TSTP Solution File: SWC413-1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SWC413-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n016.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun May  5 09:50:56 EDT 2024

% Result   : Unsatisfiable 0.58s 0.75s
% Output   : Refutation 0.58s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   45
% Syntax   : Number of formulae    :  127 (   3 unt;   1 typ;   0 def)
%            Number of atoms       : 1323 (  54 equ)
%            Maximal formula atoms :    9 (  10 avg)
%            Number of connectives :  484 ( 211   ~; 261   |;   0   &)
%                                         (  12 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :  924 ( 924 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    2 (   1   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :   29 (  27 usr;  23 prp; 0-3 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :  100 (  99   !;   0   ?;  94   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
tff(pred_def_20,type,
    sQ0_eqProxy: 
      !>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).

tff(f454,plain,
    $false,
    inference(avatar_sat_refutation,[],[f320,f325,f330,f335,f340,f365,f370,f375,f380,f385,f402,f403,f404,f405,f406,f407,f408,f409,f410,f411,f412,f413,f414,f415,f416,f417,f418,f419,f420,f421,f438,f453]) ).

tff(f453,plain,
    ( ~ spl1_1
    | ~ spl1_11
    | ~ spl1_12
    | ~ spl1_13
    | ~ spl1_14
    | ~ spl1_15 ),
    inference(avatar_contradiction_clause,[],[f452]) ).

tff(f452,plain,
    ( $false
    | ~ spl1_1
    | ~ spl1_11
    | ~ spl1_12
    | ~ spl1_13
    | ~ spl1_14
    | ~ spl1_15 ),
    inference(subsumption_resolution,[],[f451,f384]) ).

tff(f384,plain,
    ( sQ0_eqProxy($i,sk3,app(app(cons(sk9,nil),cons(sk8,nil)),sk10))
    | ~ spl1_15 ),
    inference(avatar_component_clause,[],[f382]) ).

tff(f382,plain,
    ( spl1_15
  <=> sQ0_eqProxy($i,sk3,app(app(cons(sk9,nil),cons(sk8,nil)),sk10)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_15])]) ).

tff(f451,plain,
    ( ~ sQ0_eqProxy($i,sk3,app(app(cons(sk9,nil),cons(sk8,nil)),sk10))
    | ~ spl1_1
    | ~ spl1_11
    | ~ spl1_12
    | ~ spl1_13
    | ~ spl1_14 ),
    inference(subsumption_resolution,[],[f450,f374]) ).

tff(f374,plain,
    ( ssList(sk10)
    | ~ spl1_13 ),
    inference(avatar_component_clause,[],[f372]) ).

tff(f372,plain,
    ( spl1_13
  <=> ssList(sk10) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_13])]) ).

tff(f450,plain,
    ( ~ ssList(sk10)
    | ~ sQ0_eqProxy($i,sk3,app(app(cons(sk9,nil),cons(sk8,nil)),sk10))
    | ~ spl1_1
    | ~ spl1_11
    | ~ spl1_12
    | ~ spl1_14 ),
    inference(subsumption_resolution,[],[f449,f369]) ).

tff(f369,plain,
    ( ssItem(sk9)
    | ~ spl1_12 ),
    inference(avatar_component_clause,[],[f367]) ).

tff(f367,plain,
    ( spl1_12
  <=> ssItem(sk9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_12])]) ).

tff(f449,plain,
    ( ~ ssItem(sk9)
    | ~ ssList(sk10)
    | ~ sQ0_eqProxy($i,sk3,app(app(cons(sk9,nil),cons(sk8,nil)),sk10))
    | ~ spl1_1
    | ~ spl1_11
    | ~ spl1_14 ),
    inference(subsumption_resolution,[],[f445,f364]) ).

tff(f364,plain,
    ( ssItem(sk8)
    | ~ spl1_11 ),
    inference(avatar_component_clause,[],[f362]) ).

tff(f362,plain,
    ( spl1_11
  <=> ssItem(sk8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_11])]) ).

tff(f445,plain,
    ( ~ ssItem(sk8)
    | ~ ssItem(sk9)
    | ~ ssList(sk10)
    | ~ sQ0_eqProxy($i,sk3,app(app(cons(sk9,nil),cons(sk8,nil)),sk10))
    | ~ spl1_1
    | ~ spl1_14 ),
    inference(resolution,[],[f316,f379]) ).

tff(f379,plain,
    ( sQ0_eqProxy($i,sk4,app(app(cons(sk8,nil),cons(sk9,nil)),sk10))
    | ~ spl1_14 ),
    inference(avatar_component_clause,[],[f377]) ).

tff(f377,plain,
    ( spl1_14
  <=> sQ0_eqProxy($i,sk4,app(app(cons(sk8,nil),cons(sk9,nil)),sk10)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_14])]) ).

tff(f316,plain,
    ( ! [X8: $i,X6: $i,X7: $i] :
        ( ~ sQ0_eqProxy($i,sk4,app(app(cons(X6,nil),cons(X7,nil)),X8))
        | ~ ssItem(X6)
        | ~ ssItem(X7)
        | ~ ssList(X8)
        | ~ sQ0_eqProxy($i,sk3,app(app(cons(X7,nil),cons(X6,nil)),X8)) )
    | ~ spl1_1 ),
    inference(avatar_component_clause,[],[f315]) ).

tff(f315,plain,
    ( spl1_1
  <=> ! [X6,X8,X7] :
        ( ~ sQ0_eqProxy($i,sk3,app(app(cons(X7,nil),cons(X6,nil)),X8))
        | ~ ssItem(X6)
        | ~ ssItem(X7)
        | ~ ssList(X8)
        | ~ sQ0_eqProxy($i,sk4,app(app(cons(X6,nil),cons(X7,nil)),X8)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_1])]) ).

tff(f438,plain,
    ( ~ spl1_4
    | ~ spl1_2
    | ~ spl1_3
    | ~ spl1_5
    | ~ spl1_6 ),
    inference(avatar_split_clause,[],[f437,f337,f332,f322,f318,f327]) ).

tff(f327,plain,
    ( spl1_4
  <=> ssItem(sk12) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_4])]) ).

tff(f318,plain,
    ( spl1_2
  <=> ! [X9,X11,X10] :
        ( ~ sQ0_eqProxy($i,sk4,app(app(cons(X9,nil),cons(X10,nil)),X11))
        | ~ ssItem(X9)
        | ~ ssItem(X10)
        | ~ ssList(X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_2])]) ).

tff(f322,plain,
    ( spl1_3
  <=> ssItem(sk11) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_3])]) ).

tff(f332,plain,
    ( spl1_5
  <=> ssList(sk13) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_5])]) ).

tff(f337,plain,
    ( spl1_6
  <=> sQ0_eqProxy($i,sk4,app(app(cons(sk11,nil),cons(sk12,nil)),sk13)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_6])]) ).

tff(f437,plain,
    ( ~ ssItem(sk12)
    | ~ spl1_2
    | ~ spl1_3
    | ~ spl1_5
    | ~ spl1_6 ),
    inference(subsumption_resolution,[],[f433,f334]) ).

tff(f334,plain,
    ( ssList(sk13)
    | ~ spl1_5 ),
    inference(avatar_component_clause,[],[f332]) ).

tff(f433,plain,
    ( ~ ssItem(sk12)
    | ~ ssList(sk13)
    | ~ spl1_2
    | ~ spl1_3
    | ~ spl1_6 ),
    inference(subsumption_resolution,[],[f432,f324]) ).

tff(f324,plain,
    ( ssItem(sk11)
    | ~ spl1_3 ),
    inference(avatar_component_clause,[],[f322]) ).

tff(f432,plain,
    ( ~ ssItem(sk11)
    | ~ ssItem(sk12)
    | ~ ssList(sk13)
    | ~ spl1_2
    | ~ spl1_6 ),
    inference(resolution,[],[f319,f339]) ).

tff(f339,plain,
    ( sQ0_eqProxy($i,sk4,app(app(cons(sk11,nil),cons(sk12,nil)),sk13))
    | ~ spl1_6 ),
    inference(avatar_component_clause,[],[f337]) ).

tff(f319,plain,
    ( ! [X10: $i,X11: $i,X9: $i] :
        ( ~ sQ0_eqProxy($i,sk4,app(app(cons(X9,nil),cons(X10,nil)),X11))
        | ~ ssItem(X9)
        | ~ ssItem(X10)
        | ~ ssList(X11) )
    | ~ spl1_2 ),
    inference(avatar_component_clause,[],[f318]) ).

tff(f421,plain,
    ( spl1_15
    | spl1_6 ),
    inference(avatar_split_clause,[],[f296,f337,f382]) ).

tff(f296,plain,
    ( sQ0_eqProxy($i,sk4,app(app(cons(sk11,nil),cons(sk12,nil)),sk13))
    | sQ0_eqProxy($i,sk3,app(app(cons(sk9,nil),cons(sk8,nil)),sk10)) ),
    inference(equality_proxy_replacement,[],[f261,f264]) ).

tff(f264,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( sQ0_eqProxy(X0,X1,X2)
    <=> ( X1 = X2 ) ),
    introduced(equality_proxy_definition,[new_symbols(naming,[sQ0_eqProxy])]) ).

tff(f261,plain,
    ( ( sk4 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13) )
    | ( sk3 = app(app(cons(sk9,nil),cons(sk8,nil)),sk10) ) ),
    inference(definition_unfolding,[],[f241,f190]) ).

tff(f190,axiom,
    sk2 = sk4,
    file('/export/starexec/sandbox/tmp/tmp.lyhpdBWSpE/Vampire---4.8_1401',co1_5) ).

tff(f241,axiom,
    ( ( sk2 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13) )
    | ( sk3 = app(app(cons(sk9,nil),cons(sk8,nil)),sk10) ) ),
    file('/export/starexec/sandbox/tmp/tmp.lyhpdBWSpE/Vampire---4.8_1401',co1_56) ).

tff(f420,plain,
    ( spl1_14
    | spl1_6 ),
    inference(avatar_split_clause,[],[f295,f337,f377]) ).

tff(f295,plain,
    ( sQ0_eqProxy($i,sk4,app(app(cons(sk11,nil),cons(sk12,nil)),sk13))
    | sQ0_eqProxy($i,sk4,app(app(cons(sk8,nil),cons(sk9,nil)),sk10)) ),
    inference(equality_proxy_replacement,[],[f260,f264]) ).

tff(f260,plain,
    ( ( sk4 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13) )
    | ( sk4 = app(app(cons(sk8,nil),cons(sk9,nil)),sk10) ) ),
    inference(definition_unfolding,[],[f240,f190]) ).

tff(f240,axiom,
    ( ( sk2 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13) )
    | ( sk4 = app(app(cons(sk8,nil),cons(sk9,nil)),sk10) ) ),
    file('/export/starexec/sandbox/tmp/tmp.lyhpdBWSpE/Vampire---4.8_1401',co1_55) ).

tff(f419,plain,
    ( spl1_13
    | spl1_6 ),
    inference(avatar_split_clause,[],[f294,f337,f372]) ).

tff(f294,plain,
    ( sQ0_eqProxy($i,sk4,app(app(cons(sk11,nil),cons(sk12,nil)),sk13))
    | ssList(sk10) ),
    inference(equality_proxy_replacement,[],[f259,f264]) ).

tff(f259,plain,
    ( ( sk4 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13) )
    | ssList(sk10) ),
    inference(definition_unfolding,[],[f239,f190]) ).

tff(f239,axiom,
    ( ( sk2 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13) )
    | ssList(sk10) ),
    file('/export/starexec/sandbox/tmp/tmp.lyhpdBWSpE/Vampire---4.8_1401',co1_54) ).

tff(f418,plain,
    ( spl1_15
    | spl1_5 ),
    inference(avatar_split_clause,[],[f293,f332,f382]) ).

tff(f293,plain,
    ( ssList(sk13)
    | sQ0_eqProxy($i,sk3,app(app(cons(sk9,nil),cons(sk8,nil)),sk10)) ),
    inference(equality_proxy_replacement,[],[f238,f264]) ).

tff(f238,axiom,
    ( ssList(sk13)
    | ( sk3 = app(app(cons(sk9,nil),cons(sk8,nil)),sk10) ) ),
    file('/export/starexec/sandbox/tmp/tmp.lyhpdBWSpE/Vampire---4.8_1401',co1_53) ).

tff(f417,plain,
    ( spl1_14
    | spl1_5 ),
    inference(avatar_split_clause,[],[f292,f332,f377]) ).

tff(f292,plain,
    ( ssList(sk13)
    | sQ0_eqProxy($i,sk4,app(app(cons(sk8,nil),cons(sk9,nil)),sk10)) ),
    inference(equality_proxy_replacement,[],[f237,f264]) ).

tff(f237,axiom,
    ( ssList(sk13)
    | ( sk4 = app(app(cons(sk8,nil),cons(sk9,nil)),sk10) ) ),
    file('/export/starexec/sandbox/tmp/tmp.lyhpdBWSpE/Vampire---4.8_1401',co1_52) ).

tff(f416,plain,
    ( spl1_13
    | spl1_5 ),
    inference(avatar_split_clause,[],[f236,f332,f372]) ).

tff(f236,axiom,
    ( ssList(sk13)
    | ssList(sk10) ),
    file('/export/starexec/sandbox/tmp/tmp.lyhpdBWSpE/Vampire---4.8_1401',co1_51) ).

tff(f415,plain,
    ( spl1_12
    | spl1_6 ),
    inference(avatar_split_clause,[],[f291,f337,f367]) ).

tff(f291,plain,
    ( sQ0_eqProxy($i,sk4,app(app(cons(sk11,nil),cons(sk12,nil)),sk13))
    | ssItem(sk9) ),
    inference(equality_proxy_replacement,[],[f258,f264]) ).

tff(f258,plain,
    ( ( sk4 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13) )
    | ssItem(sk9) ),
    inference(definition_unfolding,[],[f235,f190]) ).

tff(f235,axiom,
    ( ( sk2 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13) )
    | ssItem(sk9) ),
    file('/export/starexec/sandbox/tmp/tmp.lyhpdBWSpE/Vampire---4.8_1401',co1_50) ).

tff(f414,plain,
    ( spl1_12
    | spl1_5 ),
    inference(avatar_split_clause,[],[f234,f332,f367]) ).

tff(f234,axiom,
    ( ssList(sk13)
    | ssItem(sk9) ),
    file('/export/starexec/sandbox/tmp/tmp.lyhpdBWSpE/Vampire---4.8_1401',co1_49) ).

tff(f413,plain,
    ( spl1_15
    | spl1_4 ),
    inference(avatar_split_clause,[],[f290,f327,f382]) ).

tff(f290,plain,
    ( ssItem(sk12)
    | sQ0_eqProxy($i,sk3,app(app(cons(sk9,nil),cons(sk8,nil)),sk10)) ),
    inference(equality_proxy_replacement,[],[f233,f264]) ).

tff(f233,axiom,
    ( ssItem(sk12)
    | ( sk3 = app(app(cons(sk9,nil),cons(sk8,nil)),sk10) ) ),
    file('/export/starexec/sandbox/tmp/tmp.lyhpdBWSpE/Vampire---4.8_1401',co1_48) ).

tff(f412,plain,
    ( spl1_14
    | spl1_4 ),
    inference(avatar_split_clause,[],[f289,f327,f377]) ).

tff(f289,plain,
    ( ssItem(sk12)
    | sQ0_eqProxy($i,sk4,app(app(cons(sk8,nil),cons(sk9,nil)),sk10)) ),
    inference(equality_proxy_replacement,[],[f232,f264]) ).

tff(f232,axiom,
    ( ssItem(sk12)
    | ( sk4 = app(app(cons(sk8,nil),cons(sk9,nil)),sk10) ) ),
    file('/export/starexec/sandbox/tmp/tmp.lyhpdBWSpE/Vampire---4.8_1401',co1_47) ).

tff(f411,plain,
    ( spl1_13
    | spl1_4 ),
    inference(avatar_split_clause,[],[f231,f327,f372]) ).

tff(f231,axiom,
    ( ssItem(sk12)
    | ssList(sk10) ),
    file('/export/starexec/sandbox/tmp/tmp.lyhpdBWSpE/Vampire---4.8_1401',co1_46) ).

tff(f410,plain,
    ( spl1_12
    | spl1_4 ),
    inference(avatar_split_clause,[],[f230,f327,f367]) ).

tff(f230,axiom,
    ( ssItem(sk12)
    | ssItem(sk9) ),
    file('/export/starexec/sandbox/tmp/tmp.lyhpdBWSpE/Vampire---4.8_1401',co1_45) ).

tff(f409,plain,
    ( spl1_11
    | spl1_6 ),
    inference(avatar_split_clause,[],[f288,f337,f362]) ).

tff(f288,plain,
    ( sQ0_eqProxy($i,sk4,app(app(cons(sk11,nil),cons(sk12,nil)),sk13))
    | ssItem(sk8) ),
    inference(equality_proxy_replacement,[],[f257,f264]) ).

tff(f257,plain,
    ( ( sk4 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13) )
    | ssItem(sk8) ),
    inference(definition_unfolding,[],[f229,f190]) ).

tff(f229,axiom,
    ( ( sk2 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13) )
    | ssItem(sk8) ),
    file('/export/starexec/sandbox/tmp/tmp.lyhpdBWSpE/Vampire---4.8_1401',co1_44) ).

tff(f408,plain,
    ( spl1_11
    | spl1_5 ),
    inference(avatar_split_clause,[],[f228,f332,f362]) ).

tff(f228,axiom,
    ( ssList(sk13)
    | ssItem(sk8) ),
    file('/export/starexec/sandbox/tmp/tmp.lyhpdBWSpE/Vampire---4.8_1401',co1_43) ).

tff(f407,plain,
    ( spl1_11
    | spl1_4 ),
    inference(avatar_split_clause,[],[f227,f327,f362]) ).

tff(f227,axiom,
    ( ssItem(sk12)
    | ssItem(sk8) ),
    file('/export/starexec/sandbox/tmp/tmp.lyhpdBWSpE/Vampire---4.8_1401',co1_42) ).

tff(f406,plain,
    ( spl1_15
    | spl1_3 ),
    inference(avatar_split_clause,[],[f287,f322,f382]) ).

tff(f287,plain,
    ( ssItem(sk11)
    | sQ0_eqProxy($i,sk3,app(app(cons(sk9,nil),cons(sk8,nil)),sk10)) ),
    inference(equality_proxy_replacement,[],[f226,f264]) ).

tff(f226,axiom,
    ( ssItem(sk11)
    | ( sk3 = app(app(cons(sk9,nil),cons(sk8,nil)),sk10) ) ),
    file('/export/starexec/sandbox/tmp/tmp.lyhpdBWSpE/Vampire---4.8_1401',co1_41) ).

tff(f405,plain,
    ( spl1_14
    | spl1_3 ),
    inference(avatar_split_clause,[],[f286,f322,f377]) ).

tff(f286,plain,
    ( ssItem(sk11)
    | sQ0_eqProxy($i,sk4,app(app(cons(sk8,nil),cons(sk9,nil)),sk10)) ),
    inference(equality_proxy_replacement,[],[f225,f264]) ).

tff(f225,axiom,
    ( ssItem(sk11)
    | ( sk4 = app(app(cons(sk8,nil),cons(sk9,nil)),sk10) ) ),
    file('/export/starexec/sandbox/tmp/tmp.lyhpdBWSpE/Vampire---4.8_1401',co1_40) ).

tff(f404,plain,
    ( spl1_13
    | spl1_3 ),
    inference(avatar_split_clause,[],[f224,f322,f372]) ).

tff(f224,axiom,
    ( ssItem(sk11)
    | ssList(sk10) ),
    file('/export/starexec/sandbox/tmp/tmp.lyhpdBWSpE/Vampire---4.8_1401',co1_39) ).

tff(f403,plain,
    ( spl1_12
    | spl1_3 ),
    inference(avatar_split_clause,[],[f223,f322,f367]) ).

tff(f223,axiom,
    ( ssItem(sk11)
    | ssItem(sk9) ),
    file('/export/starexec/sandbox/tmp/tmp.lyhpdBWSpE/Vampire---4.8_1401',co1_38) ).

tff(f402,plain,
    ( spl1_11
    | spl1_3 ),
    inference(avatar_split_clause,[],[f222,f322,f362]) ).

tff(f222,axiom,
    ( ssItem(sk11)
    | ssItem(sk8) ),
    file('/export/starexec/sandbox/tmp/tmp.lyhpdBWSpE/Vampire---4.8_1401',co1_37) ).

tff(f385,plain,
    ( spl1_15
    | spl1_2 ),
    inference(avatar_split_clause,[],[f278,f318,f382]) ).

tff(f278,plain,
    ! [X8: $i,X6: $i,X7: $i] :
      ( ~ sQ0_eqProxy($i,sk4,app(app(cons(X6,nil),cons(X7,nil)),X8))
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6)
      | sQ0_eqProxy($i,sk3,app(app(cons(sk9,nil),cons(sk8,nil)),sk10)) ),
    inference(equality_proxy_replacement,[],[f205,f264]) ).

tff(f205,axiom,
    ! [X8: $i,X6: $i,X7: $i] :
      ( ( sk4 != app(app(cons(X6,nil),cons(X7,nil)),X8) )
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6)
      | ( sk3 = app(app(cons(sk9,nil),cons(sk8,nil)),sk10) ) ),
    file('/export/starexec/sandbox/tmp/tmp.lyhpdBWSpE/Vampire---4.8_1401',co1_20) ).

tff(f380,plain,
    ( spl1_14
    | spl1_2 ),
    inference(avatar_split_clause,[],[f277,f318,f377]) ).

tff(f277,plain,
    ! [X8: $i,X6: $i,X7: $i] :
      ( ~ sQ0_eqProxy($i,sk4,app(app(cons(X6,nil),cons(X7,nil)),X8))
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6)
      | sQ0_eqProxy($i,sk4,app(app(cons(sk8,nil),cons(sk9,nil)),sk10)) ),
    inference(equality_proxy_replacement,[],[f204,f264]) ).

tff(f204,axiom,
    ! [X8: $i,X6: $i,X7: $i] :
      ( ( sk4 != app(app(cons(X6,nil),cons(X7,nil)),X8) )
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6)
      | ( sk4 = app(app(cons(sk8,nil),cons(sk9,nil)),sk10) ) ),
    file('/export/starexec/sandbox/tmp/tmp.lyhpdBWSpE/Vampire---4.8_1401',co1_19) ).

tff(f375,plain,
    ( spl1_13
    | spl1_2 ),
    inference(avatar_split_clause,[],[f276,f318,f372]) ).

tff(f276,plain,
    ! [X8: $i,X6: $i,X7: $i] :
      ( ~ sQ0_eqProxy($i,sk4,app(app(cons(X6,nil),cons(X7,nil)),X8))
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6)
      | ssList(sk10) ),
    inference(equality_proxy_replacement,[],[f203,f264]) ).

tff(f203,axiom,
    ! [X8: $i,X6: $i,X7: $i] :
      ( ( sk4 != app(app(cons(X6,nil),cons(X7,nil)),X8) )
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6)
      | ssList(sk10) ),
    file('/export/starexec/sandbox/tmp/tmp.lyhpdBWSpE/Vampire---4.8_1401',co1_18) ).

tff(f370,plain,
    ( spl1_12
    | spl1_2 ),
    inference(avatar_split_clause,[],[f275,f318,f367]) ).

tff(f275,plain,
    ! [X8: $i,X6: $i,X7: $i] :
      ( ~ sQ0_eqProxy($i,sk4,app(app(cons(X6,nil),cons(X7,nil)),X8))
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6)
      | ssItem(sk9) ),
    inference(equality_proxy_replacement,[],[f202,f264]) ).

tff(f202,axiom,
    ! [X8: $i,X6: $i,X7: $i] :
      ( ( sk4 != app(app(cons(X6,nil),cons(X7,nil)),X8) )
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6)
      | ssItem(sk9) ),
    file('/export/starexec/sandbox/tmp/tmp.lyhpdBWSpE/Vampire---4.8_1401',co1_17) ).

tff(f365,plain,
    ( spl1_11
    | spl1_2 ),
    inference(avatar_split_clause,[],[f274,f318,f362]) ).

tff(f274,plain,
    ! [X8: $i,X6: $i,X7: $i] :
      ( ~ sQ0_eqProxy($i,sk4,app(app(cons(X6,nil),cons(X7,nil)),X8))
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6)
      | ssItem(sk8) ),
    inference(equality_proxy_replacement,[],[f201,f264]) ).

tff(f201,axiom,
    ! [X8: $i,X6: $i,X7: $i] :
      ( ( sk4 != app(app(cons(X6,nil),cons(X7,nil)),X8) )
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6)
      | ssItem(sk8) ),
    file('/export/starexec/sandbox/tmp/tmp.lyhpdBWSpE/Vampire---4.8_1401',co1_16) ).

tff(f340,plain,
    ( spl1_1
    | spl1_6 ),
    inference(avatar_split_clause,[],[f269,f337,f315]) ).

tff(f269,plain,
    ! [X8: $i,X6: $i,X7: $i] :
      ( sQ0_eqProxy($i,sk4,app(app(cons(sk11,nil),cons(sk12,nil)),sk13))
      | ~ sQ0_eqProxy($i,sk3,app(app(cons(X7,nil),cons(X6,nil)),X8))
      | ~ sQ0_eqProxy($i,sk4,app(app(cons(X6,nil),cons(X7,nil)),X8))
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6) ),
    inference(equality_proxy_replacement,[],[f248,f264]) ).

tff(f248,plain,
    ! [X8: $i,X6: $i,X7: $i] :
      ( ( sk4 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13) )
      | ( sk3 != app(app(cons(X7,nil),cons(X6,nil)),X8) )
      | ( sk4 != app(app(cons(X6,nil),cons(X7,nil)),X8) )
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6) ),
    inference(definition_unfolding,[],[f196,f190,f191,f190]) ).

tff(f191,axiom,
    sk1 = sk3,
    file('/export/starexec/sandbox/tmp/tmp.lyhpdBWSpE/Vampire---4.8_1401',co1_6) ).

tff(f196,axiom,
    ! [X8: $i,X6: $i,X7: $i] :
      ( ( sk2 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13) )
      | ( sk1 != app(app(cons(X7,nil),cons(X6,nil)),X8) )
      | ( sk2 != app(app(cons(X6,nil),cons(X7,nil)),X8) )
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6) ),
    file('/export/starexec/sandbox/tmp/tmp.lyhpdBWSpE/Vampire---4.8_1401',co1_11) ).

tff(f335,plain,
    ( spl1_1
    | spl1_5 ),
    inference(avatar_split_clause,[],[f268,f332,f315]) ).

tff(f268,plain,
    ! [X8: $i,X6: $i,X7: $i] :
      ( ssList(sk13)
      | ~ sQ0_eqProxy($i,sk3,app(app(cons(X7,nil),cons(X6,nil)),X8))
      | ~ sQ0_eqProxy($i,sk4,app(app(cons(X6,nil),cons(X7,nil)),X8))
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6) ),
    inference(equality_proxy_replacement,[],[f247,f264]) ).

tff(f247,plain,
    ! [X8: $i,X6: $i,X7: $i] :
      ( ssList(sk13)
      | ( sk3 != app(app(cons(X7,nil),cons(X6,nil)),X8) )
      | ( sk4 != app(app(cons(X6,nil),cons(X7,nil)),X8) )
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6) ),
    inference(definition_unfolding,[],[f195,f191,f190]) ).

tff(f195,axiom,
    ! [X8: $i,X6: $i,X7: $i] :
      ( ssList(sk13)
      | ( sk1 != app(app(cons(X7,nil),cons(X6,nil)),X8) )
      | ( sk2 != app(app(cons(X6,nil),cons(X7,nil)),X8) )
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6) ),
    file('/export/starexec/sandbox/tmp/tmp.lyhpdBWSpE/Vampire---4.8_1401',co1_10) ).

tff(f330,plain,
    ( spl1_1
    | spl1_4 ),
    inference(avatar_split_clause,[],[f267,f327,f315]) ).

tff(f267,plain,
    ! [X8: $i,X6: $i,X7: $i] :
      ( ssItem(sk12)
      | ~ sQ0_eqProxy($i,sk3,app(app(cons(X7,nil),cons(X6,nil)),X8))
      | ~ sQ0_eqProxy($i,sk4,app(app(cons(X6,nil),cons(X7,nil)),X8))
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6) ),
    inference(equality_proxy_replacement,[],[f246,f264]) ).

tff(f246,plain,
    ! [X8: $i,X6: $i,X7: $i] :
      ( ssItem(sk12)
      | ( sk3 != app(app(cons(X7,nil),cons(X6,nil)),X8) )
      | ( sk4 != app(app(cons(X6,nil),cons(X7,nil)),X8) )
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6) ),
    inference(definition_unfolding,[],[f194,f191,f190]) ).

tff(f194,axiom,
    ! [X8: $i,X6: $i,X7: $i] :
      ( ssItem(sk12)
      | ( sk1 != app(app(cons(X7,nil),cons(X6,nil)),X8) )
      | ( sk2 != app(app(cons(X6,nil),cons(X7,nil)),X8) )
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6) ),
    file('/export/starexec/sandbox/tmp/tmp.lyhpdBWSpE/Vampire---4.8_1401',co1_9) ).

tff(f325,plain,
    ( spl1_1
    | spl1_3 ),
    inference(avatar_split_clause,[],[f266,f322,f315]) ).

tff(f266,plain,
    ! [X8: $i,X6: $i,X7: $i] :
      ( ssItem(sk11)
      | ~ sQ0_eqProxy($i,sk3,app(app(cons(X7,nil),cons(X6,nil)),X8))
      | ~ sQ0_eqProxy($i,sk4,app(app(cons(X6,nil),cons(X7,nil)),X8))
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6) ),
    inference(equality_proxy_replacement,[],[f245,f264]) ).

tff(f245,plain,
    ! [X8: $i,X6: $i,X7: $i] :
      ( ssItem(sk11)
      | ( sk3 != app(app(cons(X7,nil),cons(X6,nil)),X8) )
      | ( sk4 != app(app(cons(X6,nil),cons(X7,nil)),X8) )
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6) ),
    inference(definition_unfolding,[],[f193,f191,f190]) ).

tff(f193,axiom,
    ! [X8: $i,X6: $i,X7: $i] :
      ( ssItem(sk11)
      | ( sk1 != app(app(cons(X7,nil),cons(X6,nil)),X8) )
      | ( sk2 != app(app(cons(X6,nil),cons(X7,nil)),X8) )
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6) ),
    file('/export/starexec/sandbox/tmp/tmp.lyhpdBWSpE/Vampire---4.8_1401',co1_8) ).

tff(f320,plain,
    ( spl1_1
    | spl1_2 ),
    inference(avatar_split_clause,[],[f265,f318,f315]) ).

tff(f265,plain,
    ! [X10: $i,X11: $i,X8: $i,X6: $i,X9: $i,X7: $i] :
      ( ~ sQ0_eqProxy($i,sk4,app(app(cons(X9,nil),cons(X10,nil)),X11))
      | ~ ssList(X11)
      | ~ ssItem(X10)
      | ~ ssItem(X9)
      | ~ sQ0_eqProxy($i,sk3,app(app(cons(X7,nil),cons(X6,nil)),X8))
      | ~ sQ0_eqProxy($i,sk4,app(app(cons(X6,nil),cons(X7,nil)),X8))
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6) ),
    inference(equality_proxy_replacement,[],[f244,f264]) ).

tff(f244,plain,
    ! [X10: $i,X11: $i,X8: $i,X6: $i,X9: $i,X7: $i] :
      ( ( sk4 != app(app(cons(X9,nil),cons(X10,nil)),X11) )
      | ~ ssList(X11)
      | ~ ssItem(X10)
      | ~ ssItem(X9)
      | ( sk3 != app(app(cons(X7,nil),cons(X6,nil)),X8) )
      | ( sk4 != app(app(cons(X6,nil),cons(X7,nil)),X8) )
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6) ),
    inference(definition_unfolding,[],[f192,f191,f190]) ).

tff(f192,axiom,
    ! [X10: $i,X11: $i,X8: $i,X6: $i,X9: $i,X7: $i] :
      ( ( sk4 != app(app(cons(X9,nil),cons(X10,nil)),X11) )
      | ~ ssList(X11)
      | ~ ssItem(X10)
      | ~ ssItem(X9)
      | ( sk1 != app(app(cons(X7,nil),cons(X6,nil)),X8) )
      | ( sk2 != app(app(cons(X6,nil),cons(X7,nil)),X8) )
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6) ),
    file('/export/starexec/sandbox/tmp/tmp.lyhpdBWSpE/Vampire---4.8_1401',co1_7) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : SWC413-1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.15  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.36  % Computer : n016.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 20:33:53 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.15/0.37  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.lyhpdBWSpE/Vampire---4.8_1401
% 0.58/0.75  % (1660)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2996ds/34Mi)
% 0.58/0.75  % (1663)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2996ds/33Mi)
% 0.58/0.75  % (1662)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.58/0.75  % (1664)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2996ds/34Mi)
% 0.58/0.75  % (1665)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/45Mi)
% 0.58/0.75  % (1666)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2996ds/83Mi)
% 0.58/0.75  % (1661)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2996ds/51Mi)
% 0.58/0.75  % (1667)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2996ds/56Mi)
% 0.58/0.75  % (1660)First to succeed.
% 0.58/0.75  % (1660)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1650"
% 0.58/0.75  % (1667)Also succeeded, but the first one will report.
% 0.58/0.75  % (1660)Refutation found. Thanks to Tanya!
% 0.58/0.75  % SZS status Unsatisfiable for Vampire---4
% 0.58/0.75  % SZS output start Proof for Vampire---4
% See solution above
% 0.58/0.75  % (1660)------------------------------
% 0.58/0.75  % (1660)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.75  % (1660)Termination reason: Refutation
% 0.58/0.75  
% 0.58/0.75  % (1660)Memory used [KB]: 1242
% 0.58/0.75  % (1660)Time elapsed: 0.005 s
% 0.58/0.75  % (1660)Instructions burned: 12 (million)
% 0.58/0.75  % (1650)Success in time 0.381 s
% 0.58/0.75  % Vampire---4.8 exiting
%------------------------------------------------------------------------------