TSTP Solution File: SWW409-1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWW409-1 : TPTP v8.1.2. Released v5.2.0.
% 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 11:38:09 EDT 2024
% Result : Unsatisfiable 0.22s 0.42s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 65
% Syntax : Number of formulae : 168 ( 28 unt; 0 def)
% Number of atoms : 452 ( 75 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 524 ( 240 ~; 236 |; 0 &)
% ( 48 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 51 ( 49 usr; 49 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 403 ( 403 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f659,plain,
$false,
inference(avatar_sat_refutation,[],[f22,f27,f32,f37,f42,f46,f50,f54,f59,f63,f85,f95,f100,f105,f109,f113,f129,f138,f155,f168,f178,f189,f198,f202,f206,f210,f329,f343,f362,f389,f409,f429,f433,f465,f469,f473,f507,f530,f554,f591,f596,f615,f637,f641,f645,f649,f653,f657,f658]) ).
fof(f658,plain,
( spl0_1
| ~ spl0_27
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f592,f588,f327,f19]) ).
fof(f19,plain,
( spl0_1
<=> heap(sep(lseg(x2,nil),emp)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f327,plain,
( spl0_27
<=> ! [X2,X0,X1] :
( ~ heap(sep(lseg(X1,nil),sep(lseg(X0,X1),X2)))
| heap(sep(lseg(X0,nil),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f588,plain,
( spl0_40
<=> heap(sep(lseg(x1,nil),sep(lseg(x2,x1),emp))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f592,plain,
( heap(sep(lseg(x2,nil),emp))
| ~ spl0_27
| ~ spl0_40 ),
inference(resolution,[],[f590,f328]) ).
fof(f328,plain,
( ! [X2,X0,X1] :
( ~ heap(sep(lseg(X1,nil),sep(lseg(X0,X1),X2)))
| heap(sep(lseg(X0,nil),X2)) )
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f327]) ).
fof(f590,plain,
( heap(sep(lseg(x1,nil),sep(lseg(x2,x1),emp)))
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f588]) ).
fof(f657,plain,
( spl0_48
| ~ spl0_22
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f277,f196,f187,f655]) ).
fof(f655,plain,
( spl0_48
<=> ! [X4,X0,X3,X2,X1] :
( ~ heap(sep(X3,sep(lseg(X0,X1),sep(next(X0,X2),X4))))
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f187,plain,
( spl0_22
<=> ! [X0,X3,X2,X1] :
( ~ heap(sep(lseg(X0,X2),sep(next(X0,X1),X3)))
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f196,plain,
( spl0_23
<=> ! [X0,X3,X2,X1] : sep(X0,sep(X3,sep(X1,X2))) = sep(X3,sep(X1,sep(X0,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f277,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ heap(sep(X3,sep(lseg(X0,X1),sep(next(X0,X2),X4))))
| X0 = X1 )
| ~ spl0_22
| ~ spl0_23 ),
inference(superposition,[],[f188,f197]) ).
fof(f197,plain,
( ! [X2,X3,X0,X1] : sep(X0,sep(X3,sep(X1,X2))) = sep(X3,sep(X1,sep(X0,X2)))
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f196]) ).
fof(f188,plain,
( ! [X2,X3,X0,X1] :
( ~ heap(sep(lseg(X0,X2),sep(next(X0,X1),X3)))
| X0 = X2 )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f653,plain,
( spl0_47
| ~ spl0_20
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f247,f196,f166,f651]) ).
fof(f651,plain,
( spl0_47
<=> ! [X4,X0,X3,X2,X1] :
( ~ heap(sep(X4,sep(X1,sep(X2,sep(lseg(nil,X0),X3)))))
| nil = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f166,plain,
( spl0_20
<=> ! [X2,X0,X1] :
( ~ heap(sep(X1,sep(lseg(nil,X0),X2)))
| nil = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f247,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ heap(sep(X4,sep(X1,sep(X2,sep(lseg(nil,X0),X3)))))
| nil = X0 )
| ~ spl0_20
| ~ spl0_23 ),
inference(superposition,[],[f167,f197]) ).
fof(f167,plain,
( ! [X2,X0,X1] :
( ~ heap(sep(X1,sep(lseg(nil,X0),X2)))
| nil = X0 )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f166]) ).
fof(f649,plain,
( spl0_46
| ~ spl0_10
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f223,f196,f61,f647]) ).
fof(f647,plain,
( spl0_46
<=> ! [X0,X3,X2,X1] : sep(X1,sep(X2,sep(X0,X3))) = sep(X1,sep(X0,sep(X2,X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f61,plain,
( spl0_10
<=> ! [X2,X0,X1] : sep(X0,sep(X1,X2)) = sep(X1,sep(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f223,plain,
( ! [X2,X3,X0,X1] : sep(X1,sep(X2,sep(X0,X3))) = sep(X1,sep(X0,sep(X2,X3)))
| ~ spl0_10
| ~ spl0_23 ),
inference(superposition,[],[f197,f62]) ).
fof(f62,plain,
( ! [X2,X0,X1] : sep(X0,sep(X1,X2)) = sep(X1,sep(X0,X2))
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f645,plain,
( spl0_45
| ~ spl0_10
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f217,f196,f61,f643]) ).
fof(f643,plain,
( spl0_45
<=> ! [X0,X3,X2,X1] : sep(X3,sep(X1,sep(X0,X2))) = sep(X0,sep(X1,sep(X3,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f217,plain,
( ! [X2,X3,X0,X1] : sep(X3,sep(X1,sep(X0,X2))) = sep(X0,sep(X1,sep(X3,X2)))
| ~ spl0_10
| ~ spl0_23 ),
inference(superposition,[],[f197,f62]) ).
fof(f641,plain,
( spl0_44
| ~ spl0_7
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f216,f196,f48,f639]) ).
fof(f639,plain,
( spl0_44
<=> ! [X0,X3,X2,X1] : sep(X3,sep(X1,X2)) = sep(lseg(X0,X0),sep(X1,sep(X3,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f48,plain,
( spl0_7
<=> ! [X2,X3] : sep(lseg(X3,X3),X2) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f216,plain,
( ! [X2,X3,X0,X1] : sep(X3,sep(X1,X2)) = sep(lseg(X0,X0),sep(X1,sep(X3,X2)))
| ~ spl0_7
| ~ spl0_23 ),
inference(superposition,[],[f197,f49]) ).
fof(f49,plain,
( ! [X2,X3] : sep(lseg(X3,X3),X2) = X2
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f637,plain,
( spl0_43
| ~ spl0_10
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f190,f187,f61,f635]) ).
fof(f635,plain,
( spl0_43
<=> ! [X4,X0,X3,X2,X1] :
( ~ heap(sep(lseg(X0,X4),sep(X2,sep(next(X0,X1),X3))))
| X0 = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f190,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ heap(sep(lseg(X0,X4),sep(X2,sep(next(X0,X1),X3))))
| X0 = X4 )
| ~ spl0_10
| ~ spl0_22 ),
inference(superposition,[],[f188,f62]) ).
fof(f615,plain,
( spl0_42
| ~ spl0_10
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f179,f176,f61,f613]) ).
fof(f613,plain,
( spl0_42
<=> ! [X5,X4,X0,X3,X2,X1] : ~ heap(sep(next(X0,X4),sep(X5,sep(X2,sep(next(X0,X1),X3))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f176,plain,
( spl0_21
<=> ! [X4,X0,X3,X2,X1] : ~ heap(sep(next(X0,X4),sep(X2,sep(next(X0,X1),X3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f179,plain,
( ! [X2,X3,X0,X1,X4,X5] : ~ heap(sep(next(X0,X4),sep(X5,sep(X2,sep(next(X0,X1),X3)))))
| ~ spl0_10
| ~ spl0_21 ),
inference(superposition,[],[f177,f62]) ).
fof(f177,plain,
( ! [X2,X3,X0,X1,X4] : ~ heap(sep(next(X0,X4),sep(X2,sep(next(X0,X1),X3))))
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f176]) ).
fof(f596,plain,
( spl0_41
| ~ spl0_10
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f170,f166,f61,f594]) ).
fof(f594,plain,
( spl0_41
<=> ! [X0,X3,X2,X1] :
( ~ heap(sep(X3,sep(X1,sep(lseg(nil,X0),X2))))
| nil = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f170,plain,
( ! [X2,X3,X0,X1] :
( ~ heap(sep(X3,sep(X1,sep(lseg(nil,X0),X2))))
| nil = X0 )
| ~ spl0_10
| ~ spl0_20 ),
inference(superposition,[],[f167,f62]) ).
fof(f591,plain,
( spl0_4
| spl0_40
| ~ spl0_14
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f410,f407,f102,f588,f34]) ).
fof(f34,plain,
( spl0_4
<=> x1 = x3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f102,plain,
( spl0_14
<=> heap(sep(next(x1,x3),sep(lseg(x2,x1),sep(lseg(x3,nil),emp)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f407,plain,
( spl0_31
<=> ! [X4,X0,X3,X2,X1] :
( ~ heap(sep(next(X4,X0),sep(X2,sep(lseg(X0,X1),X3))))
| heap(sep(lseg(X4,X1),sep(X2,X3)))
| X0 = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f410,plain,
( heap(sep(lseg(x1,nil),sep(lseg(x2,x1),emp)))
| x1 = x3
| ~ spl0_14
| ~ spl0_31 ),
inference(resolution,[],[f408,f104]) ).
fof(f104,plain,
( heap(sep(next(x1,x3),sep(lseg(x2,x1),sep(lseg(x3,nil),emp))))
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f408,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ heap(sep(next(X4,X0),sep(X2,sep(lseg(X0,X1),X3))))
| heap(sep(lseg(X4,X1),sep(X2,X3)))
| X0 = X4 )
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f407]) ).
fof(f554,plain,
( spl0_39
| ~ spl0_13
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f258,f196,f98,f552]) ).
fof(f552,plain,
( spl0_39
<=> ! [X4,X0,X3,X2,X1] : ~ heap(sep(X4,sep(X1,sep(X2,sep(next(nil,X0),X3))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f98,plain,
( spl0_13
<=> ! [X2,X0,X1] : ~ heap(sep(X1,sep(next(nil,X0),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f258,plain,
( ! [X2,X3,X0,X1,X4] : ~ heap(sep(X4,sep(X1,sep(X2,sep(next(nil,X0),X3)))))
| ~ spl0_13
| ~ spl0_23 ),
inference(superposition,[],[f99,f197]) ).
fof(f99,plain,
( ! [X2,X0,X1] : ~ heap(sep(X1,sep(next(nil,X0),X2)))
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f530,plain,
( spl0_38
| ~ spl0_10
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f157,f153,f61,f528]) ).
fof(f528,plain,
( spl0_38
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ heap(sep(lseg(X4,X5),sep(lseg(X5,X0),sep(X2,sep(lseg(X0,X1),X3)))))
| heap(sep(lseg(X4,X0),sep(X2,sep(lseg(X0,X1),X3))))
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f153,plain,
( spl0_19
<=> ! [X5,X3,X4,X6,X2] :
( X5 = X6
| heap(sep(lseg(X3,X5),sep(lseg(X5,X6),X2)))
| ~ heap(sep(lseg(X3,X4),sep(lseg(X4,X5),sep(lseg(X5,X6),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f157,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ heap(sep(lseg(X4,X5),sep(lseg(X5,X0),sep(X2,sep(lseg(X0,X1),X3)))))
| heap(sep(lseg(X4,X0),sep(X2,sep(lseg(X0,X1),X3))))
| X0 = X1 )
| ~ spl0_10
| ~ spl0_19 ),
inference(superposition,[],[f154,f62]) ).
fof(f154,plain,
( ! [X2,X3,X6,X4,X5] :
( ~ heap(sep(lseg(X3,X4),sep(lseg(X4,X5),sep(lseg(X5,X6),X2))))
| heap(sep(lseg(X3,X5),sep(lseg(X5,X6),X2)))
| X5 = X6 )
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f153]) ).
fof(f507,plain,
( spl0_37
| ~ spl0_10
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f139,f136,f61,f505]) ).
fof(f505,plain,
( spl0_37
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ heap(sep(lseg(X4,X5),sep(lseg(X5,X0),sep(X2,sep(next(X0,X1),X3)))))
| heap(sep(lseg(X4,X0),sep(X2,sep(next(X0,X1),X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f136,plain,
( spl0_18
<=> ! [X5,X3,X4,X6,X2] :
( heap(sep(lseg(X3,X5),sep(next(X5,X6),X2)))
| ~ heap(sep(lseg(X3,X4),sep(lseg(X4,X5),sep(next(X5,X6),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f139,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ heap(sep(lseg(X4,X5),sep(lseg(X5,X0),sep(X2,sep(next(X0,X1),X3)))))
| heap(sep(lseg(X4,X0),sep(X2,sep(next(X0,X1),X3)))) )
| ~ spl0_10
| ~ spl0_18 ),
inference(superposition,[],[f137,f62]) ).
fof(f137,plain,
( ! [X2,X3,X6,X4,X5] :
( ~ heap(sep(lseg(X3,X4),sep(lseg(X4,X5),sep(next(X5,X6),X2))))
| heap(sep(lseg(X3,X5),sep(next(X5,X6),X2))) )
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f473,plain,
( spl0_36
| ~ spl0_10
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f184,f176,f61,f471]) ).
fof(f471,plain,
( spl0_36
<=> ! [X2,X4,X0,X3,X1] : ~ heap(sep(X2,sep(next(X0,X1),sep(next(X0,X3),X4)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f184,plain,
( ! [X2,X3,X0,X1,X4] : ~ heap(sep(X2,sep(next(X0,X1),sep(next(X0,X3),X4))))
| ~ spl0_10
| ~ spl0_21 ),
inference(superposition,[],[f177,f62]) ).
fof(f469,plain,
( spl0_35
| ~ spl0_10
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f163,f153,f61,f467]) ).
fof(f467,plain,
( spl0_35
<=> ! [X4,X0,X3,X2,X1] :
( ~ heap(sep(lseg(X1,X2),sep(lseg(X0,X1),sep(lseg(X2,X3),X4))))
| heap(sep(lseg(X0,X2),sep(lseg(X2,X3),X4)))
| X2 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f163,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ heap(sep(lseg(X1,X2),sep(lseg(X0,X1),sep(lseg(X2,X3),X4))))
| heap(sep(lseg(X0,X2),sep(lseg(X2,X3),X4)))
| X2 = X3 )
| ~ spl0_10
| ~ spl0_19 ),
inference(superposition,[],[f154,f62]) ).
fof(f465,plain,
( spl0_34
| ~ spl0_10
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f160,f153,f61,f463]) ).
fof(f463,plain,
( spl0_34
<=> ! [X4,X0,X3,X2,X1] :
( ~ heap(sep(lseg(X4,X0),sep(lseg(X1,X2),sep(lseg(X0,X1),X3))))
| heap(sep(lseg(X4,X1),sep(lseg(X1,X2),X3)))
| X1 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f160,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ heap(sep(lseg(X4,X0),sep(lseg(X1,X2),sep(lseg(X0,X1),X3))))
| heap(sep(lseg(X4,X1),sep(lseg(X1,X2),X3)))
| X1 = X2 )
| ~ spl0_10
| ~ spl0_19 ),
inference(superposition,[],[f154,f62]) ).
fof(f433,plain,
( spl0_33
| ~ spl0_10
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f145,f136,f61,f431]) ).
fof(f431,plain,
( spl0_33
<=> ! [X4,X0,X3,X2,X1] :
( ~ heap(sep(lseg(X1,X2),sep(lseg(X0,X1),sep(next(X2,X3),X4))))
| heap(sep(lseg(X0,X2),sep(next(X2,X3),X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f145,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ heap(sep(lseg(X1,X2),sep(lseg(X0,X1),sep(next(X2,X3),X4))))
| heap(sep(lseg(X0,X2),sep(next(X2,X3),X4))) )
| ~ spl0_10
| ~ spl0_18 ),
inference(superposition,[],[f137,f62]) ).
fof(f429,plain,
( spl0_32
| ~ spl0_10
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f142,f136,f61,f427]) ).
fof(f427,plain,
( spl0_32
<=> ! [X4,X0,X3,X2,X1] :
( ~ heap(sep(lseg(X4,X0),sep(next(X1,X2),sep(lseg(X0,X1),X3))))
| heap(sep(lseg(X4,X1),sep(next(X1,X2),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f142,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ heap(sep(lseg(X4,X0),sep(next(X1,X2),sep(lseg(X0,X1),X3))))
| heap(sep(lseg(X4,X1),sep(next(X1,X2),X3))) )
| ~ spl0_10
| ~ spl0_18 ),
inference(superposition,[],[f137,f62]) ).
fof(f409,plain,
( spl0_31
| ~ spl0_10
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f131,f127,f61,f407]) ).
fof(f127,plain,
( spl0_17
<=> ! [X3,X4,X5,X2] :
( X3 = X4
| heap(sep(lseg(X3,X5),X2))
| ~ heap(sep(next(X3,X4),sep(lseg(X4,X5),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f131,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ heap(sep(next(X4,X0),sep(X2,sep(lseg(X0,X1),X3))))
| heap(sep(lseg(X4,X1),sep(X2,X3)))
| X0 = X4 )
| ~ spl0_10
| ~ spl0_17 ),
inference(superposition,[],[f128,f62]) ).
fof(f128,plain,
( ! [X2,X3,X4,X5] :
( ~ heap(sep(next(X3,X4),sep(lseg(X4,X5),X2)))
| heap(sep(lseg(X3,X5),X2))
| X3 = X4 )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f127]) ).
fof(f389,plain,
( spl0_30
| ~ spl0_10
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f121,f111,f61,f387]) ).
fof(f387,plain,
( spl0_30
<=> ! [X0,X3,X2,X1] :
( ~ heap(sep(lseg(X3,X0),sep(X1,sep(lseg(X0,nil),X2))))
| heap(sep(lseg(X3,nil),sep(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f111,plain,
( spl0_16
<=> ! [X2,X4,X3] :
( heap(sep(lseg(X3,nil),X2))
| ~ heap(sep(lseg(X3,X4),sep(lseg(X4,nil),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f121,plain,
( ! [X2,X3,X0,X1] :
( ~ heap(sep(lseg(X3,X0),sep(X1,sep(lseg(X0,nil),X2))))
| heap(sep(lseg(X3,nil),sep(X1,X2))) )
| ~ spl0_10
| ~ spl0_16 ),
inference(superposition,[],[f112,f62]) ).
fof(f112,plain,
( ! [X2,X3,X4] :
( ~ heap(sep(lseg(X3,X4),sep(lseg(X4,nil),X2)))
| heap(sep(lseg(X3,nil),X2)) )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f362,plain,
( spl0_29
| ~ spl0_10
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f133,f127,f61,f360]) ).
fof(f360,plain,
( spl0_29
<=> ! [X0,X3,X2,X1] :
( ~ heap(sep(lseg(X1,X2),sep(next(X0,X1),X3)))
| heap(sep(lseg(X0,X2),X3))
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f133,plain,
( ! [X2,X3,X0,X1] :
( ~ heap(sep(lseg(X1,X2),sep(next(X0,X1),X3)))
| heap(sep(lseg(X0,X2),X3))
| X0 = X1 )
| ~ spl0_10
| ~ spl0_17 ),
inference(superposition,[],[f128,f62]) ).
fof(f343,plain,
( spl0_28
| ~ spl0_10
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f115,f107,f61,f341]) ).
fof(f341,plain,
( spl0_28
<=> ! [X4,X0,X3,X2,X1] :
( ~ heap(sep(lseg(X0,X4),sep(X2,sep(lseg(X0,X1),X3))))
| X0 = X4
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f107,plain,
( spl0_15
<=> ! [X3,X4,X5,X2] :
( X3 = X5
| X3 = X4
| ~ heap(sep(lseg(X3,X4),sep(lseg(X3,X5),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f115,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ heap(sep(lseg(X0,X4),sep(X2,sep(lseg(X0,X1),X3))))
| X0 = X4
| X0 = X1 )
| ~ spl0_10
| ~ spl0_15 ),
inference(superposition,[],[f108,f62]) ).
fof(f108,plain,
( ! [X2,X3,X4,X5] :
( ~ heap(sep(lseg(X3,X4),sep(lseg(X3,X5),X2)))
| X3 = X4
| X3 = X5 )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f329,plain,
( spl0_27
| ~ spl0_10
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f124,f111,f61,f327]) ).
fof(f124,plain,
( ! [X2,X0,X1] :
( ~ heap(sep(lseg(X1,nil),sep(lseg(X0,X1),X2)))
| heap(sep(lseg(X0,nil),X2)) )
| ~ spl0_10
| ~ spl0_16 ),
inference(superposition,[],[f112,f62]) ).
fof(f210,plain,
( spl0_26
| ~ spl0_7
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f130,f127,f48,f208]) ).
fof(f208,plain,
( spl0_26
<=> ! [X2,X0,X1] :
( ~ heap(sep(next(X2,X0),X1))
| heap(sep(lseg(X2,X0),X1))
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f130,plain,
( ! [X2,X0,X1] :
( ~ heap(sep(next(X2,X0),X1))
| heap(sep(lseg(X2,X0),X1))
| X0 = X2 )
| ~ spl0_7
| ~ spl0_17 ),
inference(superposition,[],[f128,f49]) ).
fof(f206,plain,
( spl0_25
| ~ spl0_10
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f147,f98,f61,f204]) ).
fof(f204,plain,
( spl0_25
<=> ! [X2,X0,X1,X3] : ~ heap(sep(X3,sep(X1,sep(next(nil,X0),X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f147,plain,
( ! [X2,X3,X0,X1] : ~ heap(sep(X3,sep(X1,sep(next(nil,X0),X2))))
| ~ spl0_10
| ~ spl0_13 ),
inference(superposition,[],[f99,f62]) ).
fof(f202,plain,
( spl0_24
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f87,f83,f61,f200]) ).
fof(f200,plain,
( spl0_24
<=> ! [X4,X0,X3,X2,X1] :
( ~ heap(sep(next(X0,X4),sep(X2,sep(lseg(X0,X1),X3))))
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f83,plain,
( spl0_11
<=> ! [X3,X4,X5,X2] :
( X3 = X5
| ~ heap(sep(next(X3,X4),sep(lseg(X3,X5),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f87,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ heap(sep(next(X0,X4),sep(X2,sep(lseg(X0,X1),X3))))
| X0 = X1 )
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f84,f62]) ).
fof(f84,plain,
( ! [X2,X3,X4,X5] :
( ~ heap(sep(next(X3,X4),sep(lseg(X3,X5),X2)))
| X3 = X5 )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f198,plain,
( spl0_23
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f65,f61,f196]) ).
fof(f65,plain,
( ! [X2,X3,X0,X1] : sep(X0,sep(X3,sep(X1,X2))) = sep(X3,sep(X1,sep(X0,X2)))
| ~ spl0_10 ),
inference(superposition,[],[f62,f62]) ).
fof(f189,plain,
( spl0_22
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f89,f83,f61,f187]) ).
fof(f89,plain,
( ! [X2,X3,X0,X1] :
( ~ heap(sep(lseg(X0,X2),sep(next(X0,X1),X3)))
| X0 = X2 )
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f84,f62]) ).
fof(f178,plain,
( spl0_21
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f76,f61,f57,f176]) ).
fof(f57,plain,
( spl0_9
<=> ! [X3,X4,X5,X2] : ~ heap(sep(next(X3,X4),sep(next(X3,X5),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f76,plain,
( ! [X2,X3,X0,X1,X4] : ~ heap(sep(next(X0,X4),sep(X2,sep(next(X0,X1),X3))))
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f58,f62]) ).
fof(f58,plain,
( ! [X2,X3,X4,X5] : ~ heap(sep(next(X3,X4),sep(next(X3,X5),X2)))
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f168,plain,
( spl0_20
| ~ spl0_8
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f73,f61,f52,f166]) ).
fof(f52,plain,
( spl0_8
<=> ! [X4,X2] :
( nil = X4
| ~ heap(sep(lseg(nil,X4),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f73,plain,
( ! [X2,X0,X1] :
( ~ heap(sep(X1,sep(lseg(nil,X0),X2)))
| nil = X0 )
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f53,f62]) ).
fof(f53,plain,
( ! [X2,X4] :
( ~ heap(sep(lseg(nil,X4),X2))
| nil = X4 )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f155,plain,
spl0_19,
inference(avatar_split_clause,[],[f11,f153]) ).
fof(f11,axiom,
! [X2,X3,X6,X4,X5] :
( X5 = X6
| heap(sep(lseg(X3,X5),sep(lseg(X5,X6),X2)))
| ~ heap(sep(lseg(X3,X4),sep(lseg(X4,X5),sep(lseg(X5,X6),X2)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unfolding_5) ).
fof(f138,plain,
spl0_18,
inference(avatar_split_clause,[],[f10,f136]) ).
fof(f10,axiom,
! [X2,X3,X6,X4,X5] :
( heap(sep(lseg(X3,X5),sep(next(X5,X6),X2)))
| ~ heap(sep(lseg(X3,X4),sep(lseg(X4,X5),sep(next(X5,X6),X2)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unfolding_4) ).
fof(f129,plain,
spl0_17,
inference(avatar_split_clause,[],[f8,f127]) ).
fof(f8,axiom,
! [X2,X3,X4,X5] :
( X3 = X4
| heap(sep(lseg(X3,X5),X2))
| ~ heap(sep(next(X3,X4),sep(lseg(X4,X5),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unfolding_2) ).
fof(f113,plain,
spl0_16,
inference(avatar_split_clause,[],[f9,f111]) ).
fof(f9,axiom,
! [X2,X3,X4] :
( heap(sep(lseg(X3,nil),X2))
| ~ heap(sep(lseg(X3,X4),sep(lseg(X4,nil),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unfolding_3) ).
fof(f109,plain,
spl0_15,
inference(avatar_split_clause,[],[f7,f107]) ).
fof(f7,axiom,
! [X2,X3,X4,X5] :
( X3 = X5
| X3 = X4
| ~ heap(sep(lseg(X3,X4),sep(lseg(X3,X5),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellformedness_5) ).
fof(f105,plain,
( spl0_14
| ~ spl0_10
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f96,f92,f61,f102]) ).
fof(f92,plain,
( spl0_12
<=> heap(sep(lseg(x2,x1),sep(lseg(x3,nil),sep(next(x1,x3),emp)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f96,plain,
( heap(sep(next(x1,x3),sep(lseg(x2,x1),sep(lseg(x3,nil),emp))))
| ~ spl0_10
| ~ spl0_12 ),
inference(forward_demodulation,[],[f94,f65]) ).
fof(f94,plain,
( heap(sep(lseg(x2,x1),sep(lseg(x3,nil),sep(next(x1,x3),emp))))
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f100,plain,
( spl0_13
| ~ spl0_6
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f75,f61,f44,f98]) ).
fof(f44,plain,
( spl0_6
<=> ! [X2,X4] : ~ heap(sep(next(nil,X4),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f75,plain,
( ! [X2,X0,X1] : ~ heap(sep(X1,sep(next(nil,X0),X2)))
| ~ spl0_6
| ~ spl0_10 ),
inference(superposition,[],[f45,f62]) ).
fof(f45,plain,
( ! [X2,X4] : ~ heap(sep(next(nil,X4),X2))
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f95,plain,
spl0_12,
inference(avatar_split_clause,[],[f16,f92]) ).
fof(f16,axiom,
heap(sep(lseg(x2,x1),sep(lseg(x3,nil),sep(next(x1,x3),emp)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_5) ).
fof(f85,plain,
spl0_11,
inference(avatar_split_clause,[],[f6,f83]) ).
fof(f6,axiom,
! [X2,X3,X4,X5] :
( X3 = X5
| ~ heap(sep(next(X3,X4),sep(lseg(X3,X5),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellformedness_4) ).
fof(f63,plain,
spl0_10,
inference(avatar_split_clause,[],[f1,f61]) ).
fof(f1,axiom,
! [X2,X0,X1] : sep(X0,sep(X1,X2)) = sep(X1,sep(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associative_commutative) ).
fof(f59,plain,
spl0_9,
inference(avatar_split_clause,[],[f5,f57]) ).
fof(f5,axiom,
! [X2,X3,X4,X5] : ~ heap(sep(next(X3,X4),sep(next(X3,X5),X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellformedness_3) ).
fof(f54,plain,
spl0_8,
inference(avatar_split_clause,[],[f4,f52]) ).
fof(f4,axiom,
! [X2,X4] :
( nil = X4
| ~ heap(sep(lseg(nil,X4),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellformedness_2) ).
fof(f50,plain,
spl0_7,
inference(avatar_split_clause,[],[f2,f48]) ).
fof(f2,axiom,
! [X2,X3] : sep(lseg(X3,X3),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',normalization) ).
fof(f46,plain,
spl0_6,
inference(avatar_split_clause,[],[f3,f44]) ).
fof(f3,axiom,
! [X2,X4] : ~ heap(sep(next(nil,X4),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellformedness_1) ).
fof(f42,plain,
~ spl0_5,
inference(avatar_split_clause,[],[f15,f39]) ).
fof(f39,plain,
( spl0_5
<=> x2 = x3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f15,axiom,
x2 != x3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_4) ).
fof(f37,plain,
~ spl0_4,
inference(avatar_split_clause,[],[f14,f34]) ).
fof(f14,axiom,
x1 != x3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_3) ).
fof(f32,plain,
~ spl0_3,
inference(avatar_split_clause,[],[f13,f29]) ).
fof(f29,plain,
( spl0_3
<=> nil = x2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f13,axiom,
nil != x2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_2) ).
fof(f27,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f12,f24]) ).
fof(f24,plain,
( spl0_2
<=> nil = x1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f12,axiom,
nil != x1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_1) ).
fof(f22,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f17,f19]) ).
fof(f17,axiom,
~ heap(sep(lseg(x2,nil),emp)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conclusion_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SWW409-1 : TPTP v8.1.2. Released v5.2.0.
% 0.04/0.15 % 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 19:36:23 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (31270)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.38 % (31273)WARNING: value z3 for option sas not known
% 0.22/0.38 % (31272)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.38 % (31274)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.38 % (31275)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.22/0.38 % (31276)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.22/0.38 % (31273)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.22/0.38 % (31271)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.38 % (31277)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.22/0.38 TRYING [1]
% 0.22/0.38 TRYING [2]
% 0.22/0.39 TRYING [1]
% 0.22/0.39 TRYING [3]
% 0.22/0.39 TRYING [2]
% 0.22/0.41 TRYING [3]
% 0.22/0.41 TRYING [4]
% 0.22/0.41 % (31275)First to succeed.
% 0.22/0.41 % (31275)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-31270"
% 0.22/0.42 % (31275)Refutation found. Thanks to Tanya!
% 0.22/0.42 % SZS status Unsatisfiable for theBenchmark
% 0.22/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.42 % (31275)------------------------------
% 0.22/0.42 % (31275)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.42 % (31275)Termination reason: Refutation
% 0.22/0.42
% 0.22/0.42 % (31275)Memory used [KB]: 1438
% 0.22/0.42 % (31275)Time elapsed: 0.038 s
% 0.22/0.42 % (31275)Instructions burned: 62 (million)
% 0.22/0.42 % (31270)Success in time 0.054 s
%------------------------------------------------------------------------------