TSTP Solution File: SWW409-1 by Vampire-SAT---4.8

View Problem - 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
%------------------------------------------------------------------------------