TSTP Solution File: SYN417+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SYN417+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s

% Computer : n008.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 19:26:32 EDT 2022

% Result   : Theorem 0.18s 0.51s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   18
% Syntax   : Number of formulae    :  105 (   1 unt;   0 def)
%            Number of atoms       :  389 ( 198 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  526 ( 242   ~; 226   |;  31   &)
%                                         (  16 <=>;  10  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :   15 (  13 usr;  14 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-1 aty)
%            Number of variables   :   70 (  50   !;  20   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f278,plain,
    $false,
    inference(avatar_sat_refutation,[],[f26,f33,f41,f42,f43,f51,f52,f53,f82,f86,f109,f137,f138,f139,f179,f255,f263,f277]) ).

fof(f277,plain,
    ( ~ spl4_2
    | ~ spl4_4
    | ~ spl4_5
    | ~ spl4_8 ),
    inference(avatar_contradiction_clause,[],[f276]) ).

fof(f276,plain,
    ( $false
    | ~ spl4_2
    | ~ spl4_4
    | ~ spl4_5
    | ~ spl4_8 ),
    inference(trivial_inequality_removal,[],[f275]) ).

fof(f275,plain,
    ( sK3 != sK3
    | ~ spl4_2
    | ~ spl4_4
    | ~ spl4_5
    | ~ spl4_8 ),
    inference(superposition,[],[f226,f272]) ).

fof(f272,plain,
    ( sK3 = sK1(sK3)
    | ~ spl4_4
    | ~ spl4_5
    | ~ spl4_8 ),
    inference(trivial_inequality_removal,[],[f268]) ).

fof(f268,plain,
    ( sK3 = sK1(sK3)
    | sK1(sK3) != sK1(sK3)
    | ~ spl4_4
    | ~ spl4_5
    | ~ spl4_8 ),
    inference(superposition,[],[f50,f265]) ).

fof(f265,plain,
    ( sK1(sK3) = g(f(sK1(sK3)))
    | ~ spl4_4
    | ~ spl4_5 ),
    inference(trivial_inequality_removal,[],[f264]) ).

fof(f264,plain,
    ( sK3 != sK3
    | sK1(sK3) = g(f(sK1(sK3)))
    | ~ spl4_4
    | ~ spl4_5 ),
    inference(superposition,[],[f32,f37]) ).

fof(f37,plain,
    ( sK3 = g(f(sK3))
    | ~ spl4_5 ),
    inference(avatar_component_clause,[],[f35]) ).

fof(f35,plain,
    ( spl4_5
  <=> sK3 = g(f(sK3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_5])]) ).

fof(f32,plain,
    ( ! [X2] :
        ( g(f(X2)) != X2
        | g(f(sK1(X2))) = sK1(X2) )
    | ~ spl4_4 ),
    inference(avatar_component_clause,[],[f31]) ).

fof(f31,plain,
    ( spl4_4
  <=> ! [X2] :
        ( g(f(sK1(X2))) = sK1(X2)
        | g(f(X2)) != X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_4])]) ).

fof(f50,plain,
    ( ! [X7] :
        ( g(f(X7)) != X7
        | sK3 = X7 )
    | ~ spl4_8 ),
    inference(avatar_component_clause,[],[f49]) ).

fof(f49,plain,
    ( spl4_8
  <=> ! [X7] :
        ( sK3 = X7
        | g(f(X7)) != X7 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_8])]) ).

fof(f226,plain,
    ( sK3 != sK1(sK3)
    | ~ spl4_2
    | ~ spl4_5 ),
    inference(trivial_inequality_removal,[],[f223]) ).

fof(f223,plain,
    ( sK3 != sK1(sK3)
    | sK3 != sK3
    | ~ spl4_2
    | ~ spl4_5 ),
    inference(superposition,[],[f25,f37]) ).

fof(f25,plain,
    ( ! [X2] :
        ( g(f(X2)) != X2
        | sK1(X2) != X2 )
    | ~ spl4_2 ),
    inference(avatar_component_clause,[],[f24]) ).

fof(f24,plain,
    ( spl4_2
  <=> ! [X2] :
        ( g(f(X2)) != X2
        | sK1(X2) != X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).

fof(f263,plain,
    ( ~ spl4_3
    | ~ spl4_5
    | ~ spl4_18 ),
    inference(avatar_contradiction_clause,[],[f262]) ).

fof(f262,plain,
    ( $false
    | ~ spl4_3
    | ~ spl4_5
    | ~ spl4_18 ),
    inference(trivial_inequality_removal,[],[f259]) ).

fof(f259,plain,
    ( f(sK3) != f(sK3)
    | ~ spl4_3
    | ~ spl4_5
    | ~ spl4_18 ),
    inference(superposition,[],[f116,f247]) ).

fof(f247,plain,
    ( f(sK3) = sK0(f(sK3))
    | ~ spl4_18 ),
    inference(avatar_component_clause,[],[f246]) ).

fof(f246,plain,
    ( spl4_18
  <=> f(sK3) = sK0(f(sK3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_18])]) ).

fof(f116,plain,
    ( f(sK3) != sK0(f(sK3))
    | ~ spl4_3
    | ~ spl4_5 ),
    inference(trivial_inequality_removal,[],[f113]) ).

fof(f113,plain,
    ( f(sK3) != f(sK3)
    | f(sK3) != sK0(f(sK3))
    | ~ spl4_3
    | ~ spl4_5 ),
    inference(superposition,[],[f29,f37]) ).

fof(f29,plain,
    ( ! [X0] :
        ( f(g(X0)) != X0
        | sK0(X0) != X0 )
    | ~ spl4_3 ),
    inference(avatar_component_clause,[],[f28]) ).

fof(f28,plain,
    ( spl4_3
  <=> ! [X0] :
        ( f(g(X0)) != X0
        | sK0(X0) != X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_3])]) ).

fof(f255,plain,
    ( spl4_18
    | ~ spl4_1
    | ~ spl4_5
    | ~ spl4_8 ),
    inference(avatar_split_clause,[],[f238,f49,f35,f21,f246]) ).

fof(f21,plain,
    ( spl4_1
  <=> ! [X0] :
        ( f(g(X0)) != X0
        | sK0(X0) = f(g(sK0(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).

fof(f238,plain,
    ( f(sK3) = sK0(f(sK3))
    | ~ spl4_1
    | ~ spl4_5
    | ~ spl4_8 ),
    inference(backward_demodulation,[],[f229,f234]) ).

fof(f234,plain,
    ( sK3 = g(sK0(f(sK3)))
    | ~ spl4_1
    | ~ spl4_5
    | ~ spl4_8 ),
    inference(trivial_inequality_removal,[],[f233]) ).

fof(f233,plain,
    ( g(sK0(f(sK3))) != g(sK0(f(sK3)))
    | sK3 = g(sK0(f(sK3)))
    | ~ spl4_1
    | ~ spl4_5
    | ~ spl4_8 ),
    inference(superposition,[],[f50,f229]) ).

fof(f229,plain,
    ( f(g(sK0(f(sK3)))) = sK0(f(sK3))
    | ~ spl4_1
    | ~ spl4_5 ),
    inference(trivial_inequality_removal,[],[f228]) ).

fof(f228,plain,
    ( f(sK3) != f(sK3)
    | f(g(sK0(f(sK3)))) = sK0(f(sK3))
    | ~ spl4_1
    | ~ spl4_5 ),
    inference(superposition,[],[f22,f37]) ).

fof(f22,plain,
    ( ! [X0] :
        ( f(g(X0)) != X0
        | sK0(X0) = f(g(sK0(X0))) )
    | ~ spl4_1 ),
    inference(avatar_component_clause,[],[f21]) ).

fof(f179,plain,
    ( spl4_14
    | ~ spl4_8
    | ~ spl4_12
    | ~ spl4_13 ),
    inference(avatar_split_clause,[],[f178,f129,f125,f49,f134]) ).

fof(f134,plain,
    ( spl4_14
  <=> sK0(sK2) = sK2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_14])]) ).

fof(f125,plain,
    ( spl4_12
  <=> f(sK3) = sK2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_12])]) ).

fof(f129,plain,
    ( spl4_13
  <=> f(g(sK0(sK2))) = sK0(sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_13])]) ).

fof(f178,plain,
    ( sK0(sK2) = sK2
    | ~ spl4_8
    | ~ spl4_12
    | ~ spl4_13 ),
    inference(forward_demodulation,[],[f175,f126]) ).

fof(f126,plain,
    ( f(sK3) = sK2
    | ~ spl4_12 ),
    inference(avatar_component_clause,[],[f125]) ).

fof(f175,plain,
    ( f(sK3) = sK0(sK2)
    | ~ spl4_8
    | ~ spl4_13 ),
    inference(backward_demodulation,[],[f131,f169]) ).

fof(f169,plain,
    ( sK3 = g(sK0(sK2))
    | ~ spl4_8
    | ~ spl4_13 ),
    inference(trivial_inequality_removal,[],[f167]) ).

fof(f167,plain,
    ( g(sK0(sK2)) != g(sK0(sK2))
    | sK3 = g(sK0(sK2))
    | ~ spl4_8
    | ~ spl4_13 ),
    inference(superposition,[],[f50,f131]) ).

fof(f131,plain,
    ( f(g(sK0(sK2))) = sK0(sK2)
    | ~ spl4_13 ),
    inference(avatar_component_clause,[],[f129]) ).

fof(f139,plain,
    ( spl4_13
    | ~ spl4_1
    | ~ spl4_7 ),
    inference(avatar_split_clause,[],[f97,f45,f21,f129]) ).

fof(f45,plain,
    ( spl4_7
  <=> f(g(sK2)) = sK2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_7])]) ).

fof(f97,plain,
    ( f(g(sK0(sK2))) = sK0(sK2)
    | ~ spl4_1
    | ~ spl4_7 ),
    inference(trivial_inequality_removal,[],[f96]) ).

fof(f96,plain,
    ( f(g(sK0(sK2))) = sK0(sK2)
    | sK2 != sK2
    | ~ spl4_1
    | ~ spl4_7 ),
    inference(superposition,[],[f22,f47]) ).

fof(f47,plain,
    ( f(g(sK2)) = sK2
    | ~ spl4_7 ),
    inference(avatar_component_clause,[],[f45]) ).

fof(f138,plain,
    ( spl4_12
    | ~ spl4_7
    | ~ spl4_8 ),
    inference(avatar_split_clause,[],[f121,f49,f45,f125]) ).

fof(f121,plain,
    ( f(sK3) = sK2
    | ~ spl4_7
    | ~ spl4_8 ),
    inference(backward_demodulation,[],[f47,f119]) ).

fof(f119,plain,
    ( sK3 = g(sK2)
    | ~ spl4_7
    | ~ spl4_8 ),
    inference(trivial_inequality_removal,[],[f117]) ).

fof(f117,plain,
    ( g(sK2) != g(sK2)
    | sK3 = g(sK2)
    | ~ spl4_7
    | ~ spl4_8 ),
    inference(superposition,[],[f50,f47]) ).

fof(f137,plain,
    ( ~ spl4_14
    | ~ spl4_12
    | ~ spl4_3
    | ~ spl4_7
    | ~ spl4_8 ),
    inference(avatar_split_clause,[],[f123,f49,f45,f28,f125,f134]) ).

fof(f123,plain,
    ( f(sK3) != sK2
    | sK0(sK2) != sK2
    | ~ spl4_3
    | ~ spl4_7
    | ~ spl4_8 ),
    inference(superposition,[],[f29,f119]) ).

fof(f109,plain,
    ( ~ spl4_1
    | ~ spl4_3
    | ~ spl4_6
    | ~ spl4_7 ),
    inference(avatar_contradiction_clause,[],[f108]) ).

fof(f108,plain,
    ( $false
    | ~ spl4_1
    | ~ spl4_3
    | ~ spl4_6
    | ~ spl4_7 ),
    inference(trivial_inequality_removal,[],[f107]) ).

fof(f107,plain,
    ( sK2 != sK2
    | ~ spl4_1
    | ~ spl4_3
    | ~ spl4_6
    | ~ spl4_7 ),
    inference(superposition,[],[f91,f102]) ).

fof(f102,plain,
    ( sK0(sK2) = sK2
    | ~ spl4_1
    | ~ spl4_6
    | ~ spl4_7 ),
    inference(trivial_inequality_removal,[],[f100]) ).

fof(f100,plain,
    ( sK0(sK2) = sK2
    | sK0(sK2) != sK0(sK2)
    | ~ spl4_1
    | ~ spl4_6
    | ~ spl4_7 ),
    inference(superposition,[],[f40,f97]) ).

fof(f40,plain,
    ( ! [X5] :
        ( f(g(X5)) != X5
        | sK2 = X5 )
    | ~ spl4_6 ),
    inference(avatar_component_clause,[],[f39]) ).

fof(f39,plain,
    ( spl4_6
  <=> ! [X5] :
        ( f(g(X5)) != X5
        | sK2 = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_6])]) ).

fof(f91,plain,
    ( sK0(sK2) != sK2
    | ~ spl4_3
    | ~ spl4_7 ),
    inference(trivial_inequality_removal,[],[f90]) ).

fof(f90,plain,
    ( sK2 != sK2
    | sK0(sK2) != sK2
    | ~ spl4_3
    | ~ spl4_7 ),
    inference(superposition,[],[f29,f47]) ).

fof(f86,plain,
    ( ~ spl4_2
    | ~ spl4_7
    | ~ spl4_9 ),
    inference(avatar_contradiction_clause,[],[f85]) ).

fof(f85,plain,
    ( $false
    | ~ spl4_2
    | ~ spl4_7
    | ~ spl4_9 ),
    inference(trivial_inequality_removal,[],[f84]) ).

fof(f84,plain,
    ( g(sK2) != g(sK2)
    | ~ spl4_2
    | ~ spl4_7
    | ~ spl4_9 ),
    inference(superposition,[],[f56,f70]) ).

fof(f70,plain,
    ( g(sK2) = sK1(g(sK2))
    | ~ spl4_9 ),
    inference(avatar_component_clause,[],[f69]) ).

fof(f69,plain,
    ( spl4_9
  <=> g(sK2) = sK1(g(sK2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_9])]) ).

fof(f56,plain,
    ( g(sK2) != sK1(g(sK2))
    | ~ spl4_2
    | ~ spl4_7 ),
    inference(trivial_inequality_removal,[],[f55]) ).

fof(f55,plain,
    ( g(sK2) != sK1(g(sK2))
    | g(sK2) != g(sK2)
    | ~ spl4_2
    | ~ spl4_7 ),
    inference(superposition,[],[f25,f47]) ).

fof(f82,plain,
    ( spl4_9
    | ~ spl4_4
    | ~ spl4_6
    | ~ spl4_7 ),
    inference(avatar_split_clause,[],[f65,f45,f39,f31,f69]) ).

fof(f65,plain,
    ( g(sK2) = sK1(g(sK2))
    | ~ spl4_4
    | ~ spl4_6
    | ~ spl4_7 ),
    inference(backward_demodulation,[],[f58,f63]) ).

fof(f63,plain,
    ( sK2 = f(sK1(g(sK2)))
    | ~ spl4_4
    | ~ spl4_6
    | ~ spl4_7 ),
    inference(trivial_inequality_removal,[],[f61]) ).

fof(f61,plain,
    ( sK2 = f(sK1(g(sK2)))
    | f(sK1(g(sK2))) != f(sK1(g(sK2)))
    | ~ spl4_4
    | ~ spl4_6
    | ~ spl4_7 ),
    inference(superposition,[],[f40,f58]) ).

fof(f58,plain,
    ( g(f(sK1(g(sK2)))) = sK1(g(sK2))
    | ~ spl4_4
    | ~ spl4_7 ),
    inference(trivial_inequality_removal,[],[f57]) ).

fof(f57,plain,
    ( g(sK2) != g(sK2)
    | g(f(sK1(g(sK2)))) = sK1(g(sK2))
    | ~ spl4_4
    | ~ spl4_7 ),
    inference(superposition,[],[f32,f47]) ).

fof(f53,plain,
    ( spl4_5
    | spl4_7 ),
    inference(avatar_split_clause,[],[f14,f45,f35]) ).

fof(f14,plain,
    ( f(g(sK2)) = sK2
    | sK3 = g(f(sK3)) ),
    inference(cnf_transformation,[],[f11]) ).

fof(f11,plain,
    ( ( ! [X0] :
          ( f(g(X0)) != X0
          | ( sK0(X0) = f(g(sK0(X0)))
            & sK0(X0) != X0 ) )
      | ! [X2] :
          ( ( g(f(sK1(X2))) = sK1(X2)
            & sK1(X2) != X2 )
          | g(f(X2)) != X2 ) )
    & ( ( f(g(sK2)) = sK2
        & ! [X5] :
            ( f(g(X5)) != X5
            | sK2 = X5 ) )
      | ( ! [X7] :
            ( g(f(X7)) != X7
            | sK3 = X7 )
        & sK3 = g(f(sK3)) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f6,f10,f9,f8,f7]) ).

fof(f7,plain,
    ! [X0] :
      ( ? [X1] :
          ( f(g(X1)) = X1
          & X0 != X1 )
     => ( sK0(X0) = f(g(sK0(X0)))
        & sK0(X0) != X0 ) ),
    introduced(choice_axiom,[]) ).

fof(f8,plain,
    ! [X2] :
      ( ? [X3] :
          ( g(f(X3)) = X3
          & X2 != X3 )
     => ( g(f(sK1(X2))) = sK1(X2)
        & sK1(X2) != X2 ) ),
    introduced(choice_axiom,[]) ).

fof(f9,plain,
    ( ? [X4] :
        ( f(g(X4)) = X4
        & ! [X5] :
            ( f(g(X5)) != X5
            | X4 = X5 ) )
   => ( f(g(sK2)) = sK2
      & ! [X5] :
          ( f(g(X5)) != X5
          | sK2 = X5 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f10,plain,
    ( ? [X6] :
        ( ! [X7] :
            ( g(f(X7)) != X7
            | X6 = X7 )
        & g(f(X6)) = X6 )
   => ( ! [X7] :
          ( g(f(X7)) != X7
          | sK3 = X7 )
      & sK3 = g(f(sK3)) ) ),
    introduced(choice_axiom,[]) ).

fof(f6,plain,
    ( ( ! [X0] :
          ( f(g(X0)) != X0
          | ? [X1] :
              ( f(g(X1)) = X1
              & X0 != X1 ) )
      | ! [X2] :
          ( ? [X3] :
              ( g(f(X3)) = X3
              & X2 != X3 )
          | g(f(X2)) != X2 ) )
    & ( ? [X4] :
          ( f(g(X4)) = X4
          & ! [X5] :
              ( f(g(X5)) != X5
              | X4 = X5 ) )
      | ? [X6] :
          ( ! [X7] :
              ( g(f(X7)) != X7
              | X6 = X7 )
          & g(f(X6)) = X6 ) ) ),
    inference(rectify,[],[f5]) ).

fof(f5,plain,
    ( ( ! [X2] :
          ( f(g(X2)) != X2
          | ? [X3] :
              ( f(g(X3)) = X3
              & X2 != X3 ) )
      | ! [X0] :
          ( ? [X1] :
              ( g(f(X1)) = X1
              & X0 != X1 )
          | g(f(X0)) != X0 ) )
    & ( ? [X2] :
          ( f(g(X2)) = X2
          & ! [X3] :
              ( f(g(X3)) != X3
              | X2 = X3 ) )
      | ? [X0] :
          ( ! [X1] :
              ( g(f(X1)) != X1
              | X0 = X1 )
          & g(f(X0)) = X0 ) ) ),
    inference(nnf_transformation,[],[f4]) ).

fof(f4,plain,
    ( ? [X0] :
        ( ! [X1] :
            ( g(f(X1)) != X1
            | X0 = X1 )
        & g(f(X0)) = X0 )
  <~> ? [X2] :
        ( f(g(X2)) = X2
        & ! [X3] :
            ( f(g(X3)) != X3
            | X2 = X3 ) ) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f3,plain,
    ~ ( ? [X0] :
          ( ! [X1] :
              ( g(f(X1)) = X1
             => X0 = X1 )
          & g(f(X0)) = X0 )
    <=> ? [X2] :
          ( f(g(X2)) = X2
          & ! [X3] :
              ( f(g(X3)) = X3
             => X2 = X3 ) ) ),
    inference(rectify,[],[f2]) ).

fof(f2,negated_conjecture,
    ~ ( ? [X0] :
          ( ! [X1] :
              ( g(f(X1)) = X1
             => X0 = X1 )
          & g(f(X0)) = X0 )
    <=> ? [X0] :
          ( ! [X1] :
              ( f(g(X1)) = X1
             => X0 = X1 )
          & f(g(X0)) = X0 ) ),
    inference(negated_conjecture,[],[f1]) ).

fof(f1,conjecture,
    ( ? [X0] :
        ( ! [X1] :
            ( g(f(X1)) = X1
           => X0 = X1 )
        & g(f(X0)) = X0 )
  <=> ? [X0] :
        ( ! [X1] :
            ( f(g(X1)) = X1
           => X0 = X1 )
        & f(g(X0)) = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cute) ).

fof(f52,plain,
    ( spl4_8
    | spl4_6 ),
    inference(avatar_split_clause,[],[f13,f39,f49]) ).

fof(f13,plain,
    ! [X7,X5] :
      ( sK2 = X5
      | sK3 = X7
      | g(f(X7)) != X7
      | f(g(X5)) != X5 ),
    inference(cnf_transformation,[],[f11]) ).

fof(f51,plain,
    ( spl4_7
    | spl4_8 ),
    inference(avatar_split_clause,[],[f15,f49,f45]) ).

fof(f15,plain,
    ! [X7] :
      ( sK3 = X7
      | f(g(sK2)) = sK2
      | g(f(X7)) != X7 ),
    inference(cnf_transformation,[],[f11]) ).

fof(f43,plain,
    ( spl4_2
    | spl4_3 ),
    inference(avatar_split_clause,[],[f16,f28,f24]) ).

fof(f16,plain,
    ! [X2,X0] :
      ( sK0(X0) != X0
      | g(f(X2)) != X2
      | sK1(X2) != X2
      | f(g(X0)) != X0 ),
    inference(cnf_transformation,[],[f11]) ).

fof(f42,plain,
    ( spl4_1
    | spl4_4 ),
    inference(avatar_split_clause,[],[f19,f31,f21]) ).

fof(f19,plain,
    ! [X2,X0] :
      ( g(f(sK1(X2))) = sK1(X2)
      | g(f(X2)) != X2
      | f(g(X0)) != X0
      | sK0(X0) = f(g(sK0(X0))) ),
    inference(cnf_transformation,[],[f11]) ).

fof(f41,plain,
    ( spl4_5
    | spl4_6 ),
    inference(avatar_split_clause,[],[f12,f39,f35]) ).

fof(f12,plain,
    ! [X5] :
      ( f(g(X5)) != X5
      | sK3 = g(f(sK3))
      | sK2 = X5 ),
    inference(cnf_transformation,[],[f11]) ).

fof(f33,plain,
    ( spl4_3
    | spl4_4 ),
    inference(avatar_split_clause,[],[f17,f31,f28]) ).

fof(f17,plain,
    ! [X2,X0] :
      ( g(f(sK1(X2))) = sK1(X2)
      | f(g(X0)) != X0
      | sK0(X0) != X0
      | g(f(X2)) != X2 ),
    inference(cnf_transformation,[],[f11]) ).

fof(f26,plain,
    ( spl4_1
    | spl4_2 ),
    inference(avatar_split_clause,[],[f18,f24,f21]) ).

fof(f18,plain,
    ! [X2,X0] :
      ( g(f(X2)) != X2
      | sK1(X2) != X2
      | f(g(X0)) != X0
      | sK0(X0) = f(g(sK0(X0))) ),
    inference(cnf_transformation,[],[f11]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem    : SYN417+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.33  % Computer : n008.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Tue Aug 30 21:56:25 EDT 2022
% 0.12/0.33  % CPUTime    : 
% 0.18/0.49  % (23845)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.18/0.50  % (23827)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.18/0.50  % (23847)dis+21_1:1_ep=RS:nwc=10.0:s2a=on:s2at=1.5:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.18/0.50  % (23829)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.18/0.50  % (23830)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.18/0.50  % (23839)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.18/0.50  % (23845)First to succeed.
% 0.18/0.50  % (23850)dis+21_1:1_aac=none:abs=on:er=known:fde=none:fsr=off:nwc=5.0:s2a=on:s2at=4.0:sp=const_frequency:to=lpo:urr=ec_only:i=25:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/25Mi)
% 0.18/0.51  % (23845)Refutation found. Thanks to Tanya!
% 0.18/0.51  % SZS status Theorem for theBenchmark
% 0.18/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.51  % (23845)------------------------------
% 0.18/0.51  % (23845)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.51  % (23845)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.51  % (23845)Termination reason: Refutation
% 0.18/0.51  
% 0.18/0.51  % (23845)Memory used [KB]: 6012
% 0.18/0.51  % (23845)Time elapsed: 0.068 s
% 0.18/0.51  % (23845)Instructions burned: 5 (million)
% 0.18/0.51  % (23845)------------------------------
% 0.18/0.51  % (23845)------------------------------
% 0.18/0.51  % (23822)Success in time 0.171 s
%------------------------------------------------------------------------------