TSTP Solution File: SEU212+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU212+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n029.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 : Tue Apr 30 15:23:51 EDT 2024
% Result : Theorem 0.13s 0.38s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 127
% Syntax : Number of formulae : 440 ( 67 unt; 0 def)
% Number of atoms : 1460 ( 161 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 1833 ( 813 ~; 823 |; 68 &)
% ( 102 <=>; 25 =>; 0 <=; 2 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 98 ( 96 usr; 91 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 10 con; 0-2 aty)
% Number of variables : 448 ( 405 !; 43 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f813,plain,
$false,
inference(avatar_sat_refutation,[],[f144,f149,f154,f159,f164,f169,f174,f179,f184,f189,f194,f199,f204,f213,f220,f224,f229,f232,f240,f244,f248,f252,f262,f267,f271,f275,f279,f292,f296,f302,f307,f311,f315,f327,f332,f338,f345,f350,f357,f362,f371,f376,f381,f392,f397,f408,f413,f424,f430,f438,f443,f457,f461,f471,f487,f492,f497,f502,f508,f513,f518,f524,f525,f526,f545,f549,f553,f558,f562,f566,f579,f583,f602,f603,f611,f615,f619,f631,f638,f639,f648,f652,f663,f664,f674,f679,f687,f691,f697,f701,f712,f731,f741,f745,f754,f767,f776,f787,f811,f812]) ).
fof(f812,plain,
( ~ spl13_88
| spl13_18
| ~ spl13_80 ),
inference(avatar_split_clause,[],[f747,f694,f226,f773]) ).
fof(f773,plain,
( spl13_88
<=> sK1 = sK5(sK2,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_88])]) ).
fof(f226,plain,
( spl13_18
<=> sK1 = apply(sK2,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_18])]) ).
fof(f694,plain,
( spl13_80
<=> apply(sK2,sK0) = sK5(sK2,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_80])]) ).
fof(f747,plain,
( sK1 != sK5(sK2,sK0)
| spl13_18
| ~ spl13_80 ),
inference(superposition,[],[f227,f696]) ).
fof(f696,plain,
( apply(sK2,sK0) = sK5(sK2,sK0)
| ~ spl13_80 ),
inference(avatar_component_clause,[],[f694]) ).
fof(f227,plain,
( sK1 != apply(sK2,sK0)
| spl13_18 ),
inference(avatar_component_clause,[],[f226]) ).
fof(f811,plain,
( spl13_90
| ~ spl13_28
| ~ spl13_65 ),
inference(avatar_split_clause,[],[f574,f564,f290,f809]) ).
fof(f809,plain,
( spl13_90
<=> ! [X0] :
( empty(X0)
| ~ in(X0,sK6(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_90])]) ).
fof(f290,plain,
( spl13_28
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_28])]) ).
fof(f564,plain,
( spl13_65
<=> ! [X0] :
( empty(X0)
| in(sK6(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_65])]) ).
fof(f574,plain,
( ! [X0] :
( empty(X0)
| ~ in(X0,sK6(X0)) )
| ~ spl13_28
| ~ spl13_65 ),
inference(resolution,[],[f565,f291]) ).
fof(f291,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) )
| ~ spl13_28 ),
inference(avatar_component_clause,[],[f290]) ).
fof(f565,plain,
( ! [X0] :
( in(sK6(X0),X0)
| empty(X0) )
| ~ spl13_65 ),
inference(avatar_component_clause,[],[f564]) ).
fof(f787,plain,
( spl13_89
| ~ spl13_3
| ~ spl13_59
| ~ spl13_64 ),
inference(avatar_split_clause,[],[f571,f560,f510,f151,f784]) ).
fof(f784,plain,
( spl13_89
<=> sK8 = relation_dom(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_89])]) ).
fof(f151,plain,
( spl13_3
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_3])]) ).
fof(f510,plain,
( spl13_59
<=> empty_set = sK8 ),
introduced(avatar_definition,[new_symbols(naming,[spl13_59])]) ).
fof(f560,plain,
( spl13_64
<=> ! [X0] :
( relation_dom(X0) = sK8
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_64])]) ).
fof(f571,plain,
( sK8 = relation_dom(sK8)
| ~ spl13_3
| ~ spl13_59
| ~ spl13_64 ),
inference(forward_demodulation,[],[f568,f512]) ).
fof(f512,plain,
( empty_set = sK8
| ~ spl13_59 ),
inference(avatar_component_clause,[],[f510]) ).
fof(f568,plain,
( sK8 = relation_dom(empty_set)
| ~ spl13_3
| ~ spl13_64 ),
inference(resolution,[],[f561,f153]) ).
fof(f153,plain,
( empty(empty_set)
| ~ spl13_3 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f561,plain,
( ! [X0] :
( ~ empty(X0)
| relation_dom(X0) = sK8 )
| ~ spl13_64 ),
inference(avatar_component_clause,[],[f560]) ).
fof(f776,plain,
( ~ spl13_1
| ~ spl13_2
| ~ spl13_15
| spl13_88
| ~ spl13_16
| ~ spl13_80
| ~ spl13_81 ),
inference(avatar_split_clause,[],[f708,f699,f694,f217,f773,f210,f146,f141]) ).
fof(f141,plain,
( spl13_1
<=> relation(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_1])]) ).
fof(f146,plain,
( spl13_2
<=> function(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_2])]) ).
fof(f210,plain,
( spl13_15
<=> in(sK0,relation_dom(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_15])]) ).
fof(f217,plain,
( spl13_16
<=> in(unordered_pair(singleton(sK0),unordered_pair(sK1,sK0)),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_16])]) ).
fof(f699,plain,
( spl13_81
<=> ! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X2)
| apply(X2,X0) = X1
| ~ in(X0,relation_dom(X2))
| ~ function(X2)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_81])]) ).
fof(f708,plain,
( sK1 = sK5(sK2,sK0)
| ~ in(sK0,relation_dom(sK2))
| ~ function(sK2)
| ~ relation(sK2)
| ~ spl13_16
| ~ spl13_80
| ~ spl13_81 ),
inference(forward_demodulation,[],[f704,f696]) ).
fof(f704,plain,
( sK1 = apply(sK2,sK0)
| ~ in(sK0,relation_dom(sK2))
| ~ function(sK2)
| ~ relation(sK2)
| ~ spl13_16
| ~ spl13_81 ),
inference(resolution,[],[f700,f218]) ).
fof(f218,plain,
( in(unordered_pair(singleton(sK0),unordered_pair(sK1,sK0)),sK2)
| ~ spl13_16 ),
inference(avatar_component_clause,[],[f217]) ).
fof(f700,plain,
( ! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X2)
| apply(X2,X0) = X1
| ~ in(X0,relation_dom(X2))
| ~ function(X2)
| ~ relation(X2) )
| ~ spl13_81 ),
inference(avatar_component_clause,[],[f699]) ).
fof(f767,plain,
( spl13_87
| ~ spl13_36
| ~ spl13_47 ),
inference(avatar_split_clause,[],[f414,f411,f336,f765]) ).
fof(f765,plain,
( spl13_87
<=> ! [X2,X0,X1] :
( relation_dom(relation_dom(X0)) = X1
| ~ in(sK3(relation_dom(X0),X1),X1)
| ~ relation(relation_dom(X0))
| sK8 = apply(X0,unordered_pair(singleton(sK3(relation_dom(X0),X1)),unordered_pair(sK3(relation_dom(X0),X1),X2)))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_87])]) ).
fof(f336,plain,
( spl13_36
<=> ! [X0,X1] :
( apply(X0,X1) = sK8
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_36])]) ).
fof(f411,plain,
( spl13_47
<=> ! [X0,X1,X3] :
( ~ in(unordered_pair(singleton(sK3(X0,X1)),unordered_pair(sK3(X0,X1),X3)),X0)
| relation_dom(X0) = X1
| ~ in(sK3(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_47])]) ).
fof(f414,plain,
( ! [X2,X0,X1] :
( relation_dom(relation_dom(X0)) = X1
| ~ in(sK3(relation_dom(X0),X1),X1)
| ~ relation(relation_dom(X0))
| sK8 = apply(X0,unordered_pair(singleton(sK3(relation_dom(X0),X1)),unordered_pair(sK3(relation_dom(X0),X1),X2)))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl13_36
| ~ spl13_47 ),
inference(resolution,[],[f412,f337]) ).
fof(f337,plain,
( ! [X0,X1] :
( in(X1,relation_dom(X0))
| apply(X0,X1) = sK8
| ~ function(X0)
| ~ relation(X0) )
| ~ spl13_36 ),
inference(avatar_component_clause,[],[f336]) ).
fof(f412,plain,
( ! [X3,X0,X1] :
( ~ in(unordered_pair(singleton(sK3(X0,X1)),unordered_pair(sK3(X0,X1),X3)),X0)
| relation_dom(X0) = X1
| ~ in(sK3(X0,X1),X1)
| ~ relation(X0) )
| ~ spl13_47 ),
inference(avatar_component_clause,[],[f411]) ).
fof(f754,plain,
( spl13_86
| ~ spl13_36
| ~ spl13_45 ),
inference(avatar_split_clause,[],[f398,f395,f336,f752]) ).
fof(f752,plain,
( spl13_86
<=> ! [X2,X0,X1] :
( apply(relation_dom(X0),X1) = X2
| ~ in(X1,relation_dom(relation_dom(X0)))
| ~ function(relation_dom(X0))
| ~ relation(relation_dom(X0))
| sK8 = apply(X0,unordered_pair(singleton(X1),unordered_pair(X1,X2)))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_86])]) ).
fof(f395,plain,
( spl13_45
<=> ! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X0)
| apply(X0,X1) = X2
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_45])]) ).
fof(f398,plain,
( ! [X2,X0,X1] :
( apply(relation_dom(X0),X1) = X2
| ~ in(X1,relation_dom(relation_dom(X0)))
| ~ function(relation_dom(X0))
| ~ relation(relation_dom(X0))
| sK8 = apply(X0,unordered_pair(singleton(X1),unordered_pair(X1,X2)))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl13_36
| ~ spl13_45 ),
inference(resolution,[],[f396,f337]) ).
fof(f396,plain,
( ! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X0)
| apply(X0,X1) = X2
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl13_45 ),
inference(avatar_component_clause,[],[f395]) ).
fof(f745,plain,
( spl13_85
| ~ spl13_28
| ~ spl13_49 ),
inference(avatar_split_clause,[],[f432,f428,f290,f743]) ).
fof(f743,plain,
( spl13_85
<=> ! [X0,X1] :
( relation_dom(X0) = X1
| in(sK3(X0,X1),X1)
| ~ relation(X0)
| ~ in(X0,unordered_pair(singleton(sK3(X0,X1)),unordered_pair(sK4(X0,X1),sK3(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_85])]) ).
fof(f428,plain,
( spl13_49
<=> ! [X0,X1] :
( in(unordered_pair(singleton(sK3(X0,X1)),unordered_pair(sK4(X0,X1),sK3(X0,X1))),X0)
| relation_dom(X0) = X1
| in(sK3(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_49])]) ).
fof(f432,plain,
( ! [X0,X1] :
( relation_dom(X0) = X1
| in(sK3(X0,X1),X1)
| ~ relation(X0)
| ~ in(X0,unordered_pair(singleton(sK3(X0,X1)),unordered_pair(sK4(X0,X1),sK3(X0,X1)))) )
| ~ spl13_28
| ~ spl13_49 ),
inference(resolution,[],[f429,f291]) ).
fof(f429,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(sK3(X0,X1)),unordered_pair(sK4(X0,X1),sK3(X0,X1))),X0)
| relation_dom(X0) = X1
| in(sK3(X0,X1),X1)
| ~ relation(X0) )
| ~ spl13_49 ),
inference(avatar_component_clause,[],[f428]) ).
fof(f741,plain,
( spl13_84
| ~ spl13_29
| ~ spl13_49 ),
inference(avatar_split_clause,[],[f431,f428,f294,f739]) ).
fof(f739,plain,
( spl13_84
<=> ! [X0,X1] :
( relation_dom(X0) = X1
| in(sK3(X0,X1),X1)
| ~ relation(X0)
| element(unordered_pair(singleton(sK3(X0,X1)),unordered_pair(sK4(X0,X1),sK3(X0,X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_84])]) ).
fof(f294,plain,
( spl13_29
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_29])]) ).
fof(f431,plain,
( ! [X0,X1] :
( relation_dom(X0) = X1
| in(sK3(X0,X1),X1)
| ~ relation(X0)
| element(unordered_pair(singleton(sK3(X0,X1)),unordered_pair(sK4(X0,X1),sK3(X0,X1))),X0) )
| ~ spl13_29
| ~ spl13_49 ),
inference(resolution,[],[f429,f295]) ).
fof(f295,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) )
| ~ spl13_29 ),
inference(avatar_component_clause,[],[f294]) ).
fof(f731,plain,
( spl13_83
| ~ spl13_32
| ~ spl13_47 ),
inference(avatar_split_clause,[],[f417,f411,f309,f729]) ).
fof(f729,plain,
( spl13_83
<=> ! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(sK3(X0,X1)),unordered_pair(X2,sK3(X0,X1))),X0)
| relation_dom(X0) = X1
| ~ in(sK3(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_83])]) ).
fof(f309,plain,
( spl13_32
<=> ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_32])]) ).
fof(f417,plain,
( ! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(sK3(X0,X1)),unordered_pair(X2,sK3(X0,X1))),X0)
| relation_dom(X0) = X1
| ~ in(sK3(X0,X1),X1)
| ~ relation(X0) )
| ~ spl13_32
| ~ spl13_47 ),
inference(superposition,[],[f412,f310]) ).
fof(f310,plain,
( ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0)
| ~ spl13_32 ),
inference(avatar_component_clause,[],[f309]) ).
fof(f712,plain,
( spl13_82
| ~ spl13_36
| ~ spl13_38 ),
inference(avatar_split_clause,[],[f351,f348,f336,f710]) ).
fof(f710,plain,
( spl13_82
<=> ! [X2,X0,X1] :
( in(X0,relation_dom(relation_dom(X1)))
| ~ relation(relation_dom(X1))
| sK8 = apply(X1,unordered_pair(singleton(X0),unordered_pair(X0,X2)))
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_82])]) ).
fof(f348,plain,
( spl13_38
<=> ! [X6,X0,X5] :
( ~ in(unordered_pair(singleton(X5),unordered_pair(X5,X6)),X0)
| in(X5,relation_dom(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_38])]) ).
fof(f351,plain,
( ! [X2,X0,X1] :
( in(X0,relation_dom(relation_dom(X1)))
| ~ relation(relation_dom(X1))
| sK8 = apply(X1,unordered_pair(singleton(X0),unordered_pair(X0,X2)))
| ~ function(X1)
| ~ relation(X1) )
| ~ spl13_36
| ~ spl13_38 ),
inference(resolution,[],[f349,f337]) ).
fof(f349,plain,
( ! [X0,X6,X5] :
( ~ in(unordered_pair(singleton(X5),unordered_pair(X5,X6)),X0)
| in(X5,relation_dom(X0))
| ~ relation(X0) )
| ~ spl13_38 ),
inference(avatar_component_clause,[],[f348]) ).
fof(f701,plain,
( spl13_81
| ~ spl13_32
| ~ spl13_45 ),
inference(avatar_split_clause,[],[f401,f395,f309,f699]) ).
fof(f401,plain,
( ! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X2)
| apply(X2,X0) = X1
| ~ in(X0,relation_dom(X2))
| ~ function(X2)
| ~ relation(X2) )
| ~ spl13_32
| ~ spl13_45 ),
inference(superposition,[],[f396,f310]) ).
fof(f697,plain,
( ~ spl13_1
| ~ spl13_2
| spl13_80
| ~ spl13_15
| ~ spl13_74 ),
inference(avatar_split_clause,[],[f665,f650,f210,f694,f146,f141]) ).
fof(f650,plain,
( spl13_74
<=> ! [X0,X1] :
( apply(X0,X1) = sK5(X0,X1)
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_74])]) ).
fof(f665,plain,
( apply(sK2,sK0) = sK5(sK2,sK0)
| ~ function(sK2)
| ~ relation(sK2)
| ~ spl13_15
| ~ spl13_74 ),
inference(resolution,[],[f212,f651]) ).
fof(f651,plain,
( ! [X0,X1] :
( ~ in(X1,relation_dom(X0))
| apply(X0,X1) = sK5(X0,X1)
| ~ function(X0)
| ~ relation(X0) )
| ~ spl13_74 ),
inference(avatar_component_clause,[],[f650]) ).
fof(f212,plain,
( in(sK0,relation_dom(sK2))
| ~ spl13_15 ),
inference(avatar_component_clause,[],[f210]) ).
fof(f691,plain,
( spl13_79
| ~ spl13_28
| ~ spl13_42 ),
inference(avatar_split_clause,[],[f384,f374,f290,f689]) ).
fof(f689,plain,
( spl13_79
<=> ! [X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X1,unordered_pair(singleton(X0),unordered_pair(X0,apply(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_79])]) ).
fof(f374,plain,
( spl13_42
<=> ! [X0,X1] :
( in(unordered_pair(singleton(X1),unordered_pair(X1,apply(X0,X1))),X0)
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_42])]) ).
fof(f384,plain,
( ! [X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X1,unordered_pair(singleton(X0),unordered_pair(X0,apply(X1,X0)))) )
| ~ spl13_28
| ~ spl13_42 ),
inference(resolution,[],[f375,f291]) ).
fof(f375,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(X1),unordered_pair(X1,apply(X0,X1))),X0)
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl13_42 ),
inference(avatar_component_clause,[],[f374]) ).
fof(f687,plain,
( spl13_78
| ~ spl13_29
| ~ spl13_42 ),
inference(avatar_split_clause,[],[f383,f374,f294,f685]) ).
fof(f685,plain,
( spl13_78
<=> ! [X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| element(unordered_pair(singleton(X0),unordered_pair(X0,apply(X1,X0))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_78])]) ).
fof(f383,plain,
( ! [X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| element(unordered_pair(singleton(X0),unordered_pair(X0,apply(X1,X0))),X1) )
| ~ spl13_29
| ~ spl13_42 ),
inference(resolution,[],[f375,f295]) ).
fof(f679,plain,
( spl13_77
| ~ spl13_40
| ~ spl13_47 ),
inference(avatar_split_clause,[],[f420,f411,f360,f677]) ).
fof(f677,plain,
( spl13_77
<=> ! [X0,X1] :
( relation_dom(X0) = X1
| ~ in(sK3(X0,X1),X1)
| ~ relation(X0)
| ~ in(sK3(X0,X1),relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_77])]) ).
fof(f360,plain,
( spl13_40
<=> ! [X5,X0] :
( in(unordered_pair(singleton(X5),unordered_pair(X5,sK5(X0,X5))),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_40])]) ).
fof(f420,plain,
( ! [X0,X1] :
( relation_dom(X0) = X1
| ~ in(sK3(X0,X1),X1)
| ~ relation(X0)
| ~ in(sK3(X0,X1),relation_dom(X0)) )
| ~ spl13_40
| ~ spl13_47 ),
inference(duplicate_literal_removal,[],[f415]) ).
fof(f415,plain,
( ! [X0,X1] :
( relation_dom(X0) = X1
| ~ in(sK3(X0,X1),X1)
| ~ relation(X0)
| ~ in(sK3(X0,X1),relation_dom(X0))
| ~ relation(X0) )
| ~ spl13_40
| ~ spl13_47 ),
inference(resolution,[],[f412,f361]) ).
fof(f361,plain,
( ! [X0,X5] :
( in(unordered_pair(singleton(X5),unordered_pair(X5,sK5(X0,X5))),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) )
| ~ spl13_40 ),
inference(avatar_component_clause,[],[f360]) ).
fof(f674,plain,
( spl13_76
| ~ spl13_28
| ~ spl13_40 ),
inference(avatar_split_clause,[],[f365,f360,f290,f672]) ).
fof(f672,plain,
( spl13_76
<=> ! [X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ relation(X1)
| ~ in(X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_76])]) ).
fof(f365,plain,
( ! [X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ relation(X1)
| ~ in(X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X1,X0)))) )
| ~ spl13_28
| ~ spl13_40 ),
inference(resolution,[],[f361,f291]) ).
fof(f664,plain,
( ~ spl13_1
| spl13_15
| ~ spl13_16
| ~ spl13_72 ),
inference(avatar_split_clause,[],[f640,f629,f217,f210,f141]) ).
fof(f629,plain,
( spl13_72
<=> ! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X2)
| in(X0,relation_dom(X2))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_72])]) ).
fof(f640,plain,
( in(sK0,relation_dom(sK2))
| ~ relation(sK2)
| ~ spl13_16
| ~ spl13_72 ),
inference(resolution,[],[f218,f630]) ).
fof(f630,plain,
( ! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X2)
| in(X0,relation_dom(X2))
| ~ relation(X2) )
| ~ spl13_72 ),
inference(avatar_component_clause,[],[f629]) ).
fof(f663,plain,
( spl13_75
| ~ spl13_29
| ~ spl13_40 ),
inference(avatar_split_clause,[],[f364,f360,f294,f661]) ).
fof(f661,plain,
( spl13_75
<=> ! [X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ relation(X1)
| element(unordered_pair(singleton(X0),unordered_pair(X0,sK5(X1,X0))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_75])]) ).
fof(f364,plain,
( ! [X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ relation(X1)
| element(unordered_pair(singleton(X0),unordered_pair(X0,sK5(X1,X0))),X1) )
| ~ spl13_29
| ~ spl13_40 ),
inference(resolution,[],[f361,f295]) ).
fof(f652,plain,
( spl13_74
| ~ spl13_40
| ~ spl13_45 ),
inference(avatar_split_clause,[],[f404,f395,f360,f650]) ).
fof(f404,plain,
( ! [X0,X1] :
( apply(X0,X1) = sK5(X0,X1)
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl13_40
| ~ spl13_45 ),
inference(duplicate_literal_removal,[],[f399]) ).
fof(f399,plain,
( ! [X0,X1] :
( apply(X0,X1) = sK5(X0,X1)
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| ~ relation(X0) )
| ~ spl13_40
| ~ spl13_45 ),
inference(resolution,[],[f396,f361]) ).
fof(f648,plain,
( ~ spl13_73
| ~ spl13_16
| ~ spl13_28 ),
inference(avatar_split_clause,[],[f451,f290,f217,f645]) ).
fof(f645,plain,
( spl13_73
<=> in(sK2,unordered_pair(singleton(sK0),unordered_pair(sK1,sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_73])]) ).
fof(f451,plain,
( ~ in(sK2,unordered_pair(singleton(sK0),unordered_pair(sK1,sK0)))
| ~ spl13_16
| ~ spl13_28 ),
inference(resolution,[],[f218,f291]) ).
fof(f639,plain,
( spl13_16
| ~ spl13_14
| ~ spl13_32 ),
inference(avatar_split_clause,[],[f534,f309,f206,f217]) ).
fof(f206,plain,
( spl13_14
<=> in(unordered_pair(unordered_pair(sK0,sK1),singleton(sK0)),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_14])]) ).
fof(f534,plain,
( in(unordered_pair(singleton(sK0),unordered_pair(sK1,sK0)),sK2)
| ~ spl13_14
| ~ spl13_32 ),
inference(forward_demodulation,[],[f533,f310]) ).
fof(f533,plain,
( in(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)),sK2)
| ~ spl13_14
| ~ spl13_32 ),
inference(forward_demodulation,[],[f208,f310]) ).
fof(f208,plain,
( in(unordered_pair(unordered_pair(sK0,sK1),singleton(sK0)),sK2)
| ~ spl13_14 ),
inference(avatar_component_clause,[],[f206]) ).
fof(f638,plain,
( ~ spl13_1
| spl13_15
| ~ spl13_54
| ~ spl13_72 ),
inference(avatar_split_clause,[],[f634,f629,f484,f210,f141]) ).
fof(f484,plain,
( spl13_54
<=> in(unordered_pair(singleton(sK0),unordered_pair(sK8,sK0)),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_54])]) ).
fof(f634,plain,
( in(sK0,relation_dom(sK2))
| ~ relation(sK2)
| ~ spl13_54
| ~ spl13_72 ),
inference(resolution,[],[f630,f485]) ).
fof(f485,plain,
( in(unordered_pair(singleton(sK0),unordered_pair(sK8,sK0)),sK2)
| ~ spl13_54 ),
inference(avatar_component_clause,[],[f484]) ).
fof(f631,plain,
( spl13_72
| ~ spl13_32
| ~ spl13_38 ),
inference(avatar_split_clause,[],[f352,f348,f309,f629]) ).
fof(f352,plain,
( ! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X2)
| in(X0,relation_dom(X2))
| ~ relation(X2) )
| ~ spl13_32
| ~ spl13_38 ),
inference(superposition,[],[f349,f310]) ).
fof(f619,plain,
( spl13_71
| ~ spl13_27
| ~ spl13_49 ),
inference(avatar_split_clause,[],[f433,f428,f277,f617]) ).
fof(f617,plain,
( spl13_71
<=> ! [X0,X1] :
( relation_dom(X0) = X1
| in(sK3(X0,X1),X1)
| ~ relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_71])]) ).
fof(f277,plain,
( spl13_27
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_27])]) ).
fof(f433,plain,
( ! [X0,X1] :
( relation_dom(X0) = X1
| in(sK3(X0,X1),X1)
| ~ relation(X0)
| ~ empty(X0) )
| ~ spl13_27
| ~ spl13_49 ),
inference(resolution,[],[f429,f278]) ).
fof(f278,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) )
| ~ spl13_27 ),
inference(avatar_component_clause,[],[f277]) ).
fof(f615,plain,
( spl13_70
| ~ spl13_28
| ~ spl13_36 ),
inference(avatar_split_clause,[],[f340,f336,f290,f613]) ).
fof(f613,plain,
( spl13_70
<=> ! [X0,X1] :
( apply(X0,X1) = sK8
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_70])]) ).
fof(f340,plain,
( ! [X0,X1] :
( apply(X0,X1) = sK8
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),X1) )
| ~ spl13_28
| ~ spl13_36 ),
inference(resolution,[],[f337,f291]) ).
fof(f611,plain,
( spl13_69
| ~ spl13_29
| ~ spl13_36 ),
inference(avatar_split_clause,[],[f339,f336,f294,f609]) ).
fof(f609,plain,
( spl13_69
<=> ! [X0,X1] :
( apply(X0,X1) = sK8
| ~ function(X0)
| ~ relation(X0)
| element(X1,relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_69])]) ).
fof(f339,plain,
( ! [X0,X1] :
( apply(X0,X1) = sK8
| ~ function(X0)
| ~ relation(X0)
| element(X1,relation_dom(X0)) )
| ~ spl13_29
| ~ spl13_36 ),
inference(resolution,[],[f337,f295]) ).
fof(f603,plain,
( spl13_54
| ~ spl13_16
| ~ spl13_52 ),
inference(avatar_split_clause,[],[f465,f454,f217,f484]) ).
fof(f454,plain,
( spl13_52
<=> sK1 = sK8 ),
introduced(avatar_definition,[new_symbols(naming,[spl13_52])]) ).
fof(f465,plain,
( in(unordered_pair(singleton(sK0),unordered_pair(sK8,sK0)),sK2)
| ~ spl13_16
| ~ spl13_52 ),
inference(superposition,[],[f218,f456]) ).
fof(f456,plain,
( sK1 = sK8
| ~ spl13_52 ),
inference(avatar_component_clause,[],[f454]) ).
fof(f602,plain,
( spl13_68
| ~ spl13_27
| ~ spl13_36 ),
inference(avatar_split_clause,[],[f341,f336,f277,f600]) ).
fof(f600,plain,
( spl13_68
<=> ! [X0,X1] :
( apply(X0,X1) = sK8
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_68])]) ).
fof(f341,plain,
( ! [X0,X1] :
( apply(X0,X1) = sK8
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) )
| ~ spl13_27
| ~ spl13_36 ),
inference(resolution,[],[f337,f278]) ).
fof(f583,plain,
( spl13_67
| ~ spl13_27
| ~ spl13_40 ),
inference(avatar_split_clause,[],[f366,f360,f277,f581]) ).
fof(f581,plain,
( spl13_67
<=> ! [X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ relation(X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_67])]) ).
fof(f366,plain,
( ! [X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ relation(X1)
| ~ empty(X1) )
| ~ spl13_27
| ~ spl13_40 ),
inference(resolution,[],[f361,f278]) ).
fof(f579,plain,
( spl13_66
| ~ spl13_25
| ~ spl13_33 ),
inference(avatar_split_clause,[],[f319,f313,f269,f577]) ).
fof(f577,plain,
( spl13_66
<=> ! [X0,X1] :
( relation_dom(X1) = X0
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_66])]) ).
fof(f269,plain,
( spl13_25
<=> ! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_25])]) ).
fof(f313,plain,
( spl13_33
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_33])]) ).
fof(f319,plain,
( ! [X0,X1] :
( relation_dom(X1) = X0
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl13_25
| ~ spl13_33 ),
inference(resolution,[],[f314,f270]) ).
fof(f270,plain,
( ! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) )
| ~ spl13_25 ),
inference(avatar_component_clause,[],[f269]) ).
fof(f314,plain,
( ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) )
| ~ spl13_33 ),
inference(avatar_component_clause,[],[f313]) ).
fof(f566,plain,
( spl13_65
| ~ spl13_21
| ~ spl13_34 ),
inference(avatar_split_clause,[],[f328,f325,f246,f564]) ).
fof(f246,plain,
( spl13_21
<=> ! [X0] : element(sK6(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_21])]) ).
fof(f325,plain,
( spl13_34
<=> ! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_34])]) ).
fof(f328,plain,
( ! [X0] :
( empty(X0)
| in(sK6(X0),X0) )
| ~ spl13_21
| ~ spl13_34 ),
inference(resolution,[],[f326,f247]) ).
fof(f247,plain,
( ! [X0] : element(sK6(X0),X0)
| ~ spl13_21 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f326,plain,
( ! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) )
| ~ spl13_34 ),
inference(avatar_component_clause,[],[f325]) ).
fof(f562,plain,
( spl13_64
| ~ spl13_6
| ~ spl13_23
| ~ spl13_25 ),
inference(avatar_split_clause,[],[f287,f269,f260,f166,f560]) ).
fof(f166,plain,
( spl13_6
<=> empty(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_6])]) ).
fof(f260,plain,
( spl13_23
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_23])]) ).
fof(f287,plain,
( ! [X0] :
( relation_dom(X0) = sK8
| ~ empty(X0) )
| ~ spl13_6
| ~ spl13_23
| ~ spl13_25 ),
inference(forward_demodulation,[],[f284,f281]) ).
fof(f281,plain,
( empty_set = sK8
| ~ spl13_6
| ~ spl13_23 ),
inference(resolution,[],[f261,f168]) ).
fof(f168,plain,
( empty(sK8)
| ~ spl13_6 ),
inference(avatar_component_clause,[],[f166]) ).
fof(f261,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl13_23 ),
inference(avatar_component_clause,[],[f260]) ).
fof(f284,plain,
( ! [X0] :
( ~ empty(X0)
| relation_dom(X0) = empty_set )
| ~ spl13_23
| ~ spl13_25 ),
inference(resolution,[],[f270,f261]) ).
fof(f558,plain,
( spl13_15
| spl13_30
| ~ spl13_34
| ~ spl13_51 ),
inference(avatar_split_clause,[],[f466,f440,f325,f299,f210]) ).
fof(f299,plain,
( spl13_30
<=> empty(relation_dom(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_30])]) ).
fof(f440,plain,
( spl13_51
<=> element(sK0,relation_dom(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_51])]) ).
fof(f466,plain,
( empty(relation_dom(sK2))
| in(sK0,relation_dom(sK2))
| ~ spl13_34
| ~ spl13_51 ),
inference(resolution,[],[f442,f326]) ).
fof(f442,plain,
( element(sK0,relation_dom(sK2))
| ~ spl13_51 ),
inference(avatar_component_clause,[],[f440]) ).
fof(f553,plain,
( spl13_63
| ~ spl13_6
| ~ spl13_33 ),
inference(avatar_split_clause,[],[f321,f313,f166,f551]) ).
fof(f551,plain,
( spl13_63
<=> ! [X0] :
( sK8 = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_63])]) ).
fof(f321,plain,
( ! [X0] :
( sK8 = X0
| ~ empty(X0) )
| ~ spl13_6
| ~ spl13_33 ),
inference(resolution,[],[f314,f168]) ).
fof(f549,plain,
( spl13_62
| ~ spl13_19
| ~ spl13_25 ),
inference(avatar_split_clause,[],[f286,f269,f238,f547]) ).
fof(f547,plain,
( spl13_62
<=> ! [X0] :
( ~ empty(X0)
| function(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_62])]) ).
fof(f238,plain,
( spl13_19
<=> ! [X0] :
( function(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_19])]) ).
fof(f286,plain,
( ! [X0] :
( ~ empty(X0)
| function(relation_dom(X0)) )
| ~ spl13_19
| ~ spl13_25 ),
inference(resolution,[],[f270,f239]) ).
fof(f239,plain,
( ! [X0] :
( ~ empty(X0)
| function(X0) )
| ~ spl13_19 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f545,plain,
( ~ spl13_61
| ~ spl13_16
| ~ spl13_28
| ~ spl13_52 ),
inference(avatar_split_clause,[],[f527,f454,f290,f217,f542]) ).
fof(f542,plain,
( spl13_61
<=> in(sK2,unordered_pair(singleton(sK0),unordered_pair(sK8,sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_61])]) ).
fof(f527,plain,
( ~ in(sK2,unordered_pair(singleton(sK0),unordered_pair(sK8,sK0)))
| ~ spl13_16
| ~ spl13_28
| ~ spl13_52 ),
inference(forward_demodulation,[],[f451,f456]) ).
fof(f526,plain,
( ~ spl13_1
| ~ spl13_2
| ~ spl13_15
| spl13_16
| ~ spl13_18
| ~ spl13_32
| ~ spl13_42 ),
inference(avatar_split_clause,[],[f388,f374,f309,f226,f217,f210,f146,f141]) ).
fof(f388,plain,
( in(unordered_pair(singleton(sK0),unordered_pair(sK1,sK0)),sK2)
| ~ in(sK0,relation_dom(sK2))
| ~ function(sK2)
| ~ relation(sK2)
| ~ spl13_18
| ~ spl13_32
| ~ spl13_42 ),
inference(forward_demodulation,[],[f386,f310]) ).
fof(f386,plain,
( in(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)),sK2)
| ~ in(sK0,relation_dom(sK2))
| ~ function(sK2)
| ~ relation(sK2)
| ~ spl13_18
| ~ spl13_42 ),
inference(superposition,[],[f375,f228]) ).
fof(f228,plain,
( sK1 = apply(sK2,sK0)
| ~ spl13_18 ),
inference(avatar_component_clause,[],[f226]) ).
fof(f525,plain,
( ~ spl13_16
| spl13_14
| ~ spl13_32 ),
inference(avatar_split_clause,[],[f478,f309,f206,f217]) ).
fof(f478,plain,
( ~ in(unordered_pair(singleton(sK0),unordered_pair(sK1,sK0)),sK2)
| spl13_14
| ~ spl13_32 ),
inference(forward_demodulation,[],[f477,f310]) ).
fof(f477,plain,
( ~ in(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)),sK2)
| spl13_14
| ~ spl13_32 ),
inference(forward_demodulation,[],[f207,f310]) ).
fof(f207,plain,
( ~ in(unordered_pair(unordered_pair(sK0,sK1),singleton(sK0)),sK2)
| spl13_14 ),
inference(avatar_component_clause,[],[f206]) ).
fof(f524,plain,
( ~ spl13_1
| ~ spl13_2
| ~ spl13_15
| spl13_54
| ~ spl13_18
| ~ spl13_32
| ~ spl13_42
| ~ spl13_52 ),
inference(avatar_split_clause,[],[f472,f454,f374,f309,f226,f484,f210,f146,f141]) ).
fof(f472,plain,
( in(unordered_pair(singleton(sK0),unordered_pair(sK8,sK0)),sK2)
| ~ in(sK0,relation_dom(sK2))
| ~ function(sK2)
| ~ relation(sK2)
| ~ spl13_18
| ~ spl13_32
| ~ spl13_42
| ~ spl13_52 ),
inference(forward_demodulation,[],[f388,f456]) ).
fof(f518,plain,
( spl13_60
| ~ spl13_6
| ~ spl13_9
| ~ spl13_23 ),
inference(avatar_split_clause,[],[f283,f260,f181,f166,f515]) ).
fof(f515,plain,
( spl13_60
<=> sK8 = sK10 ),
introduced(avatar_definition,[new_symbols(naming,[spl13_60])]) ).
fof(f181,plain,
( spl13_9
<=> empty(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_9])]) ).
fof(f283,plain,
( sK8 = sK10
| ~ spl13_6
| ~ spl13_9
| ~ spl13_23 ),
inference(forward_demodulation,[],[f282,f281]) ).
fof(f282,plain,
( empty_set = sK10
| ~ spl13_9
| ~ spl13_23 ),
inference(resolution,[],[f261,f183]) ).
fof(f183,plain,
( empty(sK10)
| ~ spl13_9 ),
inference(avatar_component_clause,[],[f181]) ).
fof(f513,plain,
( spl13_59
| ~ spl13_6
| ~ spl13_23 ),
inference(avatar_split_clause,[],[f281,f260,f166,f510]) ).
fof(f508,plain,
( spl13_58
| ~ spl13_6
| ~ spl13_20 ),
inference(avatar_split_clause,[],[f257,f242,f166,f505]) ).
fof(f505,plain,
( spl13_58
<=> relation(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_58])]) ).
fof(f242,plain,
( spl13_20
<=> ! [X0] :
( relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_20])]) ).
fof(f257,plain,
( relation(sK8)
| ~ spl13_6
| ~ spl13_20 ),
inference(resolution,[],[f243,f168]) ).
fof(f243,plain,
( ! [X0] :
( ~ empty(X0)
| relation(X0) )
| ~ spl13_20 ),
inference(avatar_component_clause,[],[f242]) ).
fof(f502,plain,
( spl13_57
| ~ spl13_9
| ~ spl13_19 ),
inference(avatar_split_clause,[],[f255,f238,f181,f499]) ).
fof(f499,plain,
( spl13_57
<=> function(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_57])]) ).
fof(f255,plain,
( function(sK10)
| ~ spl13_9
| ~ spl13_19 ),
inference(resolution,[],[f239,f183]) ).
fof(f497,plain,
( spl13_56
| ~ spl13_6
| ~ spl13_19 ),
inference(avatar_split_clause,[],[f254,f238,f166,f494]) ).
fof(f494,plain,
( spl13_56
<=> function(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_56])]) ).
fof(f254,plain,
( function(sK8)
| ~ spl13_6
| ~ spl13_19 ),
inference(resolution,[],[f239,f168]) ).
fof(f492,plain,
( ~ spl13_55
| ~ spl13_52
| spl13_53 ),
inference(avatar_split_clause,[],[f473,f468,f454,f489]) ).
fof(f489,plain,
( spl13_55
<=> element(unordered_pair(singleton(sK0),unordered_pair(sK8,sK0)),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_55])]) ).
fof(f468,plain,
( spl13_53
<=> element(unordered_pair(singleton(sK0),unordered_pair(sK1,sK0)),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_53])]) ).
fof(f473,plain,
( ~ element(unordered_pair(singleton(sK0),unordered_pair(sK8,sK0)),sK2)
| ~ spl13_52
| spl13_53 ),
inference(forward_demodulation,[],[f469,f456]) ).
fof(f469,plain,
( ~ element(unordered_pair(singleton(sK0),unordered_pair(sK1,sK0)),sK2)
| spl13_53 ),
inference(avatar_component_clause,[],[f468]) ).
fof(f487,plain,
( ~ spl13_54
| spl13_16
| ~ spl13_52 ),
inference(avatar_split_clause,[],[f474,f454,f217,f484]) ).
fof(f474,plain,
( ~ in(unordered_pair(singleton(sK0),unordered_pair(sK8,sK0)),sK2)
| spl13_16
| ~ spl13_52 ),
inference(forward_demodulation,[],[f219,f456]) ).
fof(f219,plain,
( ~ in(unordered_pair(singleton(sK0),unordered_pair(sK1,sK0)),sK2)
| spl13_16 ),
inference(avatar_component_clause,[],[f217]) ).
fof(f471,plain,
( spl13_53
| ~ spl13_16
| ~ spl13_29 ),
inference(avatar_split_clause,[],[f450,f294,f217,f468]) ).
fof(f450,plain,
( element(unordered_pair(singleton(sK0),unordered_pair(sK1,sK0)),sK2)
| ~ spl13_16
| ~ spl13_29 ),
inference(resolution,[],[f218,f295]) ).
fof(f461,plain,
( ~ spl13_15
| ~ spl13_16
| ~ spl13_18 ),
inference(avatar_split_clause,[],[f445,f226,f217,f210]) ).
fof(f445,plain,
( ~ in(unordered_pair(singleton(sK0),unordered_pair(sK1,sK0)),sK2)
| ~ in(sK0,relation_dom(sK2))
| ~ spl13_18 ),
inference(trivial_inequality_removal,[],[f444]) ).
fof(f444,plain,
( sK1 != sK1
| ~ in(unordered_pair(singleton(sK0),unordered_pair(sK1,sK0)),sK2)
| ~ in(sK0,relation_dom(sK2))
| ~ spl13_18 ),
inference(forward_demodulation,[],[f234,f228]) ).
fof(f234,plain,
( ~ in(unordered_pair(singleton(sK0),unordered_pair(sK1,sK0)),sK2)
| sK1 != apply(sK2,sK0)
| ~ in(sK0,relation_dom(sK2)) ),
inference(forward_demodulation,[],[f233,f109]) ).
fof(f109,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f233,plain,
( ~ in(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)),sK2)
| sK1 != apply(sK2,sK0)
| ~ in(sK0,relation_dom(sK2)) ),
inference(forward_demodulation,[],[f125,f109]) ).
fof(f125,plain,
( sK1 != apply(sK2,sK0)
| ~ in(sK0,relation_dom(sK2))
| ~ in(unordered_pair(unordered_pair(sK0,sK1),singleton(sK0)),sK2) ),
inference(definition_unfolding,[],[f85,f110]) ).
fof(f110,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f85,plain,
( sK1 != apply(sK2,sK0)
| ~ in(sK0,relation_dom(sK2))
| ~ in(ordered_pair(sK0,sK1),sK2) ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
( ( sK1 != apply(sK2,sK0)
| ~ in(sK0,relation_dom(sK2))
| ~ in(ordered_pair(sK0,sK1),sK2) )
& ( ( sK1 = apply(sK2,sK0)
& in(sK0,relation_dom(sK2)) )
| in(ordered_pair(sK0,sK1),sK2) )
& function(sK2)
& relation(sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f57,f58]) ).
fof(f58,plain,
( ? [X0,X1,X2] :
( ( apply(X2,X0) != X1
| ~ in(X0,relation_dom(X2))
| ~ in(ordered_pair(X0,X1),X2) )
& ( ( apply(X2,X0) = X1
& in(X0,relation_dom(X2)) )
| in(ordered_pair(X0,X1),X2) )
& function(X2)
& relation(X2) )
=> ( ( sK1 != apply(sK2,sK0)
| ~ in(sK0,relation_dom(sK2))
| ~ in(ordered_pair(sK0,sK1),sK2) )
& ( ( sK1 = apply(sK2,sK0)
& in(sK0,relation_dom(sK2)) )
| in(ordered_pair(sK0,sK1),sK2) )
& function(sK2)
& relation(sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f57,plain,
? [X0,X1,X2] :
( ( apply(X2,X0) != X1
| ~ in(X0,relation_dom(X2))
| ~ in(ordered_pair(X0,X1),X2) )
& ( ( apply(X2,X0) = X1
& in(X0,relation_dom(X2)) )
| in(ordered_pair(X0,X1),X2) )
& function(X2)
& relation(X2) ),
inference(flattening,[],[f56]) ).
fof(f56,plain,
? [X0,X1,X2] :
( ( apply(X2,X0) != X1
| ~ in(X0,relation_dom(X2))
| ~ in(ordered_pair(X0,X1),X2) )
& ( ( apply(X2,X0) = X1
& in(X0,relation_dom(X2)) )
| in(ordered_pair(X0,X1),X2) )
& function(X2)
& relation(X2) ),
inference(nnf_transformation,[],[f40]) ).
fof(f40,plain,
? [X0,X1,X2] :
( ( in(ordered_pair(X0,X1),X2)
<~> ( apply(X2,X0) = X1
& in(X0,relation_dom(X2)) ) )
& function(X2)
& relation(X2) ),
inference(flattening,[],[f39]) ).
fof(f39,plain,
? [X0,X1,X2] :
( ( in(ordered_pair(X0,X1),X2)
<~> ( apply(X2,X0) = X1
& in(X0,relation_dom(X2)) ) )
& function(X2)
& relation(X2) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,negated_conjecture,
~ ! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(ordered_pair(X0,X1),X2)
<=> ( apply(X2,X0) = X1
& in(X0,relation_dom(X2)) ) ) ),
inference(negated_conjecture,[],[f35]) ).
fof(f35,conjecture,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(ordered_pair(X0,X1),X2)
<=> ( apply(X2,X0) = X1
& in(X0,relation_dom(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_funct_1) ).
fof(f457,plain,
( ~ spl13_1
| ~ spl13_2
| spl13_52
| spl13_15
| ~ spl13_18
| ~ spl13_36 ),
inference(avatar_split_clause,[],[f449,f336,f226,f210,f454,f146,f141]) ).
fof(f449,plain,
( sK1 = sK8
| ~ function(sK2)
| ~ relation(sK2)
| spl13_15
| ~ spl13_18
| ~ spl13_36 ),
inference(forward_demodulation,[],[f448,f228]) ).
fof(f448,plain,
( apply(sK2,sK0) = sK8
| ~ function(sK2)
| ~ relation(sK2)
| spl13_15
| ~ spl13_36 ),
inference(resolution,[],[f211,f337]) ).
fof(f211,plain,
( ~ in(sK0,relation_dom(sK2))
| spl13_15 ),
inference(avatar_component_clause,[],[f210]) ).
fof(f443,plain,
( spl13_51
| ~ spl13_15
| ~ spl13_29 ),
inference(avatar_split_clause,[],[f303,f294,f210,f440]) ).
fof(f303,plain,
( element(sK0,relation_dom(sK2))
| ~ spl13_15
| ~ spl13_29 ),
inference(resolution,[],[f295,f212]) ).
fof(f438,plain,
( ~ spl13_50
| ~ spl13_15
| ~ spl13_28 ),
inference(avatar_split_clause,[],[f297,f290,f210,f435]) ).
fof(f435,plain,
( spl13_50
<=> in(relation_dom(sK2),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_50])]) ).
fof(f297,plain,
( ~ in(relation_dom(sK2),sK0)
| ~ spl13_15
| ~ spl13_28 ),
inference(resolution,[],[f291,f212]) ).
fof(f430,plain,
( spl13_49
| ~ spl13_32
| ~ spl13_48 ),
inference(avatar_split_clause,[],[f426,f422,f309,f428]) ).
fof(f422,plain,
( spl13_48
<=> ! [X0,X1] :
( relation_dom(X0) = X1
| in(unordered_pair(unordered_pair(sK3(X0,X1),sK4(X0,X1)),singleton(sK3(X0,X1))),X0)
| in(sK3(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_48])]) ).
fof(f426,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(sK3(X0,X1)),unordered_pair(sK4(X0,X1),sK3(X0,X1))),X0)
| relation_dom(X0) = X1
| in(sK3(X0,X1),X1)
| ~ relation(X0) )
| ~ spl13_32
| ~ spl13_48 ),
inference(forward_demodulation,[],[f425,f310]) ).
fof(f425,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(sK3(X0,X1)),unordered_pair(sK3(X0,X1),sK4(X0,X1))),X0)
| relation_dom(X0) = X1
| in(sK3(X0,X1),X1)
| ~ relation(X0) )
| ~ spl13_32
| ~ spl13_48 ),
inference(forward_demodulation,[],[f423,f310]) ).
fof(f423,plain,
( ! [X0,X1] :
( relation_dom(X0) = X1
| in(unordered_pair(unordered_pair(sK3(X0,X1),sK4(X0,X1)),singleton(sK3(X0,X1))),X0)
| in(sK3(X0,X1),X1)
| ~ relation(X0) )
| ~ spl13_48 ),
inference(avatar_component_clause,[],[f422]) ).
fof(f424,plain,
spl13_48,
inference(avatar_split_clause,[],[f129,f422]) ).
fof(f129,plain,
! [X0,X1] :
( relation_dom(X0) = X1
| in(unordered_pair(unordered_pair(sK3(X0,X1),sK4(X0,X1)),singleton(sK3(X0,X1))),X0)
| in(sK3(X0,X1),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f99,f110]) ).
fof(f99,plain,
! [X0,X1] :
( relation_dom(X0) = X1
| in(ordered_pair(sK3(X0,X1),sK4(X0,X1)),X0)
| in(sK3(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ( ( ! [X3] : ~ in(ordered_pair(sK3(X0,X1),X3),X0)
| ~ in(sK3(X0,X1),X1) )
& ( in(ordered_pair(sK3(X0,X1),sK4(X0,X1)),X0)
| in(sK3(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK5(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f61,f64,f63,f62]) ).
fof(f62,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) )
=> ( ( ! [X3] : ~ in(ordered_pair(sK3(X0,X1),X3),X0)
| ~ in(sK3(X0,X1),X1) )
& ( ? [X4] : in(ordered_pair(sK3(X0,X1),X4),X0)
| in(sK3(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f63,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(sK3(X0,X1),X4),X0)
=> in(ordered_pair(sK3(X0,X1),sK4(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f64,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X5,X7),X0)
=> in(ordered_pair(X5,sK5(X0,X5)),X0) ),
introduced(choice_axiom,[]) ).
fof(f61,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( ? [X7] : in(ordered_pair(X5,X7),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f60]) ).
fof(f60,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0] :
( ! [X1] :
( relation_dom(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation_dom(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f413,plain,
( spl13_47
| ~ spl13_32
| ~ spl13_46 ),
inference(avatar_split_clause,[],[f409,f406,f309,f411]) ).
fof(f406,plain,
( spl13_46
<=> ! [X0,X1,X3] :
( relation_dom(X0) = X1
| ~ in(unordered_pair(unordered_pair(sK3(X0,X1),X3),singleton(sK3(X0,X1))),X0)
| ~ in(sK3(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_46])]) ).
fof(f409,plain,
( ! [X3,X0,X1] :
( ~ in(unordered_pair(singleton(sK3(X0,X1)),unordered_pair(sK3(X0,X1),X3)),X0)
| relation_dom(X0) = X1
| ~ in(sK3(X0,X1),X1)
| ~ relation(X0) )
| ~ spl13_32
| ~ spl13_46 ),
inference(forward_demodulation,[],[f407,f310]) ).
fof(f407,plain,
( ! [X3,X0,X1] :
( relation_dom(X0) = X1
| ~ in(unordered_pair(unordered_pair(sK3(X0,X1),X3),singleton(sK3(X0,X1))),X0)
| ~ in(sK3(X0,X1),X1)
| ~ relation(X0) )
| ~ spl13_46 ),
inference(avatar_component_clause,[],[f406]) ).
fof(f408,plain,
spl13_46,
inference(avatar_split_clause,[],[f128,f406]) ).
fof(f128,plain,
! [X3,X0,X1] :
( relation_dom(X0) = X1
| ~ in(unordered_pair(unordered_pair(sK3(X0,X1),X3),singleton(sK3(X0,X1))),X0)
| ~ in(sK3(X0,X1),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f100,f110]) ).
fof(f100,plain,
! [X3,X0,X1] :
( relation_dom(X0) = X1
| ~ in(ordered_pair(sK3(X0,X1),X3),X0)
| ~ in(sK3(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f397,plain,
( spl13_45
| ~ spl13_32
| ~ spl13_44 ),
inference(avatar_split_clause,[],[f393,f390,f309,f395]) ).
fof(f390,plain,
( spl13_44
<=> ! [X2,X0,X1] :
( apply(X0,X1) = X2
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X0)
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_44])]) ).
fof(f393,plain,
( ! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X0)
| apply(X0,X1) = X2
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl13_32
| ~ spl13_44 ),
inference(forward_demodulation,[],[f391,f310]) ).
fof(f391,plain,
( ! [X2,X0,X1] :
( apply(X0,X1) = X2
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X0)
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl13_44 ),
inference(avatar_component_clause,[],[f390]) ).
fof(f392,plain,
spl13_44,
inference(avatar_split_clause,[],[f132,f390]) ).
fof(f132,plain,
! [X2,X0,X1] :
( apply(X0,X1) = X2
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X0)
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f103,f110]) ).
fof(f103,plain,
! [X2,X0,X1] :
( apply(X0,X1) = X2
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0] :
( ! [X1,X2] :
( ( ( ( apply(X0,X1) = X2
| empty_set != X2 )
& ( empty_set = X2
| apply(X0,X1) != X2 ) )
| in(X1,relation_dom(X0)) )
& ( ( ( apply(X0,X1) = X2
| ~ in(ordered_pair(X1,X2),X0) )
& ( in(ordered_pair(X1,X2),X0)
| apply(X0,X1) != X2 ) )
| ~ in(X1,relation_dom(X0)) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(nnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0] :
( ! [X1,X2] :
( ( ( apply(X0,X1) = X2
<=> empty_set = X2 )
| in(X1,relation_dom(X0)) )
& ( ( apply(X0,X1) = X2
<=> in(ordered_pair(X1,X2),X0) )
| ~ in(X1,relation_dom(X0)) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f48]) ).
fof(f48,plain,
! [X0] :
( ! [X1,X2] :
( ( ( apply(X0,X1) = X2
<=> empty_set = X2 )
| in(X1,relation_dom(X0)) )
& ( ( apply(X0,X1) = X2
<=> in(ordered_pair(X1,X2),X0) )
| ~ in(X1,relation_dom(X0)) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( ( ~ in(X1,relation_dom(X0))
=> ( apply(X0,X1) = X2
<=> empty_set = X2 ) )
& ( in(X1,relation_dom(X0))
=> ( apply(X0,X1) = X2
<=> in(ordered_pair(X1,X2),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_funct_1) ).
fof(f381,plain,
( ~ spl13_43
| ~ spl13_25
| spl13_30 ),
inference(avatar_split_clause,[],[f334,f299,f269,f378]) ).
fof(f378,plain,
( spl13_43
<=> empty(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_43])]) ).
fof(f334,plain,
( ~ empty(sK2)
| ~ spl13_25
| spl13_30 ),
inference(resolution,[],[f301,f270]) ).
fof(f301,plain,
( ~ empty(relation_dom(sK2))
| spl13_30 ),
inference(avatar_component_clause,[],[f299]) ).
fof(f376,plain,
( spl13_42
| ~ spl13_32
| ~ spl13_41 ),
inference(avatar_split_clause,[],[f372,f369,f309,f374]) ).
fof(f369,plain,
( spl13_41
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(X1,apply(X0,X1)),singleton(X1)),X0)
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_41])]) ).
fof(f372,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(X1),unordered_pair(X1,apply(X0,X1))),X0)
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl13_32
| ~ spl13_41 ),
inference(forward_demodulation,[],[f370,f310]) ).
fof(f370,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(X1,apply(X0,X1)),singleton(X1)),X0)
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl13_41 ),
inference(avatar_component_clause,[],[f369]) ).
fof(f371,plain,
spl13_41,
inference(avatar_split_clause,[],[f139,f369]) ).
fof(f139,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(X1,apply(X0,X1)),singleton(X1)),X0)
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f133]) ).
fof(f133,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X0)
| apply(X0,X1) != X2
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f102,f110]) ).
fof(f102,plain,
! [X2,X0,X1] :
( in(ordered_pair(X1,X2),X0)
| apply(X0,X1) != X2
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f362,plain,
( spl13_40
| ~ spl13_32
| ~ spl13_39 ),
inference(avatar_split_clause,[],[f358,f355,f309,f360]) ).
fof(f355,plain,
( spl13_39
<=> ! [X5,X0] :
( in(unordered_pair(unordered_pair(X5,sK5(X0,X5)),singleton(X5)),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_39])]) ).
fof(f358,plain,
( ! [X0,X5] :
( in(unordered_pair(singleton(X5),unordered_pair(X5,sK5(X0,X5))),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) )
| ~ spl13_32
| ~ spl13_39 ),
inference(forward_demodulation,[],[f356,f310]) ).
fof(f356,plain,
( ! [X0,X5] :
( in(unordered_pair(unordered_pair(X5,sK5(X0,X5)),singleton(X5)),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) )
| ~ spl13_39 ),
inference(avatar_component_clause,[],[f355]) ).
fof(f357,plain,
spl13_39,
inference(avatar_split_clause,[],[f136,f355]) ).
fof(f136,plain,
! [X0,X5] :
( in(unordered_pair(unordered_pair(X5,sK5(X0,X5)),singleton(X5)),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f131]) ).
fof(f131,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(X5,sK5(X0,X5)),singleton(X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f97,f110]) ).
fof(f97,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,sK5(X0,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f350,plain,
( spl13_38
| ~ spl13_32
| ~ spl13_37 ),
inference(avatar_split_clause,[],[f346,f343,f309,f348]) ).
fof(f343,plain,
( spl13_37
<=> ! [X5,X0,X6] :
( in(X5,relation_dom(X0))
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_37])]) ).
fof(f346,plain,
( ! [X0,X6,X5] :
( ~ in(unordered_pair(singleton(X5),unordered_pair(X5,X6)),X0)
| in(X5,relation_dom(X0))
| ~ relation(X0) )
| ~ spl13_32
| ~ spl13_37 ),
inference(forward_demodulation,[],[f344,f310]) ).
fof(f344,plain,
( ! [X0,X6,X5] :
( in(X5,relation_dom(X0))
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| ~ relation(X0) )
| ~ spl13_37 ),
inference(avatar_component_clause,[],[f343]) ).
fof(f345,plain,
spl13_37,
inference(avatar_split_clause,[],[f135,f343]) ).
fof(f135,plain,
! [X0,X6,X5] :
( in(X5,relation_dom(X0))
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f130]) ).
fof(f130,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f98,f110]) ).
fof(f98,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X5,X6),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f338,plain,
( spl13_36
| ~ spl13_6
| ~ spl13_23
| ~ spl13_35 ),
inference(avatar_split_clause,[],[f333,f330,f260,f166,f336]) ).
fof(f330,plain,
( spl13_35
<=> ! [X0,X1] :
( apply(X0,X1) = empty_set
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_35])]) ).
fof(f333,plain,
( ! [X0,X1] :
( apply(X0,X1) = sK8
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl13_6
| ~ spl13_23
| ~ spl13_35 ),
inference(forward_demodulation,[],[f331,f281]) ).
fof(f331,plain,
( ! [X0,X1] :
( apply(X0,X1) = empty_set
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl13_35 ),
inference(avatar_component_clause,[],[f330]) ).
fof(f332,plain,
spl13_35,
inference(avatar_split_clause,[],[f137,f330]) ).
fof(f137,plain,
! [X0,X1] :
( apply(X0,X1) = empty_set
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f105]) ).
fof(f105,plain,
! [X2,X0,X1] :
( apply(X0,X1) = X2
| empty_set != X2
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f327,plain,
spl13_34,
inference(avatar_split_clause,[],[f111,f325]) ).
fof(f111,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f50]) ).
fof(f50,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f315,plain,
spl13_33,
inference(avatar_split_clause,[],[f114,f313]) ).
fof(f114,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(f311,plain,
spl13_32,
inference(avatar_split_clause,[],[f109,f309]) ).
fof(f307,plain,
spl13_31,
inference(avatar_split_clause,[],[f101,f305]) ).
fof(f305,plain,
( spl13_31
<=> ! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_31])]) ).
fof(f101,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f46]) ).
fof(f46,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f302,plain,
( ~ spl13_30
| ~ spl13_15
| ~ spl13_27 ),
inference(avatar_split_clause,[],[f288,f277,f210,f299]) ).
fof(f288,plain,
( ~ empty(relation_dom(sK2))
| ~ spl13_15
| ~ spl13_27 ),
inference(resolution,[],[f278,f212]) ).
fof(f296,plain,
spl13_29,
inference(avatar_split_clause,[],[f113,f294]) ).
fof(f113,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f292,plain,
spl13_28,
inference(avatar_split_clause,[],[f112,f290]) ).
fof(f112,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,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/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f279,plain,
spl13_27,
inference(avatar_split_clause,[],[f115,f277]) ).
fof(f115,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f275,plain,
spl13_26,
inference(avatar_split_clause,[],[f96,f273]) ).
fof(f273,plain,
( spl13_26
<=> ! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_26])]) ).
fof(f96,plain,
! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0] :
( ( relation(relation_dom(X0))
& empty(relation_dom(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f271,plain,
spl13_25,
inference(avatar_split_clause,[],[f95,f269]) ).
fof(f95,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f267,plain,
( spl13_24
| ~ spl13_3
| ~ spl13_19 ),
inference(avatar_split_clause,[],[f253,f238,f151,f264]) ).
fof(f264,plain,
( spl13_24
<=> function(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_24])]) ).
fof(f253,plain,
( function(empty_set)
| ~ spl13_3
| ~ spl13_19 ),
inference(resolution,[],[f239,f153]) ).
fof(f262,plain,
spl13_23,
inference(avatar_split_clause,[],[f94,f260]) ).
fof(f94,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f252,plain,
spl13_22,
inference(avatar_split_clause,[],[f107,f250]) ).
fof(f250,plain,
( spl13_22
<=> ! [X0,X1] : ~ empty(unordered_pair(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_22])]) ).
fof(f107,plain,
! [X0,X1] : ~ empty(unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0,X1] : ~ empty(unordered_pair(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_subset_1) ).
fof(f248,plain,
spl13_21,
inference(avatar_split_clause,[],[f106,f246]) ).
fof(f106,plain,
! [X0] : element(sK6(X0),X0),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0] : element(sK6(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f15,f67]) ).
fof(f67,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK6(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f15,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f244,plain,
spl13_20,
inference(avatar_split_clause,[],[f93,f242]) ).
fof(f93,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(f240,plain,
spl13_19,
inference(avatar_split_clause,[],[f92,f238]) ).
fof(f92,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( empty(X0)
=> function(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(f232,plain,
( spl13_16
| ~ spl13_14 ),
inference(avatar_split_clause,[],[f231,f206,f217]) ).
fof(f231,plain,
( in(unordered_pair(singleton(sK0),unordered_pair(sK1,sK0)),sK2)
| ~ spl13_14 ),
inference(forward_demodulation,[],[f230,f109]) ).
fof(f230,plain,
( in(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)),sK2)
| ~ spl13_14 ),
inference(forward_demodulation,[],[f208,f109]) ).
fof(f229,plain,
( spl13_14
| spl13_18 ),
inference(avatar_split_clause,[],[f126,f226,f206]) ).
fof(f126,plain,
( sK1 = apply(sK2,sK0)
| in(unordered_pair(unordered_pair(sK0,sK1),singleton(sK0)),sK2) ),
inference(definition_unfolding,[],[f84,f110]) ).
fof(f84,plain,
( sK1 = apply(sK2,sK0)
| in(ordered_pair(sK0,sK1),sK2) ),
inference(cnf_transformation,[],[f59]) ).
fof(f224,plain,
spl13_17,
inference(avatar_split_clause,[],[f91,f222]) ).
fof(f222,plain,
( spl13_17
<=> ! [X0] : ~ empty(singleton(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_17])]) ).
fof(f91,plain,
! [X0] : ~ empty(singleton(X0)),
inference(cnf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] : ~ empty(singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
fof(f220,plain,
( ~ spl13_16
| spl13_14 ),
inference(avatar_split_clause,[],[f215,f206,f217]) ).
fof(f215,plain,
( ~ in(unordered_pair(singleton(sK0),unordered_pair(sK1,sK0)),sK2)
| spl13_14 ),
inference(forward_demodulation,[],[f214,f109]) ).
fof(f214,plain,
( ~ in(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)),sK2)
| spl13_14 ),
inference(forward_demodulation,[],[f207,f109]) ).
fof(f213,plain,
( spl13_14
| spl13_15 ),
inference(avatar_split_clause,[],[f127,f210,f206]) ).
fof(f127,plain,
( in(sK0,relation_dom(sK2))
| in(unordered_pair(unordered_pair(sK0,sK1),singleton(sK0)),sK2) ),
inference(definition_unfolding,[],[f83,f110]) ).
fof(f83,plain,
( in(sK0,relation_dom(sK2))
| in(ordered_pair(sK0,sK1),sK2) ),
inference(cnf_transformation,[],[f59]) ).
fof(f204,plain,
spl13_13,
inference(avatar_split_clause,[],[f124,f201]) ).
fof(f201,plain,
( spl13_13
<=> function(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_13])]) ).
fof(f124,plain,
function(sK12),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
( function(sK12)
& relation(sK12) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f24,f79]) ).
fof(f79,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK12)
& relation(sK12) ) ),
introduced(choice_axiom,[]) ).
fof(f24,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(f199,plain,
spl13_12,
inference(avatar_split_clause,[],[f123,f196]) ).
fof(f196,plain,
( spl13_12
<=> relation(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_12])]) ).
fof(f123,plain,
relation(sK12),
inference(cnf_transformation,[],[f80]) ).
fof(f194,plain,
spl13_11,
inference(avatar_split_clause,[],[f122,f191]) ).
fof(f191,plain,
( spl13_11
<=> relation(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_11])]) ).
fof(f122,plain,
relation(sK11),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
relation(sK11),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f37,f77]) ).
fof(f77,plain,
( ? [X0] : relation(X0)
=> relation(sK11) ),
introduced(choice_axiom,[]) ).
fof(f37,plain,
? [X0] : relation(X0),
inference(pure_predicate_removal,[],[f29]) ).
fof(f29,axiom,
? [X0] :
( relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
fof(f189,plain,
spl13_10,
inference(avatar_split_clause,[],[f121,f186]) ).
fof(f186,plain,
( spl13_10
<=> relation(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_10])]) ).
fof(f121,plain,
relation(sK10),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
( relation(sK10)
& empty(sK10) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f25,f75]) ).
fof(f75,plain,
( ? [X0] :
( relation(X0)
& empty(X0) )
=> ( relation(sK10)
& empty(sK10) ) ),
introduced(choice_axiom,[]) ).
fof(f25,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f184,plain,
spl13_9,
inference(avatar_split_clause,[],[f120,f181]) ).
fof(f120,plain,
empty(sK10),
inference(cnf_transformation,[],[f76]) ).
fof(f179,plain,
spl13_8,
inference(avatar_split_clause,[],[f119,f176]) ).
fof(f176,plain,
( spl13_8
<=> relation(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_8])]) ).
fof(f119,plain,
relation(sK9),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
( relation(sK9)
& ~ empty(sK9) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f27,f73]) ).
fof(f73,plain,
( ? [X0] :
( relation(X0)
& ~ empty(X0) )
=> ( relation(sK9)
& ~ empty(sK9) ) ),
introduced(choice_axiom,[]) ).
fof(f27,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f174,plain,
~ spl13_7,
inference(avatar_split_clause,[],[f118,f171]) ).
fof(f171,plain,
( spl13_7
<=> empty(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_7])]) ).
fof(f118,plain,
~ empty(sK9),
inference(cnf_transformation,[],[f74]) ).
fof(f169,plain,
spl13_6,
inference(avatar_split_clause,[],[f117,f166]) ).
fof(f117,plain,
empty(sK8),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
empty(sK8),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f26,f71]) ).
fof(f71,plain,
( ? [X0] : empty(X0)
=> empty(sK8) ),
introduced(choice_axiom,[]) ).
fof(f26,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f164,plain,
~ spl13_5,
inference(avatar_split_clause,[],[f116,f161]) ).
fof(f161,plain,
( spl13_5
<=> empty(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_5])]) ).
fof(f116,plain,
~ empty(sK7),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
~ empty(sK7),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f28,f69]) ).
fof(f69,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK7) ),
introduced(choice_axiom,[]) ).
fof(f28,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f159,plain,
spl13_4,
inference(avatar_split_clause,[],[f88,f156]) ).
fof(f156,plain,
( spl13_4
<=> relation(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_4])]) ).
fof(f88,plain,
relation(empty_set),
inference(cnf_transformation,[],[f21]) ).
fof(f21,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f154,plain,
spl13_3,
inference(avatar_split_clause,[],[f86,f151]) ).
fof(f86,plain,
empty(empty_set),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f149,plain,
spl13_2,
inference(avatar_split_clause,[],[f82,f146]) ).
fof(f82,plain,
function(sK2),
inference(cnf_transformation,[],[f59]) ).
fof(f144,plain,
spl13_1,
inference(avatar_split_clause,[],[f81,f141]) ).
fof(f81,plain,
relation(sK2),
inference(cnf_transformation,[],[f59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SEU212+1 : TPTP v8.1.2. Released v3.3.0.
% 0.09/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.33 % Computer : n029.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Apr 29 21:01:04 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % (17530)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.35 % (17532)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.35 % (17531)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.35 % (17533)WARNING: value z3 for option sas not known
% 0.13/0.35 % (17536)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)
% 0.13/0.36 % (17537)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)
% 0.13/0.36 % (17535)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)
% 0.13/0.36 % (17534)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.36 % (17533)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)
% 0.13/0.36 TRYING [1]
% 0.13/0.36 TRYING [2]
% 0.13/0.36 TRYING [1]
% 0.13/0.36 TRYING [2]
% 0.13/0.36 TRYING [1]
% 0.13/0.36 TRYING [3]
% 0.13/0.36 TRYING [3]
% 0.13/0.36 TRYING [2]
% 0.13/0.37 TRYING [4]
% 0.13/0.37 % (17535)First to succeed.
% 0.13/0.37 TRYING [4]
% 0.13/0.37 TRYING [3]
% 0.13/0.38 % (17533)Also succeeded, but the first one will report.
% 0.13/0.38 % (17537)Also succeeded, but the first one will report.
% 0.13/0.38 % (17535)Refutation found. Thanks to Tanya!
% 0.13/0.38 % SZS status Theorem for theBenchmark
% 0.13/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.38 % (17535)------------------------------
% 0.13/0.38 % (17535)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.13/0.38 % (17535)Termination reason: Refutation
% 0.13/0.38
% 0.13/0.38 % (17535)Memory used [KB]: 1111
% 0.13/0.38 % (17535)Time elapsed: 0.024 s
% 0.13/0.38 % (17535)Instructions burned: 40 (million)
% 0.13/0.38 % (17535)------------------------------
% 0.13/0.38 % (17535)------------------------------
% 0.13/0.38 % (17530)Success in time 0.042 s
%------------------------------------------------------------------------------