TSTP Solution File: SYO500_8.008 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SYO500_8.008 : TPTP v8.1.2. Released v8.0.0.
% 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 : n012.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 12:21:56 EDT 2024

% Result   : Theorem 0.55s 0.74s
% Output   : Refutation 0.55s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   57
% Syntax   : Number of formulae    :  317 (   3 unt;   8 typ;   0 def)
%            Number of atoms       : 1147 (   2 equ)
%            Maximal formula atoms :    3 (   3 avg)
%            Number of connectives :  948 ( 386   ~; 512   |;   0   &)
%                                         (  49 <=>;   0  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    4 (   4 avg)
%            Maximal term depth    :    0 (   0 avg)
%            Number of FOOLs       :  276 ( 276 fml;   0 var)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   91 (  88 usr;  82 prp; 0-2 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :    0 (   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(pred_def_2,type,
    f0: $o > $o ).

tff(pred_def_3,type,
    f1: $o > $o ).

tff(pred_def_4,type,
    f2: $o > $o ).

tff(pred_def_5,type,
    f3: $o > $o ).

tff(pred_def_6,type,
    f4: $o > $o ).

tff(pred_def_7,type,
    f5: $o > $o ).

tff(pred_def_8,type,
    f6: $o > $o ).

tff(pred_def_9,type,
    f7: $o > $o ).

tff(f453,plain,
    $false,
    inference(avatar_sat_refutation,[],[f145,f150,f151,f152,f157,f158,f159,f160,f165,f166,f167,f168,f177,f182,f183,f184,f189,f190,f191,f192,f197,f198,f199,f200,f205,f206,f207,f208,f213,f214,f215,f216,f225,f230,f231,f232,f237,f238,f239,f240,f245,f246,f247,f248,f257,f262,f263,f264,f269,f270,f271,f272,f277,f278,f279,f280,f285,f286,f287,f288,f293,f294,f295,f296,f305,f310,f311,f312,f317,f318,f319,f320,f325,f326,f327,f328,f337,f342,f343,f344,f349,f350,f351,f352,f357,f358,f359,f360,f365,f366,f367,f368,f373,f374,f375,f376,f385,f390,f391,f392,f397,f398,f399,f400,f405,f406,f407,f408,f417,f422,f423,f424,f429,f430,f431,f432,f437,f438,f439,f440,f445,f446,f447,f448,f449,f450,f451,f452]) ).

tff(f452,plain,
    ( spl31_47
    | ~ spl31_45
    | ~ spl31_48 ),
    inference(avatar_split_clause,[],[f5,f442,f419,f434]) ).

tff(f434,plain,
    ( spl31_47
  <=> sP30 ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_47])]) ).

tff(f419,plain,
    ( spl31_45
  <=> f7($true) ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_45])]) ).

tff(f442,plain,
    ( spl31_48
  <=> x ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_48])]) ).

tff(f5,plain,
    ( ~ x
    | ~ f7($true)
    | sP30 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f4,plain,
    ( f0(f0(f0(f1(f2(f2(f2(f3(f4(f4(f4(f5(f6(f6(f6(f7(x))))))))))))))))
  <~> f0(f1(f1(f1(f2(f3(f3(f3(f4(f5(f5(f5(f6(f7(f7(f7(x)))))))))))))))) ),
    inference(ennf_transformation,[],[f3]) ).

tff(f3,plain,
    ~ ( f0(f0(f0(f1(f2(f2(f2(f3(f4(f4(f4(f5(f6(f6(f6(f7(x))))))))))))))))
    <=> f0(f1(f1(f1(f2(f3(f3(f3(f4(f5(f5(f5(f6(f7(f7(f7(x)))))))))))))))) ),
    inference(flattening,[],[f2]) ).

tff(f2,negated_conjecture,
    f0(f0(f0(f1(f2(f2(f2(f3(f4(f4(f4(f5(f6(f6(f6(f7(x)))))))))))))))) != f0(f1(f1(f1(f2(f3(f3(f3(f4(f5(f5(f5(f6(f7(f7(f7(x)))))))))))))))),
    inference(negated_conjecture,[],[f1]) ).

tff(f1,conjecture,
    f0(f0(f0(f1(f2(f2(f2(f3(f4(f4(f4(f5(f6(f6(f6(f7(x)))))))))))))))) = f0(f1(f1(f1(f2(f3(f3(f3(f4(f5(f5(f5(f6(f7(f7(f7(x)))))))))))))))),
    file('/export/starexec/sandbox/tmp/tmp.FKr2wfVR2W/Vampire---4.8_29241',kaminski8) ).

tff(f451,plain,
    ( spl31_47
    | ~ spl31_43
    | spl31_48 ),
    inference(avatar_split_clause,[],[f6,f442,f410,f434]) ).

tff(f410,plain,
    ( spl31_43
  <=> f7($false) ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_43])]) ).

tff(f6,plain,
    ( x
    | ~ f7($false)
    | sP30 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f450,plain,
    ( ~ spl31_47
    | spl31_45
    | ~ spl31_48 ),
    inference(avatar_split_clause,[],[f7,f442,f419,f434]) ).

tff(f7,plain,
    ( ~ x
    | f7($true)
    | ~ sP30 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f449,plain,
    ( ~ spl31_47
    | spl31_43
    | spl31_48 ),
    inference(avatar_split_clause,[],[f8,f442,f410,f434]) ).

tff(f8,plain,
    ( x
    | f7($false)
    | ~ sP30 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f448,plain,
    ( spl31_46
    | ~ spl31_45
    | ~ spl31_48 ),
    inference(avatar_split_clause,[],[f9,f442,f419,f426]) ).

tff(f426,plain,
    ( spl31_46
  <=> sP29 ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_46])]) ).

tff(f9,plain,
    ( ~ x
    | ~ f7($true)
    | sP29 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f447,plain,
    ( spl31_46
    | ~ spl31_43
    | spl31_48 ),
    inference(avatar_split_clause,[],[f10,f442,f410,f426]) ).

tff(f10,plain,
    ( x
    | ~ f7($false)
    | sP29 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f446,plain,
    ( ~ spl31_46
    | spl31_45
    | ~ spl31_48 ),
    inference(avatar_split_clause,[],[f11,f442,f419,f426]) ).

tff(f11,plain,
    ( ~ x
    | f7($true)
    | ~ sP29 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f445,plain,
    ( ~ spl31_46
    | spl31_43
    | spl31_48 ),
    inference(avatar_split_clause,[],[f12,f442,f410,f426]) ).

tff(f12,plain,
    ( x
    | f7($false)
    | ~ sP29 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f440,plain,
    ( spl31_44
    | ~ spl31_45
    | ~ spl31_47 ),
    inference(avatar_split_clause,[],[f13,f434,f419,f414]) ).

tff(f414,plain,
    ( spl31_44
  <=> sP28 ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_44])]) ).

tff(f13,plain,
    ( ~ sP30
    | ~ f7($true)
    | sP28 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f439,plain,
    ( spl31_44
    | ~ spl31_43
    | spl31_47 ),
    inference(avatar_split_clause,[],[f14,f434,f410,f414]) ).

tff(f14,plain,
    ( sP30
    | ~ f7($false)
    | sP28 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f438,plain,
    ( ~ spl31_44
    | spl31_45
    | ~ spl31_47 ),
    inference(avatar_split_clause,[],[f15,f434,f419,f414]) ).

tff(f15,plain,
    ( ~ sP30
    | f7($true)
    | ~ sP28 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f437,plain,
    ( ~ spl31_44
    | spl31_43
    | spl31_47 ),
    inference(avatar_split_clause,[],[f16,f434,f410,f414]) ).

tff(f16,plain,
    ( sP30
    | f7($false)
    | ~ sP28 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f432,plain,
    ( spl31_42
    | ~ spl31_40
    | ~ spl31_46 ),
    inference(avatar_split_clause,[],[f17,f426,f387,f402]) ).

tff(f402,plain,
    ( spl31_42
  <=> sP27 ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_42])]) ).

tff(f387,plain,
    ( spl31_40
  <=> f6($true) ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_40])]) ).

tff(f17,plain,
    ( ~ sP29
    | ~ f6($true)
    | sP27 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f431,plain,
    ( spl31_42
    | ~ spl31_38
    | spl31_46 ),
    inference(avatar_split_clause,[],[f18,f426,f378,f402]) ).

tff(f378,plain,
    ( spl31_38
  <=> f6($false) ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_38])]) ).

tff(f18,plain,
    ( sP29
    | ~ f6($false)
    | sP27 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f430,plain,
    ( ~ spl31_42
    | spl31_40
    | ~ spl31_46 ),
    inference(avatar_split_clause,[],[f19,f426,f387,f402]) ).

tff(f19,plain,
    ( ~ sP29
    | f6($true)
    | ~ sP27 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f429,plain,
    ( ~ spl31_42
    | spl31_38
    | spl31_46 ),
    inference(avatar_split_clause,[],[f20,f426,f378,f402]) ).

tff(f20,plain,
    ( sP29
    | f6($false)
    | ~ sP27 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f424,plain,
    ( spl31_41
    | ~ spl31_45
    | ~ spl31_44 ),
    inference(avatar_split_clause,[],[f21,f414,f419,f394]) ).

tff(f394,plain,
    ( spl31_41
  <=> sP26 ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_41])]) ).

tff(f21,plain,
    ( ~ sP28
    | ~ f7($true)
    | sP26 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f423,plain,
    ( spl31_41
    | ~ spl31_43
    | spl31_44 ),
    inference(avatar_split_clause,[],[f22,f414,f410,f394]) ).

tff(f22,plain,
    ( sP28
    | ~ f7($false)
    | sP26 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f422,plain,
    ( ~ spl31_41
    | spl31_45
    | ~ spl31_44 ),
    inference(avatar_split_clause,[],[f23,f414,f419,f394]) ).

tff(f23,plain,
    ( ~ sP28
    | f7($true)
    | ~ sP26 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f417,plain,
    ( ~ spl31_41
    | spl31_43
    | spl31_44 ),
    inference(avatar_split_clause,[],[f24,f414,f410,f394]) ).

tff(f24,plain,
    ( sP28
    | f7($false)
    | ~ sP26 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f408,plain,
    ( spl31_39
    | ~ spl31_40
    | ~ spl31_42 ),
    inference(avatar_split_clause,[],[f25,f402,f387,f382]) ).

tff(f382,plain,
    ( spl31_39
  <=> sP25 ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_39])]) ).

tff(f25,plain,
    ( ~ sP27
    | ~ f6($true)
    | sP25 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f407,plain,
    ( spl31_39
    | ~ spl31_38
    | spl31_42 ),
    inference(avatar_split_clause,[],[f26,f402,f378,f382]) ).

tff(f26,plain,
    ( sP27
    | ~ f6($false)
    | sP25 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f406,plain,
    ( ~ spl31_39
    | spl31_40
    | ~ spl31_42 ),
    inference(avatar_split_clause,[],[f27,f402,f387,f382]) ).

tff(f27,plain,
    ( ~ sP27
    | f6($true)
    | ~ sP25 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f405,plain,
    ( ~ spl31_39
    | spl31_38
    | spl31_42 ),
    inference(avatar_split_clause,[],[f28,f402,f378,f382]) ).

tff(f28,plain,
    ( sP27
    | f6($false)
    | ~ sP25 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f400,plain,
    ( spl31_37
    | ~ spl31_40
    | ~ spl31_41 ),
    inference(avatar_split_clause,[],[f29,f394,f387,f370]) ).

tff(f370,plain,
    ( spl31_37
  <=> sP24 ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_37])]) ).

tff(f29,plain,
    ( ~ sP26
    | ~ f6($true)
    | sP24 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f399,plain,
    ( spl31_37
    | ~ spl31_38
    | spl31_41 ),
    inference(avatar_split_clause,[],[f30,f394,f378,f370]) ).

tff(f30,plain,
    ( sP26
    | ~ f6($false)
    | sP24 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f398,plain,
    ( ~ spl31_37
    | spl31_40
    | ~ spl31_41 ),
    inference(avatar_split_clause,[],[f31,f394,f387,f370]) ).

tff(f31,plain,
    ( ~ sP26
    | f6($true)
    | ~ sP24 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f397,plain,
    ( ~ spl31_37
    | spl31_38
    | spl31_41 ),
    inference(avatar_split_clause,[],[f32,f394,f378,f370]) ).

tff(f32,plain,
    ( sP26
    | f6($false)
    | ~ sP24 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f392,plain,
    ( spl31_36
    | ~ spl31_40
    | ~ spl31_39 ),
    inference(avatar_split_clause,[],[f33,f382,f387,f362]) ).

tff(f362,plain,
    ( spl31_36
  <=> sP23 ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_36])]) ).

tff(f33,plain,
    ( ~ sP25
    | ~ f6($true)
    | sP23 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f391,plain,
    ( spl31_36
    | ~ spl31_38
    | spl31_39 ),
    inference(avatar_split_clause,[],[f34,f382,f378,f362]) ).

tff(f34,plain,
    ( sP25
    | ~ f6($false)
    | sP23 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f390,plain,
    ( ~ spl31_36
    | spl31_40
    | ~ spl31_39 ),
    inference(avatar_split_clause,[],[f35,f382,f387,f362]) ).

tff(f35,plain,
    ( ~ sP25
    | f6($true)
    | ~ sP23 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f385,plain,
    ( ~ spl31_36
    | spl31_38
    | spl31_39 ),
    inference(avatar_split_clause,[],[f36,f382,f378,f362]) ).

tff(f36,plain,
    ( sP25
    | f6($false)
    | ~ sP23 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f376,plain,
    ( spl31_35
    | ~ spl31_33
    | ~ spl31_37 ),
    inference(avatar_split_clause,[],[f37,f370,f339,f354]) ).

tff(f354,plain,
    ( spl31_35
  <=> sP22 ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_35])]) ).

tff(f339,plain,
    ( spl31_33
  <=> f5($true) ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_33])]) ).

tff(f37,plain,
    ( ~ sP24
    | ~ f5($true)
    | sP22 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f375,plain,
    ( spl31_35
    | ~ spl31_31
    | spl31_37 ),
    inference(avatar_split_clause,[],[f38,f370,f330,f354]) ).

tff(f330,plain,
    ( spl31_31
  <=> f5($false) ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_31])]) ).

tff(f38,plain,
    ( sP24
    | ~ f5($false)
    | sP22 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f374,plain,
    ( ~ spl31_35
    | spl31_33
    | ~ spl31_37 ),
    inference(avatar_split_clause,[],[f39,f370,f339,f354]) ).

tff(f39,plain,
    ( ~ sP24
    | f5($true)
    | ~ sP22 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f373,plain,
    ( ~ spl31_35
    | spl31_31
    | spl31_37 ),
    inference(avatar_split_clause,[],[f40,f370,f330,f354]) ).

tff(f40,plain,
    ( sP24
    | f5($false)
    | ~ sP22 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f368,plain,
    ( spl31_34
    | ~ spl31_33
    | ~ spl31_36 ),
    inference(avatar_split_clause,[],[f41,f362,f339,f346]) ).

tff(f346,plain,
    ( spl31_34
  <=> sP21 ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_34])]) ).

tff(f41,plain,
    ( ~ sP23
    | ~ f5($true)
    | sP21 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f367,plain,
    ( spl31_34
    | ~ spl31_31
    | spl31_36 ),
    inference(avatar_split_clause,[],[f42,f362,f330,f346]) ).

tff(f42,plain,
    ( sP23
    | ~ f5($false)
    | sP21 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f366,plain,
    ( ~ spl31_34
    | spl31_33
    | ~ spl31_36 ),
    inference(avatar_split_clause,[],[f43,f362,f339,f346]) ).

tff(f43,plain,
    ( ~ sP23
    | f5($true)
    | ~ sP21 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f365,plain,
    ( ~ spl31_34
    | spl31_31
    | spl31_36 ),
    inference(avatar_split_clause,[],[f44,f362,f330,f346]) ).

tff(f44,plain,
    ( sP23
    | f5($false)
    | ~ sP21 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f360,plain,
    ( spl31_32
    | ~ spl31_33
    | ~ spl31_35 ),
    inference(avatar_split_clause,[],[f45,f354,f339,f334]) ).

tff(f334,plain,
    ( spl31_32
  <=> sP20 ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_32])]) ).

tff(f45,plain,
    ( ~ sP22
    | ~ f5($true)
    | sP20 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f359,plain,
    ( spl31_32
    | ~ spl31_31
    | spl31_35 ),
    inference(avatar_split_clause,[],[f46,f354,f330,f334]) ).

tff(f46,plain,
    ( sP22
    | ~ f5($false)
    | sP20 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f358,plain,
    ( ~ spl31_32
    | spl31_33
    | ~ spl31_35 ),
    inference(avatar_split_clause,[],[f47,f354,f339,f334]) ).

tff(f47,plain,
    ( ~ sP22
    | f5($true)
    | ~ sP20 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f357,plain,
    ( ~ spl31_32
    | spl31_31
    | spl31_35 ),
    inference(avatar_split_clause,[],[f48,f354,f330,f334]) ).

tff(f48,plain,
    ( sP22
    | f5($false)
    | ~ sP20 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f352,plain,
    ( spl31_30
    | ~ spl31_28
    | ~ spl31_34 ),
    inference(avatar_split_clause,[],[f49,f346,f307,f322]) ).

tff(f322,plain,
    ( spl31_30
  <=> sP19 ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_30])]) ).

tff(f307,plain,
    ( spl31_28
  <=> f4($true) ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_28])]) ).

tff(f49,plain,
    ( ~ sP21
    | ~ f4($true)
    | sP19 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f351,plain,
    ( spl31_30
    | ~ spl31_26
    | spl31_34 ),
    inference(avatar_split_clause,[],[f50,f346,f298,f322]) ).

tff(f298,plain,
    ( spl31_26
  <=> f4($false) ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_26])]) ).

tff(f50,plain,
    ( sP21
    | ~ f4($false)
    | sP19 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f350,plain,
    ( ~ spl31_30
    | spl31_28
    | ~ spl31_34 ),
    inference(avatar_split_clause,[],[f51,f346,f307,f322]) ).

tff(f51,plain,
    ( ~ sP21
    | f4($true)
    | ~ sP19 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f349,plain,
    ( ~ spl31_30
    | spl31_26
    | spl31_34 ),
    inference(avatar_split_clause,[],[f52,f346,f298,f322]) ).

tff(f52,plain,
    ( sP21
    | f4($false)
    | ~ sP19 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f344,plain,
    ( spl31_29
    | ~ spl31_33
    | ~ spl31_32 ),
    inference(avatar_split_clause,[],[f53,f334,f339,f314]) ).

tff(f314,plain,
    ( spl31_29
  <=> sP18 ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_29])]) ).

tff(f53,plain,
    ( ~ sP20
    | ~ f5($true)
    | sP18 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f343,plain,
    ( spl31_29
    | ~ spl31_31
    | spl31_32 ),
    inference(avatar_split_clause,[],[f54,f334,f330,f314]) ).

tff(f54,plain,
    ( sP20
    | ~ f5($false)
    | sP18 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f342,plain,
    ( ~ spl31_29
    | spl31_33
    | ~ spl31_32 ),
    inference(avatar_split_clause,[],[f55,f334,f339,f314]) ).

tff(f55,plain,
    ( ~ sP20
    | f5($true)
    | ~ sP18 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f337,plain,
    ( ~ spl31_29
    | spl31_31
    | spl31_32 ),
    inference(avatar_split_clause,[],[f56,f334,f330,f314]) ).

tff(f56,plain,
    ( sP20
    | f5($false)
    | ~ sP18 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f328,plain,
    ( spl31_27
    | ~ spl31_28
    | ~ spl31_30 ),
    inference(avatar_split_clause,[],[f57,f322,f307,f302]) ).

tff(f302,plain,
    ( spl31_27
  <=> sP17 ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_27])]) ).

tff(f57,plain,
    ( ~ sP19
    | ~ f4($true)
    | sP17 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f327,plain,
    ( spl31_27
    | ~ spl31_26
    | spl31_30 ),
    inference(avatar_split_clause,[],[f58,f322,f298,f302]) ).

tff(f58,plain,
    ( sP19
    | ~ f4($false)
    | sP17 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f326,plain,
    ( ~ spl31_27
    | spl31_28
    | ~ spl31_30 ),
    inference(avatar_split_clause,[],[f59,f322,f307,f302]) ).

tff(f59,plain,
    ( ~ sP19
    | f4($true)
    | ~ sP17 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f325,plain,
    ( ~ spl31_27
    | spl31_26
    | spl31_30 ),
    inference(avatar_split_clause,[],[f60,f322,f298,f302]) ).

tff(f60,plain,
    ( sP19
    | f4($false)
    | ~ sP17 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f320,plain,
    ( spl31_25
    | ~ spl31_28
    | ~ spl31_29 ),
    inference(avatar_split_clause,[],[f61,f314,f307,f290]) ).

tff(f290,plain,
    ( spl31_25
  <=> sP16 ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_25])]) ).

tff(f61,plain,
    ( ~ sP18
    | ~ f4($true)
    | sP16 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f319,plain,
    ( spl31_25
    | ~ spl31_26
    | spl31_29 ),
    inference(avatar_split_clause,[],[f62,f314,f298,f290]) ).

tff(f62,plain,
    ( sP18
    | ~ f4($false)
    | sP16 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f318,plain,
    ( ~ spl31_25
    | spl31_28
    | ~ spl31_29 ),
    inference(avatar_split_clause,[],[f63,f314,f307,f290]) ).

tff(f63,plain,
    ( ~ sP18
    | f4($true)
    | ~ sP16 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f317,plain,
    ( ~ spl31_25
    | spl31_26
    | spl31_29 ),
    inference(avatar_split_clause,[],[f64,f314,f298,f290]) ).

tff(f64,plain,
    ( sP18
    | f4($false)
    | ~ sP16 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f312,plain,
    ( spl31_24
    | ~ spl31_28
    | ~ spl31_27 ),
    inference(avatar_split_clause,[],[f65,f302,f307,f282]) ).

tff(f282,plain,
    ( spl31_24
  <=> sP15 ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_24])]) ).

tff(f65,plain,
    ( ~ sP17
    | ~ f4($true)
    | sP15 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f311,plain,
    ( spl31_24
    | ~ spl31_26
    | spl31_27 ),
    inference(avatar_split_clause,[],[f66,f302,f298,f282]) ).

tff(f66,plain,
    ( sP17
    | ~ f4($false)
    | sP15 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f310,plain,
    ( ~ spl31_24
    | spl31_28
    | ~ spl31_27 ),
    inference(avatar_split_clause,[],[f67,f302,f307,f282]) ).

tff(f67,plain,
    ( ~ sP17
    | f4($true)
    | ~ sP15 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f305,plain,
    ( ~ spl31_24
    | spl31_26
    | spl31_27 ),
    inference(avatar_split_clause,[],[f68,f302,f298,f282]) ).

tff(f68,plain,
    ( sP17
    | f4($false)
    | ~ sP15 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f296,plain,
    ( spl31_23
    | ~ spl31_21
    | ~ spl31_25 ),
    inference(avatar_split_clause,[],[f69,f290,f259,f274]) ).

tff(f274,plain,
    ( spl31_23
  <=> sP14 ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_23])]) ).

tff(f259,plain,
    ( spl31_21
  <=> f3($true) ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_21])]) ).

tff(f69,plain,
    ( ~ sP16
    | ~ f3($true)
    | sP14 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f295,plain,
    ( spl31_23
    | ~ spl31_19
    | spl31_25 ),
    inference(avatar_split_clause,[],[f70,f290,f250,f274]) ).

tff(f250,plain,
    ( spl31_19
  <=> f3($false) ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_19])]) ).

tff(f70,plain,
    ( sP16
    | ~ f3($false)
    | sP14 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f294,plain,
    ( ~ spl31_23
    | spl31_21
    | ~ spl31_25 ),
    inference(avatar_split_clause,[],[f71,f290,f259,f274]) ).

tff(f71,plain,
    ( ~ sP16
    | f3($true)
    | ~ sP14 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f293,plain,
    ( ~ spl31_23
    | spl31_19
    | spl31_25 ),
    inference(avatar_split_clause,[],[f72,f290,f250,f274]) ).

tff(f72,plain,
    ( sP16
    | f3($false)
    | ~ sP14 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f288,plain,
    ( spl31_22
    | ~ spl31_21
    | ~ spl31_24 ),
    inference(avatar_split_clause,[],[f73,f282,f259,f266]) ).

tff(f266,plain,
    ( spl31_22
  <=> sP13 ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_22])]) ).

tff(f73,plain,
    ( ~ sP15
    | ~ f3($true)
    | sP13 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f287,plain,
    ( spl31_22
    | ~ spl31_19
    | spl31_24 ),
    inference(avatar_split_clause,[],[f74,f282,f250,f266]) ).

tff(f74,plain,
    ( sP15
    | ~ f3($false)
    | sP13 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f286,plain,
    ( ~ spl31_22
    | spl31_21
    | ~ spl31_24 ),
    inference(avatar_split_clause,[],[f75,f282,f259,f266]) ).

tff(f75,plain,
    ( ~ sP15
    | f3($true)
    | ~ sP13 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f285,plain,
    ( ~ spl31_22
    | spl31_19
    | spl31_24 ),
    inference(avatar_split_clause,[],[f76,f282,f250,f266]) ).

tff(f76,plain,
    ( sP15
    | f3($false)
    | ~ sP13 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f280,plain,
    ( spl31_20
    | ~ spl31_21
    | ~ spl31_23 ),
    inference(avatar_split_clause,[],[f77,f274,f259,f254]) ).

tff(f254,plain,
    ( spl31_20
  <=> sP12 ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_20])]) ).

tff(f77,plain,
    ( ~ sP14
    | ~ f3($true)
    | sP12 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f279,plain,
    ( spl31_20
    | ~ spl31_19
    | spl31_23 ),
    inference(avatar_split_clause,[],[f78,f274,f250,f254]) ).

tff(f78,plain,
    ( sP14
    | ~ f3($false)
    | sP12 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f278,plain,
    ( ~ spl31_20
    | spl31_21
    | ~ spl31_23 ),
    inference(avatar_split_clause,[],[f79,f274,f259,f254]) ).

tff(f79,plain,
    ( ~ sP14
    | f3($true)
    | ~ sP12 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f277,plain,
    ( ~ spl31_20
    | spl31_19
    | spl31_23 ),
    inference(avatar_split_clause,[],[f80,f274,f250,f254]) ).

tff(f80,plain,
    ( sP14
    | f3($false)
    | ~ sP12 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f272,plain,
    ( spl31_18
    | ~ spl31_16
    | ~ spl31_22 ),
    inference(avatar_split_clause,[],[f81,f266,f227,f242]) ).

tff(f242,plain,
    ( spl31_18
  <=> sP11 ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_18])]) ).

tff(f227,plain,
    ( spl31_16
  <=> f2($true) ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_16])]) ).

tff(f81,plain,
    ( ~ sP13
    | ~ f2($true)
    | sP11 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f271,plain,
    ( spl31_18
    | ~ spl31_14
    | spl31_22 ),
    inference(avatar_split_clause,[],[f82,f266,f218,f242]) ).

tff(f218,plain,
    ( spl31_14
  <=> f2($false) ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_14])]) ).

tff(f82,plain,
    ( sP13
    | ~ f2($false)
    | sP11 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f270,plain,
    ( ~ spl31_18
    | spl31_16
    | ~ spl31_22 ),
    inference(avatar_split_clause,[],[f83,f266,f227,f242]) ).

tff(f83,plain,
    ( ~ sP13
    | f2($true)
    | ~ sP11 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f269,plain,
    ( ~ spl31_18
    | spl31_14
    | spl31_22 ),
    inference(avatar_split_clause,[],[f84,f266,f218,f242]) ).

tff(f84,plain,
    ( sP13
    | f2($false)
    | ~ sP11 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f264,plain,
    ( spl31_17
    | ~ spl31_21
    | ~ spl31_20 ),
    inference(avatar_split_clause,[],[f85,f254,f259,f234]) ).

tff(f234,plain,
    ( spl31_17
  <=> sP10 ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_17])]) ).

tff(f85,plain,
    ( ~ sP12
    | ~ f3($true)
    | sP10 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f263,plain,
    ( spl31_17
    | ~ spl31_19
    | spl31_20 ),
    inference(avatar_split_clause,[],[f86,f254,f250,f234]) ).

tff(f86,plain,
    ( sP12
    | ~ f3($false)
    | sP10 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f262,plain,
    ( ~ spl31_17
    | spl31_21
    | ~ spl31_20 ),
    inference(avatar_split_clause,[],[f87,f254,f259,f234]) ).

tff(f87,plain,
    ( ~ sP12
    | f3($true)
    | ~ sP10 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f257,plain,
    ( ~ spl31_17
    | spl31_19
    | spl31_20 ),
    inference(avatar_split_clause,[],[f88,f254,f250,f234]) ).

tff(f88,plain,
    ( sP12
    | f3($false)
    | ~ sP10 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f248,plain,
    ( spl31_15
    | ~ spl31_16
    | ~ spl31_18 ),
    inference(avatar_split_clause,[],[f89,f242,f227,f222]) ).

tff(f222,plain,
    ( spl31_15
  <=> sP9 ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_15])]) ).

tff(f89,plain,
    ( ~ sP11
    | ~ f2($true)
    | sP9 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f247,plain,
    ( spl31_15
    | ~ spl31_14
    | spl31_18 ),
    inference(avatar_split_clause,[],[f90,f242,f218,f222]) ).

tff(f90,plain,
    ( sP11
    | ~ f2($false)
    | sP9 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f246,plain,
    ( ~ spl31_15
    | spl31_16
    | ~ spl31_18 ),
    inference(avatar_split_clause,[],[f91,f242,f227,f222]) ).

tff(f91,plain,
    ( ~ sP11
    | f2($true)
    | ~ sP9 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f245,plain,
    ( ~ spl31_15
    | spl31_14
    | spl31_18 ),
    inference(avatar_split_clause,[],[f92,f242,f218,f222]) ).

tff(f92,plain,
    ( sP11
    | f2($false)
    | ~ sP9 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f240,plain,
    ( spl31_13
    | ~ spl31_16
    | ~ spl31_17 ),
    inference(avatar_split_clause,[],[f93,f234,f227,f210]) ).

tff(f210,plain,
    ( spl31_13
  <=> sP8 ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_13])]) ).

tff(f93,plain,
    ( ~ sP10
    | ~ f2($true)
    | sP8 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f239,plain,
    ( spl31_13
    | ~ spl31_14
    | spl31_17 ),
    inference(avatar_split_clause,[],[f94,f234,f218,f210]) ).

tff(f94,plain,
    ( sP10
    | ~ f2($false)
    | sP8 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f238,plain,
    ( ~ spl31_13
    | spl31_16
    | ~ spl31_17 ),
    inference(avatar_split_clause,[],[f95,f234,f227,f210]) ).

tff(f95,plain,
    ( ~ sP10
    | f2($true)
    | ~ sP8 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f237,plain,
    ( ~ spl31_13
    | spl31_14
    | spl31_17 ),
    inference(avatar_split_clause,[],[f96,f234,f218,f210]) ).

tff(f96,plain,
    ( sP10
    | f2($false)
    | ~ sP8 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f232,plain,
    ( spl31_12
    | ~ spl31_16
    | ~ spl31_15 ),
    inference(avatar_split_clause,[],[f97,f222,f227,f202]) ).

tff(f202,plain,
    ( spl31_12
  <=> sP7 ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_12])]) ).

tff(f97,plain,
    ( ~ sP9
    | ~ f2($true)
    | sP7 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f231,plain,
    ( spl31_12
    | ~ spl31_14
    | spl31_15 ),
    inference(avatar_split_clause,[],[f98,f222,f218,f202]) ).

tff(f98,plain,
    ( sP9
    | ~ f2($false)
    | sP7 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f230,plain,
    ( ~ spl31_12
    | spl31_16
    | ~ spl31_15 ),
    inference(avatar_split_clause,[],[f99,f222,f227,f202]) ).

tff(f99,plain,
    ( ~ sP9
    | f2($true)
    | ~ sP7 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f225,plain,
    ( ~ spl31_12
    | spl31_14
    | spl31_15 ),
    inference(avatar_split_clause,[],[f100,f222,f218,f202]) ).

tff(f100,plain,
    ( sP9
    | f2($false)
    | ~ sP7 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f216,plain,
    ( spl31_11
    | ~ spl31_9
    | ~ spl31_13 ),
    inference(avatar_split_clause,[],[f101,f210,f179,f194]) ).

tff(f194,plain,
    ( spl31_11
  <=> sP6 ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_11])]) ).

tff(f179,plain,
    ( spl31_9
  <=> f1($true) ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_9])]) ).

tff(f101,plain,
    ( ~ sP8
    | ~ f1($true)
    | sP6 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f215,plain,
    ( spl31_11
    | ~ spl31_7
    | spl31_13 ),
    inference(avatar_split_clause,[],[f102,f210,f170,f194]) ).

tff(f170,plain,
    ( spl31_7
  <=> f1($false) ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_7])]) ).

tff(f102,plain,
    ( sP8
    | ~ f1($false)
    | sP6 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f214,plain,
    ( ~ spl31_11
    | spl31_9
    | ~ spl31_13 ),
    inference(avatar_split_clause,[],[f103,f210,f179,f194]) ).

tff(f103,plain,
    ( ~ sP8
    | f1($true)
    | ~ sP6 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f213,plain,
    ( ~ spl31_11
    | spl31_7
    | spl31_13 ),
    inference(avatar_split_clause,[],[f104,f210,f170,f194]) ).

tff(f104,plain,
    ( sP8
    | f1($false)
    | ~ sP6 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f208,plain,
    ( spl31_10
    | ~ spl31_9
    | ~ spl31_12 ),
    inference(avatar_split_clause,[],[f105,f202,f179,f186]) ).

tff(f186,plain,
    ( spl31_10
  <=> sP5 ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_10])]) ).

tff(f105,plain,
    ( ~ sP7
    | ~ f1($true)
    | sP5 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f207,plain,
    ( spl31_10
    | ~ spl31_7
    | spl31_12 ),
    inference(avatar_split_clause,[],[f106,f202,f170,f186]) ).

tff(f106,plain,
    ( sP7
    | ~ f1($false)
    | sP5 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f206,plain,
    ( ~ spl31_10
    | spl31_9
    | ~ spl31_12 ),
    inference(avatar_split_clause,[],[f107,f202,f179,f186]) ).

tff(f107,plain,
    ( ~ sP7
    | f1($true)
    | ~ sP5 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f205,plain,
    ( ~ spl31_10
    | spl31_7
    | spl31_12 ),
    inference(avatar_split_clause,[],[f108,f202,f170,f186]) ).

tff(f108,plain,
    ( sP7
    | f1($false)
    | ~ sP5 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f200,plain,
    ( spl31_8
    | ~ spl31_9
    | ~ spl31_11 ),
    inference(avatar_split_clause,[],[f109,f194,f179,f174]) ).

tff(f174,plain,
    ( spl31_8
  <=> sP4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_8])]) ).

tff(f109,plain,
    ( ~ sP6
    | ~ f1($true)
    | sP4 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f199,plain,
    ( spl31_8
    | ~ spl31_7
    | spl31_11 ),
    inference(avatar_split_clause,[],[f110,f194,f170,f174]) ).

tff(f110,plain,
    ( sP6
    | ~ f1($false)
    | sP4 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f198,plain,
    ( ~ spl31_8
    | spl31_9
    | ~ spl31_11 ),
    inference(avatar_split_clause,[],[f111,f194,f179,f174]) ).

tff(f111,plain,
    ( ~ sP6
    | f1($true)
    | ~ sP4 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f197,plain,
    ( ~ spl31_8
    | spl31_7
    | spl31_11 ),
    inference(avatar_split_clause,[],[f112,f194,f170,f174]) ).

tff(f112,plain,
    ( sP6
    | f1($false)
    | ~ sP4 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f192,plain,
    ( spl31_6
    | ~ spl31_4
    | ~ spl31_10 ),
    inference(avatar_split_clause,[],[f113,f186,f147,f162]) ).

tff(f162,plain,
    ( spl31_6
  <=> sP3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_6])]) ).

tff(f147,plain,
    ( spl31_4
  <=> f0($true) ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_4])]) ).

tff(f113,plain,
    ( ~ sP5
    | ~ f0($true)
    | sP3 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f191,plain,
    ( spl31_6
    | ~ spl31_1
    | spl31_10 ),
    inference(avatar_split_clause,[],[f114,f186,f134,f162]) ).

tff(f134,plain,
    ( spl31_1
  <=> f0($false) ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_1])]) ).

tff(f114,plain,
    ( sP5
    | ~ f0($false)
    | sP3 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f190,plain,
    ( ~ spl31_6
    | spl31_4
    | ~ spl31_10 ),
    inference(avatar_split_clause,[],[f115,f186,f147,f162]) ).

tff(f115,plain,
    ( ~ sP5
    | f0($true)
    | ~ sP3 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f189,plain,
    ( ~ spl31_6
    | spl31_1
    | spl31_10 ),
    inference(avatar_split_clause,[],[f116,f186,f134,f162]) ).

tff(f116,plain,
    ( sP5
    | f0($false)
    | ~ sP3 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f184,plain,
    ( spl31_5
    | ~ spl31_9
    | ~ spl31_8 ),
    inference(avatar_split_clause,[],[f117,f174,f179,f154]) ).

tff(f154,plain,
    ( spl31_5
  <=> sP2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_5])]) ).

tff(f117,plain,
    ( ~ sP4
    | ~ f1($true)
    | sP2 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f183,plain,
    ( spl31_5
    | ~ spl31_7
    | spl31_8 ),
    inference(avatar_split_clause,[],[f118,f174,f170,f154]) ).

tff(f118,plain,
    ( sP4
    | ~ f1($false)
    | sP2 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f182,plain,
    ( ~ spl31_5
    | spl31_9
    | ~ spl31_8 ),
    inference(avatar_split_clause,[],[f119,f174,f179,f154]) ).

tff(f119,plain,
    ( ~ sP4
    | f1($true)
    | ~ sP2 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f177,plain,
    ( ~ spl31_5
    | spl31_7
    | spl31_8 ),
    inference(avatar_split_clause,[],[f120,f174,f170,f154]) ).

tff(f120,plain,
    ( sP4
    | f1($false)
    | ~ sP2 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f168,plain,
    ( spl31_2
    | ~ spl31_4
    | ~ spl31_6 ),
    inference(avatar_split_clause,[],[f121,f162,f147,f138]) ).

tff(f138,plain,
    ( spl31_2
  <=> sP1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_2])]) ).

tff(f121,plain,
    ( ~ sP3
    | ~ f0($true)
    | sP1 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f167,plain,
    ( spl31_2
    | ~ spl31_1
    | spl31_6 ),
    inference(avatar_split_clause,[],[f122,f162,f134,f138]) ).

tff(f122,plain,
    ( sP3
    | ~ f0($false)
    | sP1 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f166,plain,
    ( ~ spl31_2
    | spl31_4
    | ~ spl31_6 ),
    inference(avatar_split_clause,[],[f123,f162,f147,f138]) ).

tff(f123,plain,
    ( ~ sP3
    | f0($true)
    | ~ sP1 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f165,plain,
    ( ~ spl31_2
    | spl31_1
    | spl31_6 ),
    inference(avatar_split_clause,[],[f124,f162,f134,f138]) ).

tff(f124,plain,
    ( sP3
    | f0($false)
    | ~ sP1 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f160,plain,
    ( spl31_3
    | ~ spl31_4
    | ~ spl31_5 ),
    inference(avatar_split_clause,[],[f125,f154,f147,f142]) ).

tff(f142,plain,
    ( spl31_3
  <=> sP0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_3])]) ).

tff(f125,plain,
    ( ~ sP2
    | ~ f0($true)
    | sP0 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f159,plain,
    ( spl31_3
    | ~ spl31_1
    | spl31_5 ),
    inference(avatar_split_clause,[],[f126,f154,f134,f142]) ).

tff(f126,plain,
    ( sP2
    | ~ f0($false)
    | sP0 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f158,plain,
    ( ~ spl31_3
    | spl31_4
    | ~ spl31_5 ),
    inference(avatar_split_clause,[],[f127,f154,f147,f142]) ).

tff(f127,plain,
    ( ~ sP2
    | f0($true)
    | ~ sP0 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f157,plain,
    ( ~ spl31_3
    | spl31_1
    | spl31_5 ),
    inference(avatar_split_clause,[],[f128,f154,f134,f142]) ).

tff(f128,plain,
    ( sP2
    | f0($false)
    | ~ sP0 ),
    inference(cnf_transformation,[],[f4]) ).

tff(f152,plain,
    ( ~ spl31_4
    | ~ spl31_2
    | ~ spl31_3 ),
    inference(avatar_split_clause,[],[f129,f142,f138,f147]) ).

tff(f129,plain,
    ( ~ sP0
    | ~ sP1
    | ~ f0($true) ),
    inference(cnf_transformation,[],[f4]) ).

tff(f151,plain,
    ( ~ spl31_1
    | spl31_2
    | ~ spl31_3 ),
    inference(avatar_split_clause,[],[f130,f142,f138,f134]) ).

tff(f130,plain,
    ( ~ sP0
    | sP1
    | ~ f0($false) ),
    inference(cnf_transformation,[],[f4]) ).

tff(f150,plain,
    ( spl31_4
    | ~ spl31_2
    | spl31_3 ),
    inference(avatar_split_clause,[],[f131,f142,f138,f147]) ).

tff(f131,plain,
    ( sP0
    | ~ sP1
    | f0($true) ),
    inference(cnf_transformation,[],[f4]) ).

tff(f145,plain,
    ( spl31_1
    | spl31_2
    | spl31_3 ),
    inference(avatar_split_clause,[],[f132,f142,f138,f134]) ).

tff(f132,plain,
    ( sP0
    | sP1
    | f0($false) ),
    inference(cnf_transformation,[],[f4]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SYO500_8.008 : TPTP v8.1.2. Released v8.0.0.
% 0.12/0.14  % 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
% 0.13/0.35  % Computer : n012.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Fri May  3 16:11:07 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.35  This is a TX0_THM_EQU_NAR problem
% 0.13/0.36  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.FKr2wfVR2W/Vampire---4.8_29241
% 0.55/0.73  % (29356)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)
% 0.55/0.73  % (29349)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)
% 0.55/0.73  % (29349)Refutation not found, incomplete strategy% (29349)------------------------------
% 0.55/0.73  % (29349)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.55/0.73  % (29349)Termination reason: Refutation not found, incomplete strategy
% 0.55/0.73  
% 0.55/0.73  % (29349)Memory used [KB]: 984
% 0.55/0.73  % (29349)Time elapsed: 0.003 s
% 0.55/0.73  % (29349)Instructions burned: 3 (million)
% 0.55/0.73  % (29356)Refutation not found, incomplete strategy% (29356)------------------------------
% 0.55/0.73  % (29356)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.55/0.73  % (29356)Termination reason: Refutation not found, incomplete strategy
% 0.55/0.73  
% 0.55/0.73  % (29356)Memory used [KB]: 964
% 0.55/0.73  % (29356)Time elapsed: 0.004 s
% 0.55/0.73  % (29356)Instructions burned: 3 (million)
% 0.55/0.73  % (29356)------------------------------
% 0.55/0.73  % (29356)------------------------------
% 0.55/0.73  % (29349)------------------------------
% 0.55/0.73  % (29349)------------------------------
% 0.55/0.73  % (29355)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)
% 0.55/0.73  % (29351)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.55/0.73  % (29355)First to succeed.
% 0.55/0.73  % (29357)lrs+21_1:16_sil=2000:sp=occurrence:urr=on:flr=on:i=55:sd=1:nm=0:ins=3:ss=included:rawr=on:br=off_0 on Vampire---4 for (2996ds/55Mi)
% 0.55/0.73  % (29358)dis+3_25:4_sil=16000:sos=all:erd=off:i=50:s2at=4.0:bd=off:nm=60:sup=off:cond=on:av=off:ins=2:nwc=10.0:etr=on:to=lpo:s2agt=20:fd=off:bsr=unit_only:slsq=on:slsqr=28,19:awrs=converge:awrsf=500:tgt=ground:bs=unit_only_0 on Vampire---4 for (2996ds/50Mi)
% 0.55/0.73  % (29352)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)
% 0.55/0.73  % (29358)Refutation not found, incomplete strategy% (29358)------------------------------
% 0.55/0.73  % (29358)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.55/0.73  % (29354)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)
% 0.55/0.73  % (29358)Termination reason: Refutation not found, incomplete strategy
% 0.55/0.73  
% 0.55/0.73  % (29358)Memory used [KB]: 1089
% 0.55/0.73  % (29358)Time elapsed: 0.003 s
% 0.55/0.73  % (29358)Instructions burned: 4 (million)
% 0.55/0.73  % (29358)------------------------------
% 0.55/0.73  % (29358)------------------------------
% 0.55/0.73  % (29351)Refutation not found, incomplete strategy% (29351)------------------------------
% 0.55/0.73  % (29351)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.55/0.73  % (29351)Termination reason: Refutation not found, incomplete strategy
% 0.55/0.73  
% 0.55/0.73  % (29351)Memory used [KB]: 1151
% 0.55/0.73  % (29351)Time elapsed: 0.005 s
% 0.55/0.73  % (29351)Instructions burned: 7 (million)
% 0.55/0.73  % (29351)------------------------------
% 0.55/0.73  % (29351)------------------------------
% 0.55/0.73  % (29352)Refutation not found, incomplete strategy% (29352)------------------------------
% 0.55/0.73  % (29352)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.55/0.73  % (29352)Termination reason: Refutation not found, incomplete strategy
% 0.55/0.73  
% 0.55/0.73  % (29352)Memory used [KB]: 968
% 0.55/0.73  % (29352)Time elapsed: 0.003 s
% 0.55/0.73  % (29352)Instructions burned: 3 (million)
% 0.55/0.73  % (29350)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)
% 0.55/0.73  % (29354)Refutation not found, incomplete strategy% (29354)------------------------------
% 0.55/0.73  % (29354)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.55/0.73  % (29354)Termination reason: Refutation not found, incomplete strategy
% 0.55/0.73  
% 0.55/0.73  % (29354)Memory used [KB]: 1046
% 0.55/0.73  % (29354)Time elapsed: 0.002 s
% 0.55/0.73  % (29352)------------------------------
% 0.55/0.73  % (29352)------------------------------
% 0.55/0.73  % (29354)Instructions burned: 4 (million)
% 0.55/0.73  % (29354)------------------------------
% 0.55/0.73  % (29354)------------------------------
% 0.55/0.74  % (29353)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)
% 0.55/0.74  % (29359)lrs+1010_1:2_sil=4000:tgt=ground:nwc=10.0:st=2.0:i=208:sd=1:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/208Mi)
% 0.55/0.74  % (29362)lrs+1011_87677:1048576_sil=8000:sos=on:spb=non_intro:nwc=10.0:kmz=on:i=42:ep=RS:nm=0:ins=1:uhcvi=on:rawr=on:fde=unused:afp=2000:afq=1.444:plsq=on:nicw=on_0 on Vampire---4 for (2996ds/42Mi)
% 0.55/0.74  % (29360)lrs-1011_1:1_sil=4000:plsq=on:plsqr=32,1:sp=frequency:plsql=on:nwc=10.0:i=52:aac=none:afr=on:ss=axioms:er=filter:sgt=16:rawr=on:etr=on:lma=on_0 on Vampire---4 for (2996ds/52Mi)
% 0.55/0.74  % (29361)lrs-1010_1:1_to=lpo:sil=2000:sp=reverse_arity:sos=on:urr=ec_only:i=518:sd=2:bd=off:ss=axioms:sgt=16_0 on Vampire---4 for (2996ds/518Mi)
% 0.55/0.74  % (29359)Refutation not found, incomplete strategy% (29359)------------------------------
% 0.55/0.74  % (29359)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.55/0.74  % (29359)Termination reason: Refutation not found, incomplete strategy
% 0.55/0.74  
% 0.55/0.74  % (29359)Memory used [KB]: 969
% 0.55/0.74  % (29359)Time elapsed: 0.003 s
% 0.55/0.74  % (29359)Instructions burned: 3 (million)
% 0.55/0.74  % (29353)Refutation not found, incomplete strategy% (29353)------------------------------
% 0.55/0.74  % (29353)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.55/0.74  % (29353)Termination reason: Refutation not found, incomplete strategy
% 0.55/0.74  
% 0.55/0.74  % (29353)Memory used [KB]: 1052
% 0.55/0.74  % (29353)Time elapsed: 0.003 s
% 0.55/0.74  % (29353)Instructions burned: 4 (million)
% 0.55/0.74  % (29359)------------------------------
% 0.55/0.74  % (29359)------------------------------
% 0.55/0.74  % (29355)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-29348"
% 0.55/0.74  % (29353)------------------------------
% 0.55/0.74  % (29353)------------------------------
% 0.55/0.74  % (29362)Refutation not found, incomplete strategy% (29362)------------------------------
% 0.55/0.74  % (29362)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.55/0.74  % (29362)Termination reason: Refutation not found, incomplete strategy
% 0.55/0.74  
% 0.55/0.74  % (29362)Memory used [KB]: 1069
% 0.55/0.74  % (29362)Time elapsed: 0.002 s
% 0.55/0.74  % (29362)Instructions burned: 5 (million)
% 0.55/0.74  % (29362)------------------------------
% 0.55/0.74  % (29362)------------------------------
% 0.55/0.74  % (29361)Refutation not found, incomplete strategy% (29361)------------------------------
% 0.55/0.74  % (29361)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.55/0.74  % (29361)Termination reason: Refutation not found, incomplete strategy
% 0.55/0.74  
% 0.55/0.74  % (29361)Memory used [KB]: 971
% 0.55/0.74  % (29361)Time elapsed: 0.003 s
% 0.55/0.74  % (29361)Instructions burned: 3 (million)
% 0.55/0.74  % (29355)Refutation found. Thanks to Tanya!
% 0.55/0.74  % SZS status Theorem for Vampire---4
% 0.55/0.74  % SZS output start Proof for Vampire---4
% See solution above
% 0.55/0.74  % (29355)------------------------------
% 0.55/0.74  % (29355)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.55/0.74  % (29355)Termination reason: Refutation
% 0.55/0.74  
% 0.55/0.74  % (29355)Memory used [KB]: 1087
% 0.55/0.74  % (29355)Time elapsed: 0.008 s
% 0.55/0.74  % (29355)Instructions burned: 13 (million)
% 0.55/0.74  % (29348)Success in time 0.376 s
% 0.55/0.74  % Vampire---4.8 exiting
%------------------------------------------------------------------------------