TSTP Solution File: GRP628+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : GRP628+1 : TPTP v8.1.0. Released v3.4.0.
% 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 : n013.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 16:17:11 EDT 2022

% Result   : Theorem 0.16s 0.45s
% Output   : Refutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   25
% Syntax   : Number of formulae    :  113 (  18 unt;   0 def)
%            Number of atoms       :  552 (  50 equ)
%            Maximal formula atoms :   18 (   4 avg)
%            Number of connectives :  722 ( 283   ~; 296   |; 100   &)
%                                         (  15 <=>;  28  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   26 (  24 usr;  16 prp; 0-4 aty)
%            Number of functors    :   10 (  10 usr;   3 con; 0-2 aty)
%            Number of variables   :   90 (  75   !;  15   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f931,plain,
    $false,
    inference(avatar_sat_refutation,[],[f622,f628,f630,f632,f695,f697,f727,f747,f768,f796,f805,f808,f866,f908,f924,f930]) ).

fof(f930,plain,
    ( ~ spl27_14
    | ~ spl27_16
    | ~ spl27_13
    | ~ spl27_17
    | spl27_15
    | spl27_44 ),
    inference(avatar_split_clause,[],[f929,f905,f605,f613,f597,f609,f601]) ).

fof(f601,plain,
    ( spl27_14
  <=> v4_group_1(sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_14])]) ).

fof(f609,plain,
    ( spl27_16
  <=> v3_group_1(sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_16])]) ).

fof(f597,plain,
    ( spl27_13
  <=> v1_group_1(sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_13])]) ).

fof(f613,plain,
    ( spl27_17
  <=> l1_group_1(sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_17])]) ).

fof(f605,plain,
    ( spl27_15
  <=> v3_struct_0(sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_15])]) ).

fof(f905,plain,
    ( spl27_44
  <=> m1_group_2(k5_autgroup(sK0),k3_autgroup(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_44])]) ).

fof(f929,plain,
    ( v3_struct_0(sK0)
    | ~ l1_group_1(sK0)
    | ~ v1_group_1(sK0)
    | ~ v3_group_1(sK0)
    | ~ v4_group_1(sK0)
    | spl27_44 ),
    inference(resolution,[],[f907,f315]) ).

fof(f315,plain,
    ! [X0] :
      ( m1_group_2(k5_autgroup(X0),k3_autgroup(X0))
      | v3_struct_0(X0)
      | ~ l1_group_1(X0)
      | ~ v3_group_1(X0)
      | ~ v4_group_1(X0)
      | ~ v1_group_1(X0) ),
    inference(cnf_transformation,[],[f146]) ).

fof(f146,plain,
    ! [X0] :
      ( ( m1_group_2(k5_autgroup(X0),k3_autgroup(X0))
        & v1_group_1(k5_autgroup(X0)) )
      | ~ v4_group_1(X0)
      | ~ v3_group_1(X0)
      | ~ v1_group_1(X0)
      | v3_struct_0(X0)
      | ~ l1_group_1(X0) ),
    inference(flattening,[],[f145]) ).

fof(f145,plain,
    ! [X0] :
      ( ( m1_group_2(k5_autgroup(X0),k3_autgroup(X0))
        & v1_group_1(k5_autgroup(X0)) )
      | ~ v1_group_1(X0)
      | ~ v3_group_1(X0)
      | ~ l1_group_1(X0)
      | v3_struct_0(X0)
      | ~ v4_group_1(X0) ),
    inference(ennf_transformation,[],[f95]) ).

fof(f95,plain,
    ! [X0] :
      ( ( v1_group_1(X0)
        & v3_group_1(X0)
        & l1_group_1(X0)
        & ~ v3_struct_0(X0)
        & v4_group_1(X0) )
     => ( m1_group_2(k5_autgroup(X0),k3_autgroup(X0))
        & v1_group_1(k5_autgroup(X0)) ) ),
    inference(pure_predicate_removal,[],[f25]) ).

fof(f25,axiom,
    ! [X0] :
      ( ( v1_group_1(X0)
        & v3_group_1(X0)
        & l1_group_1(X0)
        & ~ v3_struct_0(X0)
        & v4_group_1(X0) )
     => ( v1_group_1(k5_autgroup(X0))
        & m1_group_2(k5_autgroup(X0),k3_autgroup(X0))
        & v1_group_3(k5_autgroup(X0),k3_autgroup(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_autgroup) ).

fof(f907,plain,
    ( ~ m1_group_2(k5_autgroup(sK0),k3_autgroup(sK0))
    | spl27_44 ),
    inference(avatar_component_clause,[],[f905]) ).

fof(f924,plain,
    ( ~ spl27_16
    | ~ spl27_17
    | spl27_15
    | ~ spl27_13
    | ~ spl27_14
    | spl27_43 ),
    inference(avatar_split_clause,[],[f923,f901,f601,f597,f605,f613,f609]) ).

fof(f901,plain,
    ( spl27_43
  <=> v4_group_1(k3_autgroup(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_43])]) ).

fof(f923,plain,
    ( ~ v4_group_1(sK0)
    | ~ v1_group_1(sK0)
    | v3_struct_0(sK0)
    | ~ l1_group_1(sK0)
    | ~ v3_group_1(sK0)
    | spl27_43 ),
    inference(resolution,[],[f903,f328]) ).

fof(f328,plain,
    ! [X0] :
      ( v4_group_1(k3_autgroup(X0))
      | ~ v4_group_1(X0)
      | ~ v1_group_1(X0)
      | v3_struct_0(X0)
      | ~ l1_group_1(X0)
      | ~ v3_group_1(X0) ),
    inference(cnf_transformation,[],[f119]) ).

fof(f119,plain,
    ! [X0] :
      ( ~ v4_group_1(X0)
      | ~ v3_group_1(X0)
      | ( v3_group_1(k3_autgroup(X0))
        & l1_group_1(k3_autgroup(X0))
        & ~ v3_struct_0(k3_autgroup(X0))
        & v1_group_1(k3_autgroup(X0))
        & v4_group_1(k3_autgroup(X0)) )
      | v3_struct_0(X0)
      | ~ v1_group_1(X0)
      | ~ l1_group_1(X0) ),
    inference(flattening,[],[f118]) ).

fof(f118,plain,
    ! [X0] :
      ( ( v3_group_1(k3_autgroup(X0))
        & l1_group_1(k3_autgroup(X0))
        & ~ v3_struct_0(k3_autgroup(X0))
        & v1_group_1(k3_autgroup(X0))
        & v4_group_1(k3_autgroup(X0)) )
      | ~ v3_group_1(X0)
      | ~ v4_group_1(X0)
      | ~ l1_group_1(X0)
      | ~ v1_group_1(X0)
      | v3_struct_0(X0) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f22,axiom,
    ! [X0] :
      ( ( v3_group_1(X0)
        & v4_group_1(X0)
        & l1_group_1(X0)
        & v1_group_1(X0)
        & ~ v3_struct_0(X0) )
     => ( v3_group_1(k3_autgroup(X0))
        & l1_group_1(k3_autgroup(X0))
        & ~ v3_struct_0(k3_autgroup(X0))
        & v1_group_1(k3_autgroup(X0))
        & v4_group_1(k3_autgroup(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_autgroup) ).

fof(f903,plain,
    ( ~ v4_group_1(k3_autgroup(sK0))
    | spl27_43 ),
    inference(avatar_component_clause,[],[f901]) ).

fof(f908,plain,
    ( ~ spl27_43
    | ~ spl27_33
    | ~ spl27_30
    | ~ spl27_34
    | ~ spl27_44
    | spl27_35
    | ~ spl27_24
    | ~ spl27_29 ),
    inference(avatar_split_clause,[],[f895,f761,f725,f793,f905,f789,f765,f785,f901]) ).

fof(f785,plain,
    ( spl27_33
  <=> l1_group_1(k3_autgroup(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_33])]) ).

fof(f765,plain,
    ( spl27_30
  <=> m1_subset_1(sK1,u1_struct_0(k3_autgroup(sK0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_30])]) ).

fof(f789,plain,
    ( spl27_34
  <=> v3_group_1(k3_autgroup(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_34])]) ).

fof(f793,plain,
    ( spl27_35
  <=> v3_struct_0(k3_autgroup(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_35])]) ).

fof(f725,plain,
    ( spl27_24
  <=> ! [X0] :
        ( ~ m1_group_2(k5_autgroup(sK0),X0)
        | ~ l1_group_1(X0)
        | v3_struct_0(X0)
        | ~ m1_subset_1(sK1,u1_struct_0(X0))
        | ~ v4_group_1(X0)
        | k2_funct_1(sK1) != k3_group_1(X0,sK1)
        | ~ v3_group_1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_24])]) ).

fof(f761,plain,
    ( spl27_29
  <=> k3_group_1(k3_autgroup(sK0),sK1) = k2_funct_1(sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_29])]) ).

fof(f895,plain,
    ( v3_struct_0(k3_autgroup(sK0))
    | ~ m1_group_2(k5_autgroup(sK0),k3_autgroup(sK0))
    | ~ v3_group_1(k3_autgroup(sK0))
    | ~ m1_subset_1(sK1,u1_struct_0(k3_autgroup(sK0)))
    | ~ l1_group_1(k3_autgroup(sK0))
    | ~ v4_group_1(k3_autgroup(sK0))
    | ~ spl27_24
    | ~ spl27_29 ),
    inference(trivial_inequality_removal,[],[f891]) ).

fof(f891,plain,
    ( v3_struct_0(k3_autgroup(sK0))
    | ~ v4_group_1(k3_autgroup(sK0))
    | ~ l1_group_1(k3_autgroup(sK0))
    | ~ m1_group_2(k5_autgroup(sK0),k3_autgroup(sK0))
    | k2_funct_1(sK1) != k2_funct_1(sK1)
    | ~ m1_subset_1(sK1,u1_struct_0(k3_autgroup(sK0)))
    | ~ v3_group_1(k3_autgroup(sK0))
    | ~ spl27_24
    | ~ spl27_29 ),
    inference(superposition,[],[f726,f763]) ).

fof(f763,plain,
    ( k3_group_1(k3_autgroup(sK0),sK1) = k2_funct_1(sK1)
    | ~ spl27_29 ),
    inference(avatar_component_clause,[],[f761]) ).

fof(f726,plain,
    ( ! [X0] :
        ( k2_funct_1(sK1) != k3_group_1(X0,sK1)
        | ~ m1_subset_1(sK1,u1_struct_0(X0))
        | v3_struct_0(X0)
        | ~ l1_group_1(X0)
        | ~ v4_group_1(X0)
        | ~ m1_group_2(k5_autgroup(sK0),X0)
        | ~ v3_group_1(X0) )
    | ~ spl27_24 ),
    inference(avatar_component_clause,[],[f725]) ).

fof(f866,plain,
    ( ~ spl27_17
    | ~ spl27_16
    | ~ spl27_13
    | spl27_15
    | ~ spl27_14
    | ~ spl27_35 ),
    inference(avatar_split_clause,[],[f865,f793,f601,f605,f597,f609,f613]) ).

fof(f865,plain,
    ( ~ v4_group_1(sK0)
    | v3_struct_0(sK0)
    | ~ v1_group_1(sK0)
    | ~ v3_group_1(sK0)
    | ~ l1_group_1(sK0)
    | ~ spl27_35 ),
    inference(resolution,[],[f795,f330]) ).

fof(f330,plain,
    ! [X0] :
      ( ~ v3_struct_0(k3_autgroup(X0))
      | ~ v1_group_1(X0)
      | ~ v4_group_1(X0)
      | ~ v3_group_1(X0)
      | v3_struct_0(X0)
      | ~ l1_group_1(X0) ),
    inference(cnf_transformation,[],[f119]) ).

fof(f795,plain,
    ( v3_struct_0(k3_autgroup(sK0))
    | ~ spl27_35 ),
    inference(avatar_component_clause,[],[f793]) ).

fof(f808,plain,
    ( spl27_15
    | ~ spl27_16
    | ~ spl27_13
    | ~ spl27_17
    | ~ spl27_14
    | spl27_34 ),
    inference(avatar_split_clause,[],[f807,f789,f601,f613,f597,f609,f605]) ).

fof(f807,plain,
    ( ~ v4_group_1(sK0)
    | ~ l1_group_1(sK0)
    | ~ v1_group_1(sK0)
    | ~ v3_group_1(sK0)
    | v3_struct_0(sK0)
    | spl27_34 ),
    inference(resolution,[],[f791,f332]) ).

fof(f332,plain,
    ! [X0] :
      ( v3_group_1(k3_autgroup(X0))
      | ~ v4_group_1(X0)
      | v3_struct_0(X0)
      | ~ v3_group_1(X0)
      | ~ l1_group_1(X0)
      | ~ v1_group_1(X0) ),
    inference(cnf_transformation,[],[f119]) ).

fof(f791,plain,
    ( ~ v3_group_1(k3_autgroup(sK0))
    | spl27_34 ),
    inference(avatar_component_clause,[],[f789]) ).

fof(f805,plain,
    ( ~ spl27_17
    | spl27_15
    | ~ spl27_13
    | ~ spl27_14
    | ~ spl27_16
    | spl27_33 ),
    inference(avatar_split_clause,[],[f804,f785,f609,f601,f597,f605,f613]) ).

fof(f804,plain,
    ( ~ v3_group_1(sK0)
    | ~ v4_group_1(sK0)
    | ~ v1_group_1(sK0)
    | v3_struct_0(sK0)
    | ~ l1_group_1(sK0)
    | spl27_33 ),
    inference(resolution,[],[f787,f331]) ).

fof(f331,plain,
    ! [X0] :
      ( l1_group_1(k3_autgroup(X0))
      | ~ v4_group_1(X0)
      | ~ v3_group_1(X0)
      | ~ l1_group_1(X0)
      | v3_struct_0(X0)
      | ~ v1_group_1(X0) ),
    inference(cnf_transformation,[],[f119]) ).

fof(f787,plain,
    ( ~ l1_group_1(k3_autgroup(sK0))
    | spl27_33 ),
    inference(avatar_component_clause,[],[f785]) ).

fof(f796,plain,
    ( ~ spl27_33
    | ~ spl27_34
    | spl27_30
    | ~ spl27_13
    | spl27_35
    | spl27_15
    | ~ spl27_17
    | ~ spl27_14
    | ~ spl27_16 ),
    inference(avatar_split_clause,[],[f783,f609,f601,f613,f605,f793,f597,f765,f789,f785]) ).

fof(f783,plain,
    ( ~ v3_group_1(sK0)
    | ~ v4_group_1(sK0)
    | ~ l1_group_1(sK0)
    | v3_struct_0(sK0)
    | v3_struct_0(k3_autgroup(sK0))
    | ~ v1_group_1(sK0)
    | m1_subset_1(sK1,u1_struct_0(k3_autgroup(sK0)))
    | ~ v3_group_1(k3_autgroup(sK0))
    | ~ l1_group_1(k3_autgroup(sK0)) ),
    inference(resolution,[],[f617,f315]) ).

fof(f617,plain,
    ! [X0] :
      ( ~ m1_group_2(k5_autgroup(sK0),X0)
      | m1_subset_1(sK1,u1_struct_0(X0))
      | ~ v3_group_1(X0)
      | v3_struct_0(X0)
      | ~ l1_group_1(X0) ),
    inference(resolution,[],[f384,f392]) ).

fof(f392,plain,
    m1_subset_1(sK1,u1_struct_0(k5_autgroup(sK0))),
    inference(definition_unfolding,[],[f271,f269]) ).

fof(f269,plain,
    sK2 = sK1,
    inference(cnf_transformation,[],[f191]) ).

fof(f191,plain,
    ( ~ v3_struct_0(sK0)
    & m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
    & m1_subset_1(sK2,u1_struct_0(k5_autgroup(sK0)))
    & k3_group_1(k5_autgroup(sK0),sK2) != k2_funct_1(sK1)
    & sK2 = sK1
    & v4_group_1(sK0)
    & v3_group_1(sK0)
    & l1_group_1(sK0)
    & v1_group_1(sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f137,f190,f189,f188]) ).

fof(f188,plain,
    ( ? [X0] :
        ( ~ v3_struct_0(X0)
        & ? [X1] :
            ( m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
            & ? [X2] :
                ( m1_subset_1(X2,u1_struct_0(k5_autgroup(X0)))
                & k2_funct_1(X1) != k3_group_1(k5_autgroup(X0),X2)
                & X1 = X2 ) )
        & v4_group_1(X0)
        & v3_group_1(X0)
        & l1_group_1(X0)
        & v1_group_1(X0) )
   => ( ~ v3_struct_0(sK0)
      & ? [X1] :
          ( m2_fraenkel(X1,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
          & ? [X2] :
              ( m1_subset_1(X2,u1_struct_0(k5_autgroup(sK0)))
              & k2_funct_1(X1) != k3_group_1(k5_autgroup(sK0),X2)
              & X1 = X2 ) )
      & v4_group_1(sK0)
      & v3_group_1(sK0)
      & l1_group_1(sK0)
      & v1_group_1(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f189,plain,
    ( ? [X1] :
        ( m2_fraenkel(X1,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
        & ? [X2] :
            ( m1_subset_1(X2,u1_struct_0(k5_autgroup(sK0)))
            & k2_funct_1(X1) != k3_group_1(k5_autgroup(sK0),X2)
            & X1 = X2 ) )
   => ( m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
      & ? [X2] :
          ( m1_subset_1(X2,u1_struct_0(k5_autgroup(sK0)))
          & k2_funct_1(sK1) != k3_group_1(k5_autgroup(sK0),X2)
          & sK1 = X2 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f190,plain,
    ( ? [X2] :
        ( m1_subset_1(X2,u1_struct_0(k5_autgroup(sK0)))
        & k2_funct_1(sK1) != k3_group_1(k5_autgroup(sK0),X2)
        & sK1 = X2 )
   => ( m1_subset_1(sK2,u1_struct_0(k5_autgroup(sK0)))
      & k3_group_1(k5_autgroup(sK0),sK2) != k2_funct_1(sK1)
      & sK2 = sK1 ) ),
    introduced(choice_axiom,[]) ).

fof(f137,plain,
    ? [X0] :
      ( ~ v3_struct_0(X0)
      & ? [X1] :
          ( m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
          & ? [X2] :
              ( m1_subset_1(X2,u1_struct_0(k5_autgroup(X0)))
              & k2_funct_1(X1) != k3_group_1(k5_autgroup(X0),X2)
              & X1 = X2 ) )
      & v4_group_1(X0)
      & v3_group_1(X0)
      & l1_group_1(X0)
      & v1_group_1(X0) ),
    inference(flattening,[],[f136]) ).

fof(f136,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( k2_funct_1(X1) != k3_group_1(k5_autgroup(X0),X2)
              & X1 = X2
              & m1_subset_1(X2,u1_struct_0(k5_autgroup(X0))) )
          & m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0)) )
      & ~ v3_struct_0(X0)
      & v1_group_1(X0)
      & v4_group_1(X0)
      & l1_group_1(X0)
      & v3_group_1(X0) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f2,negated_conjecture,
    ~ ! [X0] :
        ( ( ~ v3_struct_0(X0)
          & v1_group_1(X0)
          & v4_group_1(X0)
          & l1_group_1(X0)
          & v3_group_1(X0) )
       => ! [X1] :
            ( m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
           => ! [X2] :
                ( m1_subset_1(X2,u1_struct_0(k5_autgroup(X0)))
               => ( X1 = X2
                 => k2_funct_1(X1) = k3_group_1(k5_autgroup(X0),X2) ) ) ) ),
    inference(negated_conjecture,[],[f1]) ).

fof(f1,conjecture,
    ! [X0] :
      ( ( ~ v3_struct_0(X0)
        & v1_group_1(X0)
        & v4_group_1(X0)
        & l1_group_1(X0)
        & v3_group_1(X0) )
     => ! [X1] :
          ( m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
         => ! [X2] :
              ( m1_subset_1(X2,u1_struct_0(k5_autgroup(X0)))
             => ( X1 = X2
               => k2_funct_1(X1) = k3_group_1(k5_autgroup(X0),X2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_autgroup) ).

fof(f271,plain,
    m1_subset_1(sK2,u1_struct_0(k5_autgroup(sK0))),
    inference(cnf_transformation,[],[f191]) ).

fof(f384,plain,
    ! [X2,X0,X1] :
      ( ~ m1_subset_1(X2,u1_struct_0(X1))
      | v3_struct_0(X0)
      | ~ m1_group_2(X1,X0)
      | m1_subset_1(X2,u1_struct_0(X0))
      | ~ l1_group_1(X0)
      | ~ v3_group_1(X0) ),
    inference(cnf_transformation,[],[f113]) ).

fof(f113,plain,
    ! [X0] :
      ( v3_struct_0(X0)
      | ~ v3_group_1(X0)
      | ~ l1_group_1(X0)
      | ! [X1] :
          ( ! [X2] :
              ( ~ m1_subset_1(X2,u1_struct_0(X1))
              | m1_subset_1(X2,u1_struct_0(X0)) )
          | ~ m1_group_2(X1,X0) ) ),
    inference(flattening,[],[f112]) ).

fof(f112,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ~ m1_subset_1(X2,u1_struct_0(X1))
              | m1_subset_1(X2,u1_struct_0(X0)) )
          | ~ m1_group_2(X1,X0) )
      | ~ l1_group_1(X0)
      | ~ v3_group_1(X0)
      | v3_struct_0(X0) ),
    inference(ennf_transformation,[],[f73]) ).

fof(f73,axiom,
    ! [X0] :
      ( ( l1_group_1(X0)
        & v3_group_1(X0)
        & ~ v3_struct_0(X0) )
     => ! [X1] :
          ( m1_group_2(X1,X0)
         => ! [X2] :
              ( m1_subset_1(X2,u1_struct_0(X1))
             => m1_subset_1(X2,u1_struct_0(X0)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_group_2) ).

fof(f768,plain,
    ( ~ spl27_14
    | spl27_29
    | spl27_15
    | ~ spl27_13
    | ~ spl27_30
    | ~ spl27_16
    | ~ spl27_17
    | ~ spl27_22 ),
    inference(avatar_split_clause,[],[f755,f692,f613,f609,f765,f597,f605,f761,f601]) ).

fof(f692,plain,
    ( spl27_22
  <=> m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_22])]) ).

fof(f755,plain,
    ( ~ l1_group_1(sK0)
    | ~ v3_group_1(sK0)
    | ~ m1_subset_1(sK1,u1_struct_0(k3_autgroup(sK0)))
    | ~ v1_group_1(sK0)
    | v3_struct_0(sK0)
    | k3_group_1(k3_autgroup(sK0),sK1) = k2_funct_1(sK1)
    | ~ v4_group_1(sK0)
    | ~ spl27_22 ),
    inference(resolution,[],[f694,f394]) ).

fof(f394,plain,
    ! [X2,X0] :
      ( ~ m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
      | v3_struct_0(X0)
      | ~ v1_group_1(X0)
      | ~ v3_group_1(X0)
      | ~ l1_group_1(X0)
      | ~ v4_group_1(X0)
      | ~ m1_subset_1(X2,u1_struct_0(k3_autgroup(X0)))
      | k3_group_1(k3_autgroup(X0),X2) = k2_funct_1(X2) ),
    inference(equality_resolution,[],[f290]) ).

fof(f290,plain,
    ! [X2,X0,X1] :
      ( ~ v1_group_1(X0)
      | X1 != X2
      | k2_funct_1(X1) = k3_group_1(k3_autgroup(X0),X2)
      | ~ m1_subset_1(X2,u1_struct_0(k3_autgroup(X0)))
      | ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
      | ~ v3_group_1(X0)
      | v3_struct_0(X0)
      | ~ l1_group_1(X0)
      | ~ v4_group_1(X0) ),
    inference(cnf_transformation,[],[f159]) ).

fof(f159,plain,
    ! [X0] :
      ( ~ v1_group_1(X0)
      | ! [X1] :
          ( ! [X2] :
              ( X1 != X2
              | k2_funct_1(X1) = k3_group_1(k3_autgroup(X0),X2)
              | ~ m1_subset_1(X2,u1_struct_0(k3_autgroup(X0))) )
          | ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) )
      | ~ v3_group_1(X0)
      | v3_struct_0(X0)
      | ~ l1_group_1(X0)
      | ~ v4_group_1(X0) ),
    inference(flattening,[],[f158]) ).

fof(f158,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( k2_funct_1(X1) = k3_group_1(k3_autgroup(X0),X2)
              | X1 != X2
              | ~ m1_subset_1(X2,u1_struct_0(k3_autgroup(X0))) )
          | ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) )
      | ~ v4_group_1(X0)
      | ~ l1_group_1(X0)
      | ~ v3_group_1(X0)
      | ~ v1_group_1(X0)
      | v3_struct_0(X0) ),
    inference(ennf_transformation,[],[f67]) ).

fof(f67,axiom,
    ! [X0] :
      ( ( v4_group_1(X0)
        & l1_group_1(X0)
        & v3_group_1(X0)
        & v1_group_1(X0)
        & ~ v3_struct_0(X0) )
     => ! [X1] :
          ( m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
         => ! [X2] :
              ( m1_subset_1(X2,u1_struct_0(k3_autgroup(X0)))
             => ( X1 = X2
               => k2_funct_1(X1) = k3_group_1(k3_autgroup(X0),X2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_autgroup) ).

fof(f694,plain,
    ( m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
    | ~ spl27_22 ),
    inference(avatar_component_clause,[],[f692]) ).

fof(f747,plain,
    spl27_23,
    inference(avatar_contradiction_clause,[],[f746]) ).

fof(f746,plain,
    ( $false
    | spl27_23 ),
    inference(resolution,[],[f723,f392]) ).

fof(f723,plain,
    ( ~ m1_subset_1(sK1,u1_struct_0(k5_autgroup(sK0)))
    | spl27_23 ),
    inference(avatar_component_clause,[],[f721]) ).

fof(f721,plain,
    ( spl27_23
  <=> m1_subset_1(sK1,u1_struct_0(k5_autgroup(sK0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl27_23])]) ).

fof(f727,plain,
    ( ~ spl27_23
    | spl27_24 ),
    inference(avatar_split_clause,[],[f710,f725,f721]) ).

fof(f710,plain,
    ! [X0] :
      ( ~ m1_group_2(k5_autgroup(sK0),X0)
      | ~ v3_group_1(X0)
      | k2_funct_1(sK1) != k3_group_1(X0,sK1)
      | ~ v4_group_1(X0)
      | ~ m1_subset_1(sK1,u1_struct_0(X0))
      | v3_struct_0(X0)
      | ~ l1_group_1(X0)
      | ~ m1_subset_1(sK1,u1_struct_0(k5_autgroup(sK0))) ),
    inference(superposition,[],[f393,f395]) ).

fof(f395,plain,
    ! [X2,X3,X0] :
      ( k3_group_1(X2,X3) = k3_group_1(X0,X3)
      | ~ m1_subset_1(X3,u1_struct_0(X2))
      | v3_struct_0(X0)
      | ~ v4_group_1(X0)
      | ~ m1_group_2(X2,X0)
      | ~ l1_group_1(X0)
      | ~ v3_group_1(X0)
      | ~ m1_subset_1(X3,u1_struct_0(X0)) ),
    inference(equality_resolution,[],[f365]) ).

fof(f365,plain,
    ! [X2,X3,X0,X1] :
      ( v3_struct_0(X0)
      | ~ v3_group_1(X0)
      | ~ l1_group_1(X0)
      | ~ m1_subset_1(X1,u1_struct_0(X0))
      | X1 != X3
      | k3_group_1(X0,X1) = k3_group_1(X2,X3)
      | ~ m1_subset_1(X3,u1_struct_0(X2))
      | ~ m1_group_2(X2,X0)
      | ~ v4_group_1(X0) ),
    inference(cnf_transformation,[],[f177]) ).

fof(f177,plain,
    ! [X0] :
      ( v3_struct_0(X0)
      | ~ v3_group_1(X0)
      | ~ l1_group_1(X0)
      | ! [X1] :
          ( ~ m1_subset_1(X1,u1_struct_0(X0))
          | ! [X2] :
              ( ! [X3] :
                  ( X1 != X3
                  | k3_group_1(X0,X1) = k3_group_1(X2,X3)
                  | ~ m1_subset_1(X3,u1_struct_0(X2)) )
              | ~ m1_group_2(X2,X0) ) )
      | ~ v4_group_1(X0) ),
    inference(flattening,[],[f176]) ).

fof(f176,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( k3_group_1(X0,X1) = k3_group_1(X2,X3)
                  | X1 != X3
                  | ~ m1_subset_1(X3,u1_struct_0(X2)) )
              | ~ m1_group_2(X2,X0) )
          | ~ m1_subset_1(X1,u1_struct_0(X0)) )
      | ~ v4_group_1(X0)
      | ~ l1_group_1(X0)
      | v3_struct_0(X0)
      | ~ v3_group_1(X0) ),
    inference(ennf_transformation,[],[f74]) ).

fof(f74,axiom,
    ! [X0] :
      ( ( v4_group_1(X0)
        & l1_group_1(X0)
        & ~ v3_struct_0(X0)
        & v3_group_1(X0) )
     => ! [X1] :
          ( m1_subset_1(X1,u1_struct_0(X0))
         => ! [X2] :
              ( m1_group_2(X2,X0)
             => ! [X3] :
                  ( m1_subset_1(X3,u1_struct_0(X2))
                 => ( X1 = X3
                   => k3_group_1(X0,X1) = k3_group_1(X2,X3) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_group_2) ).

fof(f393,plain,
    k2_funct_1(sK1) != k3_group_1(k5_autgroup(sK0),sK1),
    inference(definition_unfolding,[],[f270,f269]) ).

fof(f270,plain,
    k3_group_1(k5_autgroup(sK0),sK2) != k2_funct_1(sK1),
    inference(cnf_transformation,[],[f191]) ).

fof(f697,plain,
    ~ spl27_15,
    inference(avatar_contradiction_clause,[],[f696]) ).

fof(f696,plain,
    ( $false
    | ~ spl27_15 ),
    inference(resolution,[],[f607,f273]) ).

fof(f273,plain,
    ~ v3_struct_0(sK0),
    inference(cnf_transformation,[],[f191]) ).

fof(f607,plain,
    ( v3_struct_0(sK0)
    | ~ spl27_15 ),
    inference(avatar_component_clause,[],[f605]) ).

fof(f695,plain,
    ( ~ spl27_14
    | ~ spl27_13
    | spl27_22
    | ~ spl27_16
    | ~ spl27_17
    | spl27_15 ),
    inference(avatar_split_clause,[],[f688,f605,f613,f609,f692,f597,f601]) ).

fof(f688,plain,
    ( v3_struct_0(sK0)
    | ~ l1_group_1(sK0)
    | ~ v3_group_1(sK0)
    | m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
    | ~ v1_group_1(sK0)
    | ~ v4_group_1(sK0) ),
    inference(resolution,[],[f299,f272]) ).

fof(f272,plain,
    m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)),
    inference(cnf_transformation,[],[f191]) ).

fof(f299,plain,
    ! [X0,X1] :
      ( ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
      | ~ v3_group_1(X0)
      | v3_struct_0(X0)
      | ~ v1_group_1(X0)
      | m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
      | ~ v4_group_1(X0)
      | ~ l1_group_1(X0) ),
    inference(cnf_transformation,[],[f173]) ).

fof(f173,plain,
    ! [X0] :
      ( v3_struct_0(X0)
      | ~ v4_group_1(X0)
      | ! [X1] :
          ( m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
          | ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0)) )
      | ~ v3_group_1(X0)
      | ~ v1_group_1(X0)
      | ~ l1_group_1(X0) ),
    inference(flattening,[],[f172]) ).

fof(f172,plain,
    ! [X0] :
      ( ! [X1] :
          ( m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
          | ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0)) )
      | ~ l1_group_1(X0)
      | ~ v3_group_1(X0)
      | v3_struct_0(X0)
      | ~ v4_group_1(X0)
      | ~ v1_group_1(X0) ),
    inference(ennf_transformation,[],[f68]) ).

fof(f68,axiom,
    ! [X0] :
      ( ( l1_group_1(X0)
        & v3_group_1(X0)
        & ~ v3_struct_0(X0)
        & v4_group_1(X0)
        & v1_group_1(X0) )
     => ! [X1] :
          ( m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
         => m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_autgroup) ).

fof(f632,plain,
    spl27_17,
    inference(avatar_contradiction_clause,[],[f631]) ).

fof(f631,plain,
    ( $false
    | spl27_17 ),
    inference(resolution,[],[f615,f266]) ).

fof(f266,plain,
    l1_group_1(sK0),
    inference(cnf_transformation,[],[f191]) ).

fof(f615,plain,
    ( ~ l1_group_1(sK0)
    | spl27_17 ),
    inference(avatar_component_clause,[],[f613]) ).

fof(f630,plain,
    spl27_16,
    inference(avatar_contradiction_clause,[],[f629]) ).

fof(f629,plain,
    ( $false
    | spl27_16 ),
    inference(resolution,[],[f611,f267]) ).

fof(f267,plain,
    v3_group_1(sK0),
    inference(cnf_transformation,[],[f191]) ).

fof(f611,plain,
    ( ~ v3_group_1(sK0)
    | spl27_16 ),
    inference(avatar_component_clause,[],[f609]) ).

fof(f628,plain,
    spl27_14,
    inference(avatar_contradiction_clause,[],[f627]) ).

fof(f627,plain,
    ( $false
    | spl27_14 ),
    inference(resolution,[],[f603,f268]) ).

fof(f268,plain,
    v4_group_1(sK0),
    inference(cnf_transformation,[],[f191]) ).

fof(f603,plain,
    ( ~ v4_group_1(sK0)
    | spl27_14 ),
    inference(avatar_component_clause,[],[f601]) ).

fof(f622,plain,
    spl27_13,
    inference(avatar_contradiction_clause,[],[f621]) ).

fof(f621,plain,
    ( $false
    | spl27_13 ),
    inference(resolution,[],[f599,f265]) ).

fof(f265,plain,
    v1_group_1(sK0),
    inference(cnf_transformation,[],[f191]) ).

fof(f599,plain,
    ( ~ v1_group_1(sK0)
    | spl27_13 ),
    inference(avatar_component_clause,[],[f597]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11  % Problem    : GRP628+1 : TPTP v8.1.0. Released v3.4.0.
% 0.02/0.11  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.11/0.32  % Computer : n013.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Mon Aug 29 22:32:46 EDT 2022
% 0.11/0.32  % CPUTime    : 
% 0.16/0.42  % (7812)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.16/0.43  % (7812)Instruction limit reached!
% 0.16/0.43  % (7812)------------------------------
% 0.16/0.43  % (7812)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.16/0.43  % (7812)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.16/0.43  % (7812)Termination reason: Unknown
% 0.16/0.43  % (7812)Termination phase: Property scanning
% 0.16/0.43  
% 0.16/0.43  % (7812)Memory used [KB]: 1535
% 0.16/0.43  % (7812)Time elapsed: 0.005 s
% 0.16/0.43  % (7812)Instructions burned: 4 (million)
% 0.16/0.43  % (7812)------------------------------
% 0.16/0.43  % (7812)------------------------------
% 0.16/0.43  % (7821)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)
% 0.16/0.45  % (7821)First to succeed.
% 0.16/0.45  % (7821)Refutation found. Thanks to Tanya!
% 0.16/0.45  % SZS status Theorem for theBenchmark
% 0.16/0.45  % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.45  % (7821)------------------------------
% 0.16/0.45  % (7821)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.16/0.45  % (7821)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.16/0.45  % (7821)Termination reason: Refutation
% 0.16/0.45  
% 0.16/0.45  % (7821)Memory used [KB]: 6524
% 0.16/0.45  % (7821)Time elapsed: 0.077 s
% 0.16/0.45  % (7821)Instructions burned: 21 (million)
% 0.16/0.45  % (7821)------------------------------
% 0.16/0.45  % (7821)------------------------------
% 0.16/0.45  % (7797)Success in time 0.127 s
%------------------------------------------------------------------------------