],[f223,f84]) ).
fof(f84,plain,
( ! [X2,X0,X1] : compose(X0,compose(X1,X2)) = compose(compose(X0,X1),X2)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f2054,plain,
( spl0_84
| ~ spl0_14
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f230,f222,f83,f2052]) ).
fof(f2052,plain,
( spl0_84
<=> ! [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_84])]) ).
fof(f230,plain,
( ! [X2,X0,X1] : compose(X0,compose(X1,X2)) = compose(compose(X0,X1),compose(X2,domain(compose(X0,compose(X1,X2)))))
| ~ spl0_14
| ~ spl0_29 ),
inference(superposition,[],[f223,f84]) ).
fof(f1979,plain,
( spl0_83
| ~ spl0_23
| ~ spl0_25
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f660,f605,f162,f147,f1976]) ).
fof(f1976,plain,
( spl0_83
<=> domain(c) = domain(domain(c)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f605,plain,
( spl0_54
<=> ! [X0] :
( codomain(domain(X0)) = domain(codomain(domain(X0)))
| ~ there_exists(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f660,plain,
( domain(c) = domain(domain(c))
| ~ spl0_23
| ~ spl0_25
| ~ spl0_54 ),
inference(forward_demodulation,[],[f645,f280]) ).
fof(f645,plain,
( codomain(domain(c)) = domain(codomain(domain(c)))
| ~ spl0_25
| ~ spl0_54 ),
inference(resolution,[],[f606,f164]) ).
fof(f606,plain,
( ! [X0] :
( ~ there_exists(X0)
| codomain(domain(X0)) = domain(codomain(domain(X0))) )
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f605]) ).
fof(f1833,plain,
( spl0_82
| ~ spl0_14
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f270,f259,f83,f1831]) ).
fof(f1831,plain,
( spl0_82
<=> ! [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_82])]) ).
fof(f270,plain,
( ! [X2,X3,X0,X1] :
( ~ there_exists(compose(X3,compose(X0,compose(X1,X2))))
| codomain(X2) = domain(compose(X3,compose(X0,X1))) )
| ~ spl0_14
| ~ spl0_30 ),
inference(superposition,[],[f260,f84]) ).
fof(f1829,plain,
( spl0_81
| ~ spl0_14
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f246,f222,f83,f1827]) ).
fof(f1827,plain,
( spl0_81
<=> ! [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_81])]) ).
fof(f246,plain,
( ! [X0,X1] : compose(X0,X1) = compose(X0,compose(X1,compose(domain(compose(X0,X1)),domain(compose(X0,X1)))))
| ~ spl0_14
| ~ spl0_29 ),
inference(forward_demodulation,[],[f227,f84]) ).
fof(f227,plain,
( ! [X0,X1] : compose(X0,X1) = compose(X0,compose(compose(X1,domain(compose(X0,X1))),domain(compose(X0,X1))))
| ~ spl0_29 ),
inference(superposition,[],[f223,f223]) ).
fof(f1432,plain,
( spl0_80
| ~ spl0_27
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f269,f259,f178,f1430]) ).
fof(f1430,plain,
( spl0_80
<=> ! [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_80])]) ).
fof(f269,plain,
( ! [X2,X0,X1] :
( ~ there_exists(compose(X2,compose(X0,X1)))
| codomain(compose(X0,X1)) = domain(compose(X2,codomain(X0))) )
| ~ spl0_27
| ~ spl0_30 ),
inference(superposition,[],[f260,f179]) ).
fof(f1428,plain,
( spl0_79
| ~ spl0_26
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f266,f259,f174,f1426]) ).
fof(f1426,plain,
( spl0_79
<=> ! [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_79])]) ).
fof(f266,plain,
( ! [X2,X0,X1] :
( ~ there_exists(compose(X2,compose(X0,X1)))
| codomain(compose(domain(X0),X1)) = domain(compose(X2,X0)) )
| ~ spl0_26
| ~ spl0_30 ),
inference(superposition,[],[f260,f175]) ).
fof(f1424,plain,
( spl0_78
| ~ spl0_14
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f200,f178,f83,f1422]) ).
fof(f1422,plain,
( spl0_78
<=> ! [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_78])]) ).
fof(f200,plain,
( ! [X2,X0,X1] : compose(X0,compose(X1,X2)) = compose(codomain(compose(X0,X1)),compose(X0,compose(X1,X2)))
| ~ spl0_14
| ~ spl0_27 ),
inference(superposition,[],[f179,f84]) ).
fof(f1420,plain,
( spl0_77
| ~ spl0_23
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f280,f162,f147,f1417]) ).
fof(f1417,plain,
( spl0_77
<=> domain(c) = codomain(domain(c)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f1415,plain,
( spl0_76
| ~ spl0_14
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f192,f174,f83,f1413]) ).
fof(f1413,plain,
( spl0_76
<=> ! [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_76])]) ).
fof(f192,plain,
( ! [X2,X0,X1] : compose(X0,compose(X1,X2)) = compose(X0,compose(X1,compose(domain(compose(X0,X1)),X2)))
| ~ spl0_14
| ~ spl0_26 ),
inference(forward_demodulation,[],[f185,f84]) ).
fof(f185,plain,
( ! [X2,X0,X1] : compose(compose(X0,X1),X2) = compose(X0,compose(X1,compose(domain(compose(X0,X1)),X2)))
| ~ spl0_14
| ~ spl0_26 ),
inference(superposition,[],[f175,f84]) ).
fof(f1252,plain,
( spl0_75
| ~ spl0_14
| ~ spl0_26
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f245,f222,f174,f83,f1250]) ).
fof(f1250,plain,
( spl0_75
<=> ! [X0,X1] : compose(X0,X1) = compose(X0,compose(domain(X0),compose(X1,domain(compose(X0,X1))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f245,plain,
( ! [X0,X1] : compose(X0,X1) = compose(X0,compose(domain(X0),compose(X1,domain(compose(X0,X1)))))
| ~ spl0_14
| ~ spl0_26
| ~ spl0_29 ),
inference(forward_demodulation,[],[f226,f84]) ).
fof(f226,plain,
( ! [X0,X1] : compose(X0,X1) = compose(X0,compose(compose(domain(X0),X1),domain(compose(X0,X1))))
| ~ spl0_26
| ~ spl0_29 ),
inference(superposition,[],[f223,f175]) ).
fof(f1248,plain,
( spl0_74
| ~ spl0_14
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f213,f206,f83,f1246]) ).
fof(f1246,plain,
( spl0_74
<=> ! [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_74])]) ).
fof(f206,plain,
( spl0_28
<=> ! [X2,X0,X1] :
( ~ there_exists(compose(X0,compose(X1,X2)))
| there_exists(domain(compose(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f213,plain,
( ! [X2,X3,X0,X1] :
( ~ there_exists(compose(X3,compose(X0,compose(X1,X2))))
| there_exists(domain(compose(X3,compose(X0,X1)))) )
| ~ spl0_14
| ~ spl0_28 ),
inference(superposition,[],[f207,f84]) ).
fof(f207,plain,
( ! [X2,X0,X1] :
( ~ there_exists(compose(X0,compose(X1,X2)))
| there_exists(domain(compose(X0,X1))) )
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f206]) ).
fof(f1176,plain,
( spl0_73
| ~ spl0_10
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f274,f259,f57,f1174]) ).
fof(f1174,plain,
( spl0_73
<=> ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| codomain(X1) = domain(compose(codomain(compose(X0,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f274,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| codomain(X1) = domain(compose(codomain(compose(X0,X1)),X0)) )
| ~ spl0_10
| ~ spl0_30 ),
inference(superposition,[],[f260,f58]) ).
fof(f1172,plain,
( spl0_72
| ~ spl0_12
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f240,f222,f70,f1170]) ).
fof(f1170,plain,
( spl0_72
<=> ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| domain(X0) = codomain(compose(X1,domain(compose(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f70,plain,
( spl0_12
<=> ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| domain(X0) = codomain(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f240,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| domain(X0) = codomain(compose(X1,domain(compose(X0,X1)))) )
| ~ spl0_12
| ~ spl0_29 ),
inference(superposition,[],[f71,f223]) ).
fof(f71,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| domain(X0) = codomain(X1) )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f1080,plain,
( spl0_71
| ~ spl0_24
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f279,f162,f151,f1077]) ).
fof(f1077,plain,
( spl0_71
<=> codomain(c) = domain(codomain(c)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f279,plain,
( codomain(c) = domain(codomain(c))
| ~ spl0_24
| ~ spl0_25 ),
inference(resolution,[],[f164,f152]) ).
fof(f1075,plain,
( spl0_70
| ~ spl0_26
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f255,f222,f174,f1073]) ).
fof(f1073,plain,
( spl0_70
<=> ! [X0,X1] : compose(X0,X1) = compose(X0,compose(X1,domain(compose(domain(X0),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f255,plain,
( ! [X0,X1] : compose(X0,X1) = compose(X0,compose(X1,domain(compose(domain(X0),X1))))
| ~ spl0_26
| ~ spl0_29 ),
inference(forward_demodulation,[],[f242,f175]) ).
fof(f242,plain,
( ! [X0,X1] : compose(X0,compose(domain(X0),X1)) = compose(X0,compose(X1,domain(compose(domain(X0),X1))))
| ~ spl0_26
| ~ spl0_29 ),
inference(superposition,[],[f175,f223]) ).
fof(f848,plain,
( spl0_69
| ~ spl0_10
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f268,f259,f57,f846]) ).
fof(f846,plain,
( spl0_69
<=> ! [X0,X1] :
( ~ there_exists(compose(X1,X0))
| codomain(X0) = domain(compose(X1,codomain(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f268,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X1,X0))
| codomain(X0) = domain(compose(X1,codomain(X0))) )
| ~ spl0_10
| ~ spl0_30 ),
inference(superposition,[],[f260,f58]) ).
fof(f844,plain,
( spl0_68
| ~ spl0_18
| ~ spl0_19
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f264,f147,f118,f113,f841]) ).
fof(f841,plain,
( spl0_68
<=> codomain(b) = codomain(codomain(b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f264,plain,
( codomain(b) = codomain(codomain(b))
| ~ spl0_18
| ~ spl0_19
| ~ spl0_23 ),
inference(forward_demodulation,[],[f263,f115]) ).
fof(f263,plain,
( domain(a) = codomain(domain(a))
| ~ spl0_19
| ~ spl0_23 ),
inference(resolution,[],[f120,f148]) ).
fof(f839,plain,
( spl0_67
| ~ spl0_9
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f265,f259,f53,f837]) ).
fof(f265,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X1,X0))
| codomain(domain(X0)) = domain(compose(X1,X0)) )
| ~ spl0_9
| ~ spl0_30 ),
inference(superposition,[],[f260,f54]) ).
fof(f835,plain,
( spl0_66
| ~ spl0_10
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f216,f206,f57,f833]) ).
fof(f833,plain,
( spl0_66
<=> ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| there_exists(domain(compose(codomain(compose(X0,X1)),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f216,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| there_exists(domain(compose(codomain(compose(X0,X1)),X0))) )
| ~ spl0_10
| ~ spl0_28 ),
inference(superposition,[],[f207,f58]) ).
fof(f831,plain,
( spl0_65
| ~ spl0_27
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f212,f206,f178,f829]) ).
fof(f829,plain,
( spl0_65
<=> ! [X2,X0,X1] :
( ~ there_exists(compose(X2,compose(X0,X1)))
| there_exists(domain(compose(X2,codomain(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f212,plain,
( ! [X2,X0,X1] :
( ~ there_exists(compose(X2,compose(X0,X1)))
| there_exists(domain(compose(X2,codomain(X0)))) )
| ~ spl0_27
| ~ spl0_28 ),
inference(superposition,[],[f207,f179]) ).
fof(f827,plain,
( spl0_64
| ~ spl0_12
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f202,f178,f70,f825]) ).
fof(f202,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| domain(codomain(X0)) = codomain(compose(X0,X1)) )
| ~ spl0_12
| ~ spl0_27 ),
inference(superposition,[],[f71,f179]) ).
fof(f823,plain,
( spl0_63
| ~ spl0_12
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f187,f174,f70,f821]) ).
fof(f821,plain,
( spl0_63
<=> ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| domain(X0) = codomain(compose(domain(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f187,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| domain(X0) = codomain(compose(domain(X0),X1)) )
| ~ spl0_12
| ~ spl0_26 ),
inference(superposition,[],[f71,f175]) ).
fof(f819,plain,
( spl0_62
| ~ spl0_22
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f170,f151,f142,f817]) ).
fof(f817,plain,
( spl0_62
<=> ! [X0] :
( codomain(domain(codomain(X0))) = domain(codomain(domain(codomain(X0))))
| ~ there_exists(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f142,plain,
( spl0_22
<=> ! [X0] :
( ~ there_exists(X0)
| there_exists(domain(codomain(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f170,plain,
( ! [X0] :
( codomain(domain(codomain(X0))) = domain(codomain(domain(codomain(X0))))
| ~ there_exists(X0) )
| ~ spl0_22
| ~ spl0_24 ),
inference(resolution,[],[f152,f143]) ).
fof(f143,plain,
( ! [X0] :
( there_exists(domain(codomain(X0)))
| ~ there_exists(X0) )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f815,plain,
( spl0_61
| ~ spl0_22
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f158,f147,f142,f813]) ).
fof(f813,plain,
( spl0_61
<=> ! [X0] :
( domain(domain(codomain(X0))) = codomain(domain(domain(codomain(X0))))
| ~ there_exists(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f158,plain,
( ! [X0] :
( domain(domain(codomain(X0))) = codomain(domain(domain(codomain(X0))))
| ~ there_exists(X0) )
| ~ spl0_22
| ~ spl0_23 ),
inference(resolution,[],[f148,f143]) ).
fof(f796,plain,
( ~ spl0_17
| spl0_60
| ~ spl0_15
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f131,f123,f96,f794,f107]) ).
fof(f107,plain,
( spl0_17
<=> there_exists(codomain(c)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f794,plain,
( spl0_60
<=> ! [X0] :
( codomain(X0) != codomain(c)
| there_exists(compose(b,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f96,plain,
( spl0_15
<=> ! [X0,X1] :
( ~ there_exists(domain(X0))
| there_exists(compose(X0,X1))
| domain(X0) != codomain(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f131,plain,
( ! [X0] :
( codomain(X0) != codomain(c)
| there_exists(compose(b,X0))
| ~ there_exists(codomain(c)) )
| ~ spl0_15
| ~ spl0_20 ),
inference(superposition,[],[f97,f125]) ).
fof(f97,plain,
( ! [X0,X1] :
( domain(X0) != codomain(X1)
| there_exists(compose(X0,X1))
| ~ there_exists(domain(X0)) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f780,plain,
( spl0_59
| ~ spl0_19
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f262,f151,f118,f777]) ).
fof(f775,plain,
( ~ spl0_31
| spl0_58
| ~ spl0_15
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f128,f113,f96,f773,f282]) ).
fof(f282,plain,
( spl0_31
<=> there_exists(codomain(b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f128,plain,
( ! [X0] :
( codomain(X0) != codomain(b)
| there_exists(compose(a,X0))
| ~ there_exists(codomain(b)) )
| ~ spl0_15
| ~ spl0_18 ),
inference(superposition,[],[f97,f115]) ).
fof(f685,plain,
( spl0_57
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f199,f178,f683]) ).
fof(f683,plain,
( spl0_57
<=> ! [X0,X1] : compose(X0,X1) = compose(codomain(codomain(X0)),compose(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f199,plain,
( ! [X0,X1] : compose(X0,X1) = compose(codomain(codomain(X0)),compose(X0,X1))
| ~ spl0_27 ),
inference(superposition,[],[f179,f179]) ).
fof(f681,plain,
( spl0_56
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f191,f174,f679]) ).
fof(f679,plain,
( spl0_56
<=> ! [X0,X1] : compose(X0,X1) = compose(X0,compose(domain(domain(X0)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f191,plain,
( ! [X0,X1] : compose(X0,X1) = compose(X0,compose(domain(domain(X0)),X1))
| ~ spl0_26 ),
inference(forward_demodulation,[],[f184,f175]) ).
fof(f184,plain,
( ! [X0,X1] : compose(X0,compose(domain(X0),X1)) = compose(X0,compose(domain(domain(X0)),X1))
| ~ spl0_26 ),
inference(superposition,[],[f175,f175]) ).
fof(f611,plain,
( spl0_55
| ~ spl0_10
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f211,f206,f57,f609]) ).
fof(f609,plain,
( spl0_55
<=> ! [X0,X1] :
( ~ there_exists(compose(X1,X0))
| there_exists(domain(compose(X1,codomain(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f211,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X1,X0))
| there_exists(domain(compose(X1,codomain(X0)))) )
| ~ spl0_10
| ~ spl0_28 ),
inference(superposition,[],[f207,f58]) ).
fof(f607,plain,
( spl0_54
| ~ spl0_21
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f169,f151,f135,f605]) ).
fof(f135,plain,
( spl0_21
<=> ! [X0] :
( ~ there_exists(X0)
| there_exists(domain(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f169,plain,
( ! [X0] :
( codomain(domain(X0)) = domain(codomain(domain(X0)))
| ~ there_exists(X0) )
| ~ spl0_21
| ~ spl0_24 ),
inference(resolution,[],[f152,f136]) ).
fof(f136,plain,
( ! [X0] :
( there_exists(domain(X0))
| ~ there_exists(X0) )
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f599,plain,
( spl0_53
| ~ spl0_21
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f157,f147,f135,f597]) ).
fof(f157,plain,
( ! [X0] :
( domain(domain(X0)) = codomain(domain(domain(X0)))
| ~ there_exists(X0) )
| ~ spl0_21
| ~ spl0_23 ),
inference(resolution,[],[f148,f136]) ).
fof(f505,plain,
( spl0_52
| ~ spl0_20
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f182,f174,f123,f503]) ).
fof(f503,plain,
( spl0_52
<=> ! [X0] : compose(b,X0) = compose(b,compose(codomain(c),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f182,plain,
( ! [X0] : compose(b,X0) = compose(b,compose(codomain(c),X0))
| ~ spl0_20
| ~ spl0_26 ),
inference(superposition,[],[f175,f125]) ).
fof(f501,plain,
( spl0_51
| ~ spl0_18
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f181,f174,f113,f499]) ).
fof(f499,plain,
( spl0_51
<=> ! [X0] : compose(a,X0) = compose(a,compose(codomain(b),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f181,plain,
( ! [X0] : compose(a,X0) = compose(a,compose(codomain(b),X0))
| ~ spl0_18
| ~ spl0_26 ),
inference(superposition,[],[f175,f115]) ).
fof(f497,plain,
( spl0_50
| ~ spl0_3
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f167,f151,f27,f494]) ).
fof(f494,plain,
( spl0_50
<=> codomain(compose(b,c)) = domain(codomain(compose(b,c))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f167,plain,
( codomain(compose(b,c)) = domain(codomain(compose(b,c)))
| ~ spl0_3
| ~ spl0_24 ),
inference(resolution,[],[f152,f29]) ).
fof(f492,plain,
( spl0_49
| ~ spl0_2
| ~ spl0_19
| ~ spl0_24
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f443,f428,f151,f118,f22,f489]) ).
fof(f443,plain,
( there_exists(codomain(a))
| ~ spl0_2
| ~ spl0_19
| ~ spl0_24
| ~ spl0_44 ),
inference(forward_demodulation,[],[f431,f262]) ).
fof(f431,plain,
( there_exists(domain(codomain(a)))
| ~ spl0_2
| ~ spl0_44 ),
inference(resolution,[],[f429,f24]) ).
fof(f487,plain,
( spl0_48
| ~ spl0_2
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f166,f151,f22,f484]) ).
fof(f484,plain,
( spl0_48
<=> codomain(compose(a,b)) = domain(codomain(compose(a,b))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f166,plain,
( codomain(compose(a,b)) = domain(codomain(compose(a,b)))
| ~ spl0_2
| ~ spl0_24 ),
inference(resolution,[],[f152,f24]) ).
fof(f482,plain,
( spl0_47
| ~ spl0_3
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f155,f147,f27,f479]) ).
fof(f479,plain,
( spl0_47
<=> domain(compose(b,c)) = codomain(domain(compose(b,c))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f155,plain,
( domain(compose(b,c)) = codomain(domain(compose(b,c)))
| ~ spl0_3
| ~ spl0_23 ),
inference(resolution,[],[f148,f29]) ).
fof(f477,plain,
( spl0_46
| ~ spl0_2
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f154,f147,f22,f474]) ).
fof(f474,plain,
( spl0_46
<=> domain(compose(a,b)) = codomain(domain(compose(a,b))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f154,plain,
( domain(compose(a,b)) = codomain(domain(compose(a,b)))
| ~ spl0_2
| ~ spl0_23 ),
inference(resolution,[],[f148,f24]) ).
fof(f448,plain,
( spl0_45
| ~ spl0_9
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f225,f222,f53,f446]) ).
fof(f446,plain,
( spl0_45
<=> ! [X0] : compose(X0,compose(domain(X0),domain(X0))) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f225,plain,
( ! [X0] : compose(X0,compose(domain(X0),domain(X0))) = X0
| ~ spl0_9
| ~ spl0_29 ),
inference(superposition,[],[f223,f54]) ).
fof(f430,plain,
( spl0_44
| ~ spl0_11
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f203,f178,f62,f428]) ).
fof(f203,plain,
( ! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| there_exists(domain(codomain(X0))) )
| ~ spl0_11
| ~ spl0_27 ),
inference(superposition,[],[f63,f179]) ).
fof(f406,plain,
( spl0_43
| ~ spl0_18
| ~ spl0_19
| ~ spl0_23
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f398,f394,f147,f118,f113,f403]) ).
fof(f394,plain,
( spl0_42
<=> codomain(codomain(b)) = domain(codomain(codomain(b))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f398,plain,
( codomain(b) = domain(codomain(b))
| ~ spl0_18
| ~ spl0_19
| ~ spl0_23
| ~ spl0_42 ),
inference(forward_demodulation,[],[f396,f264]) ).
fof(f396,plain,
( codomain(codomain(b)) = domain(codomain(codomain(b)))
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f394]) ).
fof(f397,plain,
( spl0_42
| ~ spl0_13
| ~ spl0_18
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f172,f151,f113,f74,f394]) ).
fof(f74,plain,
( spl0_13
<=> there_exists(domain(a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f172,plain,
( codomain(codomain(b)) = domain(codomain(codomain(b)))
| ~ spl0_13
| ~ spl0_18
| ~ spl0_24 ),
inference(forward_demodulation,[],[f168,f115]) ).
fof(f168,plain,
( codomain(domain(a)) = domain(codomain(domain(a)))
| ~ spl0_13
| ~ spl0_24 ),
inference(resolution,[],[f152,f76]) ).
fof(f76,plain,
( there_exists(domain(a))
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f391,plain,
( spl0_41
| ~ spl0_17
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f171,f151,f107,f388]) ).
fof(f388,plain,
( spl0_41
<=> codomain(codomain(c)) = domain(codomain(codomain(c))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f171,plain,
( codomain(codomain(c)) = domain(codomain(codomain(c)))
| ~ spl0_17
| ~ spl0_24 ),
inference(resolution,[],[f152,f109]) ).
fof(f109,plain,
( there_exists(codomain(c))
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f386,plain,
( spl0_40
| ~ spl0_13
| ~ spl0_18
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f160,f147,f113,f74,f383]) ).
fof(f383,plain,
( spl0_40
<=> domain(codomain(b)) = codomain(domain(codomain(b))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f160,plain,
( domain(codomain(b)) = codomain(domain(codomain(b)))
| ~ spl0_13
| ~ spl0_18
| ~ spl0_23 ),
inference(forward_demodulation,[],[f156,f115]) ).
fof(f156,plain,
( domain(domain(a)) = codomain(domain(domain(a)))
| ~ spl0_13
| ~ spl0_23 ),
inference(resolution,[],[f148,f76]) ).
fof(f372,plain,
( spl0_39
| ~ spl0_24
| ~ spl0_25
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f367,f363,f162,f151,f369]) ).
fof(f363,plain,
( spl0_38
<=> domain(codomain(c)) = codomain(domain(codomain(c))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f367,plain,
( codomain(c) = codomain(codomain(c))
| ~ spl0_24
| ~ spl0_25
| ~ spl0_38 ),
inference(forward_demodulation,[],[f365,f279]) ).
fof(f365,plain,
( domain(codomain(c)) = codomain(domain(codomain(c)))
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f363]) ).
fof(f366,plain,
( spl0_38
| ~ spl0_17
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f159,f147,f107,f363]) ).
fof(f159,plain,
( domain(codomain(c)) = codomain(domain(codomain(c)))
| ~ spl0_17
| ~ spl0_23 ),
inference(resolution,[],[f148,f109]) ).
fof(f337,plain,
( spl0_37
| ~ spl0_10
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f198,f178,f57,f335]) ).
fof(f198,plain,
( ! [X0] : compose(codomain(codomain(X0)),X0) = X0
| ~ spl0_10
| ~ spl0_27 ),
inference(superposition,[],[f179,f58]) ).
fof(f333,plain,
( spl0_36
| ~ spl0_9
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f190,f174,f53,f331]) ).
fof(f190,plain,
( ! [X0] : compose(X0,domain(domain(X0))) = X0
| ~ spl0_9
| ~ spl0_26 ),
inference(forward_demodulation,[],[f183,f54]) ).
fof(f183,plain,
( ! [X0] : compose(X0,domain(X0)) = compose(X0,domain(domain(X0)))
| ~ spl0_9
| ~ spl0_26 ),
inference(superposition,[],[f175,f54]) ).
fof(f329,plain,
( spl0_35
| ~ spl0_6
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f286,f282,f40,f326]) ).
fof(f326,plain,
( spl0_35
<=> there_exists(b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f40,plain,
( spl0_6
<=> ! [X0] :
( there_exists(X0)
| ~ there_exists(codomain(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f286,plain,
( there_exists(b)
| ~ spl0_6
| ~ spl0_31 ),
inference(resolution,[],[f284,f41]) ).
fof(f41,plain,
( ! [X0] :
( ~ there_exists(codomain(X0))
| there_exists(X0) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f40]) ).
fof(f284,plain,
( there_exists(codomain(b))
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f282]) ).
fof(f305,plain,
( spl0_34
| ~ spl0_9
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f132,f123,f53,f302]) ).
fof(f302,plain,
( spl0_34
<=> b = compose(b,codomain(c)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f132,plain,
( b = compose(b,codomain(c))
| ~ spl0_9
| ~ spl0_20 ),
inference(superposition,[],[f54,f125]) ).
fof(f300,plain,
( spl0_33
| ~ spl0_9
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f129,f113,f53,f297]) ).
fof(f297,plain,
( spl0_33
<=> a = compose(a,codomain(b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f129,plain,
( a = compose(a,codomain(b))
| ~ spl0_9
| ~ spl0_18 ),
inference(superposition,[],[f54,f115]) ).
fof(f292,plain,
( spl0_32
| ~ spl0_5
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f145,f142,f36,f290]) ).
fof(f290,plain,
( spl0_32
<=> ! [X0] :
( ~ there_exists(X0)
| there_exists(codomain(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f36,plain,
( spl0_5
<=> ! [X0] :
( there_exists(X0)
| ~ there_exists(domain(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f145,plain,
( ! [X0] :
( ~ there_exists(X0)
| there_exists(codomain(X0)) )
| ~ spl0_5
| ~ spl0_22 ),
inference(resolution,[],[f143,f37]) ).
fof(f37,plain,
( ! [X0] :
( ~ there_exists(domain(X0))
| there_exists(X0) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f36]) ).
fof(f285,plain,
( spl0_31
| ~ spl0_13
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f127,f113,f74,f282]) ).
fof(f127,plain,
( there_exists(codomain(b))
| ~ spl0_13
| ~ spl0_18 ),
inference(superposition,[],[f76,f115]) ).
fof(f261,plain,
( spl0_30
| ~ spl0_12
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f91,f83,f70,f259]) ).
fof(f91,plain,
( ! [X2,X0,X1] :
( ~ there_exists(compose(X0,compose(X1,X2)))
| domain(compose(X0,X1)) = codomain(X2) )
| ~ spl0_12
| ~ spl0_14 ),
inference(superposition,[],[f71,f84]) ).
fof(f224,plain,
( spl0_29
| ~ spl0_9
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f89,f83,f53,f222]) ).
fof(f89,plain,
( ! [X0,X1] : compose(X0,X1) = compose(X0,compose(X1,domain(compose(X0,X1))))
| ~ spl0_9
| ~ spl0_14 ),
inference(superposition,[],[f84,f54]) ).
fof(f208,plain,
( spl0_28
| ~ spl0_11
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f92,f83,f62,f206]) ).
fof(f92,plain,
( ! [X2,X0,X1] :
( ~ there_exists(compose(X0,compose(X1,X2)))
| there_exists(domain(compose(X0,X1))) )
| ~ spl0_11
| ~ spl0_14 ),
inference(superposition,[],[f63,f84]) ).
fof(f180,plain,
( spl0_27
| ~ spl0_10
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f87,f83,f57,f178]) ).
fof(f87,plain,
( ! [X0,X1] : compose(X0,X1) = compose(codomain(X0),compose(X0,X1))
| ~ spl0_10
| ~ spl0_14 ),
inference(superposition,[],[f84,f58]) ).
fof(f176,plain,
( spl0_26
| ~ spl0_9
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f86,f83,f53,f174]) ).
fof(f86,plain,
( ! [X0,X1] : compose(X0,X1) = compose(X0,compose(domain(X0),X1))
| ~ spl0_9
| ~ spl0_14 ),
inference(superposition,[],[f84,f54]) ).
fof(f165,plain,
( spl0_25
| ~ spl0_6
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f111,f107,f40,f162]) ).
fof(f111,plain,
( there_exists(c)
| ~ spl0_6
| ~ spl0_17 ),
inference(resolution,[],[f109,f41]) ).
fof(f153,plain,
( spl0_24
| ~ spl0_10
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f81,f70,f57,f151]) ).
fof(f81,plain,
( ! [X0] :
( ~ there_exists(X0)
| codomain(X0) = domain(codomain(X0)) )
| ~ spl0_10
| ~ spl0_12 ),
inference(superposition,[],[f71,f58]) ).
fof(f149,plain,
( spl0_23
| ~ spl0_9
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f80,f70,f53,f147]) ).
fof(f80,plain,
( ! [X0] :
( ~ there_exists(X0)
| domain(X0) = codomain(domain(X0)) )
| ~ spl0_9
| ~ spl0_12 ),
inference(superposition,[],[f71,f54]) ).
fof(f144,plain,
( spl0_22
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f68,f62,f57,f142]) ).
fof(f68,plain,
( ! [X0] :
( ~ there_exists(X0)
| there_exists(domain(codomain(X0))) )
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f63,f58]) ).
fof(f137,plain,
( spl0_21
| ~ spl0_9
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f67,f62,f53,f135]) ).
fof(f67,plain,
( ! [X0] :
( ~ there_exists(X0)
| there_exists(domain(X0)) )
| ~ spl0_9
| ~ spl0_11 ),
inference(superposition,[],[f63,f54]) ).
fof(f126,plain,
( spl0_20
| ~ spl0_3
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f79,f70,f27,f123]) ).
fof(f79,plain,
( domain(b) = codomain(c)
| ~ spl0_3
| ~ spl0_12 ),
inference(resolution,[],[f71,f29]) ).
fof(f121,plain,
( spl0_19
| ~ spl0_5
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f105,f74,f36,f118]) ).
fof(f105,plain,
( there_exists(a)
| ~ spl0_5
| ~ spl0_13 ),
inference(resolution,[],[f76,f37]) ).
fof(f116,plain,
( spl0_18
| ~ spl0_2
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f78,f70,f22,f113]) ).
fof(f78,plain,
( domain(a) = codomain(b)
| ~ spl0_2
| ~ spl0_12 ),
inference(resolution,[],[f71,f24]) ).
fof(f110,plain,
( spl0_17
| ~ spl0_3
| ~ spl0_12
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f104,f100,f70,f27,f107]) ).
fof(f100,plain,
( spl0_16
<=> there_exists(domain(b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f104,plain,
( there_exists(codomain(c))
| ~ spl0_3
| ~ spl0_12
| ~ spl0_16 ),
inference(forward_demodulation,[],[f102,f79]) ).
fof(f102,plain,
( there_exists(domain(b))
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f100]) ).
fof(f103,plain,
( spl0_16
| ~ spl0_3
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f66,f62,f27,f100]) ).
fof(f66,plain,
( there_exists(domain(b))
| ~ spl0_3
| ~ spl0_11 ),
inference(resolution,[],[f63,f29]) ).
fof(f98,plain,
spl0_15,
inference(avatar_split_clause,[],[f8,f96]) ).
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(f85,plain,
spl0_14,
inference(avatar_split_clause,[],[f9,f83]) ).
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(f77,plain,
( spl0_13
| ~ spl0_2
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f65,f62,f22,f74]) ).
fof(f65,plain,
( there_exists(domain(a))
| ~ spl0_2
| ~ spl0_11 ),
inference(resolution,[],[f63,f24]) ).
fof(f72,plain,
spl0_12,
inference(avatar_split_clause,[],[f7,f70]) ).
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(f64,plain,
spl0_11,
inference(avatar_split_clause,[],[f6,f62]) ).
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(f59,plain,
spl0_10,
inference(avatar_split_clause,[],[f11,f57]) ).
fof(f11,axiom,
! [X0] : compose(codomain(X0),X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_codomain) ).
fof(f55,plain,
spl0_9,
inference(avatar_split_clause,[],[f10,f53]) ).
fof(f10,axiom,
! [X0] : compose(X0,domain(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_domain) ).
fof(f51,plain,
spl0_8,
inference(avatar_split_clause,[],[f2,f49]) ).
fof(f49,plain,
( spl0_8
<=> ! [X0,X1] :
( ~ equivalent(X0,X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f2,axiom,
! [X0,X1] :
( ~ equivalent(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_implies_existence2) ).
fof(f46,plain,
spl0_7,
inference(avatar_split_clause,[],[f15,f44]) ).
fof(f44,plain,
( spl0_7
<=> ! [X1] :
( ~ there_exists(X1)
| equivalent(X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f15,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(f42,plain,
spl0_6,
inference(avatar_split_clause,[],[f5,f40]) ).
fof(f5,axiom,
! [X0] :
( there_exists(X0)
| ~ there_exists(codomain(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain_has_elements) ).
fof(f38,plain,
spl0_5,
inference(avatar_split_clause,[],[f4,f36]) ).
fof(f4,axiom,
! [X0] :
( there_exists(X0)
| ~ there_exists(domain(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_has_elements) ).
fof(f34,plain,
spl0_4,
inference(avatar_split_clause,[],[f1,f32]) ).
fof(f32,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(f30,plain,
spl0_3,
inference(avatar_split_clause,[],[f13,f27]) ).
fof(f13,axiom,
there_exists(compose(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assume_bc_exists) ).
fof(f25,plain,
spl0_2,
inference(avatar_split_clause,[],[f12,f22]) ).
fof(f12,axiom,
there_exists(compose(a,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assume_ab_exists) ).
fof(f20,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f14,f17]) ).
fof(f14,axiom,
~ there_exists(compose(a,compose(b,c))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_bc_exists) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : CAT018-4 : 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 : n018.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 18:10:08 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (4547)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.38 % (4552)WARNING: value z3 for option sas not known
% 0.22/0.38 % (4550)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.38 % (4553)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.38 % (4551)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 % (4552)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 % (4556)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 % (4557)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 TRYING [1]
% 0.22/0.38 TRYING [2]
% 0.22/0.38 % (4555)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 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 [4]
% 0.22/0.40 TRYING [5]
% 0.22/0.41 TRYING [1]
% 0.22/0.41 TRYING [2]
% 0.22/0.41 TRYING [3]
% 0.22/0.42 TRYING [4]
% 0.22/0.43 TRYING [5]
% 0.22/0.43 TRYING [6]
% 0.22/0.43 TRYING [5]
% 0.22/0.46 % (4555)First to succeed.
% 0.22/0.47 TRYING [6]
% 0.22/0.47 % (4555)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4547"
% 0.22/0.47 % (4555)Refutation found. Thanks to Tanya!
% 0.22/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.22/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.47 % (4555)------------------------------
% 0.22/0.47 % (4555)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.47 % (4555)Termination reason: Refutation
% 0.22/0.47
% 0.22/0.47 % (4555)Memory used [KB]: 2110
% 0.22/0.47 % (4555)Time elapsed: 0.088 s
% 0.22/0.47 % (4555)Instructions burned: 147 (million)
% 0.22/0.47 % (4547)Success in time 0.107 s
%------------------------------------------------------------------------------