TSTP Solution File: GRP237-1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : GRP237-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s

% Computer : n009.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 : Wed Aug 31 16:20:59 EDT 2022

% Result   : Unsatisfiable 0.19s 0.52s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   66
% Syntax   : Number of formulae    :  258 (   6 unt;   0 def)
%            Number of atoms       :  800 ( 299 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives : 1020 ( 478   ~; 514   |;   0   &)
%                                         (  28 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   30 (  28 usr;  29 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;  10 con; 0-2 aty)
%            Number of variables   :   65 (  65   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f728,plain,
    $false,
    inference(avatar_sat_refutation,[],[f58,f63,f68,f73,f78,f79,f95,f100,f104,f109,f114,f115,f116,f120,f125,f130,f131,f136,f137,f138,f139,f140,f142,f143,f144,f145,f146,f147,f148,f149,f150,f151,f152,f153,f154,f155,f157,f158,f167,f177,f186,f191,f248,f268,f271,f307,f325,f404,f508,f512,f549,f608,f657,f702,f722,f727]) ).

fof(f727,plain,
    ( ~ spl3_24
    | ~ spl3_11
    | spl3_19
    | ~ spl3_23
    | ~ spl3_24 ),
    inference(avatar_split_clause,[],[f726,f198,f193,f170,f97,f198]) ).

fof(f97,plain,
    ( spl3_11
  <=> sk_c9 = inverse(sk_c6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_11])]) ).

fof(f170,plain,
    ( spl3_19
  <=> sk_c9 = inverse(sk_c8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_19])]) ).

fof(f193,plain,
    ( spl3_23
  <=> sk_c9 = sk_c8 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_23])]) ).

fof(f198,plain,
    ( spl3_24
  <=> identity = sk_c9 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_24])]) ).

fof(f726,plain,
    ( identity != sk_c9
    | ~ spl3_11
    | spl3_19
    | ~ spl3_23
    | ~ spl3_24 ),
    inference(forward_demodulation,[],[f725,f686]) ).

fof(f686,plain,
    ( identity = inverse(identity)
    | ~ spl3_11
    | ~ spl3_24 ),
    inference(backward_demodulation,[],[f557,f681]) ).

fof(f681,plain,
    ( identity = sk_c6
    | ~ spl3_11
    | ~ spl3_24 ),
    inference(superposition,[],[f1,f564]) ).

fof(f564,plain,
    ( identity = multiply(identity,sk_c6)
    | ~ spl3_11
    | ~ spl3_24 ),
    inference(backward_demodulation,[],[f441,f199]) ).

fof(f199,plain,
    ( identity = sk_c9
    | ~ spl3_24 ),
    inference(avatar_component_clause,[],[f198]) ).

fof(f441,plain,
    ( identity = multiply(sk_c9,sk_c6)
    | ~ spl3_11 ),
    inference(superposition,[],[f2,f99]) ).

fof(f99,plain,
    ( sk_c9 = inverse(sk_c6)
    | ~ spl3_11 ),
    inference(avatar_component_clause,[],[f97]) ).

fof(f2,axiom,
    ! [X0] : identity = multiply(inverse(X0),X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).

fof(f1,axiom,
    ! [X0] : multiply(identity,X0) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).

fof(f557,plain,
    ( identity = inverse(sk_c6)
    | ~ spl3_11
    | ~ spl3_24 ),
    inference(backward_demodulation,[],[f99,f199]) ).

fof(f725,plain,
    ( sk_c9 != inverse(identity)
    | spl3_19
    | ~ spl3_23
    | ~ spl3_24 ),
    inference(forward_demodulation,[],[f172,f560]) ).

fof(f560,plain,
    ( identity = sk_c8
    | ~ spl3_23
    | ~ spl3_24 ),
    inference(backward_demodulation,[],[f194,f199]) ).

fof(f194,plain,
    ( sk_c9 = sk_c8
    | ~ spl3_23 ),
    inference(avatar_component_clause,[],[f193]) ).

fof(f172,plain,
    ( sk_c9 != inverse(sk_c8)
    | spl3_19 ),
    inference(avatar_component_clause,[],[f170]) ).

fof(f722,plain,
    ( spl3_20
    | ~ spl3_23
    | ~ spl3_24 ),
    inference(avatar_contradiction_clause,[],[f721]) ).

fof(f721,plain,
    ( $false
    | spl3_20
    | ~ spl3_23
    | ~ spl3_24 ),
    inference(trivial_inequality_removal,[],[f720]) ).

fof(f720,plain,
    ( identity != identity
    | spl3_20
    | ~ spl3_23
    | ~ spl3_24 ),
    inference(superposition,[],[f708,f560]) ).

fof(f708,plain,
    ( identity != sk_c8
    | spl3_20
    | ~ spl3_24 ),
    inference(forward_demodulation,[],[f707,f1]) ).

fof(f707,plain,
    ( sk_c8 != multiply(identity,identity)
    | spl3_20
    | ~ spl3_24 ),
    inference(forward_demodulation,[],[f176,f199]) ).

fof(f176,plain,
    ( sk_c8 != multiply(sk_c9,identity)
    | spl3_20 ),
    inference(avatar_component_clause,[],[f174]) ).

fof(f174,plain,
    ( spl3_20
  <=> sk_c8 = multiply(sk_c9,identity) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_20])]) ).

fof(f702,plain,
    ( spl3_2
    | ~ spl3_11
    | ~ spl3_23
    | ~ spl3_24 ),
    inference(avatar_contradiction_clause,[],[f701]) ).

fof(f701,plain,
    ( $false
    | spl3_2
    | ~ spl3_11
    | ~ spl3_23
    | ~ spl3_24 ),
    inference(trivial_inequality_removal,[],[f698]) ).

fof(f698,plain,
    ( identity != identity
    | spl3_2
    | ~ spl3_11
    | ~ spl3_23
    | ~ spl3_24 ),
    inference(superposition,[],[f567,f686]) ).

fof(f567,plain,
    ( identity != inverse(identity)
    | spl3_2
    | ~ spl3_23
    | ~ spl3_24 ),
    inference(backward_demodulation,[],[f513,f199]) ).

fof(f513,plain,
    ( sk_c9 != inverse(sk_c9)
    | spl3_2
    | ~ spl3_23 ),
    inference(backward_demodulation,[],[f56,f194]) ).

fof(f56,plain,
    ( inverse(sk_c9) != sk_c8
    | spl3_2 ),
    inference(avatar_component_clause,[],[f55]) ).

fof(f55,plain,
    ( spl3_2
  <=> inverse(sk_c9) = sk_c8 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

fof(f657,plain,
    ( ~ spl3_24
    | ~ spl3_6
    | ~ spl3_23
    | ~ spl3_24
    | spl3_28 ),
    inference(avatar_split_clause,[],[f656,f245,f198,f193,f75,f198]) ).

fof(f75,plain,
    ( spl3_6
  <=> sk_c9 = inverse(sk_c2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).

fof(f245,plain,
    ( spl3_28
  <=> sk_c9 = multiply(sk_c8,inverse(sk_c8)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_28])]) ).

fof(f656,plain,
    ( identity != sk_c9
    | ~ spl3_6
    | ~ spl3_23
    | ~ spl3_24
    | spl3_28 ),
    inference(forward_demodulation,[],[f655,f1]) ).

fof(f655,plain,
    ( sk_c9 != multiply(identity,identity)
    | ~ spl3_6
    | ~ spl3_23
    | ~ spl3_24
    | spl3_28 ),
    inference(forward_demodulation,[],[f622,f654]) ).

fof(f654,plain,
    ( identity = inverse(identity)
    | ~ spl3_6
    | ~ spl3_24 ),
    inference(forward_demodulation,[],[f630,f199]) ).

fof(f630,plain,
    ( sk_c9 = inverse(identity)
    | ~ spl3_6
    | ~ spl3_24 ),
    inference(forward_demodulation,[],[f77,f627]) ).

fof(f627,plain,
    ( identity = sk_c2
    | ~ spl3_6
    | ~ spl3_24 ),
    inference(forward_demodulation,[],[f626,f2]) ).

fof(f626,plain,
    ( sk_c2 = multiply(inverse(identity),identity)
    | ~ spl3_6
    | ~ spl3_24 ),
    inference(forward_demodulation,[],[f483,f199]) ).

fof(f483,plain,
    ( sk_c2 = multiply(inverse(sk_c9),identity)
    | ~ spl3_6 ),
    inference(superposition,[],[f218,f161]) ).

fof(f161,plain,
    ( identity = multiply(sk_c9,sk_c2)
    | ~ spl3_6 ),
    inference(superposition,[],[f2,f77]) ).

fof(f218,plain,
    ! [X6,X7] : multiply(inverse(X6),multiply(X6,X7)) = X7,
    inference(forward_demodulation,[],[f208,f1]) ).

fof(f208,plain,
    ! [X6,X7] : multiply(inverse(X6),multiply(X6,X7)) = multiply(identity,X7),
    inference(superposition,[],[f3,f2]) ).

fof(f3,axiom,
    ! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).

fof(f77,plain,
    ( sk_c9 = inverse(sk_c2)
    | ~ spl3_6 ),
    inference(avatar_component_clause,[],[f75]) ).

fof(f622,plain,
    ( sk_c9 != multiply(identity,inverse(identity))
    | ~ spl3_23
    | ~ spl3_24
    | spl3_28 ),
    inference(forward_demodulation,[],[f247,f560]) ).

fof(f247,plain,
    ( sk_c9 != multiply(sk_c8,inverse(sk_c8))
    | spl3_28 ),
    inference(avatar_component_clause,[],[f245]) ).

fof(f608,plain,
    ( ~ spl3_3
    | spl3_21
    | ~ spl3_24 ),
    inference(avatar_contradiction_clause,[],[f607]) ).

fof(f607,plain,
    ( $false
    | ~ spl3_3
    | spl3_21
    | ~ spl3_24 ),
    inference(trivial_inequality_removal,[],[f606]) ).

fof(f606,plain,
    ( identity != identity
    | ~ spl3_3
    | spl3_21
    | ~ spl3_24 ),
    inference(superposition,[],[f559,f592]) ).

fof(f592,plain,
    ( identity = inverse(identity)
    | ~ spl3_3
    | ~ spl3_24 ),
    inference(forward_demodulation,[],[f555,f583]) ).

fof(f583,plain,
    ( identity = sk_c1
    | ~ spl3_3
    | ~ spl3_24 ),
    inference(forward_demodulation,[],[f562,f2]) ).

fof(f562,plain,
    ( sk_c1 = multiply(inverse(identity),identity)
    | ~ spl3_3
    | ~ spl3_24 ),
    inference(backward_demodulation,[],[f261,f199]) ).

fof(f261,plain,
    ( sk_c1 = multiply(inverse(sk_c9),identity)
    | ~ spl3_3 ),
    inference(superposition,[],[f218,f160]) ).

fof(f160,plain,
    ( identity = multiply(sk_c9,sk_c1)
    | ~ spl3_3 ),
    inference(superposition,[],[f2,f62]) ).

fof(f62,plain,
    ( sk_c9 = inverse(sk_c1)
    | ~ spl3_3 ),
    inference(avatar_component_clause,[],[f60]) ).

fof(f60,plain,
    ( spl3_3
  <=> sk_c9 = inverse(sk_c1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).

fof(f555,plain,
    ( identity = inverse(sk_c1)
    | ~ spl3_3
    | ~ spl3_24 ),
    inference(backward_demodulation,[],[f62,f199]) ).

fof(f559,plain,
    ( identity != inverse(identity)
    | spl3_21
    | ~ spl3_24 ),
    inference(backward_demodulation,[],[f181,f199]) ).

fof(f181,plain,
    ( sk_c9 != inverse(identity)
    | spl3_21 ),
    inference(avatar_component_clause,[],[f179]) ).

fof(f179,plain,
    ( spl3_21
  <=> sk_c9 = inverse(identity) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_21])]) ).

fof(f549,plain,
    ( spl3_24
    | ~ spl3_13
    | ~ spl3_16
    | ~ spl3_17
    | ~ spl3_23 ),
    inference(avatar_split_clause,[],[f548,f193,f127,f122,f106,f198]) ).

fof(f106,plain,
    ( spl3_13
  <=> sk_c5 = inverse(sk_c4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_13])]) ).

fof(f122,plain,
    ( spl3_16
  <=> sk_c9 = multiply(sk_c4,sk_c5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_16])]) ).

fof(f127,plain,
    ( spl3_17
  <=> sk_c9 = multiply(sk_c5,sk_c8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_17])]) ).

fof(f548,plain,
    ( identity = sk_c9
    | ~ spl3_13
    | ~ spl3_16
    | ~ spl3_17
    | ~ spl3_23 ),
    inference(forward_demodulation,[],[f546,f2]) ).

fof(f546,plain,
    ( sk_c9 = multiply(inverse(sk_c9),sk_c9)
    | ~ spl3_13
    | ~ spl3_16
    | ~ spl3_17
    | ~ spl3_23 ),
    inference(superposition,[],[f218,f530]) ).

fof(f530,plain,
    ( sk_c9 = multiply(sk_c9,sk_c9)
    | ~ spl3_13
    | ~ spl3_16
    | ~ spl3_17
    | ~ spl3_23 ),
    inference(backward_demodulation,[],[f515,f524]) ).

fof(f524,plain,
    ( sk_c9 = sk_c5
    | ~ spl3_13
    | ~ spl3_16
    | ~ spl3_17
    | ~ spl3_23 ),
    inference(backward_demodulation,[],[f449,f515]) ).

fof(f449,plain,
    ( sk_c5 = multiply(sk_c5,sk_c9)
    | ~ spl3_13
    | ~ spl3_16 ),
    inference(forward_demodulation,[],[f447,f108]) ).

fof(f108,plain,
    ( sk_c5 = inverse(sk_c4)
    | ~ spl3_13 ),
    inference(avatar_component_clause,[],[f106]) ).

fof(f447,plain,
    ( sk_c5 = multiply(inverse(sk_c4),sk_c9)
    | ~ spl3_16 ),
    inference(superposition,[],[f218,f124]) ).

fof(f124,plain,
    ( sk_c9 = multiply(sk_c4,sk_c5)
    | ~ spl3_16 ),
    inference(avatar_component_clause,[],[f122]) ).

fof(f515,plain,
    ( sk_c9 = multiply(sk_c5,sk_c9)
    | ~ spl3_17
    | ~ spl3_23 ),
    inference(backward_demodulation,[],[f129,f194]) ).

fof(f129,plain,
    ( sk_c9 = multiply(sk_c5,sk_c8)
    | ~ spl3_17 ),
    inference(avatar_component_clause,[],[f127]) ).

fof(f512,plain,
    ( spl3_23
    | ~ spl3_1
    | ~ spl3_4
    | ~ spl3_11 ),
    inference(avatar_split_clause,[],[f511,f97,f65,f51,f193]) ).

fof(f51,plain,
    ( spl3_1
  <=> sk_c8 = multiply(sk_c9,sk_c7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

fof(f65,plain,
    ( spl3_4
  <=> sk_c7 = multiply(sk_c6,sk_c9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).

fof(f511,plain,
    ( sk_c9 = sk_c8
    | ~ spl3_1
    | ~ spl3_4
    | ~ spl3_11 ),
    inference(backward_demodulation,[],[f53,f446]) ).

fof(f446,plain,
    ( sk_c9 = multiply(sk_c9,sk_c7)
    | ~ spl3_4
    | ~ spl3_11 ),
    inference(forward_demodulation,[],[f444,f99]) ).

fof(f444,plain,
    ( sk_c9 = multiply(inverse(sk_c6),sk_c7)
    | ~ spl3_4 ),
    inference(superposition,[],[f218,f67]) ).

fof(f67,plain,
    ( sk_c7 = multiply(sk_c6,sk_c9)
    | ~ spl3_4 ),
    inference(avatar_component_clause,[],[f65]) ).

fof(f53,plain,
    ( sk_c8 = multiply(sk_c9,sk_c7)
    | ~ spl3_1 ),
    inference(avatar_component_clause,[],[f51]) ).

fof(f508,plain,
    ( ~ spl3_12
    | ~ spl3_13
    | ~ spl3_16
    | ~ spl3_17
    | ~ spl3_23 ),
    inference(avatar_contradiction_clause,[],[f507]) ).

fof(f507,plain,
    ( $false
    | ~ spl3_12
    | ~ spl3_13
    | ~ spl3_16
    | ~ spl3_17
    | ~ spl3_23 ),
    inference(trivial_inequality_removal,[],[f506]) ).

fof(f506,plain,
    ( sk_c9 != sk_c9
    | ~ spl3_12
    | ~ spl3_13
    | ~ spl3_16
    | ~ spl3_17
    | ~ spl3_23 ),
    inference(superposition,[],[f505,f456]) ).

fof(f456,plain,
    ( sk_c9 = inverse(sk_c4)
    | ~ spl3_13
    | ~ spl3_16
    | ~ spl3_17
    | ~ spl3_23 ),
    inference(backward_demodulation,[],[f108,f450]) ).

fof(f450,plain,
    ( sk_c9 = sk_c5
    | ~ spl3_13
    | ~ spl3_16
    | ~ spl3_17
    | ~ spl3_23 ),
    inference(forward_demodulation,[],[f449,f430]) ).

fof(f430,plain,
    ( sk_c9 = multiply(sk_c5,sk_c9)
    | ~ spl3_17
    | ~ spl3_23 ),
    inference(forward_demodulation,[],[f129,f194]) ).

fof(f505,plain,
    ( sk_c9 != inverse(sk_c4)
    | ~ spl3_12
    | ~ spl3_13
    | ~ spl3_16
    | ~ spl3_17
    | ~ spl3_23 ),
    inference(trivial_inequality_removal,[],[f501]) ).

fof(f501,plain,
    ( sk_c9 != sk_c9
    | sk_c9 != inverse(sk_c4)
    | ~ spl3_12
    | ~ spl3_13
    | ~ spl3_16
    | ~ spl3_17
    | ~ spl3_23 ),
    inference(superposition,[],[f434,f454]) ).

fof(f454,plain,
    ( sk_c9 = multiply(sk_c4,sk_c9)
    | ~ spl3_13
    | ~ spl3_16
    | ~ spl3_17
    | ~ spl3_23 ),
    inference(backward_demodulation,[],[f124,f450]) ).

fof(f434,plain,
    ( ! [X3] :
        ( sk_c9 != multiply(X3,sk_c9)
        | sk_c9 != inverse(X3) )
    | ~ spl3_12
    | ~ spl3_23 ),
    inference(forward_demodulation,[],[f103,f194]) ).

fof(f103,plain,
    ( ! [X3] :
        ( sk_c9 != multiply(X3,sk_c8)
        | sk_c9 != inverse(X3) )
    | ~ spl3_12 ),
    inference(avatar_component_clause,[],[f102]) ).

fof(f102,plain,
    ( spl3_12
  <=> ! [X3] :
        ( sk_c9 != multiply(X3,sk_c8)
        | sk_c9 != inverse(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_12])]) ).

fof(f404,plain,
    ( ~ spl3_24
    | ~ spl3_3
    | spl3_14
    | ~ spl3_23
    | ~ spl3_24 ),
    inference(avatar_split_clause,[],[f403,f198,f193,f111,f60,f198]) ).

fof(f111,plain,
    ( spl3_14
  <=> sk_c9 = multiply(sk_c1,sk_c8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_14])]) ).

fof(f403,plain,
    ( identity != sk_c9
    | ~ spl3_3
    | spl3_14
    | ~ spl3_23
    | ~ spl3_24 ),
    inference(forward_demodulation,[],[f402,f1]) ).

fof(f402,plain,
    ( sk_c9 != multiply(identity,identity)
    | ~ spl3_3
    | spl3_14
    | ~ spl3_23
    | ~ spl3_24 ),
    inference(forward_demodulation,[],[f337,f393]) ).

fof(f393,plain,
    ( identity = sk_c1
    | ~ spl3_3
    | ~ spl3_24 ),
    inference(forward_demodulation,[],[f392,f2]) ).

fof(f392,plain,
    ( sk_c1 = multiply(inverse(identity),identity)
    | ~ spl3_3
    | ~ spl3_24 ),
    inference(forward_demodulation,[],[f261,f199]) ).

fof(f337,plain,
    ( sk_c9 != multiply(sk_c1,identity)
    | spl3_14
    | ~ spl3_23
    | ~ spl3_24 ),
    inference(forward_demodulation,[],[f112,f311]) ).

fof(f311,plain,
    ( identity = sk_c8
    | ~ spl3_23
    | ~ spl3_24 ),
    inference(backward_demodulation,[],[f194,f199]) ).

fof(f112,plain,
    ( sk_c9 != multiply(sk_c1,sk_c8)
    | spl3_14 ),
    inference(avatar_component_clause,[],[f111]) ).

fof(f325,plain,
    ( ~ spl3_24
    | ~ spl3_2
    | ~ spl3_23
    | ~ spl3_24
    | spl3_28 ),
    inference(avatar_split_clause,[],[f324,f245,f198,f193,f55,f198]) ).

fof(f324,plain,
    ( identity != sk_c9
    | ~ spl3_2
    | ~ spl3_23
    | ~ spl3_24
    | spl3_28 ),
    inference(forward_demodulation,[],[f323,f1]) ).

fof(f323,plain,
    ( sk_c9 != multiply(identity,identity)
    | ~ spl3_2
    | ~ spl3_23
    | ~ spl3_24
    | spl3_28 ),
    inference(forward_demodulation,[],[f322,f312]) ).

fof(f312,plain,
    ( identity = inverse(identity)
    | ~ spl3_2
    | ~ spl3_23
    | ~ spl3_24 ),
    inference(backward_demodulation,[],[f275,f199]) ).

fof(f275,plain,
    ( sk_c9 = inverse(sk_c9)
    | ~ spl3_2
    | ~ spl3_23 ),
    inference(backward_demodulation,[],[f57,f194]) ).

fof(f57,plain,
    ( inverse(sk_c9) = sk_c8
    | ~ spl3_2 ),
    inference(avatar_component_clause,[],[f55]) ).

fof(f322,plain,
    ( sk_c9 != multiply(identity,inverse(identity))
    | ~ spl3_23
    | ~ spl3_24
    | spl3_28 ),
    inference(forward_demodulation,[],[f247,f311]) ).

fof(f307,plain,
    ( spl3_24
    | ~ spl3_2
    | ~ spl3_3
    | ~ spl3_5
    | ~ spl3_6
    | ~ spl3_14
    | ~ spl3_18
    | ~ spl3_23 ),
    inference(avatar_split_clause,[],[f306,f193,f133,f111,f75,f70,f60,f55,f198]) ).

fof(f70,plain,
    ( spl3_5
  <=> sk_c3 = multiply(sk_c2,sk_c9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).

fof(f133,plain,
    ( spl3_18
  <=> sk_c8 = multiply(sk_c9,sk_c3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_18])]) ).

fof(f306,plain,
    ( identity = sk_c9
    | ~ spl3_2
    | ~ spl3_3
    | ~ spl3_5
    | ~ spl3_6
    | ~ spl3_14
    | ~ spl3_18
    | ~ spl3_23 ),
    inference(forward_demodulation,[],[f285,f293]) ).

fof(f293,plain,
    ( ! [X7] : multiply(inverse(sk_c9),X7) = X7
    | ~ spl3_2
    | ~ spl3_3
    | ~ spl3_5
    | ~ spl3_6
    | ~ spl3_14
    | ~ spl3_18
    | ~ spl3_23 ),
    inference(backward_demodulation,[],[f286,f290]) ).

fof(f290,plain,
    ( ! [X8] : multiply(sk_c9,X8) = X8
    | ~ spl3_2
    | ~ spl3_3
    | ~ spl3_5
    | ~ spl3_6
    | ~ spl3_14
    | ~ spl3_18
    | ~ spl3_23 ),
    inference(forward_demodulation,[],[f289,f281]) ).

fof(f281,plain,
    ( ! [X11] : multiply(sk_c9,multiply(sk_c9,X11)) = X11
    | ~ spl3_2
    | ~ spl3_23 ),
    inference(backward_demodulation,[],[f215,f194]) ).

fof(f215,plain,
    ( ! [X11] : multiply(sk_c8,multiply(sk_c9,X11)) = X11
    | ~ spl3_2 ),
    inference(forward_demodulation,[],[f212,f1]) ).

fof(f212,plain,
    ( ! [X11] : multiply(sk_c8,multiply(sk_c9,X11)) = multiply(identity,X11)
    | ~ spl3_2 ),
    inference(superposition,[],[f3,f159]) ).

fof(f159,plain,
    ( identity = multiply(sk_c8,sk_c9)
    | ~ spl3_2 ),
    inference(superposition,[],[f2,f57]) ).

fof(f289,plain,
    ( ! [X8] : multiply(sk_c9,X8) = multiply(sk_c9,multiply(sk_c9,X8))
    | ~ spl3_2
    | ~ spl3_3
    | ~ spl3_5
    | ~ spl3_6
    | ~ spl3_14
    | ~ spl3_18
    | ~ spl3_23 ),
    inference(backward_demodulation,[],[f279,f288]) ).

fof(f288,plain,
    ( ! [X13] : multiply(sk_c9,X13) = multiply(sk_c3,X13)
    | ~ spl3_2
    | ~ spl3_3
    | ~ spl3_5
    | ~ spl3_6
    | ~ spl3_14
    | ~ spl3_23 ),
    inference(backward_demodulation,[],[f226,f280]) ).

fof(f280,plain,
    ( ! [X12] : multiply(sk_c9,X12) = multiply(sk_c1,multiply(sk_c9,X12))
    | ~ spl3_14
    | ~ spl3_23 ),
    inference(backward_demodulation,[],[f213,f194]) ).

fof(f213,plain,
    ( ! [X12] : multiply(sk_c9,X12) = multiply(sk_c1,multiply(sk_c8,X12))
    | ~ spl3_14 ),
    inference(superposition,[],[f3,f113]) ).

fof(f113,plain,
    ( sk_c9 = multiply(sk_c1,sk_c8)
    | ~ spl3_14 ),
    inference(avatar_component_clause,[],[f111]) ).

fof(f226,plain,
    ( ! [X13] : multiply(sk_c1,multiply(sk_c9,X13)) = multiply(sk_c3,X13)
    | ~ spl3_2
    | ~ spl3_3
    | ~ spl3_5
    | ~ spl3_6 ),
    inference(backward_demodulation,[],[f214,f224]) ).

fof(f224,plain,
    ( sk_c1 = sk_c2
    | ~ spl3_2
    | ~ spl3_3
    | ~ spl3_6 ),
    inference(backward_demodulation,[],[f222,f221]) ).

fof(f221,plain,
    ( sk_c1 = multiply(sk_c8,identity)
    | ~ spl3_2
    | ~ spl3_3 ),
    inference(superposition,[],[f215,f160]) ).

fof(f222,plain,
    ( sk_c2 = multiply(sk_c8,identity)
    | ~ spl3_2
    | ~ spl3_6 ),
    inference(superposition,[],[f215,f161]) ).

fof(f214,plain,
    ( ! [X13] : multiply(sk_c2,multiply(sk_c9,X13)) = multiply(sk_c3,X13)
    | ~ spl3_5 ),
    inference(superposition,[],[f3,f72]) ).

fof(f72,plain,
    ( sk_c3 = multiply(sk_c2,sk_c9)
    | ~ spl3_5 ),
    inference(avatar_component_clause,[],[f70]) ).

fof(f279,plain,
    ( ! [X8] : multiply(sk_c9,X8) = multiply(sk_c9,multiply(sk_c3,X8))
    | ~ spl3_18
    | ~ spl3_23 ),
    inference(backward_demodulation,[],[f209,f194]) ).

fof(f209,plain,
    ( ! [X8] : multiply(sk_c8,X8) = multiply(sk_c9,multiply(sk_c3,X8))
    | ~ spl3_18 ),
    inference(superposition,[],[f3,f135]) ).

fof(f135,plain,
    ( sk_c8 = multiply(sk_c9,sk_c3)
    | ~ spl3_18 ),
    inference(avatar_component_clause,[],[f133]) ).

fof(f286,plain,
    ( ! [X7] : multiply(inverse(sk_c9),X7) = multiply(sk_c9,X7)
    | ~ spl3_2
    | ~ spl3_23 ),
    inference(backward_demodulation,[],[f263,f194]) ).

fof(f263,plain,
    ( ! [X7] : multiply(inverse(sk_c8),X7) = multiply(sk_c9,X7)
    | ~ spl3_2 ),
    inference(superposition,[],[f218,f215]) ).

fof(f285,plain,
    ( sk_c9 = multiply(inverse(sk_c9),identity)
    | ~ spl3_2
    | ~ spl3_23 ),
    inference(backward_demodulation,[],[f262,f194]) ).

fof(f262,plain,
    ( sk_c9 = multiply(inverse(sk_c8),identity)
    | ~ spl3_2 ),
    inference(superposition,[],[f218,f159]) ).

fof(f271,plain,
    ( spl3_23
    | ~ spl3_2
    | ~ spl3_3
    | ~ spl3_5
    | ~ spl3_6
    | ~ spl3_18 ),
    inference(avatar_split_clause,[],[f270,f133,f75,f70,f60,f55,f193]) ).

fof(f270,plain,
    ( sk_c9 = sk_c8
    | ~ spl3_2
    | ~ spl3_3
    | ~ spl3_5
    | ~ spl3_6
    | ~ spl3_18 ),
    inference(backward_demodulation,[],[f135,f269]) ).

fof(f269,plain,
    ( sk_c9 = multiply(sk_c9,sk_c3)
    | ~ spl3_2
    | ~ spl3_3
    | ~ spl3_5
    | ~ spl3_6 ),
    inference(forward_demodulation,[],[f265,f62]) ).

fof(f265,plain,
    ( sk_c9 = multiply(inverse(sk_c1),sk_c3)
    | ~ spl3_2
    | ~ spl3_3
    | ~ spl3_5
    | ~ spl3_6 ),
    inference(superposition,[],[f218,f228]) ).

fof(f228,plain,
    ( sk_c3 = multiply(sk_c1,sk_c9)
    | ~ spl3_2
    | ~ spl3_3
    | ~ spl3_5
    | ~ spl3_6 ),
    inference(backward_demodulation,[],[f72,f224]) ).

fof(f268,plain,
    ( spl3_22
    | ~ spl3_3
    | ~ spl3_14 ),
    inference(avatar_split_clause,[],[f267,f111,f60,f183]) ).

fof(f183,plain,
    ( spl3_22
  <=> sk_c8 = multiply(sk_c9,sk_c9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_22])]) ).

fof(f267,plain,
    ( sk_c8 = multiply(sk_c9,sk_c9)
    | ~ spl3_3
    | ~ spl3_14 ),
    inference(forward_demodulation,[],[f264,f62]) ).

fof(f264,plain,
    ( sk_c8 = multiply(inverse(sk_c1),sk_c9)
    | ~ spl3_14 ),
    inference(superposition,[],[f218,f113]) ).

fof(f248,plain,
    ( ~ spl3_24
    | ~ spl3_28
    | ~ spl3_15 ),
    inference(avatar_split_clause,[],[f234,f118,f245,f198]) ).

fof(f118,plain,
    ( spl3_15
  <=> ! [X6] :
        ( sk_c9 != multiply(inverse(X6),sk_c8)
        | sk_c9 != multiply(X6,inverse(X6)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_15])]) ).

fof(f234,plain,
    ( sk_c9 != multiply(sk_c8,inverse(sk_c8))
    | identity != sk_c9
    | ~ spl3_15 ),
    inference(superposition,[],[f119,f2]) ).

fof(f119,plain,
    ( ! [X6] :
        ( sk_c9 != multiply(inverse(X6),sk_c8)
        | sk_c9 != multiply(X6,inverse(X6)) )
    | ~ spl3_15 ),
    inference(avatar_component_clause,[],[f118]) ).

fof(f191,plain,
    ( ~ spl3_3
    | ~ spl3_12
    | ~ spl3_14 ),
    inference(avatar_split_clause,[],[f190,f111,f102,f60]) ).

fof(f190,plain,
    ( sk_c9 != inverse(sk_c1)
    | ~ spl3_12
    | ~ spl3_14 ),
    inference(trivial_inequality_removal,[],[f189]) ).

fof(f189,plain,
    ( sk_c9 != inverse(sk_c1)
    | sk_c9 != sk_c9
    | ~ spl3_12
    | ~ spl3_14 ),
    inference(superposition,[],[f103,f113]) ).

fof(f186,plain,
    ( ~ spl3_21
    | ~ spl3_22
    | ~ spl3_9 ),
    inference(avatar_split_clause,[],[f162,f89,f183,f179]) ).

fof(f89,plain,
    ( spl3_9
  <=> ! [X5] :
        ( sk_c9 != inverse(X5)
        | sk_c8 != multiply(sk_c9,multiply(X5,sk_c9)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_9])]) ).

fof(f162,plain,
    ( sk_c8 != multiply(sk_c9,sk_c9)
    | sk_c9 != inverse(identity)
    | ~ spl3_9 ),
    inference(superposition,[],[f90,f1]) ).

fof(f90,plain,
    ( ! [X5] :
        ( sk_c8 != multiply(sk_c9,multiply(X5,sk_c9))
        | sk_c9 != inverse(X5) )
    | ~ spl3_9 ),
    inference(avatar_component_clause,[],[f89]) ).

fof(f177,plain,
    ( ~ spl3_19
    | ~ spl3_20
    | ~ spl3_2
    | ~ spl3_9 ),
    inference(avatar_split_clause,[],[f168,f89,f55,f174,f170]) ).

fof(f168,plain,
    ( sk_c8 != multiply(sk_c9,identity)
    | sk_c9 != inverse(sk_c8)
    | ~ spl3_2
    | ~ spl3_9 ),
    inference(forward_demodulation,[],[f163,f57]) ).

fof(f163,plain,
    ( sk_c9 != inverse(inverse(sk_c9))
    | sk_c8 != multiply(sk_c9,identity)
    | ~ spl3_9 ),
    inference(superposition,[],[f90,f2]) ).

fof(f167,plain,
    ( ~ spl3_18
    | ~ spl3_5
    | ~ spl3_6
    | ~ spl3_9 ),
    inference(avatar_split_clause,[],[f166,f89,f75,f70,f133]) ).

fof(f166,plain,
    ( sk_c8 != multiply(sk_c9,sk_c3)
    | ~ spl3_5
    | ~ spl3_6
    | ~ spl3_9 ),
    inference(trivial_inequality_removal,[],[f165]) ).

fof(f165,plain,
    ( sk_c9 != sk_c9
    | sk_c8 != multiply(sk_c9,sk_c3)
    | ~ spl3_5
    | ~ spl3_6
    | ~ spl3_9 ),
    inference(forward_demodulation,[],[f164,f77]) ).

fof(f164,plain,
    ( sk_c9 != inverse(sk_c2)
    | sk_c8 != multiply(sk_c9,sk_c3)
    | ~ spl3_5
    | ~ spl3_9 ),
    inference(superposition,[],[f90,f72]) ).

fof(f158,plain,
    ( spl3_17
    | spl3_2 ),
    inference(avatar_split_clause,[],[f6,f55,f127]) ).

fof(f6,axiom,
    ( inverse(sk_c9) = sk_c8
    | sk_c9 = multiply(sk_c5,sk_c8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).

fof(f157,plain,
    ( spl3_4
    | spl3_6 ),
    inference(avatar_split_clause,[],[f38,f75,f65]) ).

fof(f38,axiom,
    ( sk_c9 = inverse(sk_c2)
    | sk_c7 = multiply(sk_c6,sk_c9) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).

fof(f155,plain,
    ( spl3_2
    | spl3_13 ),
    inference(avatar_split_clause,[],[f5,f106,f55]) ).

fof(f5,axiom,
    ( sk_c5 = inverse(sk_c4)
    | inverse(sk_c9) = sk_c8 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).

fof(f154,plain,
    ( spl3_10
    | spl3_9 ),
    inference(avatar_split_clause,[],[f48,f89,f92]) ).

fof(f92,plain,
    ( spl3_10
  <=> sP2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_10])]) ).

fof(f48,plain,
    ! [X9] :
      ( sk_c9 != inverse(X9)
      | sk_c8 != multiply(sk_c9,multiply(X9,sk_c9))
      | sP2 ),
    inference(cnf_transformation,[],[f48_D]) ).

fof(f48_D,plain,
    ( ! [X9] :
        ( sk_c9 != inverse(X9)
        | sk_c8 != multiply(sk_c9,multiply(X9,sk_c9)) )
  <=> ~ sP2 ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP2])]) ).

fof(f153,plain,
    ( spl3_5
    | spl3_17 ),
    inference(avatar_split_clause,[],[f30,f127,f70]) ).

fof(f30,axiom,
    ( sk_c9 = multiply(sk_c5,sk_c8)
    | sk_c3 = multiply(sk_c2,sk_c9) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).

fof(f152,plain,
    ( spl3_16
    | spl3_14 ),
    inference(avatar_split_clause,[],[f16,f111,f122]) ).

fof(f16,axiom,
    ( sk_c9 = multiply(sk_c1,sk_c8)
    | sk_c9 = multiply(sk_c4,sk_c5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).

fof(f151,plain,
    ( spl3_11
    | spl3_6 ),
    inference(avatar_split_clause,[],[f39,f75,f97]) ).

fof(f39,axiom,
    ( sk_c9 = inverse(sk_c2)
    | sk_c9 = inverse(sk_c6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).

fof(f150,plain,
    ( spl3_3
    | spl3_17 ),
    inference(avatar_split_clause,[],[f12,f127,f60]) ).

fof(f12,axiom,
    ( sk_c9 = multiply(sk_c5,sk_c8)
    | sk_c9 = inverse(sk_c1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).

fof(f149,plain,
    ( spl3_16
    | spl3_3 ),
    inference(avatar_split_clause,[],[f10,f60,f122]) ).

fof(f10,axiom,
    ( sk_c9 = inverse(sk_c1)
    | sk_c9 = multiply(sk_c4,sk_c5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).

fof(f148,plain,
    ( spl3_18
    | spl3_4 ),
    inference(avatar_split_clause,[],[f26,f65,f133]) ).

fof(f26,axiom,
    ( sk_c7 = multiply(sk_c6,sk_c9)
    | sk_c8 = multiply(sk_c9,sk_c3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).

fof(f147,plain,
    ( spl3_18
    | spl3_11 ),
    inference(avatar_split_clause,[],[f27,f97,f133]) ).

fof(f27,axiom,
    ( sk_c9 = inverse(sk_c6)
    | sk_c8 = multiply(sk_c9,sk_c3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).

fof(f146,plain,
    ( spl3_6
    | spl3_13 ),
    inference(avatar_split_clause,[],[f35,f106,f75]) ).

fof(f35,axiom,
    ( sk_c5 = inverse(sk_c4)
    | sk_c9 = inverse(sk_c2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).

fof(f145,plain,
    ( spl3_18
    | spl3_1 ),
    inference(avatar_split_clause,[],[f25,f51,f133]) ).

fof(f25,axiom,
    ( sk_c8 = multiply(sk_c9,sk_c7)
    | sk_c8 = multiply(sk_c9,sk_c3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).

fof(f144,plain,
    ( spl3_6
    | spl3_16 ),
    inference(avatar_split_clause,[],[f34,f122,f75]) ).

fof(f34,axiom,
    ( sk_c9 = multiply(sk_c4,sk_c5)
    | sk_c9 = inverse(sk_c2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).

fof(f143,plain,
    ( spl3_14
    | spl3_17 ),
    inference(avatar_split_clause,[],[f18,f127,f111]) ).

fof(f18,axiom,
    ( sk_c9 = multiply(sk_c5,sk_c8)
    | sk_c9 = multiply(sk_c1,sk_c8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).

fof(f142,plain,
    ( spl3_16
    | spl3_18 ),
    inference(avatar_split_clause,[],[f22,f133,f122]) ).

fof(f22,axiom,
    ( sk_c8 = multiply(sk_c9,sk_c3)
    | sk_c9 = multiply(sk_c4,sk_c5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).

fof(f140,plain,
    ( spl3_18
    | spl3_17 ),
    inference(avatar_split_clause,[],[f24,f127,f133]) ).

fof(f24,axiom,
    ( sk_c9 = multiply(sk_c5,sk_c8)
    | sk_c8 = multiply(sk_c9,sk_c3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).

fof(f139,plain,
    ( spl3_4
    | spl3_5 ),
    inference(avatar_split_clause,[],[f32,f70,f65]) ).

fof(f32,axiom,
    ( sk_c3 = multiply(sk_c2,sk_c9)
    | sk_c7 = multiply(sk_c6,sk_c9) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).

fof(f138,plain,
    ( spl3_11
    | spl3_2 ),
    inference(avatar_split_clause,[],[f9,f55,f97]) ).

fof(f9,axiom,
    ( inverse(sk_c9) = sk_c8
    | sk_c9 = inverse(sk_c6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).

fof(f137,plain,
    ( spl3_13
    | spl3_14 ),
    inference(avatar_split_clause,[],[f17,f111,f106]) ).

fof(f17,axiom,
    ( sk_c9 = multiply(sk_c1,sk_c8)
    | sk_c5 = inverse(sk_c4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).

fof(f136,plain,
    ( spl3_13
    | spl3_18 ),
    inference(avatar_split_clause,[],[f23,f133,f106]) ).

fof(f23,axiom,
    ( sk_c8 = multiply(sk_c9,sk_c3)
    | sk_c5 = inverse(sk_c4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).

fof(f131,plain,
    ( spl3_5
    | spl3_16 ),
    inference(avatar_split_clause,[],[f28,f122,f70]) ).

fof(f28,axiom,
    ( sk_c9 = multiply(sk_c4,sk_c5)
    | sk_c3 = multiply(sk_c2,sk_c9) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).

fof(f130,plain,
    ( spl3_17
    | spl3_6 ),
    inference(avatar_split_clause,[],[f36,f75,f127]) ).

fof(f36,axiom,
    ( sk_c9 = inverse(sk_c2)
    | sk_c9 = multiply(sk_c5,sk_c8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).

fof(f125,plain,
    ( spl3_2
    | spl3_16 ),
    inference(avatar_split_clause,[],[f4,f122,f55]) ).

fof(f4,axiom,
    ( sk_c9 = multiply(sk_c4,sk_c5)
    | inverse(sk_c9) = sk_c8 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).

fof(f120,plain,
    ( spl3_7
    | spl3_15 ),
    inference(avatar_split_clause,[],[f46,f118,f81]) ).

fof(f81,plain,
    ( spl3_7
  <=> sP1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).

fof(f46,plain,
    ! [X6] :
      ( sk_c9 != multiply(inverse(X6),sk_c8)
      | sk_c9 != multiply(X6,inverse(X6))
      | sP1 ),
    inference(cnf_transformation,[],[f46_D]) ).

fof(f46_D,plain,
    ( ! [X6] :
        ( sk_c9 != multiply(inverse(X6),sk_c8)
        | sk_c9 != multiply(X6,inverse(X6)) )
  <=> ~ sP1 ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP1])]) ).

fof(f116,plain,
    ( spl3_11
    | spl3_5 ),
    inference(avatar_split_clause,[],[f33,f70,f97]) ).

fof(f33,axiom,
    ( sk_c3 = multiply(sk_c2,sk_c9)
    | sk_c9 = inverse(sk_c6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).

fof(f115,plain,
    ( spl3_13
    | spl3_3 ),
    inference(avatar_split_clause,[],[f11,f60,f106]) ).

fof(f11,axiom,
    ( sk_c9 = inverse(sk_c1)
    | sk_c5 = inverse(sk_c4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).

fof(f114,plain,
    ( spl3_14
    | spl3_11 ),
    inference(avatar_split_clause,[],[f21,f97,f111]) ).

fof(f21,axiom,
    ( sk_c9 = inverse(sk_c6)
    | sk_c9 = multiply(sk_c1,sk_c8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).

fof(f109,plain,
    ( spl3_13
    | spl3_5 ),
    inference(avatar_split_clause,[],[f29,f70,f106]) ).

fof(f29,axiom,
    ( sk_c3 = multiply(sk_c2,sk_c9)
    | sk_c5 = inverse(sk_c4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).

fof(f104,plain,
    ( spl3_8
    | spl3_12 ),
    inference(avatar_split_clause,[],[f44,f102,f85]) ).

fof(f85,plain,
    ( spl3_8
  <=> sP0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_8])]) ).

fof(f44,plain,
    ! [X3] :
      ( sk_c9 != multiply(X3,sk_c8)
      | sP0
      | sk_c9 != inverse(X3) ),
    inference(cnf_transformation,[],[f44_D]) ).

fof(f44_D,plain,
    ( ! [X3] :
        ( sk_c9 != multiply(X3,sk_c8)
        | sk_c9 != inverse(X3) )
  <=> ~ sP0 ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP0])]) ).

fof(f100,plain,
    ( spl3_11
    | spl3_3 ),
    inference(avatar_split_clause,[],[f15,f60,f97]) ).

fof(f15,axiom,
    ( sk_c9 = inverse(sk_c1)
    | sk_c9 = inverse(sk_c6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).

fof(f95,plain,
    ( ~ spl3_7
    | ~ spl3_8
    | ~ spl3_2
    | spl3_9
    | ~ spl3_10 ),
    inference(avatar_split_clause,[],[f49,f92,f89,f55,f85,f81]) ).

fof(f49,plain,
    ! [X5] :
      ( ~ sP2
      | sk_c9 != inverse(X5)
      | inverse(sk_c9) != sk_c8
      | ~ sP0
      | ~ sP1
      | sk_c8 != multiply(sk_c9,multiply(X5,sk_c9)) ),
    inference(general_splitting,[],[f47,f48_D]) ).

fof(f47,plain,
    ! [X9,X5] :
      ( sk_c9 != inverse(X9)
      | sk_c9 != inverse(X5)
      | inverse(sk_c9) != sk_c8
      | sk_c8 != multiply(sk_c9,multiply(X9,sk_c9))
      | sk_c8 != multiply(sk_c9,multiply(X5,sk_c9))
      | ~ sP0
      | ~ sP1 ),
    inference(general_splitting,[],[f45,f46_D]) ).

fof(f45,plain,
    ! [X6,X9,X5] :
      ( sk_c9 != multiply(inverse(X6),sk_c8)
      | sk_c9 != multiply(X6,inverse(X6))
      | sk_c9 != inverse(X9)
      | sk_c9 != inverse(X5)
      | inverse(sk_c9) != sk_c8
      | sk_c8 != multiply(sk_c9,multiply(X9,sk_c9))
      | sk_c8 != multiply(sk_c9,multiply(X5,sk_c9))
      | ~ sP0 ),
    inference(general_splitting,[],[f43,f44_D]) ).

fof(f43,plain,
    ! [X3,X6,X9,X5] :
      ( sk_c9 != multiply(inverse(X6),sk_c8)
      | sk_c9 != multiply(X6,inverse(X6))
      | sk_c9 != multiply(X3,sk_c8)
      | sk_c9 != inverse(X9)
      | sk_c9 != inverse(X5)
      | inverse(sk_c9) != sk_c8
      | sk_c8 != multiply(sk_c9,multiply(X9,sk_c9))
      | sk_c9 != inverse(X3)
      | sk_c8 != multiply(sk_c9,multiply(X5,sk_c9)) ),
    inference(equality_resolution,[],[f42]) ).

fof(f42,plain,
    ! [X3,X6,X9,X4,X5] :
      ( sk_c9 != multiply(inverse(X6),sk_c8)
      | sk_c9 != multiply(X6,inverse(X6))
      | sk_c9 != multiply(X3,sk_c8)
      | sk_c9 != inverse(X9)
      | sk_c9 != inverse(X5)
      | inverse(sk_c9) != sk_c8
      | sk_c8 != multiply(sk_c9,multiply(X9,sk_c9))
      | sk_c9 != inverse(X3)
      | multiply(X5,sk_c9) != X4
      | sk_c8 != multiply(sk_c9,X4) ),
    inference(equality_resolution,[],[f41]) ).

fof(f41,plain,
    ! [X3,X8,X6,X9,X4,X5] :
      ( sk_c9 != multiply(inverse(X6),sk_c8)
      | sk_c9 != multiply(X6,inverse(X6))
      | sk_c9 != multiply(X3,sk_c8)
      | sk_c9 != inverse(X9)
      | sk_c9 != inverse(X5)
      | inverse(sk_c9) != sk_c8
      | sk_c8 != multiply(sk_c9,X8)
      | sk_c9 != inverse(X3)
      | multiply(X9,sk_c9) != X8
      | multiply(X5,sk_c9) != X4
      | sk_c8 != multiply(sk_c9,X4) ),
    inference(equality_resolution,[],[f40]) ).

fof(f40,axiom,
    ! [X3,X8,X6,X9,X7,X4,X5] :
      ( sk_c9 != multiply(X7,sk_c8)
      | sk_c9 != multiply(X6,X7)
      | sk_c9 != multiply(X3,sk_c8)
      | sk_c9 != inverse(X9)
      | sk_c9 != inverse(X5)
      | inverse(sk_c9) != sk_c8
      | sk_c8 != multiply(sk_c9,X8)
      | inverse(X6) != X7
      | sk_c9 != inverse(X3)
      | multiply(X9,sk_c9) != X8
      | multiply(X5,sk_c9) != X4
      | sk_c8 != multiply(sk_c9,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).

fof(f79,plain,
    ( spl3_4
    | spl3_3 ),
    inference(avatar_split_clause,[],[f14,f60,f65]) ).

fof(f14,axiom,
    ( sk_c9 = inverse(sk_c1)
    | sk_c7 = multiply(sk_c6,sk_c9) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).

fof(f78,plain,
    ( spl3_1
    | spl3_6 ),
    inference(avatar_split_clause,[],[f37,f75,f51]) ).

fof(f37,axiom,
    ( sk_c9 = inverse(sk_c2)
    | sk_c8 = multiply(sk_c9,sk_c7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).

fof(f73,plain,
    ( spl3_1
    | spl3_5 ),
    inference(avatar_split_clause,[],[f31,f70,f51]) ).

fof(f31,axiom,
    ( sk_c3 = multiply(sk_c2,sk_c9)
    | sk_c8 = multiply(sk_c9,sk_c7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).

fof(f68,plain,
    ( spl3_4
    | spl3_2 ),
    inference(avatar_split_clause,[],[f8,f55,f65]) ).

fof(f8,axiom,
    ( inverse(sk_c9) = sk_c8
    | sk_c7 = multiply(sk_c6,sk_c9) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).

fof(f63,plain,
    ( spl3_1
    | spl3_3 ),
    inference(avatar_split_clause,[],[f13,f60,f51]) ).

fof(f13,axiom,
    ( sk_c9 = inverse(sk_c1)
    | sk_c8 = multiply(sk_c9,sk_c7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).

fof(f58,plain,
    ( spl3_1
    | spl3_2 ),
    inference(avatar_split_clause,[],[f7,f55,f51]) ).

fof(f7,axiom,
    ( inverse(sk_c9) = sk_c8
    | sk_c8 = multiply(sk_c9,sk_c7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem    : GRP237-1 : TPTP v8.1.0. Released v2.5.0.
% 0.10/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.34  % Computer : n009.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Mon Aug 29 22:19:35 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.19/0.48  % (10835)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.48  % (10831)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.49  % (10852)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.19/0.49  % (10839)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.19/0.50  % (10826)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.50  % (10846)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.19/0.50  % (10830)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.19/0.51  TRYING [1]
% 0.19/0.51  TRYING [2]
% 0.19/0.51  TRYING [3]
% 0.19/0.51  % (10829)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.51  % (10847)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.19/0.51  % (10836)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.19/0.51  % (10835)First to succeed.
% 0.19/0.52  % (10828)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.52  % (10832)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.52  % (10853)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.19/0.52  % (10827)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.19/0.52  % (10835)Refutation found. Thanks to Tanya!
% 0.19/0.52  % SZS status Unsatisfiable for theBenchmark
% 0.19/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.52  % (10835)------------------------------
% 0.19/0.52  % (10835)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52  % (10835)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52  % (10835)Termination reason: Refutation
% 0.19/0.52  
% 0.19/0.52  % (10835)Memory used [KB]: 5756
% 0.19/0.52  % (10835)Time elapsed: 0.128 s
% 0.19/0.52  % (10835)Instructions burned: 19 (million)
% 0.19/0.52  % (10835)------------------------------
% 0.19/0.52  % (10835)------------------------------
% 0.19/0.52  % (10821)Success in time 0.175 s
%------------------------------------------------------------------------------