TSTP Solution File: SEU010+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU010+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n005.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 09:26:37 EDT 2024
% Result : Theorem 0.15s 0.40s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 143
% Syntax : Number of formulae : 439 ( 82 unt; 0 def)
% Number of atoms : 1222 ( 98 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 1405 ( 622 ~; 588 |; 66 &)
% ( 97 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 105 ( 103 usr; 97 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 8 con; 0-2 aty)
% Number of variables : 408 ( 385 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f876,plain,
$false,
inference(avatar_sat_refutation,[],[f155,f160,f165,f170,f175,f180,f185,f190,f195,f200,f205,f210,f215,f219,f223,f227,f231,f235,f244,f248,f252,f256,f269,f273,f277,f281,f285,f289,f293,f297,f301,f311,f323,f327,f332,f337,f341,f345,f349,f353,f357,f369,f382,f386,f390,f394,f398,f402,f422,f432,f442,f446,f450,f456,f461,f467,f472,f476,f485,f490,f496,f500,f504,f508,f515,f520,f521,f522,f523,f540,f566,f578,f582,f586,f590,f624,f628,f636,f640,f644,f648,f653,f657,f661,f700,f704,f709,f713,f717,f721,f725,f800,f804,f808,f818,f822,f856,f857,f874,f875]) ).
fof(f875,plain,
( spl10_19
| ~ spl10_1
| ~ spl10_88 ),
inference(avatar_split_clause,[],[f786,f723,f152,f237]) ).
fof(f237,plain,
( spl10_19
<=> sK0 = relation_composition(identity_relation(relation_dom(sK0)),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_19])]) ).
fof(f152,plain,
( spl10_1
<=> relation(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_1])]) ).
fof(f723,plain,
( spl10_88
<=> ! [X0] :
( relation_composition(identity_relation(relation_dom(X0)),X0) = X0
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_88])]) ).
fof(f786,plain,
( sK0 = relation_composition(identity_relation(relation_dom(sK0)),sK0)
| ~ spl10_1
| ~ spl10_88 ),
inference(resolution,[],[f724,f154]) ).
fof(f154,plain,
( relation(sK0)
| ~ spl10_1 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f724,plain,
( ! [X0] :
( ~ relation(X0)
| relation_composition(identity_relation(relation_dom(X0)),X0) = X0 )
| ~ spl10_88 ),
inference(avatar_component_clause,[],[f723]) ).
fof(f874,plain,
( ~ spl10_95
| ~ spl10_1
| spl10_96
| ~ spl10_20
| ~ spl10_47 ),
inference(avatar_split_clause,[],[f860,f392,f241,f871,f152,f867]) ).
fof(f867,plain,
( spl10_95
<=> empty(identity_relation(relation_rng(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_95])]) ).
fof(f871,plain,
( spl10_96
<=> empty(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_96])]) ).
fof(f241,plain,
( spl10_20
<=> sK0 = relation_composition(sK0,identity_relation(relation_rng(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_20])]) ).
fof(f392,plain,
( spl10_47
<=> ! [X0,X1] :
( empty(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_47])]) ).
fof(f860,plain,
( empty(sK0)
| ~ relation(sK0)
| ~ empty(identity_relation(relation_rng(sK0)))
| ~ spl10_20
| ~ spl10_47 ),
inference(superposition,[],[f393,f242]) ).
fof(f242,plain,
( sK0 = relation_composition(sK0,identity_relation(relation_rng(sK0)))
| ~ spl10_20 ),
inference(avatar_component_clause,[],[f241]) ).
fof(f393,plain,
( ! [X0,X1] :
( empty(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) )
| ~ spl10_47 ),
inference(avatar_component_clause,[],[f392]) ).
fof(f857,plain,
( spl10_20
| ~ spl10_1
| ~ spl10_87 ),
inference(avatar_split_clause,[],[f768,f719,f152,f241]) ).
fof(f719,plain,
( spl10_87
<=> ! [X0] :
( relation_composition(X0,identity_relation(relation_rng(X0))) = X0
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_87])]) ).
fof(f768,plain,
( sK0 = relation_composition(sK0,identity_relation(relation_rng(sK0)))
| ~ spl10_1
| ~ spl10_87 ),
inference(resolution,[],[f720,f154]) ).
fof(f720,plain,
( ! [X0] :
( ~ relation(X0)
| relation_composition(X0,identity_relation(relation_rng(X0))) = X0 )
| ~ spl10_87 ),
inference(avatar_component_clause,[],[f719]) ).
fof(f856,plain,
( spl10_94
| ~ spl10_1
| ~ spl10_83 ),
inference(avatar_split_clause,[],[f748,f702,f152,f854]) ).
fof(f854,plain,
( spl10_94
<=> ! [X0] :
( sK5 = relation_composition(sK0,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_94])]) ).
fof(f702,plain,
( spl10_83
<=> ! [X0,X1] :
( relation_composition(X0,X1) = sK5
| ~ relation(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_83])]) ).
fof(f748,plain,
( ! [X0] :
( sK5 = relation_composition(sK0,X0)
| ~ empty(X0) )
| ~ spl10_1
| ~ spl10_83 ),
inference(resolution,[],[f703,f154]) ).
fof(f703,plain,
( ! [X0,X1] :
( ~ relation(X0)
| relation_composition(X0,X1) = sK5
| ~ empty(X1) )
| ~ spl10_83 ),
inference(avatar_component_clause,[],[f702]) ).
fof(f822,plain,
( spl10_93
| ~ spl10_42
| ~ spl10_47 ),
inference(avatar_split_clause,[],[f414,f392,f355,f820]) ).
fof(f820,plain,
( spl10_93
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X0,X1) = X2
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_93])]) ).
fof(f355,plain,
( spl10_42
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_42])]) ).
fof(f414,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X0,X1) = X2
| ~ empty(X2) )
| ~ spl10_42
| ~ spl10_47 ),
inference(resolution,[],[f393,f356]) ).
fof(f356,plain,
( ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) )
| ~ spl10_42 ),
inference(avatar_component_clause,[],[f355]) ).
fof(f818,plain,
( spl10_92
| ~ spl10_42
| ~ spl10_45 ),
inference(avatar_split_clause,[],[f409,f384,f355,f816]) ).
fof(f816,plain,
( spl10_92
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X1,X0) = X2
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_92])]) ).
fof(f384,plain,
( spl10_45
<=> ! [X0,X1] :
( empty(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_45])]) ).
fof(f409,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X1,X0) = X2
| ~ empty(X2) )
| ~ spl10_42
| ~ spl10_45 ),
inference(resolution,[],[f385,f356]) ).
fof(f385,plain,
( ! [X0,X1] :
( empty(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) )
| ~ spl10_45 ),
inference(avatar_component_clause,[],[f384]) ).
fof(f808,plain,
( spl10_91
| ~ spl10_37
| ~ spl10_44 ),
inference(avatar_split_clause,[],[f404,f380,f335,f806]) ).
fof(f806,plain,
( spl10_91
<=> ! [X0] :
( empty(powerset(X0))
| in(sK1(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_91])]) ).
fof(f335,plain,
( spl10_37
<=> ! [X0] :
( element(sK1(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_37])]) ).
fof(f380,plain,
( spl10_44
<=> ! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_44])]) ).
fof(f404,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK1(X0),powerset(X0))
| empty(X0) )
| ~ spl10_37
| ~ spl10_44 ),
inference(resolution,[],[f381,f336]) ).
fof(f336,plain,
( ! [X0] :
( element(sK1(X0),powerset(X0))
| empty(X0) )
| ~ spl10_37 ),
inference(avatar_component_clause,[],[f335]) ).
fof(f381,plain,
( ! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) )
| ~ spl10_44 ),
inference(avatar_component_clause,[],[f380]) ).
fof(f804,plain,
( spl10_90
| ~ spl10_41
| ~ spl10_44 ),
inference(avatar_split_clause,[],[f403,f380,f351,f802]) ).
fof(f802,plain,
( spl10_90
<=> ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_90])]) ).
fof(f351,plain,
( spl10_41
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_41])]) ).
fof(f403,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) )
| ~ spl10_41
| ~ spl10_44 ),
inference(resolution,[],[f381,f352]) ).
fof(f352,plain,
( ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) )
| ~ spl10_41 ),
inference(avatar_component_clause,[],[f351]) ).
fof(f800,plain,
( spl10_89
| ~ spl10_1
| ~ spl10_82 ),
inference(avatar_split_clause,[],[f733,f698,f152,f798]) ).
fof(f798,plain,
( spl10_89
<=> ! [X0] :
( sK5 = relation_composition(X0,sK0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_89])]) ).
fof(f698,plain,
( spl10_82
<=> ! [X0,X1] :
( relation_composition(X1,X0) = sK5
| ~ relation(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_82])]) ).
fof(f733,plain,
( ! [X0] :
( sK5 = relation_composition(X0,sK0)
| ~ empty(X0) )
| ~ spl10_1
| ~ spl10_82 ),
inference(resolution,[],[f699,f154]) ).
fof(f699,plain,
( ! [X0,X1] :
( ~ relation(X0)
| relation_composition(X1,X0) = sK5
| ~ empty(X1) )
| ~ spl10_82 ),
inference(avatar_component_clause,[],[f698]) ).
fof(f725,plain,
( spl10_88
| ~ spl10_18
| ~ spl10_53 ),
inference(avatar_split_clause,[],[f452,f444,f233,f723]) ).
fof(f233,plain,
( spl10_18
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_18])]) ).
fof(f444,plain,
( spl10_53
<=> ! [X0,X1] :
( relation_composition(identity_relation(X0),X1) = X1
| ~ subset(relation_dom(X1),X0)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_53])]) ).
fof(f452,plain,
( ! [X0] :
( relation_composition(identity_relation(relation_dom(X0)),X0) = X0
| ~ relation(X0) )
| ~ spl10_18
| ~ spl10_53 ),
inference(resolution,[],[f445,f234]) ).
fof(f234,plain,
( ! [X0] : subset(X0,X0)
| ~ spl10_18 ),
inference(avatar_component_clause,[],[f233]) ).
fof(f445,plain,
( ! [X0,X1] :
( ~ subset(relation_dom(X1),X0)
| relation_composition(identity_relation(X0),X1) = X1
| ~ relation(X1) )
| ~ spl10_53 ),
inference(avatar_component_clause,[],[f444]) ).
fof(f721,plain,
( spl10_87
| ~ spl10_18
| ~ spl10_52 ),
inference(avatar_split_clause,[],[f451,f440,f233,f719]) ).
fof(f440,plain,
( spl10_52
<=> ! [X0,X1] :
( relation_composition(X1,identity_relation(X0)) = X1
| ~ subset(relation_rng(X1),X0)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_52])]) ).
fof(f451,plain,
( ! [X0] :
( relation_composition(X0,identity_relation(relation_rng(X0))) = X0
| ~ relation(X0) )
| ~ spl10_18
| ~ spl10_52 ),
inference(resolution,[],[f441,f234]) ).
fof(f441,plain,
( ! [X0,X1] :
( ~ subset(relation_rng(X1),X0)
| relation_composition(X1,identity_relation(X0)) = X1
| ~ relation(X1) )
| ~ spl10_52 ),
inference(avatar_component_clause,[],[f440]) ).
fof(f717,plain,
( spl10_86
| ~ spl10_37
| ~ spl10_51 ),
inference(avatar_split_clause,[],[f434,f430,f335,f715]) ).
fof(f715,plain,
( spl10_86
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK1(X1))
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_86])]) ).
fof(f430,plain,
( spl10_51
<=> ! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_51])]) ).
fof(f434,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK1(X1))
| empty(X1) )
| ~ spl10_37
| ~ spl10_51 ),
inference(resolution,[],[f431,f336]) ).
fof(f431,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| element(X0,X2)
| ~ in(X0,X1) )
| ~ spl10_51 ),
inference(avatar_component_clause,[],[f430]) ).
fof(f713,plain,
( spl10_85
| ~ spl10_41
| ~ spl10_51 ),
inference(avatar_split_clause,[],[f433,f430,f351,f711]) ).
fof(f711,plain,
( spl10_85
<=> ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_85])]) ).
fof(f433,plain,
( ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) )
| ~ spl10_41
| ~ spl10_51 ),
inference(resolution,[],[f431,f352]) ).
fof(f709,plain,
( spl10_84
| ~ spl10_3
| ~ spl10_57
| ~ spl10_70 ),
inference(avatar_split_clause,[],[f610,f580,f464,f162,f706]) ).
fof(f706,plain,
( spl10_84
<=> sK5 = relation_rng(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_84])]) ).
fof(f162,plain,
( spl10_3
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_3])]) ).
fof(f464,plain,
( spl10_57
<=> empty_set = sK5 ),
introduced(avatar_definition,[new_symbols(naming,[spl10_57])]) ).
fof(f580,plain,
( spl10_70
<=> ! [X0] :
( relation_rng(X0) = sK5
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_70])]) ).
fof(f610,plain,
( sK5 = relation_rng(sK5)
| ~ spl10_3
| ~ spl10_57
| ~ spl10_70 ),
inference(forward_demodulation,[],[f602,f466]) ).
fof(f466,plain,
( empty_set = sK5
| ~ spl10_57 ),
inference(avatar_component_clause,[],[f464]) ).
fof(f602,plain,
( sK5 = relation_rng(empty_set)
| ~ spl10_3
| ~ spl10_70 ),
inference(resolution,[],[f581,f164]) ).
fof(f164,plain,
( empty(empty_set)
| ~ spl10_3 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f581,plain,
( ! [X0] :
( ~ empty(X0)
| relation_rng(X0) = sK5 )
| ~ spl10_70 ),
inference(avatar_component_clause,[],[f580]) ).
fof(f704,plain,
( spl10_83
| ~ spl10_6
| ~ spl10_26
| ~ spl10_47 ),
inference(avatar_split_clause,[],[f418,f392,f275,f177,f702]) ).
fof(f177,plain,
( spl10_6
<=> empty(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_6])]) ).
fof(f275,plain,
( spl10_26
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_26])]) ).
fof(f418,plain,
( ! [X0,X1] :
( relation_composition(X0,X1) = sK5
| ~ relation(X0)
| ~ empty(X1) )
| ~ spl10_6
| ~ spl10_26
| ~ spl10_47 ),
inference(forward_demodulation,[],[f415,f304]) ).
fof(f304,plain,
( empty_set = sK5
| ~ spl10_6
| ~ spl10_26 ),
inference(resolution,[],[f276,f179]) ).
fof(f179,plain,
( empty(sK5)
| ~ spl10_6 ),
inference(avatar_component_clause,[],[f177]) ).
fof(f276,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl10_26 ),
inference(avatar_component_clause,[],[f275]) ).
fof(f415,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| empty_set = relation_composition(X0,X1) )
| ~ spl10_26
| ~ spl10_47 ),
inference(resolution,[],[f393,f276]) ).
fof(f700,plain,
( spl10_82
| ~ spl10_6
| ~ spl10_26
| ~ spl10_45 ),
inference(avatar_split_clause,[],[f413,f384,f275,f177,f698]) ).
fof(f413,plain,
( ! [X0,X1] :
( relation_composition(X1,X0) = sK5
| ~ relation(X0)
| ~ empty(X1) )
| ~ spl10_6
| ~ spl10_26
| ~ spl10_45 ),
inference(forward_demodulation,[],[f410,f304]) ).
fof(f410,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| empty_set = relation_composition(X1,X0) )
| ~ spl10_26
| ~ spl10_45 ),
inference(resolution,[],[f385,f276]) ).
fof(f661,plain,
( spl10_81
| ~ spl10_23
| ~ spl10_51 ),
inference(avatar_split_clause,[],[f435,f430,f254,f659]) ).
fof(f659,plain,
( spl10_81
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK2(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_81])]) ).
fof(f254,plain,
( spl10_23
<=> ! [X0] : element(sK2(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_23])]) ).
fof(f435,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK2(powerset(X1))) )
| ~ spl10_23
| ~ spl10_51 ),
inference(resolution,[],[f431,f255]) ).
fof(f255,plain,
( ! [X0] : element(sK2(X0),X0)
| ~ spl10_23 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f657,plain,
( spl10_80
| ~ spl10_41
| ~ spl10_50 ),
inference(avatar_split_clause,[],[f423,f420,f351,f655]) ).
fof(f655,plain,
( spl10_80
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_80])]) ).
fof(f420,plain,
( spl10_50
<=> ! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_50])]) ).
fof(f423,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) )
| ~ spl10_41
| ~ spl10_50 ),
inference(resolution,[],[f421,f352]) ).
fof(f421,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X0,X1) )
| ~ spl10_50 ),
inference(avatar_component_clause,[],[f420]) ).
fof(f653,plain,
( spl10_79
| ~ spl10_3
| ~ spl10_57
| ~ spl10_69 ),
inference(avatar_split_clause,[],[f599,f576,f464,f162,f650]) ).
fof(f650,plain,
( spl10_79
<=> sK5 = relation_dom(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_79])]) ).
fof(f576,plain,
( spl10_69
<=> ! [X0] :
( relation_dom(X0) = sK5
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_69])]) ).
fof(f599,plain,
( sK5 = relation_dom(sK5)
| ~ spl10_3
| ~ spl10_57
| ~ spl10_69 ),
inference(forward_demodulation,[],[f591,f466]) ).
fof(f591,plain,
( sK5 = relation_dom(empty_set)
| ~ spl10_3
| ~ spl10_69 ),
inference(resolution,[],[f577,f164]) ).
fof(f577,plain,
( ! [X0] :
( ~ empty(X0)
| relation_dom(X0) = sK5 )
| ~ spl10_69 ),
inference(avatar_component_clause,[],[f576]) ).
fof(f648,plain,
( spl10_78
| ~ spl10_21
| ~ spl10_47 ),
inference(avatar_split_clause,[],[f417,f392,f246,f646]) ).
fof(f646,plain,
( spl10_78
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| function(relation_composition(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_78])]) ).
fof(f246,plain,
( spl10_21
<=> ! [X0] :
( function(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_21])]) ).
fof(f417,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| function(relation_composition(X0,X1)) )
| ~ spl10_21
| ~ spl10_47 ),
inference(resolution,[],[f393,f247]) ).
fof(f247,plain,
( ! [X0] :
( ~ empty(X0)
| function(X0) )
| ~ spl10_21 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f644,plain,
( spl10_77
| ~ spl10_21
| ~ spl10_45 ),
inference(avatar_split_clause,[],[f412,f384,f246,f642]) ).
fof(f642,plain,
( spl10_77
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| function(relation_composition(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_77])]) ).
fof(f412,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| function(relation_composition(X1,X0)) )
| ~ spl10_21
| ~ spl10_45 ),
inference(resolution,[],[f385,f247]) ).
fof(f640,plain,
( spl10_76
| ~ spl10_29
| ~ spl10_42 ),
inference(avatar_split_clause,[],[f373,f355,f287,f638]) ).
fof(f638,plain,
( spl10_76
<=> ! [X0,X1] :
( relation_rng(X1) = X0
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_76])]) ).
fof(f287,plain,
( spl10_29
<=> ! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_29])]) ).
fof(f373,plain,
( ! [X0,X1] :
( relation_rng(X1) = X0
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl10_29
| ~ spl10_42 ),
inference(resolution,[],[f356,f288]) ).
fof(f288,plain,
( ! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) )
| ~ spl10_29 ),
inference(avatar_component_clause,[],[f287]) ).
fof(f636,plain,
( spl10_75
| ~ spl10_27
| ~ spl10_42 ),
inference(avatar_split_clause,[],[f372,f355,f279,f634]) ).
fof(f634,plain,
( spl10_75
<=> ! [X0,X1] :
( relation_dom(X1) = X0
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_75])]) ).
fof(f279,plain,
( spl10_27
<=> ! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_27])]) ).
fof(f372,plain,
( ! [X0,X1] :
( relation_dom(X1) = X0
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl10_27
| ~ spl10_42 ),
inference(resolution,[],[f356,f280]) ).
fof(f280,plain,
( ! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) )
| ~ spl10_27 ),
inference(avatar_component_clause,[],[f279]) ).
fof(f628,plain,
( spl10_74
| ~ spl10_23
| ~ spl10_50 ),
inference(avatar_split_clause,[],[f425,f420,f254,f626]) ).
fof(f626,plain,
( spl10_74
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK2(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_74])]) ).
fof(f425,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK2(powerset(X0))) )
| ~ spl10_23
| ~ spl10_50 ),
inference(resolution,[],[f421,f255]) ).
fof(f624,plain,
( spl10_73
| ~ spl10_6
| ~ spl10_17
| ~ spl10_26
| ~ spl10_31
| ~ spl10_44 ),
inference(avatar_split_clause,[],[f408,f380,f295,f275,f229,f177,f622]) ).
fof(f622,plain,
( spl10_73
<=> ! [X0] :
( in(sK5,powerset(X0))
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_73])]) ).
fof(f229,plain,
( spl10_17
<=> ! [X0] : empty(sK3(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_17])]) ).
fof(f295,plain,
( spl10_31
<=> ! [X0] : element(sK3(X0),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_31])]) ).
fof(f408,plain,
( ! [X0] :
( in(sK5,powerset(X0))
| empty(powerset(X0)) )
| ~ spl10_6
| ~ spl10_17
| ~ spl10_26
| ~ spl10_31
| ~ spl10_44 ),
inference(forward_demodulation,[],[f407,f304]) ).
fof(f407,plain,
( ! [X0] :
( in(empty_set,powerset(X0))
| empty(powerset(X0)) )
| ~ spl10_17
| ~ spl10_26
| ~ spl10_31
| ~ spl10_44 ),
inference(forward_demodulation,[],[f406,f303]) ).
fof(f303,plain,
( ! [X0] : empty_set = sK3(X0)
| ~ spl10_17
| ~ spl10_26 ),
inference(resolution,[],[f276,f230]) ).
fof(f230,plain,
( ! [X0] : empty(sK3(X0))
| ~ spl10_17 ),
inference(avatar_component_clause,[],[f229]) ).
fof(f406,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK3(X0),powerset(X0)) )
| ~ spl10_31
| ~ spl10_44 ),
inference(resolution,[],[f381,f296]) ).
fof(f296,plain,
( ! [X0] : element(sK3(X0),powerset(X0))
| ~ spl10_31 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f590,plain,
( spl10_72
| ~ spl10_23
| ~ spl10_44 ),
inference(avatar_split_clause,[],[f405,f380,f254,f588]) ).
fof(f588,plain,
( spl10_72
<=> ! [X0] :
( empty(X0)
| in(sK2(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_72])]) ).
fof(f405,plain,
( ! [X0] :
( empty(X0)
| in(sK2(X0),X0) )
| ~ spl10_23
| ~ spl10_44 ),
inference(resolution,[],[f381,f255]) ).
fof(f586,plain,
( spl10_71
| ~ spl10_37
| ~ spl10_40 ),
inference(avatar_split_clause,[],[f362,f347,f335,f584]) ).
fof(f584,plain,
( spl10_71
<=> ! [X0] :
( subset(sK1(X0),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_71])]) ).
fof(f347,plain,
( spl10_40
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_40])]) ).
fof(f362,plain,
( ! [X0] :
( subset(sK1(X0),X0)
| empty(X0) )
| ~ spl10_37
| ~ spl10_40 ),
inference(resolution,[],[f348,f336]) ).
fof(f348,plain,
( ! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) )
| ~ spl10_40 ),
inference(avatar_component_clause,[],[f347]) ).
fof(f582,plain,
( spl10_70
| ~ spl10_6
| ~ spl10_26
| ~ spl10_29 ),
inference(avatar_split_clause,[],[f319,f287,f275,f177,f580]) ).
fof(f319,plain,
( ! [X0] :
( relation_rng(X0) = sK5
| ~ empty(X0) )
| ~ spl10_6
| ~ spl10_26
| ~ spl10_29 ),
inference(forward_demodulation,[],[f316,f304]) ).
fof(f316,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = relation_rng(X0) )
| ~ spl10_26
| ~ spl10_29 ),
inference(resolution,[],[f288,f276]) ).
fof(f578,plain,
( spl10_69
| ~ spl10_6
| ~ spl10_26
| ~ spl10_27 ),
inference(avatar_split_clause,[],[f315,f279,f275,f177,f576]) ).
fof(f315,plain,
( ! [X0] :
( relation_dom(X0) = sK5
| ~ empty(X0) )
| ~ spl10_6
| ~ spl10_26
| ~ spl10_27 ),
inference(forward_demodulation,[],[f312,f304]) ).
fof(f312,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = relation_dom(X0) )
| ~ spl10_26
| ~ spl10_27 ),
inference(resolution,[],[f280,f276]) ).
fof(f566,plain,
( spl10_68
| ~ spl10_31
| ~ spl10_61 ),
inference(avatar_split_clause,[],[f491,f488,f295,f564]) ).
fof(f564,plain,
( spl10_68
<=> ! [X0] : element(sK5,powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_68])]) ).
fof(f488,plain,
( spl10_61
<=> ! [X0] : sK3(X0) = sK5 ),
introduced(avatar_definition,[new_symbols(naming,[spl10_61])]) ).
fof(f491,plain,
( ! [X0] : element(sK5,powerset(X0))
| ~ spl10_31
| ~ spl10_61 ),
inference(superposition,[],[f296,f489]) ).
fof(f489,plain,
( ! [X0] : sK3(X0) = sK5
| ~ spl10_61 ),
inference(avatar_component_clause,[],[f488]) ).
fof(f540,plain,
( spl10_65
| ~ spl10_26
| ~ spl10_57 ),
inference(avatar_split_clause,[],[f524,f464,f275,f506]) ).
fof(f506,plain,
( spl10_65
<=> ! [X0] :
( sK5 = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_65])]) ).
fof(f524,plain,
( ! [X0] :
( sK5 = X0
| ~ empty(X0) )
| ~ spl10_26
| ~ spl10_57 ),
inference(forward_demodulation,[],[f276,f466]) ).
fof(f523,plain,
( ~ spl10_3
| ~ spl10_66 ),
inference(avatar_contradiction_clause,[],[f516]) ).
fof(f516,plain,
( $false
| ~ spl10_3
| ~ spl10_66 ),
inference(resolution,[],[f511,f164]) ).
fof(f511,plain,
( ! [X0] : ~ empty(X0)
| ~ spl10_66 ),
inference(avatar_component_clause,[],[f510]) ).
fof(f510,plain,
( spl10_66
<=> ! [X0] : ~ empty(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_66])]) ).
fof(f522,plain,
( ~ spl10_17
| ~ spl10_66 ),
inference(avatar_contradiction_clause,[],[f517]) ).
fof(f517,plain,
( $false
| ~ spl10_17
| ~ spl10_66 ),
inference(resolution,[],[f511,f230]) ).
fof(f521,plain,
( ~ spl10_6
| ~ spl10_66 ),
inference(avatar_contradiction_clause,[],[f518]) ).
fof(f518,plain,
( $false
| ~ spl10_6
| ~ spl10_66 ),
inference(resolution,[],[f511,f179]) ).
fof(f520,plain,
( ~ spl10_9
| ~ spl10_66 ),
inference(avatar_contradiction_clause,[],[f519]) ).
fof(f519,plain,
( $false
| ~ spl10_9
| ~ spl10_66 ),
inference(resolution,[],[f511,f194]) ).
fof(f194,plain,
( empty(sK7)
| ~ spl10_9 ),
inference(avatar_component_clause,[],[f192]) ).
fof(f192,plain,
( spl10_9
<=> empty(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_9])]) ).
fof(f515,plain,
( spl10_66
| spl10_67
| ~ spl10_6
| ~ spl10_17
| ~ spl10_26
| ~ spl10_31
| ~ spl10_50 ),
inference(avatar_split_clause,[],[f428,f420,f295,f275,f229,f177,f513,f510]) ).
fof(f513,plain,
( spl10_67
<=> ! [X1] : ~ in(X1,sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_67])]) ).
fof(f428,plain,
( ! [X0,X1] :
( ~ in(X1,sK5)
| ~ empty(X0) )
| ~ spl10_6
| ~ spl10_17
| ~ spl10_26
| ~ spl10_31
| ~ spl10_50 ),
inference(forward_demodulation,[],[f427,f304]) ).
fof(f427,plain,
( ! [X0,X1] :
( ~ in(X1,empty_set)
| ~ empty(X0) )
| ~ spl10_17
| ~ spl10_26
| ~ spl10_31
| ~ spl10_50 ),
inference(forward_demodulation,[],[f426,f303]) ).
fof(f426,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK3(X0)) )
| ~ spl10_31
| ~ spl10_50 ),
inference(resolution,[],[f421,f296]) ).
fof(f508,plain,
( spl10_65
| ~ spl10_6
| ~ spl10_42 ),
inference(avatar_split_clause,[],[f375,f355,f177,f506]) ).
fof(f375,plain,
( ! [X0] :
( sK5 = X0
| ~ empty(X0) )
| ~ spl10_6
| ~ spl10_42 ),
inference(resolution,[],[f356,f179]) ).
fof(f504,plain,
( spl10_64
| ~ spl10_23
| ~ spl10_40 ),
inference(avatar_split_clause,[],[f360,f347,f254,f502]) ).
fof(f502,plain,
( spl10_64
<=> ! [X0] : subset(sK2(powerset(X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_64])]) ).
fof(f360,plain,
( ! [X0] : subset(sK2(powerset(X0)),X0)
| ~ spl10_23
| ~ spl10_40 ),
inference(resolution,[],[f348,f255]) ).
fof(f500,plain,
( spl10_63
| ~ spl10_21
| ~ spl10_29 ),
inference(avatar_split_clause,[],[f318,f287,f246,f498]) ).
fof(f498,plain,
( spl10_63
<=> ! [X0] :
( ~ empty(X0)
| function(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_63])]) ).
fof(f318,plain,
( ! [X0] :
( ~ empty(X0)
| function(relation_rng(X0)) )
| ~ spl10_21
| ~ spl10_29 ),
inference(resolution,[],[f288,f247]) ).
fof(f496,plain,
( spl10_62
| ~ spl10_21
| ~ spl10_27 ),
inference(avatar_split_clause,[],[f314,f279,f246,f494]) ).
fof(f494,plain,
( spl10_62
<=> ! [X0] :
( ~ empty(X0)
| function(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_62])]) ).
fof(f314,plain,
( ! [X0] :
( ~ empty(X0)
| function(relation_dom(X0)) )
| ~ spl10_21
| ~ spl10_27 ),
inference(resolution,[],[f280,f247]) ).
fof(f490,plain,
( spl10_61
| ~ spl10_57
| ~ spl10_60 ),
inference(avatar_split_clause,[],[f486,f483,f464,f488]) ).
fof(f483,plain,
( spl10_60
<=> ! [X0] : empty_set = sK3(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_60])]) ).
fof(f486,plain,
( ! [X0] : sK3(X0) = sK5
| ~ spl10_57
| ~ spl10_60 ),
inference(forward_demodulation,[],[f484,f466]) ).
fof(f484,plain,
( ! [X0] : empty_set = sK3(X0)
| ~ spl10_60 ),
inference(avatar_component_clause,[],[f483]) ).
fof(f485,plain,
( spl10_60
| ~ spl10_17
| ~ spl10_26 ),
inference(avatar_split_clause,[],[f303,f275,f229,f483]) ).
fof(f476,plain,
( spl10_59
| ~ spl10_6
| ~ spl10_17
| ~ spl10_26
| ~ spl10_31
| ~ spl10_40 ),
inference(avatar_split_clause,[],[f364,f347,f295,f275,f229,f177,f474]) ).
fof(f474,plain,
( spl10_59
<=> ! [X0] : subset(sK5,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_59])]) ).
fof(f364,plain,
( ! [X0] : subset(sK5,X0)
| ~ spl10_6
| ~ spl10_17
| ~ spl10_26
| ~ spl10_31
| ~ spl10_40 ),
inference(forward_demodulation,[],[f363,f304]) ).
fof(f363,plain,
( ! [X0] : subset(empty_set,X0)
| ~ spl10_17
| ~ spl10_26
| ~ spl10_31
| ~ spl10_40 ),
inference(forward_demodulation,[],[f361,f303]) ).
fof(f361,plain,
( ! [X0] : subset(sK3(X0),X0)
| ~ spl10_31
| ~ spl10_40 ),
inference(resolution,[],[f348,f296]) ).
fof(f472,plain,
( spl10_58
| ~ spl10_6
| ~ spl10_9
| ~ spl10_26 ),
inference(avatar_split_clause,[],[f306,f275,f192,f177,f469]) ).
fof(f469,plain,
( spl10_58
<=> sK5 = sK7 ),
introduced(avatar_definition,[new_symbols(naming,[spl10_58])]) ).
fof(f306,plain,
( sK5 = sK7
| ~ spl10_6
| ~ spl10_9
| ~ spl10_26 ),
inference(forward_demodulation,[],[f305,f304]) ).
fof(f305,plain,
( empty_set = sK7
| ~ spl10_9
| ~ spl10_26 ),
inference(resolution,[],[f276,f194]) ).
fof(f467,plain,
( spl10_57
| ~ spl10_6
| ~ spl10_26 ),
inference(avatar_split_clause,[],[f304,f275,f177,f464]) ).
fof(f461,plain,
( spl10_56
| ~ spl10_17
| ~ spl10_22 ),
inference(avatar_split_clause,[],[f262,f250,f229,f459]) ).
fof(f459,plain,
( spl10_56
<=> ! [X0] : relation(sK3(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_56])]) ).
fof(f250,plain,
( spl10_22
<=> ! [X0] :
( relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_22])]) ).
fof(f262,plain,
( ! [X0] : relation(sK3(X0))
| ~ spl10_17
| ~ spl10_22 ),
inference(resolution,[],[f251,f230]) ).
fof(f251,plain,
( ! [X0] :
( ~ empty(X0)
| relation(X0) )
| ~ spl10_22 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f456,plain,
( spl10_55
| ~ spl10_17
| ~ spl10_21 ),
inference(avatar_split_clause,[],[f258,f246,f229,f454]) ).
fof(f454,plain,
( spl10_55
<=> ! [X0] : function(sK3(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_55])]) ).
fof(f258,plain,
( ! [X0] : function(sK3(X0))
| ~ spl10_17
| ~ spl10_21 ),
inference(resolution,[],[f247,f230]) ).
fof(f450,plain,
spl10_54,
inference(avatar_split_clause,[],[f134,f448]) ).
fof(f448,plain,
( spl10_54
<=> ! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_54])]) ).
fof(f134,plain,
! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1] :
( ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) )
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f67]) ).
fof(f67,plain,
! [X0,X1] :
( ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) )
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1)
& function(X0)
& relation(X0) )
=> ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(f446,plain,
spl10_53,
inference(avatar_split_clause,[],[f125,f444]) ).
fof(f125,plain,
! [X0,X1] :
( relation_composition(identity_relation(X0),X1) = X1
| ~ subset(relation_dom(X1),X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0,X1] :
( relation_composition(identity_relation(X0),X1) = X1
| ~ subset(relation_dom(X1),X0)
| ~ relation(X1) ),
inference(flattening,[],[f57]) ).
fof(f57,plain,
! [X0,X1] :
( relation_composition(identity_relation(X0),X1) = X1
| ~ subset(relation_dom(X1),X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0,X1] :
( relation(X1)
=> ( subset(relation_dom(X1),X0)
=> relation_composition(identity_relation(X0),X1) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_relat_1) ).
fof(f442,plain,
spl10_52,
inference(avatar_split_clause,[],[f124,f440]) ).
fof(f124,plain,
! [X0,X1] :
( relation_composition(X1,identity_relation(X0)) = X1
| ~ subset(relation_rng(X1),X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0,X1] :
( relation_composition(X1,identity_relation(X0)) = X1
| ~ subset(relation_rng(X1),X0)
| ~ relation(X1) ),
inference(flattening,[],[f55]) ).
fof(f55,plain,
! [X0,X1] :
( relation_composition(X1,identity_relation(X0)) = X1
| ~ subset(relation_rng(X1),X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f39,axiom,
! [X0,X1] :
( relation(X1)
=> ( subset(relation_rng(X1),X0)
=> relation_composition(X1,identity_relation(X0)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_relat_1) ).
fof(f432,plain,
spl10_51,
inference(avatar_split_clause,[],[f140,f430]) ).
fof(f140,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f73]) ).
fof(f73,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f422,plain,
spl10_50,
inference(avatar_split_clause,[],[f141,f420]) ).
fof(f141,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f402,plain,
spl10_49,
inference(avatar_split_clause,[],[f135,f400]) ).
fof(f400,plain,
( spl10_49
<=> ! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_49])]) ).
fof(f135,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(flattening,[],[f69]) ).
fof(f69,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f398,plain,
spl10_48,
inference(avatar_split_clause,[],[f132,f396]) ).
fof(f396,plain,
( spl10_48
<=> ! [X0,X1] :
( relation(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_48])]) ).
fof(f132,plain,
! [X0,X1] :
( relation(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0,X1] :
( ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(flattening,[],[f65]) ).
fof(f65,plain,
! [X0,X1] :
( ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0,X1] :
( ( relation(X1)
& empty(X0) )
=> ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc10_relat_1) ).
fof(f394,plain,
spl10_47,
inference(avatar_split_clause,[],[f131,f392]) ).
fof(f131,plain,
! [X0,X1] :
( empty(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f390,plain,
spl10_46,
inference(avatar_split_clause,[],[f130,f388]) ).
fof(f388,plain,
( spl10_46
<=> ! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_46])]) ).
fof(f130,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(flattening,[],[f63]) ).
fof(f63,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0,X1] :
( ( relation(X1)
& empty(X0) )
=> ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc9_relat_1) ).
fof(f386,plain,
spl10_45,
inference(avatar_split_clause,[],[f129,f384]) ).
fof(f129,plain,
! [X0,X1] :
( empty(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f382,plain,
spl10_44,
inference(avatar_split_clause,[],[f128,f380]) ).
fof(f128,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f61]) ).
fof(f61,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f369,plain,
( spl10_43
| ~ spl10_6
| ~ spl10_22 ),
inference(avatar_split_clause,[],[f263,f250,f177,f366]) ).
fof(f366,plain,
( spl10_43
<=> relation(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_43])]) ).
fof(f263,plain,
( relation(sK5)
| ~ spl10_6
| ~ spl10_22 ),
inference(resolution,[],[f251,f179]) ).
fof(f357,plain,
spl10_42,
inference(avatar_split_clause,[],[f138,f355]) ).
fof(f138,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(f353,plain,
spl10_41,
inference(avatar_split_clause,[],[f137,f351]) ).
fof(f137,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f349,plain,
spl10_40,
inference(avatar_split_clause,[],[f136,f347]) ).
fof(f136,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f84]) ).
fof(f345,plain,
spl10_39,
inference(avatar_split_clause,[],[f119,f343]) ).
fof(f343,plain,
( spl10_39
<=> ! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_39])]) ).
fof(f119,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f53]) ).
fof(f53,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f341,plain,
spl10_38,
inference(avatar_split_clause,[],[f118,f339]) ).
fof(f339,plain,
( spl10_38
<=> ! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_38])]) ).
fof(f118,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f51]) ).
fof(f51,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_rng(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
fof(f337,plain,
spl10_37,
inference(avatar_split_clause,[],[f109,f335]) ).
fof(f109,plain,
! [X0] :
( element(sK1(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0] :
( ( ~ empty(sK1(X0))
& element(sK1(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f45,f78]) ).
fof(f78,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK1(X0))
& element(sK1(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f45,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f332,plain,
( spl10_36
| ~ spl10_9
| ~ spl10_21 ),
inference(avatar_split_clause,[],[f260,f246,f192,f329]) ).
fof(f329,plain,
( spl10_36
<=> function(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_36])]) ).
fof(f260,plain,
( function(sK7)
| ~ spl10_9
| ~ spl10_21 ),
inference(resolution,[],[f247,f194]) ).
fof(f327,plain,
spl10_35,
inference(avatar_split_clause,[],[f127,f325]) ).
fof(f325,plain,
( spl10_35
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_35])]) ).
fof(f127,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f323,plain,
spl10_34,
inference(avatar_split_clause,[],[f126,f321]) ).
fof(f321,plain,
( spl10_34
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_34])]) ).
fof(f126,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f311,plain,
( spl10_33
| ~ spl10_6
| ~ spl10_21 ),
inference(avatar_split_clause,[],[f259,f246,f177,f308]) ).
fof(f308,plain,
( spl10_33
<=> function(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_33])]) ).
fof(f259,plain,
( function(sK5)
| ~ spl10_6
| ~ spl10_21 ),
inference(resolution,[],[f247,f179]) ).
fof(f301,plain,
spl10_32,
inference(avatar_split_clause,[],[f139,f299]) ).
fof(f299,plain,
( spl10_32
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_32])]) ).
fof(f139,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f297,plain,
spl10_31,
inference(avatar_split_clause,[],[f121,f295]) ).
fof(f121,plain,
! [X0] : element(sK3(X0),powerset(X0)),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0] :
( empty(sK3(X0))
& element(sK3(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f29,f82]) ).
fof(f82,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK3(X0))
& element(sK3(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f29,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f293,plain,
spl10_30,
inference(avatar_split_clause,[],[f117,f291]) ).
fof(f291,plain,
( spl10_30
<=> ! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_30])]) ).
fof(f117,plain,
! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0] :
( ( relation(relation_rng(X0))
& empty(relation_rng(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_rng(X0))
& empty(relation_rng(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
fof(f289,plain,
spl10_29,
inference(avatar_split_clause,[],[f116,f287]) ).
fof(f116,plain,
! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f285,plain,
spl10_28,
inference(avatar_split_clause,[],[f115,f283]) ).
fof(f283,plain,
( spl10_28
<=> ! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_28])]) ).
fof(f115,plain,
! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0] :
( ( relation(relation_dom(X0))
& empty(relation_dom(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f281,plain,
spl10_27,
inference(avatar_split_clause,[],[f114,f279]) ).
fof(f114,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f277,plain,
spl10_26,
inference(avatar_split_clause,[],[f113,f275]) ).
fof(f113,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f273,plain,
spl10_25,
inference(avatar_split_clause,[],[f110,f271]) ).
fof(f271,plain,
( spl10_25
<=> ! [X0] :
( ~ empty(sK1(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_25])]) ).
fof(f110,plain,
! [X0] :
( ~ empty(sK1(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f269,plain,
( spl10_24
| ~ spl10_3
| ~ spl10_21 ),
inference(avatar_split_clause,[],[f257,f246,f162,f266]) ).
fof(f266,plain,
( spl10_24
<=> function(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_24])]) ).
fof(f257,plain,
( function(empty_set)
| ~ spl10_3
| ~ spl10_21 ),
inference(resolution,[],[f247,f164]) ).
fof(f256,plain,
spl10_23,
inference(avatar_split_clause,[],[f120,f254]) ).
fof(f120,plain,
! [X0] : element(sK2(X0),X0),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0] : element(sK2(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f8,f80]) ).
fof(f80,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK2(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f8,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f252,plain,
spl10_22,
inference(avatar_split_clause,[],[f112,f250]) ).
fof(f112,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(f248,plain,
spl10_21,
inference(avatar_split_clause,[],[f111,f246]) ).
fof(f111,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] :
( empty(X0)
=> function(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(f244,plain,
( ~ spl10_19
| ~ spl10_20 ),
inference(avatar_split_clause,[],[f99,f241,f237]) ).
fof(f99,plain,
( sK0 != relation_composition(sK0,identity_relation(relation_rng(sK0)))
| sK0 != relation_composition(identity_relation(relation_dom(sK0)),sK0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
( ( sK0 != relation_composition(sK0,identity_relation(relation_rng(sK0)))
| sK0 != relation_composition(identity_relation(relation_dom(sK0)),sK0) )
& function(sK0)
& relation(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f44,f76]) ).
fof(f76,plain,
( ? [X0] :
( ( relation_composition(X0,identity_relation(relation_rng(X0))) != X0
| relation_composition(identity_relation(relation_dom(X0)),X0) != X0 )
& function(X0)
& relation(X0) )
=> ( ( sK0 != relation_composition(sK0,identity_relation(relation_rng(sK0)))
| sK0 != relation_composition(identity_relation(relation_dom(sK0)),sK0) )
& function(sK0)
& relation(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f44,plain,
? [X0] :
( ( relation_composition(X0,identity_relation(relation_rng(X0))) != X0
| relation_composition(identity_relation(relation_dom(X0)),X0) != X0 )
& function(X0)
& relation(X0) ),
inference(flattening,[],[f43]) ).
fof(f43,plain,
? [X0] :
( ( relation_composition(X0,identity_relation(relation_rng(X0))) != X0
| relation_composition(identity_relation(relation_dom(X0)),X0) != X0 )
& function(X0)
& relation(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,negated_conjecture,
~ ! [X0] :
( ( function(X0)
& relation(X0) )
=> ( relation_composition(X0,identity_relation(relation_rng(X0))) = X0
& relation_composition(identity_relation(relation_dom(X0)),X0) = X0 ) ),
inference(negated_conjecture,[],[f36]) ).
fof(f36,conjecture,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( relation_composition(X0,identity_relation(relation_rng(X0))) = X0
& relation_composition(identity_relation(relation_dom(X0)),X0) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_funct_1) ).
fof(f235,plain,
spl10_18,
inference(avatar_split_clause,[],[f123,f233]) ).
fof(f123,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f22]) ).
fof(f22,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f231,plain,
spl10_17,
inference(avatar_split_clause,[],[f122,f229]) ).
fof(f122,plain,
! [X0] : empty(sK3(X0)),
inference(cnf_transformation,[],[f83]) ).
fof(f227,plain,
spl10_16,
inference(avatar_split_clause,[],[f108,f225]) ).
fof(f225,plain,
( spl10_16
<=> ! [X0] : function(identity_relation(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_16])]) ).
fof(f108,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0] :
( function(identity_relation(X0))
& relation(identity_relation(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(f223,plain,
spl10_15,
inference(avatar_split_clause,[],[f106,f221]) ).
fof(f221,plain,
( spl10_15
<=> ! [X0] : relation(identity_relation(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_15])]) ).
fof(f106,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0] : relation(identity_relation(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(f219,plain,
spl10_14,
inference(avatar_split_clause,[],[f105,f217]) ).
fof(f217,plain,
( spl10_14
<=> ! [X0] : ~ empty(powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_14])]) ).
fof(f105,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f215,plain,
spl10_13,
inference(avatar_split_clause,[],[f150,f212]) ).
fof(f212,plain,
( spl10_13
<=> function(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_13])]) ).
fof(f150,plain,
function(sK9),
inference(cnf_transformation,[],[f96]) ).
fof(f96,plain,
( function(sK9)
& relation(sK9) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f27,f95]) ).
fof(f95,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK9)
& relation(sK9) ) ),
introduced(choice_axiom,[]) ).
fof(f27,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(f210,plain,
spl10_12,
inference(avatar_split_clause,[],[f149,f207]) ).
fof(f207,plain,
( spl10_12
<=> relation(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_12])]) ).
fof(f149,plain,
relation(sK9),
inference(cnf_transformation,[],[f96]) ).
fof(f205,plain,
spl10_11,
inference(avatar_split_clause,[],[f148,f202]) ).
fof(f202,plain,
( spl10_11
<=> relation(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_11])]) ).
fof(f148,plain,
relation(sK8),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
relation(sK8),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f42,f93]) ).
fof(f93,plain,
( ? [X0] : relation(X0)
=> relation(sK8) ),
introduced(choice_axiom,[]) ).
fof(f42,plain,
? [X0] : relation(X0),
inference(pure_predicate_removal,[],[f32]) ).
fof(f32,axiom,
? [X0] :
( relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
fof(f200,plain,
spl10_10,
inference(avatar_split_clause,[],[f147,f197]) ).
fof(f197,plain,
( spl10_10
<=> relation(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_10])]) ).
fof(f147,plain,
relation(sK7),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
( relation(sK7)
& empty(sK7) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f30,f91]) ).
fof(f91,plain,
( ? [X0] :
( relation(X0)
& empty(X0) )
=> ( relation(sK7)
& empty(sK7) ) ),
introduced(choice_axiom,[]) ).
fof(f30,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f195,plain,
spl10_9,
inference(avatar_split_clause,[],[f146,f192]) ).
fof(f146,plain,
empty(sK7),
inference(cnf_transformation,[],[f92]) ).
fof(f190,plain,
spl10_8,
inference(avatar_split_clause,[],[f145,f187]) ).
fof(f187,plain,
( spl10_8
<=> relation(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_8])]) ).
fof(f145,plain,
relation(sK6),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
( relation(sK6)
& ~ empty(sK6) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f31,f89]) ).
fof(f89,plain,
( ? [X0] :
( relation(X0)
& ~ empty(X0) )
=> ( relation(sK6)
& ~ empty(sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f31,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f185,plain,
~ spl10_7,
inference(avatar_split_clause,[],[f144,f182]) ).
fof(f182,plain,
( spl10_7
<=> empty(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_7])]) ).
fof(f144,plain,
~ empty(sK6),
inference(cnf_transformation,[],[f90]) ).
fof(f180,plain,
spl10_6,
inference(avatar_split_clause,[],[f143,f177]) ).
fof(f143,plain,
empty(sK5),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
empty(sK5),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f33,f87]) ).
fof(f87,plain,
( ? [X0] : empty(X0)
=> empty(sK5) ),
introduced(choice_axiom,[]) ).
fof(f33,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f175,plain,
~ spl10_5,
inference(avatar_split_clause,[],[f142,f172]) ).
fof(f172,plain,
( spl10_5
<=> empty(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_5])]) ).
fof(f142,plain,
~ empty(sK4),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
~ empty(sK4),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f34,f85]) ).
fof(f85,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK4) ),
introduced(choice_axiom,[]) ).
fof(f34,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f170,plain,
spl10_4,
inference(avatar_split_clause,[],[f102,f167]) ).
fof(f167,plain,
( spl10_4
<=> relation(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_4])]) ).
fof(f102,plain,
relation(empty_set),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f165,plain,
spl10_3,
inference(avatar_split_clause,[],[f100,f162]) ).
fof(f100,plain,
empty(empty_set),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f160,plain,
spl10_2,
inference(avatar_split_clause,[],[f98,f157]) ).
fof(f157,plain,
( spl10_2
<=> function(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_2])]) ).
fof(f98,plain,
function(sK0),
inference(cnf_transformation,[],[f77]) ).
fof(f155,plain,
spl10_1,
inference(avatar_split_clause,[],[f97,f152]) ).
fof(f97,plain,
relation(sK0),
inference(cnf_transformation,[],[f77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU010+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n005.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 11:28:56 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (15464)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (15467)WARNING: value z3 for option sas not known
% 0.15/0.38 % (15465)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (15466)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (15468)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (15467)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.38 % (15469)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.38 % (15471)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)
% 0.15/0.38 % (15470)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.15/0.38 TRYING [3]
% 0.15/0.39 TRYING [1]
% 0.15/0.39 TRYING [4]
% 0.15/0.39 TRYING [2]
% 0.15/0.39 TRYING [1]
% 0.15/0.39 TRYING [2]
% 0.15/0.39 TRYING [5]
% 0.15/0.39 TRYING [3]
% 0.15/0.39 TRYING [4]
% 0.15/0.39 TRYING [3]
% 0.15/0.40 % (15469)First to succeed.
% 0.15/0.40 TRYING [5]
% 0.15/0.40 % (15469)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-15464"
% 0.15/0.40 % (15469)Refutation found. Thanks to Tanya!
% 0.15/0.40 % SZS status Theorem for theBenchmark
% 0.15/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.41 % (15469)------------------------------
% 0.15/0.41 % (15469)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.41 % (15469)Termination reason: Refutation
% 0.15/0.41
% 0.15/0.41 % (15469)Memory used [KB]: 1129
% 0.15/0.41 % (15469)Time elapsed: 0.023 s
% 0.15/0.41 % (15469)Instructions burned: 32 (million)
% 0.15/0.41 % (15464)Success in time 0.039 s
%------------------------------------------------------------------------------