TSTP Solution File: DAT080_1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : DAT080_1 : TPTP v8.1.2. Released v6.1.0.
% 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 : Tue Apr 30 11:04:00 EDT 2024

% Result   : Theorem 0.22s 0.40s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :  120
% Syntax   : Number of formulae    :  322 (  77 unt;  18 typ;   0 def)
%            Number of atoms       :  804 ( 206 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  816 ( 316   ~; 344   |;  67   &)
%                                         (  82 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number arithmetic     :  739 ( 129 atm; 131 fun; 170 num; 309 var)
%            Number of types       :    3 (   1 usr;   1 ari)
%            Number of type conns  :   29 (  16   >;  13   *;   0   +;   0  <<)
%            Number of predicates  :   79 (  74 usr;  71 prp; 0-2 aty)
%            Number of functors    :   20 (  13 usr;   6 con; 0-2 aty)
%            Number of variables   :  497 ( 453   !;  44   ?; 497   :)

% Comments : 
%------------------------------------------------------------------------------
tff(type_def_5,type,
    list: $tType ).

tff(func_def_0,type,
    nil: list ).

tff(func_def_1,type,
    cons: ( $int * list ) > list ).

tff(func_def_2,type,
    head: list > $int ).

tff(func_def_3,type,
    tail: list > list ).

tff(func_def_5,type,
    length: list > $int ).

tff(func_def_8,type,
    count: ( $int * list ) > $int ).

tff(func_def_9,type,
    append: ( list * list ) > list ).

tff(func_def_14,type,
    sK2: ( $int * list ) > $int ).

tff(func_def_15,type,
    sK3: ( $int * list ) > list ).

tff(func_def_16,type,
    sK4: ( $int * list ) > $int ).

tff(func_def_17,type,
    sK5: ( $int * list ) > list ).

tff(func_def_18,type,
    sK6: ( $int * list ) > $int ).

tff(func_def_19,type,
    sK7: ( $int * list ) > list ).

tff(pred_def_1,type,
    in: ( $int * list ) > $o ).

tff(pred_def_2,type,
    inRange: ( $int * list ) > $o ).

tff(pred_def_6,type,
    sP0: ( $int * list ) > $o ).

tff(pred_def_7,type,
    sP1: ( $int * list ) > $o ).

tff(f650,plain,
    $false,
    inference(avatar_sat_refutation,[],[f102,f106,f110,f115,f119,f123,f127,f131,f135,f139,f143,f147,f151,f155,f159,f163,f167,f174,f179,f183,f187,f191,f195,f199,f213,f217,f221,f235,f239,f243,f258,f279,f283,f287,f291,f295,f299,f337,f348,f354,f363,f367,f373,f377,f386,f393,f402,f406,f420,f424,f428,f444,f448,f452,f456,f460,f464,f510,f514,f518,f522,f545,f549,f553,f557,f563,f568,f634,f638,f642,f649]) ).

tff(f649,plain,
    ( ~ spl8_7
    | ~ spl8_38
    | ~ spl8_58 ),
    inference(avatar_contradiction_clause,[],[f648]) ).

tff(f648,plain,
    ( $false
    | ~ spl8_7
    | ~ spl8_38
    | ~ spl8_58 ),
    inference(evaluation,[],[f647]) ).

tff(f647,plain,
    ( $less(0,0)
    | ~ spl8_7
    | ~ spl8_38
    | ~ spl8_58 ),
    inference(forward_demodulation,[],[f646,f126]) ).

tff(f126,plain,
    ( ! [X0: $int] : ( 0 = count(X0,nil) )
    | ~ spl8_7 ),
    inference(avatar_component_clause,[],[f125]) ).

tff(f125,plain,
    ( spl8_7
  <=> ! [X0: $int] : ( 0 = count(X0,nil) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_7])]) ).

tff(f646,plain,
    ( $less(0,count(4,nil))
    | ~ spl8_38
    | ~ spl8_58 ),
    inference(evaluation,[],[f645]) ).

tff(f645,plain,
    ( $less(0,count(4,nil))
    | ( 4 = 3 )
    | ~ spl8_38
    | ~ spl8_58 ),
    inference(superposition,[],[f509,f336]) ).

tff(f336,plain,
    ( ! [X2: list,X0: $int,X1: $int] :
        ( ( count(X0,cons(X1,X2)) = count(X0,X2) )
        | ( X0 = X1 ) )
    | ~ spl8_38 ),
    inference(avatar_component_clause,[],[f335]) ).

tff(f335,plain,
    ( spl8_38
  <=> ! [X2: list,X0: $int,X1: $int] :
        ( ( count(X0,cons(X1,X2)) = count(X0,X2) )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_38])]) ).

tff(f509,plain,
    ( $less(0,count(4,cons(3,nil)))
    | ~ spl8_58 ),
    inference(avatar_component_clause,[],[f507]) ).

tff(f507,plain,
    ( spl8_58
  <=> $less(0,count(4,cons(3,nil))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_58])]) ).

tff(f642,plain,
    ( spl8_70
    | ~ spl8_18
    | ~ spl8_32 ),
    inference(avatar_split_clause,[],[f301,f277,f172,f640]) ).

tff(f640,plain,
    ( spl8_70
  <=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X1,X0),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_70])]) ).

tff(f172,plain,
    ( spl8_18
  <=> ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_18])]) ).

tff(f277,plain,
    ( spl8_32
  <=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_32])]) ).

tff(f301,plain,
    ( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X1,X0),X2) )
    | ~ spl8_18
    | ~ spl8_32 ),
    inference(superposition,[],[f278,f173]) ).

tff(f173,plain,
    ( ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) )
    | ~ spl8_18 ),
    inference(avatar_component_clause,[],[f172]) ).

tff(f278,plain,
    ( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) )
    | ~ spl8_32 ),
    inference(avatar_component_clause,[],[f277]) ).

tff(f638,plain,
    ( spl8_69
    | ~ spl8_27
    | ~ spl8_30 ),
    inference(avatar_split_clause,[],[f272,f241,f219,f636]) ).

tff(f636,plain,
    ( spl8_69
  <=> ! [X0: list] :
        ( ( $sum(1,length(tail(X0))) = length(X0) )
        | ( nil = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_69])]) ).

tff(f219,plain,
    ( spl8_27
  <=> ! [X0: $int,X1: list] : ( length(cons(X0,X1)) = $sum(1,length(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_27])]) ).

tff(f241,plain,
    ( spl8_30
  <=> ! [X0: list] :
        ( ( cons(head(X0),tail(X0)) = X0 )
        | ( nil = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_30])]) ).

tff(f272,plain,
    ( ! [X0: list] :
        ( ( $sum(1,length(tail(X0))) = length(X0) )
        | ( nil = X0 ) )
    | ~ spl8_27
    | ~ spl8_30 ),
    inference(superposition,[],[f220,f242]) ).

tff(f242,plain,
    ( ! [X0: list] :
        ( ( cons(head(X0),tail(X0)) = X0 )
        | ( nil = X0 ) )
    | ~ spl8_30 ),
    inference(avatar_component_clause,[],[f241]) ).

tff(f220,plain,
    ( ! [X0: $int,X1: list] : ( length(cons(X0,X1)) = $sum(1,length(X1)) )
    | ~ spl8_27 ),
    inference(avatar_component_clause,[],[f219]) ).

tff(f634,plain,
    ( spl8_68
    | ~ spl8_20
    | ~ spl8_25 ),
    inference(avatar_split_clause,[],[f222,f211,f181,f632]) ).

tff(f632,plain,
    ( spl8_68
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( ~ $less(X0,X1)
        | $less(X0,$sum(X2,1))
        | $less(X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_68])]) ).

tff(f181,plain,
    ( spl8_20
  <=> ! [X0: $int,X1: $int] :
        ( $less(X0,X1)
        | $less(X1,$sum(X0,1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_20])]) ).

tff(f211,plain,
    ( spl8_25
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( ~ $less(X0,X1)
        | ~ $less(X1,X2)
        | $less(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_25])]) ).

tff(f222,plain,
    ( ! [X2: $int,X0: $int,X1: $int] :
        ( ~ $less(X0,X1)
        | $less(X0,$sum(X2,1))
        | $less(X2,X1) )
    | ~ spl8_20
    | ~ spl8_25 ),
    inference(resolution,[],[f212,f182]) ).

tff(f182,plain,
    ( ! [X0: $int,X1: $int] :
        ( $less(X1,$sum(X0,1))
        | $less(X0,X1) )
    | ~ spl8_20 ),
    inference(avatar_component_clause,[],[f181]) ).

tff(f212,plain,
    ( ! [X2: $int,X0: $int,X1: $int] :
        ( ~ $less(X1,X2)
        | ~ $less(X0,X1)
        | $less(X0,X2) )
    | ~ spl8_25 ),
    inference(avatar_component_clause,[],[f211]) ).

tff(f568,plain,
    ( spl8_67
    | ~ spl8_12
    | ~ spl8_36 ),
    inference(avatar_split_clause,[],[f328,f293,f145,f566]) ).

tff(f566,plain,
    ( spl8_67
  <=> ! [X2: list,X0: $int,X1: list] : ( append(X1,X2) = tail(append(cons(X0,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_67])]) ).

tff(f145,plain,
    ( spl8_12
  <=> ! [X0: $int,X1: list] : ( tail(cons(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_12])]) ).

tff(f293,plain,
    ( spl8_36
  <=> ! [X2: list,X0: $int,X1: list] : ( append(cons(X0,X1),X2) = cons(X0,append(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_36])]) ).

tff(f328,plain,
    ( ! [X2: list,X0: $int,X1: list] : ( append(X1,X2) = tail(append(cons(X0,X1),X2)) )
    | ~ spl8_12
    | ~ spl8_36 ),
    inference(superposition,[],[f146,f294]) ).

tff(f294,plain,
    ( ! [X2: list,X0: $int,X1: list] : ( append(cons(X0,X1),X2) = cons(X0,append(X1,X2)) )
    | ~ spl8_36 ),
    inference(avatar_component_clause,[],[f293]) ).

tff(f146,plain,
    ( ! [X0: $int,X1: list] : ( tail(cons(X0,X1)) = X1 )
    | ~ spl8_12 ),
    inference(avatar_component_clause,[],[f145]) ).

tff(f563,plain,
    ( spl8_66
    | ~ spl8_11
    | ~ spl8_32 ),
    inference(avatar_split_clause,[],[f305,f277,f141,f561]) ).

tff(f561,plain,
    ( spl8_66
  <=> ! [X0: $int,X1: $int] : ( 0 = $sum(X0,$sum(X1,$uminus($sum(X0,X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_66])]) ).

tff(f141,plain,
    ( spl8_11
  <=> ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_11])]) ).

tff(f305,plain,
    ( ! [X0: $int,X1: $int] : ( 0 = $sum(X0,$sum(X1,$uminus($sum(X0,X1)))) )
    | ~ spl8_11
    | ~ spl8_32 ),
    inference(superposition,[],[f278,f142]) ).

tff(f142,plain,
    ( ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) )
    | ~ spl8_11 ),
    inference(avatar_component_clause,[],[f141]) ).

tff(f557,plain,
    ( spl8_65
    | ~ spl8_24
    | ~ spl8_30 ),
    inference(avatar_split_clause,[],[f273,f241,f197,f555]) ).

tff(f555,plain,
    ( spl8_65
  <=> ! [X0: list,X1: $int] :
        ( sP1(X1,X0)
        | ~ in(X1,tail(X0))
        | ( nil = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_65])]) ).

tff(f197,plain,
    ( spl8_24
  <=> ! [X2: $int,X0: $int,X3: list] :
        ( sP1(X0,cons(X2,X3))
        | ~ in(X0,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_24])]) ).

tff(f273,plain,
    ( ! [X0: list,X1: $int] :
        ( sP1(X1,X0)
        | ~ in(X1,tail(X0))
        | ( nil = X0 ) )
    | ~ spl8_24
    | ~ spl8_30 ),
    inference(superposition,[],[f198,f242]) ).

tff(f198,plain,
    ( ! [X2: $int,X3: list,X0: $int] :
        ( sP1(X0,cons(X2,X3))
        | ~ in(X0,X3) )
    | ~ spl8_24 ),
    inference(avatar_component_clause,[],[f197]) ).

tff(f553,plain,
    ( spl8_64
    | ~ spl8_18
    | ~ spl8_29 ),
    inference(avatar_split_clause,[],[f267,f237,f172,f551]) ).

tff(f551,plain,
    ( spl8_64
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( $less($sum(X2,X1),$sum(X1,X0))
        | ~ $less(X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_64])]) ).

tff(f237,plain,
    ( spl8_29
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( ~ $less(X0,X1)
        | $less($sum(X0,X2),$sum(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_29])]) ).

tff(f267,plain,
    ( ! [X2: $int,X0: $int,X1: $int] :
        ( $less($sum(X2,X1),$sum(X1,X0))
        | ~ $less(X2,X0) )
    | ~ spl8_18
    | ~ spl8_29 ),
    inference(superposition,[],[f238,f173]) ).

tff(f238,plain,
    ( ! [X2: $int,X0: $int,X1: $int] :
        ( $less($sum(X0,X2),$sum(X1,X2))
        | ~ $less(X0,X1) )
    | ~ spl8_29 ),
    inference(avatar_component_clause,[],[f237]) ).

tff(f549,plain,
    ( spl8_63
    | ~ spl8_18
    | ~ spl8_29 ),
    inference(avatar_split_clause,[],[f263,f237,f172,f547]) ).

tff(f547,plain,
    ( spl8_63
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( $less($sum(X1,X0),$sum(X2,X1))
        | ~ $less(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_63])]) ).

tff(f263,plain,
    ( ! [X2: $int,X0: $int,X1: $int] :
        ( $less($sum(X1,X0),$sum(X2,X1))
        | ~ $less(X0,X2) )
    | ~ spl8_18
    | ~ spl8_29 ),
    inference(superposition,[],[f238,f173]) ).

tff(f545,plain,
    ( spl8_62
    | ~ spl8_18
    | ~ spl8_28 ),
    inference(avatar_split_clause,[],[f245,f233,f172,f543]) ).

tff(f543,plain,
    ( spl8_62
  <=> ! [X0: $int,X1: $int] : ( $sum($uminus(X1),$uminus(X0)) = $uminus($sum(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_62])]) ).

tff(f233,plain,
    ( spl8_28
  <=> ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_28])]) ).

tff(f245,plain,
    ( ! [X0: $int,X1: $int] : ( $sum($uminus(X1),$uminus(X0)) = $uminus($sum(X1,X0)) )
    | ~ spl8_18
    | ~ spl8_28 ),
    inference(superposition,[],[f234,f173]) ).

tff(f234,plain,
    ( ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) )
    | ~ spl8_28 ),
    inference(avatar_component_clause,[],[f233]) ).

tff(f522,plain,
    ( spl8_61
    | ~ spl8_8
    | ~ spl8_36 ),
    inference(avatar_split_clause,[],[f324,f293,f129,f520]) ).

tff(f520,plain,
    ( spl8_61
  <=> ! [X0: list,X1: $int] : ( append(cons(X1,nil),X0) = cons(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_61])]) ).

tff(f129,plain,
    ( spl8_8
  <=> ! [X0: list] : ( append(nil,X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_8])]) ).

tff(f324,plain,
    ( ! [X0: list,X1: $int] : ( append(cons(X1,nil),X0) = cons(X1,X0) )
    | ~ spl8_8
    | ~ spl8_36 ),
    inference(superposition,[],[f294,f130]) ).

tff(f130,plain,
    ( ! [X0: list] : ( append(nil,X0) = X0 )
    | ~ spl8_8 ),
    inference(avatar_component_clause,[],[f129]) ).

tff(f518,plain,
    ( spl8_60
    | ~ spl8_11
    | ~ spl8_29 ),
    inference(avatar_split_clause,[],[f266,f237,f141,f516]) ).

tff(f516,plain,
    ( spl8_60
  <=> ! [X0: $int,X1: $int] :
        ( $less($sum(X1,$uminus(X0)),0)
        | ~ $less(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_60])]) ).

tff(f266,plain,
    ( ! [X0: $int,X1: $int] :
        ( $less($sum(X1,$uminus(X0)),0)
        | ~ $less(X1,X0) )
    | ~ spl8_11
    | ~ spl8_29 ),
    inference(superposition,[],[f238,f142]) ).

tff(f514,plain,
    ( spl8_59
    | ~ spl8_11
    | ~ spl8_29 ),
    inference(avatar_split_clause,[],[f262,f237,f141,f512]) ).

tff(f512,plain,
    ( spl8_59
  <=> ! [X0: $int,X1: $int] :
        ( $less(0,$sum(X1,$uminus(X0)))
        | ~ $less(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_59])]) ).

tff(f262,plain,
    ( ! [X0: $int,X1: $int] :
        ( $less(0,$sum(X1,$uminus(X0)))
        | ~ $less(X0,X1) )
    | ~ spl8_11
    | ~ spl8_29 ),
    inference(superposition,[],[f238,f142]) ).

tff(f510,plain,
    ( spl8_58
    | ~ spl8_38
    | ~ spl8_41 ),
    inference(avatar_split_clause,[],[f398,f360,f335,f507]) ).

tff(f360,plain,
    ( spl8_41
  <=> $less(0,count(4,cons(2,cons(3,nil)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_41])]) ).

tff(f398,plain,
    ( $less(0,count(4,cons(3,nil)))
    | ~ spl8_38
    | ~ spl8_41 ),
    inference(evaluation,[],[f397]) ).

tff(f397,plain,
    ( $less(0,count(4,cons(3,nil)))
    | ( 4 = 2 )
    | ~ spl8_38
    | ~ spl8_41 ),
    inference(superposition,[],[f362,f336]) ).

tff(f362,plain,
    ( $less(0,count(4,cons(2,cons(3,nil))))
    | ~ spl8_41 ),
    inference(avatar_component_clause,[],[f360]) ).

tff(f464,plain,
    ( spl8_57
    | ~ spl8_13
    | ~ spl8_36 ),
    inference(avatar_split_clause,[],[f327,f293,f149,f462]) ).

tff(f462,plain,
    ( spl8_57
  <=> ! [X2: list,X0: $int,X1: list] : ( head(append(cons(X0,X1),X2)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_57])]) ).

tff(f149,plain,
    ( spl8_13
  <=> ! [X0: $int,X1: list] : ( head(cons(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_13])]) ).

tff(f327,plain,
    ( ! [X2: list,X0: $int,X1: list] : ( head(append(cons(X0,X1),X2)) = X0 )
    | ~ spl8_13
    | ~ spl8_36 ),
    inference(superposition,[],[f150,f294]) ).

tff(f150,plain,
    ( ! [X0: $int,X1: list] : ( head(cons(X0,X1)) = X0 )
    | ~ spl8_13 ),
    inference(avatar_component_clause,[],[f149]) ).

tff(f460,plain,
    ( spl8_56
    | ~ spl8_11
    | ~ spl8_32 ),
    inference(avatar_split_clause,[],[f315,f277,f141,f458]) ).

tff(f458,plain,
    ( spl8_56
  <=> ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_56])]) ).

tff(f315,plain,
    ( ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 )
    | ~ spl8_11
    | ~ spl8_32 ),
    inference(evaluation,[],[f300]) ).

tff(f300,plain,
    ( ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = $sum(0,X1) )
    | ~ spl8_11
    | ~ spl8_32 ),
    inference(superposition,[],[f278,f142]) ).

tff(f456,plain,
    ( spl8_55
    | ~ spl8_17
    | ~ spl8_24 ),
    inference(avatar_split_clause,[],[f208,f197,f165,f454]) ).

tff(f454,plain,
    ( spl8_55
  <=> ! [X2: $int,X0: $int,X1: list] :
        ( ~ in(X0,X1)
        | in(X0,cons(X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_55])]) ).

tff(f165,plain,
    ( spl8_17
  <=> ! [X0: $int,X1: list] :
        ( in(X0,X1)
        | ~ sP1(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_17])]) ).

tff(f208,plain,
    ( ! [X2: $int,X0: $int,X1: list] :
        ( ~ in(X0,X1)
        | in(X0,cons(X2,X1)) )
    | ~ spl8_17
    | ~ spl8_24 ),
    inference(resolution,[],[f198,f166]) ).

tff(f166,plain,
    ( ! [X0: $int,X1: list] :
        ( ~ sP1(X0,X1)
        | in(X0,X1) )
    | ~ spl8_17 ),
    inference(avatar_component_clause,[],[f165]) ).

tff(f452,plain,
    ( spl8_54
    | ~ spl8_18
    | ~ spl8_21 ),
    inference(avatar_split_clause,[],[f204,f185,f172,f450]) ).

tff(f450,plain,
    ( spl8_54
  <=> ! [X0: $int,X1: $int] :
        ( ~ $less(X1,$sum(1,X0))
        | ~ $less(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_54])]) ).

tff(f185,plain,
    ( spl8_21
  <=> ! [X0: $int,X1: $int] :
        ( ~ $less(X0,X1)
        | ~ $less(X1,$sum(X0,1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_21])]) ).

tff(f204,plain,
    ( ! [X0: $int,X1: $int] :
        ( ~ $less(X1,$sum(1,X0))
        | ~ $less(X0,X1) )
    | ~ spl8_18
    | ~ spl8_21 ),
    inference(superposition,[],[f186,f173]) ).

tff(f186,plain,
    ( ! [X0: $int,X1: $int] :
        ( ~ $less(X1,$sum(X0,1))
        | ~ $less(X0,X1) )
    | ~ spl8_21 ),
    inference(avatar_component_clause,[],[f185]) ).

tff(f448,plain,
    ( spl8_53
    | ~ spl8_18
    | ~ spl8_20 ),
    inference(avatar_split_clause,[],[f201,f181,f172,f446]) ).

tff(f446,plain,
    ( spl8_53
  <=> ! [X0: $int,X1: $int] :
        ( $less(X1,$sum(1,X0))
        | $less(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_53])]) ).

tff(f201,plain,
    ( ! [X0: $int,X1: $int] :
        ( $less(X1,$sum(1,X0))
        | $less(X0,X1) )
    | ~ spl8_18
    | ~ spl8_20 ),
    inference(superposition,[],[f182,f173]) ).

tff(f444,plain,
    ( spl8_52
    | ~ spl8_23
    | ~ spl8_41 ),
    inference(avatar_split_clause,[],[f395,f360,f193,f441]) ).

tff(f441,plain,
    ( spl8_52
  <=> in(4,cons(2,cons(3,nil))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_52])]) ).

tff(f193,plain,
    ( spl8_23
  <=> ! [X0: $int,X1: list] :
        ( in(X0,X1)
        | ~ $less(0,count(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_23])]) ).

tff(f395,plain,
    ( in(4,cons(2,cons(3,nil)))
    | ~ spl8_23
    | ~ spl8_41 ),
    inference(resolution,[],[f362,f194]) ).

tff(f194,plain,
    ( ! [X0: $int,X1: list] :
        ( ~ $less(0,count(X0,X1))
        | in(X0,X1) )
    | ~ spl8_23 ),
    inference(avatar_component_clause,[],[f193]) ).

tff(f428,plain,
    ( spl8_51
    | ~ spl8_9
    | ~ spl8_36 ),
    inference(avatar_split_clause,[],[f330,f293,f133,f426]) ).

tff(f426,plain,
    ( spl8_51
  <=> ! [X2: list,X0: $int,X1: list] : ( nil != append(cons(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_51])]) ).

tff(f133,plain,
    ( spl8_9
  <=> ! [X0: $int,X1: list] : ( cons(X0,X1) != nil ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_9])]) ).

tff(f330,plain,
    ( ! [X2: list,X0: $int,X1: list] : ( nil != append(cons(X0,X1),X2) )
    | ~ spl8_9
    | ~ spl8_36 ),
    inference(superposition,[],[f134,f294]) ).

tff(f134,plain,
    ( ! [X0: $int,X1: list] : ( cons(X0,X1) != nil )
    | ~ spl8_9 ),
    inference(avatar_component_clause,[],[f133]) ).

tff(f424,plain,
    ( spl8_50
    | ~ spl8_10
    | ~ spl8_36 ),
    inference(avatar_split_clause,[],[f329,f293,f137,f422]) ).

tff(f422,plain,
    ( spl8_50
  <=> ! [X2: list,X0: $int,X1: list] : sP1(X0,append(cons(X0,X1),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_50])]) ).

tff(f137,plain,
    ( spl8_10
  <=> ! [X4: $int,X5: list] : sP1(X4,cons(X4,X5)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_10])]) ).

tff(f329,plain,
    ( ! [X2: list,X0: $int,X1: list] : sP1(X0,append(cons(X0,X1),X2))
    | ~ spl8_10
    | ~ spl8_36 ),
    inference(superposition,[],[f138,f294]) ).

tff(f138,plain,
    ( ! [X4: $int,X5: list] : sP1(X4,cons(X4,X5))
    | ~ spl8_10 ),
    inference(avatar_component_clause,[],[f137]) ).

tff(f420,plain,
    ( spl8_49
    | ~ spl8_10
    | ~ spl8_30 ),
    inference(avatar_split_clause,[],[f274,f241,f137,f418]) ).

tff(f418,plain,
    ( spl8_49
  <=> ! [X0: list] :
        ( sP1(head(X0),X0)
        | ( nil = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_49])]) ).

tff(f274,plain,
    ( ! [X0: list] :
        ( sP1(head(X0),X0)
        | ( nil = X0 ) )
    | ~ spl8_10
    | ~ spl8_30 ),
    inference(superposition,[],[f138,f242]) ).

tff(f406,plain,
    ( spl8_48
    | ~ spl8_2
    | ~ spl8_20 ),
    inference(avatar_split_clause,[],[f200,f181,f104,f404]) ).

tff(f404,plain,
    ( spl8_48
  <=> ! [X0: $int] : $less(X0,$sum(X0,1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_48])]) ).

tff(f104,plain,
    ( spl8_2
  <=> ! [X0: $int] : ~ $less(X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).

tff(f200,plain,
    ( ! [X0: $int] : $less(X0,$sum(X0,1))
    | ~ spl8_2
    | ~ spl8_20 ),
    inference(resolution,[],[f182,f105]) ).

tff(f105,plain,
    ( ! [X0: $int] : ~ $less(X0,X0)
    | ~ spl8_2 ),
    inference(avatar_component_clause,[],[f104]) ).

tff(f402,plain,
    ( spl8_47
    | ~ spl8_10
    | ~ spl8_17 ),
    inference(avatar_split_clause,[],[f170,f165,f137,f400]) ).

tff(f400,plain,
    ( spl8_47
  <=> ! [X0: $int,X1: list] : in(X0,cons(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_47])]) ).

tff(f170,plain,
    ( ! [X0: $int,X1: list] : in(X0,cons(X0,X1))
    | ~ spl8_10
    | ~ spl8_17 ),
    inference(resolution,[],[f166,f138]) ).

tff(f393,plain,
    ( spl8_46
    | ~ spl8_3
    | ~ spl8_15 ),
    inference(avatar_split_clause,[],[f168,f157,f108,f391]) ).

tff(f391,plain,
    ( spl8_46
  <=> ! [X0: $int] : inRange(X0,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_46])]) ).

tff(f108,plain,
    ( spl8_3
  <=> ! [X0: $int] : sP0(X0,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_3])]) ).

tff(f157,plain,
    ( spl8_15
  <=> ! [X0: $int,X1: list] :
        ( inRange(X0,X1)
        | ~ sP0(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_15])]) ).

tff(f168,plain,
    ( ! [X0: $int] : inRange(X0,nil)
    | ~ spl8_3
    | ~ spl8_15 ),
    inference(resolution,[],[f158,f109]) ).

tff(f109,plain,
    ( ! [X0: $int] : sP0(X0,nil)
    | ~ spl8_3 ),
    inference(avatar_component_clause,[],[f108]) ).

tff(f158,plain,
    ( ! [X0: $int,X1: list] :
        ( ~ sP0(X0,X1)
        | inRange(X0,X1) )
    | ~ spl8_15 ),
    inference(avatar_component_clause,[],[f157]) ).

tff(f386,plain,
    spl8_45,
    inference(avatar_split_clause,[],[f80,f384]) ).

tff(f384,plain,
    ( spl8_45
  <=> ! [X0: $int,X1: list] :
        ( ( cons(sK4(X0,X1),sK5(X0,X1)) = X1 )
        | ( cons(sK6(X0,X1),sK7(X0,X1)) = X1 )
        | ~ sP1(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_45])]) ).

tff(f80,plain,
    ! [X0: $int,X1: list] :
      ( ( cons(sK4(X0,X1),sK5(X0,X1)) = X1 )
      | ( cons(sK6(X0,X1),sK7(X0,X1)) = X1 )
      | ~ sP1(X0,X1) ),
    inference(cnf_transformation,[],[f59]) ).

tff(f59,plain,
    ! [X0: $int,X1: list] :
      ( ( sP1(X0,X1)
        | ( ! [X2: $int,X3: list] :
              ( ~ in(X0,X3)
              | ( cons(X2,X3) != X1 ) )
          & ! [X4: $int,X5: list] :
              ( ( X0 != X4 )
              | ( cons(X4,X5) != X1 ) ) ) )
      & ( ( in(X0,sK5(X0,X1))
          & ( cons(sK4(X0,X1),sK5(X0,X1)) = X1 ) )
        | ( ( sK6(X0,X1) = X0 )
          & ( cons(sK6(X0,X1),sK7(X0,X1)) = X1 ) )
        | ~ sP1(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f56,f58,f57]) ).

tff(f57,plain,
    ! [X0: $int,X1: list] :
      ( ? [X6: $int,X7: list] :
          ( in(X0,X7)
          & ( cons(X6,X7) = X1 ) )
     => ( in(X0,sK5(X0,X1))
        & ( cons(sK4(X0,X1),sK5(X0,X1)) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f58,plain,
    ! [X0: $int,X1: list] :
      ( ? [X8: $int,X9: list] :
          ( ( X0 = X8 )
          & ( cons(X8,X9) = X1 ) )
     => ( ( sK6(X0,X1) = X0 )
        & ( cons(sK6(X0,X1),sK7(X0,X1)) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f56,plain,
    ! [X0: $int,X1: list] :
      ( ( sP1(X0,X1)
        | ( ! [X2: $int,X3: list] :
              ( ~ in(X0,X3)
              | ( cons(X2,X3) != X1 ) )
          & ! [X4: $int,X5: list] :
              ( ( X0 != X4 )
              | ( cons(X4,X5) != X1 ) ) ) )
      & ( ? [X6: $int,X7: list] :
            ( in(X0,X7)
            & ( cons(X6,X7) = X1 ) )
        | ? [X8: $int,X9: list] :
            ( ( X0 = X8 )
            & ( cons(X8,X9) = X1 ) )
        | ~ sP1(X0,X1) ) ),
    inference(rectify,[],[f55]) ).

tff(f55,plain,
    ! [X0: $int,X1: list] :
      ( ( sP1(X0,X1)
        | ( ! [X2: $int,X3: list] :
              ( ~ in(X0,X3)
              | ( cons(X2,X3) != X1 ) )
          & ! [X4: $int,X5: list] :
              ( ( X0 != X4 )
              | ( cons(X4,X5) != X1 ) ) ) )
      & ( ? [X2: $int,X3: list] :
            ( in(X0,X3)
            & ( cons(X2,X3) = X1 ) )
        | ? [X4: $int,X5: list] :
            ( ( X0 = X4 )
            & ( cons(X4,X5) = X1 ) )
        | ~ sP1(X0,X1) ) ),
    inference(flattening,[],[f54]) ).

tff(f54,plain,
    ! [X0: $int,X1: list] :
      ( ( sP1(X0,X1)
        | ( ! [X2: $int,X3: list] :
              ( ~ in(X0,X3)
              | ( cons(X2,X3) != X1 ) )
          & ! [X4: $int,X5: list] :
              ( ( X0 != X4 )
              | ( cons(X4,X5) != X1 ) ) ) )
      & ( ? [X2: $int,X3: list] :
            ( in(X0,X3)
            & ( cons(X2,X3) = X1 ) )
        | ? [X4: $int,X5: list] :
            ( ( X0 = X4 )
            & ( cons(X4,X5) = X1 ) )
        | ~ sP1(X0,X1) ) ),
    inference(nnf_transformation,[],[f45]) ).

tff(f45,plain,
    ! [X0: $int,X1: list] :
      ( sP1(X0,X1)
    <=> ( ? [X2: $int,X3: list] :
            ( in(X0,X3)
            & ( cons(X2,X3) = X1 ) )
        | ? [X4: $int,X5: list] :
            ( ( X0 = X4 )
            & ( cons(X4,X5) = X1 ) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

tff(f377,plain,
    spl8_44,
    inference(avatar_split_clause,[],[f82,f375]) ).

tff(f375,plain,
    ( spl8_44
  <=> ! [X0: $int,X1: list] :
        ( in(X0,sK5(X0,X1))
        | ( cons(sK6(X0,X1),sK7(X0,X1)) = X1 )
        | ~ sP1(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_44])]) ).

tff(f82,plain,
    ! [X0: $int,X1: list] :
      ( in(X0,sK5(X0,X1))
      | ( cons(sK6(X0,X1),sK7(X0,X1)) = X1 )
      | ~ sP1(X0,X1) ),
    inference(cnf_transformation,[],[f59]) ).

tff(f373,plain,
    spl8_43,
    inference(avatar_split_clause,[],[f81,f371]) ).

tff(f371,plain,
    ( spl8_43
  <=> ! [X0: $int,X1: list] :
        ( ( cons(sK4(X0,X1),sK5(X0,X1)) = X1 )
        | ( sK6(X0,X1) = X0 )
        | ~ sP1(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_43])]) ).

tff(f81,plain,
    ! [X0: $int,X1: list] :
      ( ( cons(sK4(X0,X1),sK5(X0,X1)) = X1 )
      | ( sK6(X0,X1) = X0 )
      | ~ sP1(X0,X1) ),
    inference(cnf_transformation,[],[f59]) ).

tff(f367,plain,
    spl8_42,
    inference(avatar_split_clause,[],[f70,f365]) ).

tff(f365,plain,
    ( spl8_42
  <=> ! [X0: $int,X1: list] :
        ( ( cons(sK2(X0,X1),sK3(X0,X1)) = X1 )
        | ( nil = X1 )
        | ~ sP0(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_42])]) ).

tff(f70,plain,
    ! [X0: $int,X1: list] :
      ( ( cons(sK2(X0,X1),sK3(X0,X1)) = X1 )
      | ( nil = X1 )
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f51]) ).

tff(f51,plain,
    ! [X0: $int,X1: list] :
      ( ( sP0(X0,X1)
        | ( ! [X2: $int,X3: list] :
              ( ~ inRange(X0,X3)
              | ~ $less(X2,X0)
              | $less(X2,0)
              | ( cons(X2,X3) != X1 ) )
          & ( nil != X1 ) ) )
      & ( ( inRange(X0,sK3(X0,X1))
          & $less(sK2(X0,X1),X0)
          & ~ $less(sK2(X0,X1),0)
          & ( cons(sK2(X0,X1),sK3(X0,X1)) = X1 ) )
        | ( nil = X1 )
        | ~ sP0(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f49,f50]) ).

tff(f50,plain,
    ! [X0: $int,X1: list] :
      ( ? [X4: $int,X5: list] :
          ( inRange(X0,X5)
          & $less(X4,X0)
          & ~ $less(X4,0)
          & ( cons(X4,X5) = X1 ) )
     => ( inRange(X0,sK3(X0,X1))
        & $less(sK2(X0,X1),X0)
        & ~ $less(sK2(X0,X1),0)
        & ( cons(sK2(X0,X1),sK3(X0,X1)) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f49,plain,
    ! [X0: $int,X1: list] :
      ( ( sP0(X0,X1)
        | ( ! [X2: $int,X3: list] :
              ( ~ inRange(X0,X3)
              | ~ $less(X2,X0)
              | $less(X2,0)
              | ( cons(X2,X3) != X1 ) )
          & ( nil != X1 ) ) )
      & ( ? [X4: $int,X5: list] :
            ( inRange(X0,X5)
            & $less(X4,X0)
            & ~ $less(X4,0)
            & ( cons(X4,X5) = X1 ) )
        | ( nil = X1 )
        | ~ sP0(X0,X1) ) ),
    inference(rectify,[],[f48]) ).

tff(f48,plain,
    ! [X0: $int,X1: list] :
      ( ( sP0(X0,X1)
        | ( ! [X2: $int,X3: list] :
              ( ~ inRange(X0,X3)
              | ~ $less(X2,X0)
              | $less(X2,0)
              | ( cons(X2,X3) != X1 ) )
          & ( nil != X1 ) ) )
      & ( ? [X2: $int,X3: list] :
            ( inRange(X0,X3)
            & $less(X2,X0)
            & ~ $less(X2,0)
            & ( cons(X2,X3) = X1 ) )
        | ( nil = X1 )
        | ~ sP0(X0,X1) ) ),
    inference(flattening,[],[f47]) ).

tff(f47,plain,
    ! [X0: $int,X1: list] :
      ( ( sP0(X0,X1)
        | ( ! [X2: $int,X3: list] :
              ( ~ inRange(X0,X3)
              | ~ $less(X2,X0)
              | $less(X2,0)
              | ( cons(X2,X3) != X1 ) )
          & ( nil != X1 ) ) )
      & ( ? [X2: $int,X3: list] :
            ( inRange(X0,X3)
            & $less(X2,X0)
            & ~ $less(X2,0)
            & ( cons(X2,X3) = X1 ) )
        | ( nil = X1 )
        | ~ sP0(X0,X1) ) ),
    inference(nnf_transformation,[],[f43]) ).

tff(f43,plain,
    ! [X0: $int,X1: list] :
      ( sP0(X0,X1)
    <=> ( ? [X2: $int,X3: list] :
            ( inRange(X0,X3)
            & $less(X2,X0)
            & ~ $less(X2,0)
            & ( cons(X2,X3) = X1 ) )
        | ( nil = X1 ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

tff(f363,plain,
    ( spl8_41
    | ~ spl8_31
    | ~ spl8_38 ),
    inference(avatar_split_clause,[],[f344,f335,f255,f360]) ).

tff(f255,plain,
    ( spl8_31
  <=> $less(0,count(4,cons(1,cons(2,cons(3,nil))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_31])]) ).

tff(f344,plain,
    ( $less(0,count(4,cons(2,cons(3,nil))))
    | ~ spl8_31
    | ~ spl8_38 ),
    inference(evaluation,[],[f343]) ).

tff(f343,plain,
    ( $less(0,count(4,cons(2,cons(3,nil))))
    | ( 1 = 4 )
    | ~ spl8_31
    | ~ spl8_38 ),
    inference(superposition,[],[f257,f336]) ).

tff(f257,plain,
    ( $less(0,count(4,cons(1,cons(2,cons(3,nil)))))
    | ~ spl8_31 ),
    inference(avatar_component_clause,[],[f255]) ).

tff(f354,plain,
    spl8_40,
    inference(avatar_split_clause,[],[f91,f352]) ).

tff(f352,plain,
    ( spl8_40
  <=> ! [X2: $int,X0: $int,X3: list] :
        ( sP0(X0,cons(X2,X3))
        | ~ inRange(X0,X3)
        | ~ $less(X2,X0)
        | $less(X2,0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_40])]) ).

tff(f91,plain,
    ! [X2: $int,X3: list,X0: $int] :
      ( sP0(X0,cons(X2,X3))
      | ~ inRange(X0,X3)
      | ~ $less(X2,X0)
      | $less(X2,0) ),
    inference(equality_resolution,[],[f75]) ).

tff(f75,plain,
    ! [X2: $int,X3: list,X0: $int,X1: list] :
      ( sP0(X0,X1)
      | ~ inRange(X0,X3)
      | ~ $less(X2,X0)
      | $less(X2,0)
      | ( cons(X2,X3) != X1 ) ),
    inference(cnf_transformation,[],[f51]) ).

tff(f348,plain,
    spl8_39,
    inference(avatar_split_clause,[],[f83,f346]) ).

tff(f346,plain,
    ( spl8_39
  <=> ! [X0: $int,X1: list] :
        ( in(X0,sK5(X0,X1))
        | ( sK6(X0,X1) = X0 )
        | ~ sP1(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_39])]) ).

tff(f83,plain,
    ! [X0: $int,X1: list] :
      ( in(X0,sK5(X0,X1))
      | ( sK6(X0,X1) = X0 )
      | ~ sP1(X0,X1) ),
    inference(cnf_transformation,[],[f59]) ).

tff(f337,plain,
    spl8_38,
    inference(avatar_split_clause,[],[f89,f335]) ).

tff(f89,plain,
    ! [X2: list,X0: $int,X1: $int] :
      ( ( count(X0,cons(X1,X2)) = count(X0,X2) )
      | ( X0 = X1 ) ),
    inference(cnf_transformation,[],[f41]) ).

tff(f41,plain,
    ! [X0: $int,X1: $int,X2: list] :
      ( ( count(X0,cons(X1,X2)) = count(X0,X2) )
      | ( X0 = X1 ) ),
    inference(ennf_transformation,[],[f39]) ).

tff(f39,plain,
    ! [X0: $int,X1: $int,X2: list] :
      ( ( X0 != X1 )
     => ( count(X0,cons(X1,X2)) = count(X0,X2) ) ),
    inference(rectify,[],[f10]) ).

tff(f10,axiom,
    ! [X0: $int,X3: $int,X4: list,X5: $int] :
      ( ( X0 != X3 )
     => ( count(X0,cons(X3,X4)) = count(X0,X4) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_3) ).

tff(f299,plain,
    spl8_37,
    inference(avatar_split_clause,[],[f97,f297]) ).

tff(f297,plain,
    ( spl8_37
  <=> ! [X2: list,X1: $int] : ( count(X1,cons(X1,X2)) = $sum(1,count(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_37])]) ).

tff(f97,plain,
    ! [X2: list,X1: $int] : ( count(X1,cons(X1,X2)) = $sum(1,count(X1,X2)) ),
    inference(forward_demodulation,[],[f96,f19]) ).

tff(f19,plain,
    ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
    introduced(theory_axiom_135,[]) ).

tff(f96,plain,
    ! [X2: list,X1: $int] : ( count(X1,cons(X1,X2)) = $sum(count(X1,X2),1) ),
    inference(equality_resolution,[],[f90]) ).

tff(f90,plain,
    ! [X2: list,X0: $int,X1: $int] :
      ( ( count(X0,cons(X1,X2)) = $sum(count(X0,X2),1) )
      | ( X0 != X1 ) ),
    inference(cnf_transformation,[],[f42]) ).

tff(f42,plain,
    ! [X0: $int,X1: $int,X2: list] :
      ( ( count(X0,cons(X1,X2)) = $sum(count(X0,X2),1) )
      | ( X0 != X1 ) ),
    inference(ennf_transformation,[],[f40]) ).

tff(f40,plain,
    ! [X0: $int,X1: $int,X2: list] :
      ( ( X0 = X1 )
     => ( count(X0,cons(X1,X2)) = $sum(count(X0,X2),1) ) ),
    inference(rectify,[],[f11]) ).

tff(f11,axiom,
    ! [X0: $int,X3: $int,X4: list,X5: $int] :
      ( ( X0 = X3 )
     => ( count(X0,cons(X3,X4)) = $sum(count(X0,X4),1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_4) ).

tff(f295,plain,
    spl8_36,
    inference(avatar_split_clause,[],[f88,f293]) ).

tff(f88,plain,
    ! [X2: list,X0: $int,X1: list] : ( append(cons(X0,X1),X2) = cons(X0,append(X1,X2)) ),
    inference(cnf_transformation,[],[f38]) ).

tff(f38,plain,
    ! [X0: $int,X1: list,X2: list] : ( append(cons(X0,X1),X2) = cons(X0,append(X1,X2)) ),
    inference(rectify,[],[f13]) ).

tff(f13,axiom,
    ! [X6: $int,X0: list,X1: list] : ( append(cons(X6,X0),X1) = cons(X6,append(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l_7) ).

tff(f291,plain,
    spl8_35,
    inference(avatar_split_clause,[],[f73,f289]) ).

tff(f289,plain,
    ( spl8_35
  <=> ! [X0: $int,X1: list] :
        ( inRange(X0,sK3(X0,X1))
        | ( nil = X1 )
        | ~ sP0(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_35])]) ).

tff(f73,plain,
    ! [X0: $int,X1: list] :
      ( inRange(X0,sK3(X0,X1))
      | ( nil = X1 )
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f51]) ).

tff(f287,plain,
    spl8_34,
    inference(avatar_split_clause,[],[f72,f285]) ).

tff(f285,plain,
    ( spl8_34
  <=> ! [X0: $int,X1: list] :
        ( $less(sK2(X0,X1),X0)
        | ( nil = X1 )
        | ~ sP0(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_34])]) ).

tff(f72,plain,
    ! [X0: $int,X1: list] :
      ( $less(sK2(X0,X1),X0)
      | ( nil = X1 )
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f51]) ).

tff(f283,plain,
    spl8_33,
    inference(avatar_split_clause,[],[f71,f281]) ).

tff(f281,plain,
    ( spl8_33
  <=> ! [X0: $int,X1: list] :
        ( ~ $less(sK2(X0,X1),0)
        | ( nil = X1 )
        | ~ sP0(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_33])]) ).

tff(f71,plain,
    ! [X0: $int,X1: list] :
      ( ~ $less(sK2(X0,X1),0)
      | ( nil = X1 )
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f51]) ).

tff(f279,plain,
    spl8_32,
    inference(avatar_split_clause,[],[f20,f277]) ).

tff(f20,plain,
    ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
    introduced(theory_axiom_136,[]) ).

tff(f258,plain,
    ( spl8_31
    | ~ spl8_1
    | ~ spl8_22 ),
    inference(avatar_split_clause,[],[f206,f189,f99,f255]) ).

tff(f99,plain,
    ( spl8_1
  <=> in(4,cons(1,cons(2,cons(3,nil)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).

tff(f189,plain,
    ( spl8_22
  <=> ! [X0: $int,X1: list] :
        ( $less(0,count(X0,X1))
        | ~ in(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_22])]) ).

tff(f206,plain,
    ( $less(0,count(4,cons(1,cons(2,cons(3,nil)))))
    | ~ spl8_1
    | ~ spl8_22 ),
    inference(resolution,[],[f190,f101]) ).

tff(f101,plain,
    ( in(4,cons(1,cons(2,cons(3,nil))))
    | ~ spl8_1 ),
    inference(avatar_component_clause,[],[f99]) ).

tff(f190,plain,
    ( ! [X0: $int,X1: list] :
        ( ~ in(X0,X1)
        | $less(0,count(X0,X1)) )
    | ~ spl8_22 ),
    inference(avatar_component_clause,[],[f189]) ).

tff(f243,plain,
    spl8_30,
    inference(avatar_split_clause,[],[f65,f241]) ).

tff(f65,plain,
    ! [X0: list] :
      ( ( cons(head(X0),tail(X0)) = X0 )
      | ( nil = X0 ) ),
    inference(cnf_transformation,[],[f33]) ).

tff(f33,plain,
    ! [X0: list] :
      ( ( cons(head(X0),tail(X0)) = X0 )
      | ( nil = X0 ) ),
    inference(rectify,[],[f3]) ).

tff(f3,axiom,
    ! [X1: list] :
      ( ( cons(head(X1),tail(X1)) = X1 )
      | ( nil = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3) ).

tff(f239,plain,
    spl8_29,
    inference(avatar_split_clause,[],[f27,f237]) ).

tff(f27,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( ~ $less(X0,X1)
      | $less($sum(X0,X2),$sum(X1,X2)) ),
    introduced(theory_axiom_145,[]) ).

tff(f235,plain,
    spl8_28,
    inference(avatar_split_clause,[],[f22,f233]) ).

tff(f22,plain,
    ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
    introduced(theory_axiom_139,[]) ).

tff(f221,plain,
    spl8_27,
    inference(avatar_split_clause,[],[f69,f219]) ).

tff(f69,plain,
    ! [X0: $int,X1: list] : ( length(cons(X0,X1)) = $sum(1,length(X1)) ),
    inference(cnf_transformation,[],[f34]) ).

tff(f34,plain,
    ! [X0: $int,X1: list] : ( length(cons(X0,X1)) = $sum(1,length(X1)) ),
    inference(rectify,[],[f8]) ).

tff(f8,axiom,
    ! [X3: $int,X4: list] : ( length(cons(X3,X4)) = $sum(1,length(X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l_1) ).

tff(f217,plain,
    spl8_26,
    inference(avatar_split_clause,[],[f26,f215]) ).

tff(f215,plain,
    ( spl8_26
  <=> ! [X0: $int,X1: $int] :
        ( $less(X0,X1)
        | $less(X1,X0)
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_26])]) ).

tff(f26,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X0,X1)
      | $less(X1,X0)
      | ( X0 = X1 ) ),
    introduced(theory_axiom_144,[]) ).

tff(f213,plain,
    spl8_25,
    inference(avatar_split_clause,[],[f25,f211]) ).

tff(f25,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( ~ $less(X0,X1)
      | ~ $less(X1,X2)
      | $less(X0,X2) ),
    introduced(theory_axiom_143,[]) ).

tff(f199,plain,
    spl8_24,
    inference(avatar_split_clause,[],[f93,f197]) ).

tff(f93,plain,
    ! [X2: $int,X3: list,X0: $int] :
      ( sP1(X0,cons(X2,X3))
      | ~ in(X0,X3) ),
    inference(equality_resolution,[],[f85]) ).

tff(f85,plain,
    ! [X2: $int,X3: list,X0: $int,X1: list] :
      ( sP1(X0,X1)
      | ~ in(X0,X3)
      | ( cons(X2,X3) != X1 ) ),
    inference(cnf_transformation,[],[f59]) ).

tff(f195,plain,
    spl8_23,
    inference(avatar_split_clause,[],[f79,f193]) ).

tff(f79,plain,
    ! [X0: $int,X1: list] :
      ( in(X0,X1)
      | ~ $less(0,count(X0,X1)) ),
    inference(cnf_transformation,[],[f53]) ).

tff(f53,plain,
    ! [X0: $int,X1: list] :
      ( ( in(X0,X1)
        | ~ $less(0,count(X0,X1)) )
      & ( $less(0,count(X0,X1))
        | ~ in(X0,X1) ) ),
    inference(nnf_transformation,[],[f36]) ).

tff(f36,plain,
    ! [X0: $int,X1: list] :
      ( in(X0,X1)
    <=> $less(0,count(X0,X1)) ),
    inference(rectify,[],[f18]) ).

tff(f18,plain,
    ! [X5: $int,X1: list] :
      ( in(X5,X1)
    <=> $less(0,count(X5,X1)) ),
    inference(theory_normalization,[],[f14]) ).

tff(f14,axiom,
    ! [X5: $int,X1: list] :
      ( in(X5,X1)
    <=> $greater(count(X5,X1),0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_8) ).

tff(f191,plain,
    spl8_22,
    inference(avatar_split_clause,[],[f78,f189]) ).

tff(f78,plain,
    ! [X0: $int,X1: list] :
      ( $less(0,count(X0,X1))
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f53]) ).

tff(f187,plain,
    spl8_21,
    inference(avatar_split_clause,[],[f30,f185]) ).

tff(f30,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less(X0,X1)
      | ~ $less(X1,$sum(X0,1)) ),
    introduced(theory_axiom_161,[]) ).

tff(f183,plain,
    spl8_20,
    inference(avatar_split_clause,[],[f28,f181]) ).

tff(f28,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X0,X1)
      | $less(X1,$sum(X0,1)) ),
    introduced(theory_axiom_147,[]) ).

tff(f179,plain,
    ( spl8_19
    | ~ spl8_1
    | ~ spl8_16 ),
    inference(avatar_split_clause,[],[f169,f161,f99,f176]) ).

tff(f176,plain,
    ( spl8_19
  <=> sP1(4,cons(1,cons(2,cons(3,nil)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_19])]) ).

tff(f161,plain,
    ( spl8_16
  <=> ! [X0: $int,X1: list] :
        ( sP1(X0,X1)
        | ~ in(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_16])]) ).

tff(f169,plain,
    ( sP1(4,cons(1,cons(2,cons(3,nil))))
    | ~ spl8_1
    | ~ spl8_16 ),
    inference(resolution,[],[f162,f101]) ).

tff(f162,plain,
    ( ! [X0: $int,X1: list] :
        ( ~ in(X0,X1)
        | sP1(X0,X1) )
    | ~ spl8_16 ),
    inference(avatar_component_clause,[],[f161]) ).

tff(f174,plain,
    spl8_18,
    inference(avatar_split_clause,[],[f19,f172]) ).

tff(f167,plain,
    spl8_17,
    inference(avatar_split_clause,[],[f87,f165]) ).

tff(f87,plain,
    ! [X0: $int,X1: list] :
      ( in(X0,X1)
      | ~ sP1(X0,X1) ),
    inference(cnf_transformation,[],[f60]) ).

tff(f60,plain,
    ! [X0: $int,X1: list] :
      ( ( in(X0,X1)
        | ~ sP1(X0,X1) )
      & ( sP1(X0,X1)
        | ~ in(X0,X1) ) ),
    inference(nnf_transformation,[],[f46]) ).

tff(f46,plain,
    ! [X0: $int,X1: list] :
      ( in(X0,X1)
    <=> sP1(X0,X1) ),
    inference(definition_folding,[],[f37,f45]) ).

tff(f37,plain,
    ! [X0: $int,X1: list] :
      ( in(X0,X1)
    <=> ( ? [X2: $int,X3: list] :
            ( in(X0,X3)
            & ( cons(X2,X3) = X1 ) )
        | ? [X4: $int,X5: list] :
            ( ( X0 = X4 )
            & ( cons(X4,X5) = X1 ) ) ) ),
    inference(rectify,[],[f5]) ).

tff(f5,axiom,
    ! [X2: $int,X1: list] :
      ( in(X2,X1)
    <=> ( ? [X3: $int,X4: list] :
            ( in(X2,X4)
            & ( cons(X3,X4) = X1 ) )
        | ? [X3: $int,X4: list] :
            ( ( X2 = X3 )
            & ( cons(X3,X4) = X1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',in_conv) ).

tff(f163,plain,
    spl8_16,
    inference(avatar_split_clause,[],[f86,f161]) ).

tff(f86,plain,
    ! [X0: $int,X1: list] :
      ( sP1(X0,X1)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f60]) ).

tff(f159,plain,
    spl8_15,
    inference(avatar_split_clause,[],[f77,f157]) ).

tff(f77,plain,
    ! [X0: $int,X1: list] :
      ( inRange(X0,X1)
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f52]) ).

tff(f52,plain,
    ! [X0: $int,X1: list] :
      ( ( inRange(X0,X1)
        | ~ sP0(X0,X1) )
      & ( sP0(X0,X1)
        | ~ inRange(X0,X1) ) ),
    inference(nnf_transformation,[],[f44]) ).

tff(f44,plain,
    ! [X0: $int,X1: list] :
      ( inRange(X0,X1)
    <=> sP0(X0,X1) ),
    inference(definition_folding,[],[f35,f43]) ).

tff(f35,plain,
    ! [X0: $int,X1: list] :
      ( inRange(X0,X1)
    <=> ( ? [X2: $int,X3: list] :
            ( inRange(X0,X3)
            & $less(X2,X0)
            & ~ $less(X2,0)
            & ( cons(X2,X3) = X1 ) )
        | ( nil = X1 ) ) ),
    inference(rectify,[],[f17]) ).

tff(f17,plain,
    ! [X5: $int,X1: list] :
      ( inRange(X5,X1)
    <=> ( ? [X0: $int,X4: list] :
            ( inRange(X5,X4)
            & $less(X0,X5)
            & ~ $less(X0,0)
            & ( cons(X0,X4) = X1 ) )
        | ( nil = X1 ) ) ),
    inference(theory_normalization,[],[f6]) ).

tff(f6,axiom,
    ! [X5: $int,X1: list] :
      ( inRange(X5,X1)
    <=> ( ? [X0: $int,X4: list] :
            ( inRange(X5,X4)
            & $less(X0,X5)
            & $lesseq(0,X0)
            & ( cons(X0,X4) = X1 ) )
        | ( nil = X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',inRange) ).

tff(f155,plain,
    spl8_14,
    inference(avatar_split_clause,[],[f76,f153]) ).

tff(f153,plain,
    ( spl8_14
  <=> ! [X0: $int,X1: list] :
        ( sP0(X0,X1)
        | ~ inRange(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_14])]) ).

tff(f76,plain,
    ! [X0: $int,X1: list] :
      ( sP0(X0,X1)
      | ~ inRange(X0,X1) ),
    inference(cnf_transformation,[],[f52]) ).

tff(f151,plain,
    spl8_13,
    inference(avatar_split_clause,[],[f68,f149]) ).

tff(f68,plain,
    ! [X0: $int,X1: list] : ( head(cons(X0,X1)) = X0 ),
    inference(cnf_transformation,[],[f1]) ).

tff(f1,axiom,
    ! [X0: $int,X1: list] : ( head(cons(X0,X1)) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1) ).

tff(f147,plain,
    spl8_12,
    inference(avatar_split_clause,[],[f67,f145]) ).

tff(f67,plain,
    ! [X0: $int,X1: list] : ( tail(cons(X0,X1)) = X1 ),
    inference(cnf_transformation,[],[f2]) ).

tff(f2,axiom,
    ! [X0: $int,X1: list] : ( tail(cons(X0,X1)) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2) ).

tff(f143,plain,
    spl8_11,
    inference(avatar_split_clause,[],[f23,f141]) ).

tff(f23,plain,
    ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
    introduced(theory_axiom_140,[]) ).

tff(f139,plain,
    spl8_10,
    inference(avatar_split_clause,[],[f95,f137]) ).

tff(f95,plain,
    ! [X4: $int,X5: list] : sP1(X4,cons(X4,X5)),
    inference(equality_resolution,[],[f94]) ).

tff(f94,plain,
    ! [X1: list,X4: $int,X5: list] :
      ( sP1(X4,X1)
      | ( cons(X4,X5) != X1 ) ),
    inference(equality_resolution,[],[f84]) ).

tff(f84,plain,
    ! [X0: $int,X1: list,X4: $int,X5: list] :
      ( sP1(X0,X1)
      | ( X0 != X4 )
      | ( cons(X4,X5) != X1 ) ),
    inference(cnf_transformation,[],[f59]) ).

tff(f135,plain,
    spl8_9,
    inference(avatar_split_clause,[],[f66,f133]) ).

tff(f66,plain,
    ! [X0: $int,X1: list] : ( cons(X0,X1) != nil ),
    inference(cnf_transformation,[],[f4]) ).

tff(f4,axiom,
    ! [X0: $int,X1: list] : ( cons(X0,X1) != nil ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4) ).

tff(f131,plain,
    spl8_8,
    inference(avatar_split_clause,[],[f64,f129]) ).

tff(f64,plain,
    ! [X0: list] : ( append(nil,X0) = X0 ),
    inference(cnf_transformation,[],[f32]) ).

tff(f32,plain,
    ! [X0: list] : ( append(nil,X0) = X0 ),
    inference(rectify,[],[f12]) ).

tff(f12,axiom,
    ! [X1: list] : ( append(nil,X1) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l_6) ).

tff(f127,plain,
    spl8_7,
    inference(avatar_split_clause,[],[f63,f125]) ).

tff(f63,plain,
    ! [X0: $int] : ( 0 = count(X0,nil) ),
    inference(cnf_transformation,[],[f9]) ).

tff(f9,axiom,
    ! [X0: $int] : ( 0 = count(X0,nil) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a) ).

tff(f123,plain,
    spl8_6,
    inference(avatar_split_clause,[],[f29,f121]) ).

tff(f121,plain,
    ( spl8_6
  <=> ! [X0: $int] : ( $uminus($uminus(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_6])]) ).

tff(f29,plain,
    ! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
    introduced(theory_axiom_148,[]) ).

tff(f119,plain,
    spl8_5,
    inference(avatar_split_clause,[],[f21,f117]) ).

tff(f117,plain,
    ( spl8_5
  <=> ! [X0: $int] : ( $sum(X0,0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_5])]) ).

tff(f21,plain,
    ! [X0: $int] : ( $sum(X0,0) = X0 ),
    introduced(theory_axiom_137,[]) ).

tff(f115,plain,
    spl8_4,
    inference(avatar_split_clause,[],[f62,f112]) ).

tff(f112,plain,
    ( spl8_4
  <=> ( 0 = length(nil) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_4])]) ).

tff(f62,plain,
    0 = length(nil),
    inference(cnf_transformation,[],[f7]) ).

tff(f7,axiom,
    0 = length(nil),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l) ).

tff(f110,plain,
    spl8_3,
    inference(avatar_split_clause,[],[f92,f108]) ).

tff(f92,plain,
    ! [X0: $int] : sP0(X0,nil),
    inference(equality_resolution,[],[f74]) ).

tff(f74,plain,
    ! [X0: $int,X1: list] :
      ( sP0(X0,X1)
      | ( nil != X1 ) ),
    inference(cnf_transformation,[],[f51]) ).

tff(f106,plain,
    spl8_2,
    inference(avatar_split_clause,[],[f24,f104]) ).

tff(f24,plain,
    ! [X0: $int] : ~ $less(X0,X0),
    introduced(theory_axiom_142,[]) ).

tff(f102,plain,
    spl8_1,
    inference(avatar_split_clause,[],[f61,f99]) ).

tff(f61,plain,
    in(4,cons(1,cons(2,cons(3,nil)))),
    inference(cnf_transformation,[],[f31]) ).

tff(f31,plain,
    in(4,cons(1,cons(2,cons(3,nil)))),
    inference(flattening,[],[f16]) ).

tff(f16,negated_conjecture,
    ~ ~ in(4,cons(1,cons(2,cons(3,nil)))),
    inference(negated_conjecture,[],[f15]) ).

tff(f15,conjecture,
    ~ in(4,cons(1,cons(2,cons(3,nil)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : DAT080_1 : TPTP v8.1.2. Released v6.1.0.
% 0.07/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.36  % Computer : n005.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit   : 300
% 0.16/0.36  % WCLimit    : 300
% 0.16/0.36  % DateTime   : Mon Apr 29 22:03:41 EDT 2024
% 0.16/0.36  % CPUTime    : 
% 0.16/0.36  % (22575)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.38  % (22578)WARNING: value z3 for option sas not known
% 0.16/0.38  % (22577)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.38  % (22579)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.38  % (22576)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.38  % (22580)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)
% 0.16/0.38  % (22578)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)
% 0.16/0.38  % (22582)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)
% 0.16/0.38  % (22581)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)
% 0.16/0.38  % (22577)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.16/0.38  % (22576)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.16/0.38  % (22579)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.16/0.38  % (22577)Terminated due to inappropriate strategy.
% 0.16/0.38  % (22577)------------------------------
% 0.16/0.38  % (22577)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.16/0.38  % (22579)Terminated due to inappropriate strategy.
% 0.16/0.38  % (22579)------------------------------
% 0.16/0.38  % (22579)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.16/0.38  % (22576)Terminated due to inappropriate strategy.
% 0.16/0.38  % (22576)------------------------------
% 0.16/0.38  % (22576)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.16/0.38  % (22577)Termination reason: Inappropriate
% 0.16/0.38  % (22579)Termination reason: Inappropriate
% 0.16/0.38  % (22576)Termination reason: Inappropriate
% 0.16/0.38  
% 0.16/0.38  
% 0.16/0.38  
% 0.16/0.38  % (22577)Memory used [KB]: 803
% 0.16/0.38  % (22579)Memory used [KB]: 803
% 0.16/0.38  % (22576)Memory used [KB]: 803
% 0.16/0.38  % (22577)Time elapsed: 0.003 s
% 0.16/0.38  % (22579)Time elapsed: 0.003 s
% 0.16/0.38  % (22576)Time elapsed: 0.003 s
% 0.16/0.38  % (22577)Instructions burned: 3 (million)
% 0.16/0.38  % (22579)Instructions burned: 3 (million)
% 0.16/0.38  % (22576)Instructions burned: 3 (million)
% 0.16/0.38  % (22577)------------------------------
% 0.16/0.38  % (22577)------------------------------
% 0.16/0.38  % (22579)------------------------------
% 0.16/0.38  % (22579)------------------------------
% 0.16/0.38  % (22576)------------------------------
% 0.16/0.38  % (22576)------------------------------
% 0.22/0.40  % (22583)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.22/0.40  % (22584)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.22/0.40  % (22580)First to succeed.
% 0.22/0.40  % (22585)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.22/0.40  % (22583)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.22/0.40  % (22583)Terminated due to inappropriate strategy.
% 0.22/0.40  % (22583)------------------------------
% 0.22/0.40  % (22583)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.40  % (22583)Termination reason: Inappropriate
% 0.22/0.40  
% 0.22/0.40  % (22583)Memory used [KB]: 801
% 0.22/0.40  % (22583)Time elapsed: 0.002 s
% 0.22/0.40  % (22583)Instructions burned: 3 (million)
% 0.22/0.40  % (22583)------------------------------
% 0.22/0.40  % (22583)------------------------------
% 0.22/0.40  % (22580)Refutation found. Thanks to Tanya!
% 0.22/0.40  % SZS status Theorem for theBenchmark
% 0.22/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.41  % (22580)------------------------------
% 0.22/0.41  % (22580)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.41  % (22580)Termination reason: Refutation
% 0.22/0.41  
% 0.22/0.41  % (22580)Memory used [KB]: 1130
% 0.22/0.41  % (22580)Time elapsed: 0.024 s
% 0.22/0.41  % (22580)Instructions burned: 34 (million)
% 0.22/0.41  % (22580)------------------------------
% 0.22/0.41  % (22580)------------------------------
% 0.22/0.41  % (22575)Success in time 0.039 s
%------------------------------------------------------------------------------