TSTP Solution File: GRP628+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : GRP628+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n021.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 : Fri May  3 02:23:09 EDT 2024

% Result   : Theorem 7.59s 1.71s
% Output   : CNFRefutation 7.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   81 (  22 unt;   0 def)
%            Number of atoms       :  467 (  52 equ)
%            Maximal formula atoms :   18 (   5 avg)
%            Number of connectives :  635 ( 249   ~; 258   |; 100   &)
%                                         (   0 <=>;  28  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-4 aty)
%            Number of functors    :   10 (  10 usr;   3 con; 0-2 aty)
%            Number of variables   :  106 (   0 sgn  71   !;  15   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,conjecture,
    ! [X0] :
      ( ( l1_group_1(X0)
        & v4_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),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/sandbox2/benchmark/theBenchmark.p',t22_autgroup) ).

fof(f2,negated_conjecture,
    ~ ! [X0] :
        ( ( l1_group_1(X0)
          & v4_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),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(f22,axiom,
    ! [X0] :
      ( ( l1_group_1(X0)
        & v4_group_1(X0)
        & v3_group_1(X0)
        & v1_group_1(X0)
        & ~ v3_struct_0(X0) )
     => ( l1_group_1(k3_autgroup(X0))
        & v4_group_1(k3_autgroup(X0))
        & v3_group_1(k3_autgroup(X0))
        & v1_group_1(k3_autgroup(X0))
        & ~ v3_struct_0(k3_autgroup(X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_autgroup) ).

fof(f25,axiom,
    ! [X0] :
      ( ( l1_group_1(X0)
        & v4_group_1(X0)
        & v3_group_1(X0)
        & v1_group_1(X0)
        & ~ v3_struct_0(X0) )
     => ( m1_group_2(k5_autgroup(X0),k3_autgroup(X0))
        & v1_group_3(k5_autgroup(X0),k3_autgroup(X0))
        & v1_group_1(k5_autgroup(X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_autgroup) ).

fof(f67,axiom,
    ! [X0] :
      ( ( l1_group_1(X0)
        & v4_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/sandbox2/benchmark/theBenchmark.p',t11_autgroup) ).

fof(f68,axiom,
    ! [X0] :
      ( ( l1_group_1(X0)
        & v4_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),k4_autgroup(X0))
         => m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_autgroup) ).

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/sandbox2/benchmark/theBenchmark.p',t51_group_2) ).

fof(f74,axiom,
    ! [X0] :
      ( ( l1_group_1(X0)
        & v4_group_1(X0)
        & v3_group_1(X0)
        & ~ v3_struct_0(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/sandbox2/benchmark/theBenchmark.p',t57_group_2) ).

fof(f82,plain,
    ! [X0] :
      ( ( l1_group_1(X0)
        & v4_group_1(X0)
        & v3_group_1(X0)
        & v1_group_1(X0)
        & ~ v3_struct_0(X0) )
     => ( m1_group_2(k5_autgroup(X0),k3_autgroup(X0))
        & v1_group_1(k5_autgroup(X0)) ) ),
    inference(pure_predicate_removal,[],[f25]) ).

fof(f90,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)) )
      & l1_group_1(X0)
      & v4_group_1(X0)
      & v3_group_1(X0)
      & v1_group_1(X0)
      & ~ v3_struct_0(X0) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f91,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)) )
      & l1_group_1(X0)
      & v4_group_1(X0)
      & v3_group_1(X0)
      & v1_group_1(X0)
      & ~ v3_struct_0(X0) ),
    inference(flattening,[],[f90]) ).

fof(f120,plain,
    ! [X0] :
      ( ( l1_group_1(k3_autgroup(X0))
        & v4_group_1(k3_autgroup(X0))
        & v3_group_1(k3_autgroup(X0))
        & v1_group_1(k3_autgroup(X0))
        & ~ v3_struct_0(k3_autgroup(X0)) )
      | ~ l1_group_1(X0)
      | ~ v4_group_1(X0)
      | ~ v3_group_1(X0)
      | ~ v1_group_1(X0)
      | v3_struct_0(X0) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f121,plain,
    ! [X0] :
      ( ( l1_group_1(k3_autgroup(X0))
        & v4_group_1(k3_autgroup(X0))
        & v3_group_1(k3_autgroup(X0))
        & v1_group_1(k3_autgroup(X0))
        & ~ v3_struct_0(k3_autgroup(X0)) )
      | ~ l1_group_1(X0)
      | ~ v4_group_1(X0)
      | ~ v3_group_1(X0)
      | ~ v1_group_1(X0)
      | v3_struct_0(X0) ),
    inference(flattening,[],[f120]) ).

fof(f126,plain,
    ! [X0] :
      ( ( m1_group_2(k5_autgroup(X0),k3_autgroup(X0))
        & v1_group_1(k5_autgroup(X0)) )
      | ~ l1_group_1(X0)
      | ~ v4_group_1(X0)
      | ~ v3_group_1(X0)
      | ~ v1_group_1(X0)
      | v3_struct_0(X0) ),
    inference(ennf_transformation,[],[f82]) ).

fof(f127,plain,
    ! [X0] :
      ( ( m1_group_2(k5_autgroup(X0),k3_autgroup(X0))
        & v1_group_1(k5_autgroup(X0)) )
      | ~ l1_group_1(X0)
      | ~ v4_group_1(X0)
      | ~ v3_group_1(X0)
      | ~ v1_group_1(X0)
      | v3_struct_0(X0) ),
    inference(flattening,[],[f126]) ).

fof(f154,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)) )
      | ~ l1_group_1(X0)
      | ~ v4_group_1(X0)
      | ~ v3_group_1(X0)
      | ~ v1_group_1(X0)
      | v3_struct_0(X0) ),
    inference(ennf_transformation,[],[f67]) ).

fof(f155,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)) )
      | ~ l1_group_1(X0)
      | ~ v4_group_1(X0)
      | ~ v3_group_1(X0)
      | ~ v1_group_1(X0)
      | v3_struct_0(X0) ),
    inference(flattening,[],[f154]) ).

fof(f156,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)
      | ~ v4_group_1(X0)
      | ~ v3_group_1(X0)
      | ~ v1_group_1(X0)
      | v3_struct_0(X0) ),
    inference(ennf_transformation,[],[f68]) ).

fof(f157,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)
      | ~ v4_group_1(X0)
      | ~ v3_group_1(X0)
      | ~ v1_group_1(X0)
      | v3_struct_0(X0) ),
    inference(flattening,[],[f156]) ).

fof(f164,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( m1_subset_1(X2,u1_struct_0(X0))
              | ~ m1_subset_1(X2,u1_struct_0(X1)) )
          | ~ m1_group_2(X1,X0) )
      | ~ l1_group_1(X0)
      | ~ v3_group_1(X0)
      | v3_struct_0(X0) ),
    inference(ennf_transformation,[],[f73]) ).

fof(f165,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( m1_subset_1(X2,u1_struct_0(X0))
              | ~ m1_subset_1(X2,u1_struct_0(X1)) )
          | ~ m1_group_2(X1,X0) )
      | ~ l1_group_1(X0)
      | ~ v3_group_1(X0)
      | v3_struct_0(X0) ),
    inference(flattening,[],[f164]) ).

fof(f166,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)) )
      | ~ l1_group_1(X0)
      | ~ v4_group_1(X0)
      | ~ v3_group_1(X0)
      | v3_struct_0(X0) ),
    inference(ennf_transformation,[],[f74]) ).

fof(f167,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)) )
      | ~ l1_group_1(X0)
      | ~ v4_group_1(X0)
      | ~ v3_group_1(X0)
      | v3_struct_0(X0) ),
    inference(flattening,[],[f166]) ).

fof(f172,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)) )
        & l1_group_1(X0)
        & v4_group_1(X0)
        & v3_group_1(X0)
        & v1_group_1(X0)
        & ~ v3_struct_0(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( k2_funct_1(X1) != k3_group_1(k5_autgroup(sK0),X2)
              & X1 = X2
              & m1_subset_1(X2,u1_struct_0(k5_autgroup(sK0))) )
          & m2_fraenkel(X1,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)) )
      & l1_group_1(sK0)
      & v4_group_1(sK0)
      & v3_group_1(sK0)
      & v1_group_1(sK0)
      & ~ v3_struct_0(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f173,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( k2_funct_1(X1) != k3_group_1(k5_autgroup(sK0),X2)
            & X1 = X2
            & m1_subset_1(X2,u1_struct_0(k5_autgroup(sK0))) )
        & m2_fraenkel(X1,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)) )
   => ( ? [X2] :
          ( k3_group_1(k5_autgroup(sK0),X2) != k2_funct_1(sK1)
          & sK1 = X2
          & m1_subset_1(X2,u1_struct_0(k5_autgroup(sK0))) )
      & m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f174,plain,
    ( ? [X2] :
        ( k3_group_1(k5_autgroup(sK0),X2) != k2_funct_1(sK1)
        & sK1 = X2
        & m1_subset_1(X2,u1_struct_0(k5_autgroup(sK0))) )
   => ( k2_funct_1(sK1) != k3_group_1(k5_autgroup(sK0),sK2)
      & sK1 = sK2
      & m1_subset_1(sK2,u1_struct_0(k5_autgroup(sK0))) ) ),
    introduced(choice_axiom,[]) ).

fof(f175,plain,
    ( k2_funct_1(sK1) != k3_group_1(k5_autgroup(sK0),sK2)
    & sK1 = sK2
    & m1_subset_1(sK2,u1_struct_0(k5_autgroup(sK0)))
    & m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
    & l1_group_1(sK0)
    & v4_group_1(sK0)
    & v3_group_1(sK0)
    & v1_group_1(sK0)
    & ~ v3_struct_0(sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f91,f174,f173,f172]) ).

fof(f226,plain,
    ~ v3_struct_0(sK0),
    inference(cnf_transformation,[],[f175]) ).

fof(f227,plain,
    v1_group_1(sK0),
    inference(cnf_transformation,[],[f175]) ).

fof(f228,plain,
    v3_group_1(sK0),
    inference(cnf_transformation,[],[f175]) ).

fof(f229,plain,
    v4_group_1(sK0),
    inference(cnf_transformation,[],[f175]) ).

fof(f230,plain,
    l1_group_1(sK0),
    inference(cnf_transformation,[],[f175]) ).

fof(f231,plain,
    m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)),
    inference(cnf_transformation,[],[f175]) ).

fof(f232,plain,
    m1_subset_1(sK2,u1_struct_0(k5_autgroup(sK0))),
    inference(cnf_transformation,[],[f175]) ).

fof(f233,plain,
    sK1 = sK2,
    inference(cnf_transformation,[],[f175]) ).

fof(f234,plain,
    k2_funct_1(sK1) != k3_group_1(k5_autgroup(sK0),sK2),
    inference(cnf_transformation,[],[f175]) ).

fof(f263,plain,
    ! [X0] :
      ( ~ v3_struct_0(k3_autgroup(X0))
      | ~ l1_group_1(X0)
      | ~ v4_group_1(X0)
      | ~ v3_group_1(X0)
      | ~ v1_group_1(X0)
      | v3_struct_0(X0) ),
    inference(cnf_transformation,[],[f121]) ).

fof(f265,plain,
    ! [X0] :
      ( v3_group_1(k3_autgroup(X0))
      | ~ l1_group_1(X0)
      | ~ v4_group_1(X0)
      | ~ v3_group_1(X0)
      | ~ v1_group_1(X0)
      | v3_struct_0(X0) ),
    inference(cnf_transformation,[],[f121]) ).

fof(f266,plain,
    ! [X0] :
      ( v4_group_1(k3_autgroup(X0))
      | ~ l1_group_1(X0)
      | ~ v4_group_1(X0)
      | ~ v3_group_1(X0)
      | ~ v1_group_1(X0)
      | v3_struct_0(X0) ),
    inference(cnf_transformation,[],[f121]) ).

fof(f267,plain,
    ! [X0] :
      ( l1_group_1(k3_autgroup(X0))
      | ~ l1_group_1(X0)
      | ~ v4_group_1(X0)
      | ~ v3_group_1(X0)
      | ~ v1_group_1(X0)
      | v3_struct_0(X0) ),
    inference(cnf_transformation,[],[f121]) ).

fof(f271,plain,
    ! [X0] :
      ( m1_group_2(k5_autgroup(X0),k3_autgroup(X0))
      | ~ l1_group_1(X0)
      | ~ v4_group_1(X0)
      | ~ v3_group_1(X0)
      | ~ v1_group_1(X0)
      | v3_struct_0(X0) ),
    inference(cnf_transformation,[],[f127]) ).

fof(f349,plain,
    ! [X2,X0,X1] :
      ( 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))
      | ~ l1_group_1(X0)
      | ~ v4_group_1(X0)
      | ~ v3_group_1(X0)
      | ~ v1_group_1(X0)
      | v3_struct_0(X0) ),
    inference(cnf_transformation,[],[f155]) ).

fof(f350,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)
      | ~ v4_group_1(X0)
      | ~ v3_group_1(X0)
      | ~ v1_group_1(X0)
      | v3_struct_0(X0) ),
    inference(cnf_transformation,[],[f157]) ).

fof(f355,plain,
    ! [X2,X0,X1] :
      ( m1_subset_1(X2,u1_struct_0(X0))
      | ~ m1_subset_1(X2,u1_struct_0(X1))
      | ~ m1_group_2(X1,X0)
      | ~ l1_group_1(X0)
      | ~ v3_group_1(X0)
      | v3_struct_0(X0) ),
    inference(cnf_transformation,[],[f165]) ).

fof(f356,plain,
    ! [X2,X3,X0,X1] :
      ( 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))
      | ~ l1_group_1(X0)
      | ~ v4_group_1(X0)
      | ~ v3_group_1(X0)
      | v3_struct_0(X0) ),
    inference(cnf_transformation,[],[f167]) ).

fof(f361,plain,
    k3_group_1(k5_autgroup(sK0),sK2) != k2_funct_1(sK2),
    inference(definition_unfolding,[],[f234,f233]) ).

fof(f362,plain,
    m2_fraenkel(sK2,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)),
    inference(definition_unfolding,[],[f231,f233]) ).

fof(f363,plain,
    ! [X2,X0] :
      ( k3_group_1(k3_autgroup(X0),X2) = k2_funct_1(X2)
      | ~ m1_subset_1(X2,u1_struct_0(k3_autgroup(X0)))
      | ~ m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
      | ~ l1_group_1(X0)
      | ~ v4_group_1(X0)
      | ~ v3_group_1(X0)
      | ~ v1_group_1(X0)
      | v3_struct_0(X0) ),
    inference(equality_resolution,[],[f349]) ).

fof(f364,plain,
    ! [X2,X3,X0] :
      ( k3_group_1(X2,X3) = k3_group_1(X0,X3)
      | ~ m1_subset_1(X3,u1_struct_0(X2))
      | ~ m1_group_2(X2,X0)
      | ~ m1_subset_1(X3,u1_struct_0(X0))
      | ~ l1_group_1(X0)
      | ~ v4_group_1(X0)
      | ~ v3_group_1(X0)
      | v3_struct_0(X0) ),
    inference(equality_resolution,[],[f356]) ).

cnf(c_49,negated_conjecture,
    k3_group_1(k5_autgroup(sK0),sK2) != k2_funct_1(sK2),
    inference(cnf_transformation,[],[f361]) ).

cnf(c_50,negated_conjecture,
    m1_subset_1(sK2,u1_struct_0(k5_autgroup(sK0))),
    inference(cnf_transformation,[],[f232]) ).

cnf(c_51,negated_conjecture,
    m2_fraenkel(sK2,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)),
    inference(cnf_transformation,[],[f362]) ).

cnf(c_52,negated_conjecture,
    l1_group_1(sK0),
    inference(cnf_transformation,[],[f230]) ).

cnf(c_53,negated_conjecture,
    v4_group_1(sK0),
    inference(cnf_transformation,[],[f229]) ).

cnf(c_54,negated_conjecture,
    v3_group_1(sK0),
    inference(cnf_transformation,[],[f228]) ).

cnf(c_55,negated_conjecture,
    v1_group_1(sK0),
    inference(cnf_transformation,[],[f227]) ).

cnf(c_56,negated_conjecture,
    ~ v3_struct_0(sK0),
    inference(cnf_transformation,[],[f226]) ).

cnf(c_77,plain,
    ( ~ l1_group_1(X0)
    | ~ v4_group_1(X0)
    | ~ v3_group_1(X0)
    | ~ v1_group_1(X0)
    | l1_group_1(k3_autgroup(X0))
    | v3_struct_0(X0) ),
    inference(cnf_transformation,[],[f267]) ).

cnf(c_78,plain,
    ( ~ l1_group_1(X0)
    | ~ v4_group_1(X0)
    | ~ v3_group_1(X0)
    | ~ v1_group_1(X0)
    | v4_group_1(k3_autgroup(X0))
    | v3_struct_0(X0) ),
    inference(cnf_transformation,[],[f266]) ).

cnf(c_79,plain,
    ( ~ l1_group_1(X0)
    | ~ v4_group_1(X0)
    | ~ v3_group_1(X0)
    | ~ v1_group_1(X0)
    | v3_group_1(k3_autgroup(X0))
    | v3_struct_0(X0) ),
    inference(cnf_transformation,[],[f265]) ).

cnf(c_81,plain,
    ( ~ v3_struct_0(k3_autgroup(X0))
    | ~ l1_group_1(X0)
    | ~ v4_group_1(X0)
    | ~ v3_group_1(X0)
    | ~ v1_group_1(X0)
    | v3_struct_0(X0) ),
    inference(cnf_transformation,[],[f263]) ).

cnf(c_84,plain,
    ( ~ l1_group_1(X0)
    | ~ v4_group_1(X0)
    | ~ v3_group_1(X0)
    | ~ v1_group_1(X0)
    | m1_group_2(k5_autgroup(X0),k3_autgroup(X0))
    | v3_struct_0(X0) ),
    inference(cnf_transformation,[],[f271]) ).

cnf(c_163,plain,
    ( ~ m2_fraenkel(X0,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
    | ~ m1_subset_1(X0,u1_struct_0(k3_autgroup(X1)))
    | ~ l1_group_1(X1)
    | ~ v4_group_1(X1)
    | ~ v3_group_1(X1)
    | ~ v1_group_1(X1)
    | k3_group_1(k3_autgroup(X1),X0) = k2_funct_1(X0)
    | v3_struct_0(X1) ),
    inference(cnf_transformation,[],[f363]) ).

cnf(c_164,plain,
    ( ~ m2_fraenkel(X0,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
    | ~ l1_group_1(X1)
    | ~ v4_group_1(X1)
    | ~ v3_group_1(X1)
    | ~ v1_group_1(X1)
    | m2_fraenkel(X0,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
    | v3_struct_0(X1) ),
    inference(cnf_transformation,[],[f350]) ).

cnf(c_169,plain,
    ( ~ m1_subset_1(X0,u1_struct_0(X1))
    | ~ m1_group_2(X1,X2)
    | ~ l1_group_1(X2)
    | ~ v3_group_1(X2)
    | m1_subset_1(X0,u1_struct_0(X2))
    | v3_struct_0(X2) ),
    inference(cnf_transformation,[],[f355]) ).

cnf(c_170,plain,
    ( ~ m1_subset_1(X0,u1_struct_0(X1))
    | ~ m1_subset_1(X0,u1_struct_0(X2))
    | ~ m1_group_2(X2,X1)
    | ~ l1_group_1(X1)
    | ~ v4_group_1(X1)
    | ~ v3_group_1(X1)
    | k3_group_1(X1,X0) = k3_group_1(X2,X0)
    | v3_struct_0(X1) ),
    inference(cnf_transformation,[],[f364]) ).

cnf(c_232,plain,
    ( ~ l1_group_1(sK0)
    | ~ v4_group_1(sK0)
    | ~ v3_group_1(sK0)
    | ~ v1_group_1(sK0)
    | v3_group_1(k3_autgroup(sK0))
    | v3_struct_0(sK0) ),
    inference(instantiation,[status(thm)],[c_79]) ).

cnf(c_233,plain,
    ( ~ l1_group_1(sK0)
    | ~ v4_group_1(sK0)
    | ~ v3_group_1(sK0)
    | ~ v1_group_1(sK0)
    | v4_group_1(k3_autgroup(sK0))
    | v3_struct_0(sK0) ),
    inference(instantiation,[status(thm)],[c_78]) ).

cnf(c_234,plain,
    ( ~ l1_group_1(sK0)
    | ~ v4_group_1(sK0)
    | ~ v3_group_1(sK0)
    | ~ v1_group_1(sK0)
    | l1_group_1(k3_autgroup(sK0))
    | v3_struct_0(sK0) ),
    inference(instantiation,[status(thm)],[c_77]) ).

cnf(c_237,plain,
    ( ~ v3_struct_0(k3_autgroup(sK0))
    | ~ l1_group_1(sK0)
    | ~ v4_group_1(sK0)
    | ~ v3_group_1(sK0)
    | ~ v1_group_1(sK0)
    | v3_struct_0(sK0) ),
    inference(instantiation,[status(thm)],[c_81]) ).

cnf(c_238,plain,
    ( ~ l1_group_1(sK0)
    | ~ v4_group_1(sK0)
    | ~ v3_group_1(sK0)
    | ~ v1_group_1(sK0)
    | m1_group_2(k5_autgroup(sK0),k3_autgroup(sK0))
    | v3_struct_0(sK0) ),
    inference(instantiation,[status(thm)],[c_84]) ).

cnf(c_1125,plain,
    ( ~ m1_subset_1(X0,u1_struct_0(X1))
    | ~ m1_group_2(X1,X2)
    | ~ l1_group_1(X2)
    | ~ v4_group_1(X2)
    | ~ v3_group_1(X2)
    | k3_group_1(X2,X0) = k3_group_1(X1,X0)
    | v3_struct_0(X2) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_170,c_169]) ).

cnf(c_9809,plain,
    ( ~ m1_subset_1(sK2,u1_struct_0(k5_autgroup(sK0)))
    | ~ m1_group_2(k5_autgroup(sK0),X0)
    | ~ l1_group_1(X0)
    | ~ v3_group_1(X0)
    | m1_subset_1(sK2,u1_struct_0(X0))
    | v3_struct_0(X0) ),
    inference(instantiation,[status(thm)],[c_169]) ).

cnf(c_10053,plain,
    ( ~ m2_fraenkel(sK2,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
    | ~ l1_group_1(sK0)
    | ~ v4_group_1(sK0)
    | ~ v3_group_1(sK0)
    | ~ v1_group_1(sK0)
    | m2_fraenkel(sK2,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
    | v3_struct_0(sK0) ),
    inference(instantiation,[status(thm)],[c_164]) ).

cnf(c_10635,plain,
    ( ~ m2_fraenkel(sK2,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
    | ~ m1_subset_1(sK2,u1_struct_0(k3_autgroup(sK0)))
    | ~ l1_group_1(sK0)
    | ~ v4_group_1(sK0)
    | ~ v3_group_1(sK0)
    | ~ v1_group_1(sK0)
    | k3_group_1(k3_autgroup(sK0),sK2) = k2_funct_1(sK2)
    | v3_struct_0(sK0) ),
    inference(instantiation,[status(thm)],[c_163]) ).

cnf(c_10786,plain,
    ( ~ m1_subset_1(sK2,u1_struct_0(k5_autgroup(sK0)))
    | ~ m1_group_2(k5_autgroup(sK0),k3_autgroup(sK0))
    | ~ l1_group_1(k3_autgroup(sK0))
    | ~ v3_group_1(k3_autgroup(sK0))
    | m1_subset_1(sK2,u1_struct_0(k3_autgroup(sK0)))
    | v3_struct_0(k3_autgroup(sK0)) ),
    inference(instantiation,[status(thm)],[c_9809]) ).

cnf(c_13809,plain,
    ( ~ m1_group_2(k5_autgroup(sK0),X0)
    | ~ l1_group_1(X0)
    | ~ v4_group_1(X0)
    | ~ v3_group_1(X0)
    | k3_group_1(k5_autgroup(sK0),sK2) = k3_group_1(X0,sK2)
    | v3_struct_0(X0) ),
    inference(superposition,[status(thm)],[c_50,c_1125]) ).

cnf(c_13913,plain,
    ( ~ l1_group_1(k3_autgroup(sK0))
    | ~ v4_group_1(k3_autgroup(sK0))
    | ~ v3_group_1(k3_autgroup(sK0))
    | ~ l1_group_1(sK0)
    | ~ v4_group_1(sK0)
    | ~ v3_group_1(sK0)
    | ~ v1_group_1(sK0)
    | k3_group_1(k5_autgroup(sK0),sK2) = k3_group_1(k3_autgroup(sK0),sK2)
    | v3_struct_0(k3_autgroup(sK0))
    | v3_struct_0(sK0) ),
    inference(superposition,[status(thm)],[c_84,c_13809]) ).

cnf(c_13929,plain,
    k3_group_1(k5_autgroup(sK0),sK2) = k3_group_1(k3_autgroup(sK0),sK2),
    inference(global_subsumption_just,[status(thm)],[c_13913,c_55,c_54,c_53,c_52,c_56,c_232,c_233,c_234,c_237,c_13913]) ).

cnf(c_13931,plain,
    k3_group_1(k3_autgroup(sK0),sK2) != k2_funct_1(sK2),
    inference(superposition,[status(thm)],[c_13929,c_49]) ).

cnf(c_13933,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_13931,c_10786,c_10635,c_10053,c_238,c_237,c_234,c_232,c_51,c_50,c_56,c_52,c_53,c_54,c_55]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.15  % Problem  : GRP628+1 : TPTP v8.1.2. Released v3.4.0.
% 0.07/0.16  % Command  : run_iprover %s %d THM
% 0.14/0.38  % Computer : n021.cluster.edu
% 0.14/0.38  % Model    : x86_64 x86_64
% 0.14/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.38  % Memory   : 8042.1875MB
% 0.14/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.38  % CPULimit : 300
% 0.14/0.38  % WCLimit  : 300
% 0.14/0.38  % DateTime : Thu May  2 23:50:43 EDT 2024
% 0.14/0.38  % CPUTime  : 
% 0.22/0.52  Running first-order theorem proving
% 0.22/0.52  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 7.59/1.71  % SZS status Started for theBenchmark.p
% 7.59/1.71  % SZS status Theorem for theBenchmark.p
% 7.59/1.71  
% 7.59/1.71  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 7.59/1.71  
% 7.59/1.71  ------  iProver source info
% 7.59/1.71  
% 7.59/1.71  git: date: 2024-05-02 19:28:25 +0000
% 7.59/1.71  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 7.59/1.71  git: non_committed_changes: false
% 7.59/1.71  
% 7.59/1.71  ------ Parsing...
% 7.59/1.71  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 7.59/1.71  
% 7.59/1.71  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe_e  sup_sim: 0  sf_s  rm: 2 0s  sf_e  pe_s  pe_e 
% 7.59/1.71  
% 7.59/1.71  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 7.59/1.71  
% 7.59/1.71  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 7.59/1.71  ------ Proving...
% 7.59/1.71  ------ Problem Properties 
% 7.59/1.71  
% 7.59/1.71  
% 7.59/1.71  clauses                                 124
% 7.59/1.71  conjectures                             8
% 7.59/1.71  EPR                                     55
% 7.59/1.71  Horn                                    85
% 7.59/1.71  unary                                   50
% 7.59/1.71  binary                                  17
% 7.59/1.71  lits                                    358
% 7.59/1.71  lits eq                                 11
% 7.59/1.71  fd_pure                                 0
% 7.59/1.71  fd_pseudo                               0
% 7.59/1.71  fd_cond                                 1
% 7.59/1.71  fd_pseudo_cond                          3
% 7.59/1.71  AC symbols                              0
% 7.59/1.71  
% 7.59/1.71  ------ Input Options Time Limit: Unbounded
% 7.59/1.71  
% 7.59/1.71  
% 7.59/1.71  ------ 
% 7.59/1.71  Current options:
% 7.59/1.71  ------ 
% 7.59/1.71  
% 7.59/1.71  
% 7.59/1.71  
% 7.59/1.71  
% 7.59/1.71  ------ Proving...
% 7.59/1.71  
% 7.59/1.71  
% 7.59/1.71  % SZS status Theorem for theBenchmark.p
% 7.59/1.71  
% 7.59/1.71  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.59/1.71  
% 7.59/1.72  
%------------------------------------------------------------------------------