TSTP Solution File: GRP239-1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : GRP239-1 : 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 : n016.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Aug 31 16:21:00 EDT 2022

% Result   : Unsatisfiable 1.48s 0.54s
% Output   : Refutation 1.48s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   49
% Syntax   : Number of formulae    :  177 (   6 unt;   0 def)
%            Number of atoms       :  521 ( 223 equ)
%            Maximal formula atoms :   13 (   2 avg)
%            Number of connectives :  661 ( 317   ~; 316   |;   0   &)
%                                         (  28 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   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   :   60 (  60   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f821,plain,
    $false,
    inference(avatar_sat_refutation,[],[f65,f79,f84,f89,f94,f99,f109,f122,f123,f124,f126,f135,f136,f148,f157,f162,f171,f175,f176,f179,f182,f183,f308,f322,f361,f475,f486,f536,f545,f556,f560,f568,f676,f694,f703,f807]) ).

fof(f807,plain,
    ( ~ spl4_8
    | ~ spl4_21
    | ~ spl4_23
    | ~ spl4_24 ),
    inference(avatar_contradiction_clause,[],[f806]) ).

fof(f806,plain,
    ( $false
    | ~ spl4_8
    | ~ spl4_21
    | ~ spl4_23
    | ~ spl4_24 ),
    inference(subsumption_resolution,[],[f647,f310]) ).

fof(f310,plain,
    ( ! [X0] : multiply(sk_c9,X0) = X0
    | ~ spl4_24 ),
    inference(backward_demodulation,[],[f1,f212]) ).

fof(f212,plain,
    ( identity = sk_c9
    | ~ spl4_24 ),
    inference(avatar_component_clause,[],[f211]) ).

fof(f211,plain,
    ( spl4_24
  <=> identity = sk_c9 ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_24])]) ).

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

fof(f647,plain,
    ( sk_c9 != multiply(sk_c9,sk_c9)
    | ~ spl4_8
    | ~ spl4_21
    | ~ spl4_23
    | ~ spl4_24 ),
    inference(subsumption_resolution,[],[f624,f362]) ).

fof(f362,plain,
    ( sk_c9 = inverse(sk_c9)
    | ~ spl4_8
    | ~ spl4_23 ),
    inference(forward_demodulation,[],[f93,f203]) ).

fof(f203,plain,
    ( sk_c9 = sk_c8
    | ~ spl4_23 ),
    inference(avatar_component_clause,[],[f202]) ).

fof(f202,plain,
    ( spl4_23
  <=> sk_c9 = sk_c8 ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_23])]) ).

fof(f93,plain,
    ( inverse(sk_c9) = sk_c8
    | ~ spl4_8 ),
    inference(avatar_component_clause,[],[f91]) ).

fof(f91,plain,
    ( spl4_8
  <=> inverse(sk_c9) = sk_c8 ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_8])]) ).

fof(f624,plain,
    ( sk_c9 != multiply(sk_c9,sk_c9)
    | sk_c9 != inverse(sk_c9)
    | ~ spl4_21
    | ~ spl4_23
    | ~ spl4_24 ),
    inference(superposition,[],[f561,f310]) ).

fof(f561,plain,
    ( ! [X5] :
        ( sk_c9 != multiply(sk_c9,multiply(X5,sk_c9))
        | sk_c9 != inverse(X5) )
    | ~ spl4_21
    | ~ spl4_23 ),
    inference(forward_demodulation,[],[f170,f203]) ).

fof(f170,plain,
    ( ! [X5] :
        ( sk_c9 != inverse(X5)
        | sk_c8 != multiply(sk_c9,multiply(X5,sk_c9)) )
    | ~ spl4_21 ),
    inference(avatar_component_clause,[],[f169]) ).

fof(f169,plain,
    ( spl4_21
  <=> ! [X5] :
        ( sk_c9 != inverse(X5)
        | sk_c8 != multiply(sk_c9,multiply(X5,sk_c9)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_21])]) ).

fof(f703,plain,
    ( ~ spl4_24
    | spl4_29 ),
    inference(avatar_contradiction_clause,[],[f702]) ).

fof(f702,plain,
    ( $false
    | ~ spl4_24
    | spl4_29 ),
    inference(subsumption_resolution,[],[f531,f310]) ).

fof(f531,plain,
    ( sk_c9 != multiply(sk_c9,sk_c9)
    | spl4_29 ),
    inference(avatar_component_clause,[],[f529]) ).

fof(f529,plain,
    ( spl4_29
  <=> sk_c9 = multiply(sk_c9,sk_c9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_29])]) ).

fof(f694,plain,
    ( ~ spl4_8
    | ~ spl4_19
    | ~ spl4_23
    | ~ spl4_24 ),
    inference(avatar_contradiction_clause,[],[f693]) ).

fof(f693,plain,
    ( $false
    | ~ spl4_8
    | ~ spl4_19
    | ~ spl4_23
    | ~ spl4_24 ),
    inference(subsumption_resolution,[],[f692,f362]) ).

fof(f692,plain,
    ( sk_c9 != inverse(sk_c9)
    | ~ spl4_8
    | ~ spl4_19
    | ~ spl4_23
    | ~ spl4_24 ),
    inference(forward_demodulation,[],[f691,f362]) ).

fof(f691,plain,
    ( sk_c9 != inverse(inverse(sk_c9))
    | ~ spl4_19
    | ~ spl4_23
    | ~ spl4_24 ),
    inference(forward_demodulation,[],[f690,f203]) ).

fof(f690,plain,
    ( sk_c9 != inverse(inverse(sk_c8))
    | ~ spl4_19
    | ~ spl4_24 ),
    inference(subsumption_resolution,[],[f220,f212]) ).

fof(f220,plain,
    ( identity != sk_c9
    | sk_c9 != inverse(inverse(sk_c8))
    | ~ spl4_19 ),
    inference(superposition,[],[f156,f2]) ).

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

fof(f156,plain,
    ( ! [X3] :
        ( sk_c9 != multiply(X3,sk_c8)
        | sk_c9 != inverse(X3) )
    | ~ spl4_19 ),
    inference(avatar_component_clause,[],[f155]) ).

fof(f155,plain,
    ( spl4_19
  <=> ! [X3] :
        ( sk_c9 != multiply(X3,sk_c8)
        | sk_c9 != inverse(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_19])]) ).

fof(f676,plain,
    ( ~ spl4_8
    | ~ spl4_14
    | ~ spl4_23
    | ~ spl4_24 ),
    inference(avatar_contradiction_clause,[],[f675]) ).

fof(f675,plain,
    ( $false
    | ~ spl4_8
    | ~ spl4_14
    | ~ spl4_23
    | ~ spl4_24 ),
    inference(subsumption_resolution,[],[f674,f362]) ).

fof(f674,plain,
    ( sk_c9 != inverse(sk_c9)
    | ~ spl4_14
    | ~ spl4_23
    | ~ spl4_24 ),
    inference(forward_demodulation,[],[f673,f203]) ).

fof(f673,plain,
    ( inverse(sk_c9) != sk_c8
    | ~ spl4_14
    | ~ spl4_23
    | ~ spl4_24 ),
    inference(forward_demodulation,[],[f672,f212]) ).

fof(f672,plain,
    ( sk_c8 != inverse(identity)
    | ~ spl4_14
    | ~ spl4_23 ),
    inference(subsumption_resolution,[],[f189,f203]) ).

fof(f189,plain,
    ( sk_c8 != inverse(identity)
    | sk_c9 != sk_c8
    | ~ spl4_14 ),
    inference(superposition,[],[f130,f1]) ).

fof(f130,plain,
    ( ! [X7] :
        ( sk_c9 != multiply(X7,sk_c8)
        | sk_c8 != inverse(X7) )
    | ~ spl4_14 ),
    inference(avatar_component_clause,[],[f129]) ).

fof(f129,plain,
    ( spl4_14
  <=> ! [X7] :
        ( sk_c8 != inverse(X7)
        | sk_c9 != multiply(X7,sk_c8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_14])]) ).

fof(f568,plain,
    ( spl4_24
    | ~ spl4_8
    | ~ spl4_23
    | ~ spl4_29 ),
    inference(avatar_split_clause,[],[f562,f529,f202,f91,f211]) ).

fof(f562,plain,
    ( identity = sk_c9
    | ~ spl4_8
    | ~ spl4_23
    | ~ spl4_29 ),
    inference(backward_demodulation,[],[f363,f530]) ).

fof(f530,plain,
    ( sk_c9 = multiply(sk_c9,sk_c9)
    | ~ spl4_29 ),
    inference(avatar_component_clause,[],[f529]) ).

fof(f363,plain,
    ( identity = multiply(sk_c9,sk_c9)
    | ~ spl4_8
    | ~ spl4_23 ),
    inference(forward_demodulation,[],[f184,f203]) ).

fof(f184,plain,
    ( identity = multiply(sk_c8,sk_c9)
    | ~ spl4_8 ),
    inference(superposition,[],[f2,f93]) ).

fof(f560,plain,
    ( spl4_29
    | ~ spl4_13
    | ~ spl4_28 ),
    inference(avatar_split_clause,[],[f559,f525,f116,f529]) ).

fof(f116,plain,
    ( spl4_13
  <=> sk_c9 = inverse(sk_c1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_13])]) ).

fof(f525,plain,
    ( spl4_28
  <=> sk_c9 = multiply(sk_c1,sk_c9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_28])]) ).

fof(f559,plain,
    ( sk_c9 = multiply(sk_c9,sk_c9)
    | ~ spl4_13
    | ~ spl4_28 ),
    inference(forward_demodulation,[],[f557,f118]) ).

fof(f118,plain,
    ( sk_c9 = inverse(sk_c1)
    | ~ spl4_13 ),
    inference(avatar_component_clause,[],[f116]) ).

fof(f557,plain,
    ( sk_c9 = multiply(inverse(sk_c1),sk_c9)
    | ~ spl4_28 ),
    inference(superposition,[],[f252,f526]) ).

fof(f526,plain,
    ( sk_c9 = multiply(sk_c1,sk_c9)
    | ~ spl4_28 ),
    inference(avatar_component_clause,[],[f525]) ).

fof(f252,plain,
    ! [X6,X7] : multiply(inverse(X6),multiply(X6,X7)) = X7,
    inference(forward_demodulation,[],[f239,f1]) ).

fof(f239,plain,
    ! [X6,X7] : multiply(identity,X7) = multiply(inverse(X6),multiply(X6,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(f556,plain,
    ( ~ spl4_29
    | ~ spl4_8
    | ~ spl4_17
    | ~ spl4_23 ),
    inference(avatar_split_clause,[],[f468,f202,f146,f91,f529]) ).

fof(f146,plain,
    ( spl4_17
  <=> ! [X8] :
        ( sk_c8 != multiply(X8,inverse(X8))
        | sk_c8 != multiply(inverse(X8),sk_c9) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_17])]) ).

fof(f468,plain,
    ( sk_c9 != multiply(sk_c9,sk_c9)
    | ~ spl4_8
    | ~ spl4_17
    | ~ spl4_23 ),
    inference(duplicate_literal_removal,[],[f464]) ).

fof(f464,plain,
    ( sk_c9 != multiply(sk_c9,sk_c9)
    | sk_c9 != multiply(sk_c9,sk_c9)
    | ~ spl4_8
    | ~ spl4_17
    | ~ spl4_23 ),
    inference(superposition,[],[f366,f362]) ).

fof(f366,plain,
    ( ! [X8] :
        ( sk_c9 != multiply(X8,inverse(X8))
        | sk_c9 != multiply(inverse(X8),sk_c9) )
    | ~ spl4_17
    | ~ spl4_23 ),
    inference(forward_demodulation,[],[f365,f203]) ).

fof(f365,plain,
    ( ! [X8] :
        ( sk_c9 != multiply(inverse(X8),sk_c9)
        | sk_c8 != multiply(X8,inverse(X8)) )
    | ~ spl4_17
    | ~ spl4_23 ),
    inference(forward_demodulation,[],[f147,f203]) ).

fof(f147,plain,
    ( ! [X8] :
        ( sk_c8 != multiply(inverse(X8),sk_c9)
        | sk_c8 != multiply(X8,inverse(X8)) )
    | ~ spl4_17 ),
    inference(avatar_component_clause,[],[f146]) ).

fof(f545,plain,
    ( spl4_28
    | ~ spl4_6
    | ~ spl4_23 ),
    inference(avatar_split_clause,[],[f540,f202,f81,f525]) ).

fof(f81,plain,
    ( spl4_6
  <=> sk_c9 = multiply(sk_c1,sk_c8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_6])]) ).

fof(f540,plain,
    ( sk_c9 = multiply(sk_c1,sk_c9)
    | ~ spl4_6
    | ~ spl4_23 ),
    inference(backward_demodulation,[],[f83,f203]) ).

fof(f83,plain,
    ( sk_c9 = multiply(sk_c1,sk_c8)
    | ~ spl4_6 ),
    inference(avatar_component_clause,[],[f81]) ).

fof(f536,plain,
    ( spl4_23
    | ~ spl4_1
    | ~ spl4_3
    | ~ spl4_5 ),
    inference(avatar_split_clause,[],[f516,f76,f67,f58,f202]) ).

fof(f58,plain,
    ( spl4_1
  <=> sk_c8 = multiply(sk_c9,sk_c3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).

fof(f67,plain,
    ( spl4_3
  <=> sk_c9 = inverse(sk_c2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_3])]) ).

fof(f76,plain,
    ( spl4_5
  <=> sk_c3 = multiply(sk_c2,sk_c9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_5])]) ).

fof(f516,plain,
    ( sk_c9 = sk_c8
    | ~ spl4_1
    | ~ spl4_3
    | ~ spl4_5 ),
    inference(backward_demodulation,[],[f60,f499]) ).

fof(f499,plain,
    ( sk_c9 = multiply(sk_c9,sk_c3)
    | ~ spl4_3
    | ~ spl4_5 ),
    inference(forward_demodulation,[],[f497,f69]) ).

fof(f69,plain,
    ( sk_c9 = inverse(sk_c2)
    | ~ spl4_3 ),
    inference(avatar_component_clause,[],[f67]) ).

fof(f497,plain,
    ( sk_c9 = multiply(inverse(sk_c2),sk_c3)
    | ~ spl4_5 ),
    inference(superposition,[],[f252,f78]) ).

fof(f78,plain,
    ( sk_c3 = multiply(sk_c2,sk_c9)
    | ~ spl4_5 ),
    inference(avatar_component_clause,[],[f76]) ).

fof(f60,plain,
    ( sk_c8 = multiply(sk_c9,sk_c3)
    | ~ spl4_1 ),
    inference(avatar_component_clause,[],[f58]) ).

fof(f486,plain,
    ( ~ spl4_3
    | ~ spl4_8
    | spl4_23
    | ~ spl4_24 ),
    inference(avatar_contradiction_clause,[],[f485]) ).

fof(f485,plain,
    ( $false
    | ~ spl4_3
    | ~ spl4_8
    | spl4_23
    | ~ spl4_24 ),
    inference(subsumption_resolution,[],[f482,f204]) ).

fof(f204,plain,
    ( sk_c9 != sk_c8
    | spl4_23 ),
    inference(avatar_component_clause,[],[f202]) ).

fof(f482,plain,
    ( sk_c9 = sk_c8
    | ~ spl4_3
    | ~ spl4_8
    | ~ spl4_24 ),
    inference(backward_demodulation,[],[f93,f457]) ).

fof(f457,plain,
    ( sk_c9 = inverse(sk_c9)
    | ~ spl4_3
    | ~ spl4_24 ),
    inference(forward_demodulation,[],[f69,f454]) ).

fof(f454,plain,
    ( sk_c9 = sk_c2
    | ~ spl4_3
    | ~ spl4_24 ),
    inference(forward_demodulation,[],[f453,f212]) ).

fof(f453,plain,
    ( identity = sk_c2
    | ~ spl4_3
    | ~ spl4_24 ),
    inference(forward_demodulation,[],[f188,f310]) ).

fof(f188,plain,
    ( identity = multiply(sk_c9,sk_c2)
    | ~ spl4_3 ),
    inference(superposition,[],[f2,f69]) ).

fof(f475,plain,
    ( spl4_23
    | ~ spl4_4
    | ~ spl4_12
    | ~ spl4_24 ),
    inference(avatar_split_clause,[],[f431,f211,f112,f71,f202]) ).

fof(f71,plain,
    ( spl4_4
  <=> sk_c8 = multiply(sk_c6,sk_c7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_4])]) ).

fof(f112,plain,
    ( spl4_12
  <=> sk_c7 = inverse(sk_c6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_12])]) ).

fof(f431,plain,
    ( sk_c9 = sk_c8
    | ~ spl4_4
    | ~ spl4_12
    | ~ spl4_24 ),
    inference(forward_demodulation,[],[f275,f311]) ).

fof(f311,plain,
    ( ! [X0] : multiply(inverse(X0),X0) = sk_c9
    | ~ spl4_24 ),
    inference(backward_demodulation,[],[f2,f212]) ).

fof(f275,plain,
    ( sk_c8 = multiply(inverse(sk_c7),sk_c7)
    | ~ spl4_4
    | ~ spl4_12 ),
    inference(superposition,[],[f252,f253]) ).

fof(f253,plain,
    ( sk_c7 = multiply(sk_c7,sk_c8)
    | ~ spl4_4
    | ~ spl4_12 ),
    inference(superposition,[],[f247,f73]) ).

fof(f73,plain,
    ( sk_c8 = multiply(sk_c6,sk_c7)
    | ~ spl4_4 ),
    inference(avatar_component_clause,[],[f71]) ).

fof(f247,plain,
    ( ! [X14] : multiply(sk_c7,multiply(sk_c6,X14)) = X14
    | ~ spl4_12 ),
    inference(forward_demodulation,[],[f246,f1]) ).

fof(f246,plain,
    ( ! [X14] : multiply(sk_c7,multiply(sk_c6,X14)) = multiply(identity,X14)
    | ~ spl4_12 ),
    inference(superposition,[],[f3,f187]) ).

fof(f187,plain,
    ( identity = multiply(sk_c7,sk_c6)
    | ~ spl4_12 ),
    inference(superposition,[],[f2,f114]) ).

fof(f114,plain,
    ( sk_c7 = inverse(sk_c6)
    | ~ spl4_12 ),
    inference(avatar_component_clause,[],[f112]) ).

fof(f361,plain,
    ( spl4_8
    | ~ spl4_11
    | ~ spl4_23
    | ~ spl4_24 ),
    inference(avatar_contradiction_clause,[],[f360]) ).

fof(f360,plain,
    ( $false
    | spl4_8
    | ~ spl4_11
    | ~ spl4_23
    | ~ spl4_24 ),
    inference(subsumption_resolution,[],[f359,f326]) ).

fof(f326,plain,
    ( sk_c9 != inverse(sk_c9)
    | spl4_8
    | ~ spl4_23 ),
    inference(backward_demodulation,[],[f92,f203]) ).

fof(f92,plain,
    ( inverse(sk_c9) != sk_c8
    | spl4_8 ),
    inference(avatar_component_clause,[],[f91]) ).

fof(f359,plain,
    ( sk_c9 = inverse(sk_c9)
    | ~ spl4_11
    | ~ spl4_24 ),
    inference(backward_demodulation,[],[f108,f352]) ).

fof(f352,plain,
    ( sk_c9 = sk_c4
    | ~ spl4_11
    | ~ spl4_24 ),
    inference(superposition,[],[f312,f310]) ).

fof(f312,plain,
    ( sk_c9 = multiply(sk_c9,sk_c4)
    | ~ spl4_11
    | ~ spl4_24 ),
    inference(backward_demodulation,[],[f185,f212]) ).

fof(f185,plain,
    ( identity = multiply(sk_c9,sk_c4)
    | ~ spl4_11 ),
    inference(superposition,[],[f2,f108]) ).

fof(f108,plain,
    ( sk_c9 = inverse(sk_c4)
    | ~ spl4_11 ),
    inference(avatar_component_clause,[],[f106]) ).

fof(f106,plain,
    ( spl4_11
  <=> sk_c9 = inverse(sk_c4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_11])]) ).

fof(f322,plain,
    ( spl4_23
    | ~ spl4_9
    | ~ spl4_11
    | ~ spl4_24 ),
    inference(avatar_split_clause,[],[f319,f211,f106,f96,f202]) ).

fof(f96,plain,
    ( spl4_9
  <=> sk_c9 = multiply(sk_c4,sk_c8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_9])]) ).

fof(f319,plain,
    ( sk_c9 = sk_c8
    | ~ spl4_9
    | ~ spl4_11
    | ~ spl4_24 ),
    inference(backward_demodulation,[],[f278,f310]) ).

fof(f278,plain,
    ( sk_c8 = multiply(sk_c9,sk_c9)
    | ~ spl4_9
    | ~ spl4_11 ),
    inference(forward_demodulation,[],[f270,f108]) ).

fof(f270,plain,
    ( sk_c8 = multiply(inverse(sk_c4),sk_c9)
    | ~ spl4_9 ),
    inference(superposition,[],[f252,f98]) ).

fof(f98,plain,
    ( sk_c9 = multiply(sk_c4,sk_c8)
    | ~ spl4_9 ),
    inference(avatar_component_clause,[],[f96]) ).

fof(f308,plain,
    ( spl4_24
    | ~ spl4_2
    | ~ spl4_7 ),
    inference(avatar_split_clause,[],[f304,f86,f62,f211]) ).

fof(f62,plain,
    ( spl4_2
  <=> sk_c9 = multiply(sk_c5,sk_c8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).

fof(f86,plain,
    ( spl4_7
  <=> sk_c8 = inverse(sk_c5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_7])]) ).

fof(f304,plain,
    ( identity = sk_c9
    | ~ spl4_2
    | ~ spl4_7 ),
    inference(superposition,[],[f2,f284]) ).

fof(f284,plain,
    ( sk_c9 = multiply(inverse(sk_c8),sk_c8)
    | ~ spl4_2
    | ~ spl4_7 ),
    inference(superposition,[],[f252,f279]) ).

fof(f279,plain,
    ( sk_c8 = multiply(sk_c8,sk_c9)
    | ~ spl4_2
    | ~ spl4_7 ),
    inference(forward_demodulation,[],[f271,f88]) ).

fof(f88,plain,
    ( sk_c8 = inverse(sk_c5)
    | ~ spl4_7 ),
    inference(avatar_component_clause,[],[f86]) ).

fof(f271,plain,
    ( sk_c8 = multiply(inverse(sk_c5),sk_c9)
    | ~ spl4_2 ),
    inference(superposition,[],[f252,f64]) ).

fof(f64,plain,
    ( sk_c9 = multiply(sk_c5,sk_c8)
    | ~ spl4_2 ),
    inference(avatar_component_clause,[],[f62]) ).

fof(f183,plain,
    ( spl4_3
    | spl4_11 ),
    inference(avatar_split_clause,[],[f39,f106,f67]) ).

fof(f39,axiom,
    ( sk_c9 = inverse(sk_c4)
    | sk_c9 = inverse(sk_c2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).

fof(f182,plain,
    ( spl4_7
    | spl4_13 ),
    inference(avatar_split_clause,[],[f14,f116,f86]) ).

fof(f14,axiom,
    ( sk_c9 = inverse(sk_c1)
    | sk_c8 = inverse(sk_c5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).

fof(f179,plain,
    ( spl4_8
    | spl4_2 ),
    inference(avatar_split_clause,[],[f6,f62,f91]) ).

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

fof(f176,plain,
    ( spl4_8
    | spl4_4 ),
    inference(avatar_split_clause,[],[f8,f71,f91]) ).

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

fof(f175,plain,
    ( spl4_20
    | spl4_19 ),
    inference(avatar_split_clause,[],[f53,f155,f165]) ).

fof(f165,plain,
    ( spl4_20
  <=> sP2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_20])]) ).

fof(f53,plain,
    ! [X6] :
      ( sk_c9 != multiply(X6,sk_c8)
      | sk_c9 != inverse(X6)
      | sP2 ),
    inference(cnf_transformation,[],[f53_D]) ).

fof(f53_D,plain,
    ( ! [X6] :
        ( sk_c9 != multiply(X6,sk_c8)
        | sk_c9 != inverse(X6) )
  <=> ~ sP2 ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP2])]) ).

fof(f171,plain,
    ( ~ spl4_15
    | ~ spl4_16
    | ~ spl4_18
    | ~ spl4_20
    | spl4_21
    | ~ spl4_8 ),
    inference(avatar_split_clause,[],[f56,f91,f169,f165,f151,f142,f132]) ).

fof(f132,plain,
    ( spl4_15
  <=> sP3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_15])]) ).

fof(f142,plain,
    ( spl4_16
  <=> sP1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_16])]) ).

fof(f151,plain,
    ( spl4_18
  <=> sP0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_18])]) ).

fof(f56,plain,
    ! [X5] :
      ( inverse(sk_c9) != sk_c8
      | sk_c9 != inverse(X5)
      | ~ sP2
      | ~ sP0
      | ~ sP1
      | ~ sP3
      | sk_c8 != multiply(sk_c9,multiply(X5,sk_c9)) ),
    inference(general_splitting,[],[f54,f55_D]) ).

fof(f55,plain,
    ! [X7] :
      ( sP3
      | sk_c8 != inverse(X7)
      | sk_c9 != multiply(X7,sk_c8) ),
    inference(cnf_transformation,[],[f55_D]) ).

fof(f55_D,plain,
    ( ! [X7] :
        ( sk_c8 != inverse(X7)
        | sk_c9 != multiply(X7,sk_c8) )
  <=> ~ sP3 ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP3])]) ).

fof(f54,plain,
    ! [X7,X5] :
      ( inverse(sk_c9) != sk_c8
      | sk_c8 != inverse(X7)
      | sk_c9 != multiply(X7,sk_c8)
      | sk_c9 != inverse(X5)
      | sk_c8 != multiply(sk_c9,multiply(X5,sk_c9))
      | ~ sP0
      | ~ sP1
      | ~ sP2 ),
    inference(general_splitting,[],[f52,f53_D]) ).

fof(f52,plain,
    ! [X6,X7,X5] :
      ( sk_c9 != inverse(X6)
      | inverse(sk_c9) != sk_c8
      | sk_c8 != inverse(X7)
      | sk_c9 != multiply(X6,sk_c8)
      | sk_c9 != multiply(X7,sk_c8)
      | sk_c9 != inverse(X5)
      | sk_c8 != multiply(sk_c9,multiply(X5,sk_c9))
      | ~ sP0
      | ~ sP1 ),
    inference(general_splitting,[],[f50,f51_D]) ).

fof(f51,plain,
    ! [X8] :
      ( sk_c8 != multiply(X8,inverse(X8))
      | sP1
      | sk_c8 != multiply(inverse(X8),sk_c9) ),
    inference(cnf_transformation,[],[f51_D]) ).

fof(f51_D,plain,
    ( ! [X8] :
        ( sk_c8 != multiply(X8,inverse(X8))
        | sk_c8 != multiply(inverse(X8),sk_c9) )
  <=> ~ sP1 ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP1])]) ).

fof(f50,plain,
    ! [X8,X6,X7,X5] :
      ( sk_c9 != inverse(X6)
      | inverse(sk_c9) != sk_c8
      | sk_c8 != inverse(X7)
      | sk_c9 != multiply(X6,sk_c8)
      | sk_c8 != multiply(X8,inverse(X8))
      | sk_c9 != multiply(X7,sk_c8)
      | sk_c9 != inverse(X5)
      | sk_c8 != multiply(inverse(X8),sk_c9)
      | sk_c8 != multiply(sk_c9,multiply(X5,sk_c9))
      | ~ sP0 ),
    inference(general_splitting,[],[f48,f49_D]) ).

fof(f49,plain,
    ! [X3] :
      ( sk_c9 != multiply(X3,sk_c8)
      | sP0
      | sk_c9 != inverse(X3) ),
    inference(cnf_transformation,[],[f49_D]) ).

fof(f49_D,plain,
    ( ! [X3] :
        ( sk_c9 != multiply(X3,sk_c8)
        | sk_c9 != inverse(X3) )
  <=> ~ sP0 ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP0])]) ).

fof(f48,plain,
    ! [X3,X8,X6,X7,X5] :
      ( sk_c9 != inverse(X6)
      | inverse(sk_c9) != sk_c8
      | sk_c9 != inverse(X3)
      | sk_c8 != inverse(X7)
      | sk_c9 != multiply(X6,sk_c8)
      | sk_c8 != multiply(X8,inverse(X8))
      | sk_c9 != multiply(X7,sk_c8)
      | sk_c9 != inverse(X5)
      | sk_c9 != multiply(X3,sk_c8)
      | sk_c8 != multiply(inverse(X8),sk_c9)
      | sk_c8 != multiply(sk_c9,multiply(X5,sk_c9)) ),
    inference(equality_resolution,[],[f47]) ).

fof(f47,plain,
    ! [X3,X8,X6,X7,X4,X5] :
      ( sk_c9 != inverse(X6)
      | inverse(sk_c9) != sk_c8
      | sk_c9 != inverse(X3)
      | sk_c8 != inverse(X7)
      | sk_c9 != multiply(X6,sk_c8)
      | sk_c8 != multiply(X8,inverse(X8))
      | multiply(X5,sk_c9) != X4
      | sk_c9 != multiply(X7,sk_c8)
      | sk_c9 != inverse(X5)
      | sk_c9 != multiply(X3,sk_c8)
      | sk_c8 != multiply(inverse(X8),sk_c9)
      | sk_c8 != multiply(sk_c9,X4) ),
    inference(equality_resolution,[],[f46]) ).

fof(f46,axiom,
    ! [X3,X8,X6,X9,X7,X4,X5] :
      ( sk_c9 != inverse(X6)
      | inverse(sk_c9) != sk_c8
      | sk_c9 != inverse(X3)
      | inverse(X8) != X9
      | sk_c8 != inverse(X7)
      | sk_c9 != multiply(X6,sk_c8)
      | sk_c8 != multiply(X8,X9)
      | multiply(X5,sk_c9) != X4
      | sk_c9 != multiply(X7,sk_c8)
      | sk_c9 != inverse(X5)
      | sk_c9 != multiply(X3,sk_c8)
      | sk_c8 != multiply(X9,sk_c9)
      | sk_c8 != multiply(sk_c9,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_43) ).

fof(f162,plain,
    ( spl4_1
    | spl4_7 ),
    inference(avatar_split_clause,[],[f28,f86,f58]) ).

fof(f28,axiom,
    ( sk_c8 = inverse(sk_c5)
    | sk_c8 = multiply(sk_c9,sk_c3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).

fof(f157,plain,
    ( spl4_18
    | spl4_19 ),
    inference(avatar_split_clause,[],[f49,f155,f151]) ).

fof(f148,plain,
    ( spl4_16
    | spl4_17 ),
    inference(avatar_split_clause,[],[f51,f146,f142]) ).

fof(f136,plain,
    ( spl4_7
    | spl4_3 ),
    inference(avatar_split_clause,[],[f42,f67,f86]) ).

fof(f42,axiom,
    ( sk_c9 = inverse(sk_c2)
    | sk_c8 = inverse(sk_c5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_39) ).

fof(f135,plain,
    ( spl4_14
    | spl4_15 ),
    inference(avatar_split_clause,[],[f55,f132,f129]) ).

fof(f126,plain,
    ( spl4_8
    | spl4_12 ),
    inference(avatar_split_clause,[],[f9,f112,f91]) ).

fof(f9,axiom,
    ( sk_c7 = inverse(sk_c6)
    | inverse(sk_c9) = sk_c8 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).

fof(f124,plain,
    ( spl4_2
    | spl4_13 ),
    inference(avatar_split_clause,[],[f13,f116,f62]) ).

fof(f13,axiom,
    ( sk_c9 = inverse(sk_c1)
    | sk_c9 = multiply(sk_c5,sk_c8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).

fof(f123,plain,
    ( spl4_6
    | spl4_7 ),
    inference(avatar_split_clause,[],[f21,f86,f81]) ).

fof(f21,axiom,
    ( sk_c8 = inverse(sk_c5)
    | sk_c9 = multiply(sk_c1,sk_c8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).

fof(f122,plain,
    ( spl4_2
    | spl4_3 ),
    inference(avatar_split_clause,[],[f41,f67,f62]) ).

fof(f41,axiom,
    ( sk_c9 = inverse(sk_c2)
    | sk_c9 = multiply(sk_c5,sk_c8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_38) ).

fof(f109,plain,
    ( spl4_8
    | spl4_11 ),
    inference(avatar_split_clause,[],[f4,f106,f91]) ).

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

fof(f99,plain,
    ( spl4_3
    | spl4_9 ),
    inference(avatar_split_clause,[],[f40,f96,f67]) ).

fof(f40,axiom,
    ( sk_c9 = multiply(sk_c4,sk_c8)
    | sk_c9 = inverse(sk_c2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).

fof(f94,plain,
    ( spl4_8
    | spl4_7 ),
    inference(avatar_split_clause,[],[f7,f86,f91]) ).

fof(f7,axiom,
    ( sk_c8 = inverse(sk_c5)
    | inverse(sk_c9) = sk_c8 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).

fof(f89,plain,
    ( spl4_5
    | spl4_7 ),
    inference(avatar_split_clause,[],[f35,f86,f76]) ).

fof(f35,axiom,
    ( sk_c8 = inverse(sk_c5)
    | sk_c3 = multiply(sk_c2,sk_c9) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).

fof(f84,plain,
    ( spl4_2
    | spl4_6 ),
    inference(avatar_split_clause,[],[f20,f81,f62]) ).

fof(f20,axiom,
    ( sk_c9 = multiply(sk_c1,sk_c8)
    | sk_c9 = multiply(sk_c5,sk_c8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).

fof(f79,plain,
    ( spl4_5
    | spl4_2 ),
    inference(avatar_split_clause,[],[f34,f62,f76]) ).

fof(f34,axiom,
    ( sk_c9 = multiply(sk_c5,sk_c8)
    | sk_c3 = multiply(sk_c2,sk_c9) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).

fof(f65,plain,
    ( spl4_1
    | spl4_2 ),
    inference(avatar_split_clause,[],[f27,f62,f58]) ).

fof(f27,axiom,
    ( sk_c9 = multiply(sk_c5,sk_c8)
    | sk_c8 = multiply(sk_c9,sk_c3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : GRP239-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34  % Computer : n016.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon Aug 29 22:44:45 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.20/0.50  % (20156)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.20/0.50  % (20139)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.51  % (20148)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.51  % (20140)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)
% 0.20/0.52  % (20147)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.20/0.52  % (20158)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.20/0.52  % (20157)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)
% 0.20/0.52  % (20141)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)
% 0.20/0.52  % (20150)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.20/0.53  % (20135)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.20/0.53  TRYING [1]
% 0.20/0.53  % (20142)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.53  % (20159)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.20/0.53  % (20138)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)
% 0.20/0.54  % (20160)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.20/0.54  % (20161)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)
% 0.20/0.54  % (20149)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)
% 1.48/0.54  % (20163)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 1.48/0.54  TRYING [1]
% 1.48/0.54  % (20136)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)
% 1.48/0.54  % (20140)First to succeed.
% 1.48/0.54  % (20151)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.48/0.54  % (20137)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)
% 1.48/0.54  % (20140)Refutation found. Thanks to Tanya!
% 1.48/0.54  % SZS status Unsatisfiable for theBenchmark
% 1.48/0.54  % SZS output start Proof for theBenchmark
% See solution above
% 1.48/0.54  % (20140)------------------------------
% 1.48/0.54  % (20140)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.48/0.54  % (20140)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.48/0.54  % (20140)Termination reason: Refutation
% 1.48/0.54  
% 1.48/0.54  % (20140)Memory used [KB]: 5756
% 1.48/0.54  % (20140)Time elapsed: 0.132 s
% 1.48/0.54  % (20140)Instructions burned: 22 (million)
% 1.48/0.54  % (20140)------------------------------
% 1.48/0.54  % (20140)------------------------------
% 1.48/0.54  % (20131)Success in time 0.191 s
%------------------------------------------------------------------------------