TSTP Solution File: GRP622+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : GRP622+1 : TPTP v5.0.0. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art05.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory   : 2018MB
% OS       : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sat Dec 25 10:12:27 EST 2010

% Result   : Theorem 5.09s
% Output   : CNFRefutation 5.09s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :   14
% Syntax   : Number of formulae    :  118 (  11 unt;   0 def)
%            Number of atoms       :  496 (   9 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :  619 ( 241   ~; 260   |;  90   &)
%                                         (   4 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   18 (  16 usr;   1 prp; 0-4 aty)
%            Number of functors    :    9 (   9 usr;   1 con; 0-2 aty)
%            Number of variables   :  209 (   1 sgn 126   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(7,axiom,
    ! [X1,X2,X3] :
      ( m2_relset_1(X3,X1,X2)
    <=> m1_relset_1(X3,X1,X2) ),
    file('/tmp/tmp-YGLCg/sel_GRP622+1.p_1',redefinition_m2_relset_1) ).

fof(12,axiom,
    ! [X1,X2] :
      ( r2_hidden(X1,X2)
     => m1_subset_1(X1,X2) ),
    file('/tmp/tmp-YGLCg/sel_GRP622+1.p_1',t1_subset) ).

fof(13,axiom,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v1_group_1(X1)
        & v3_group_1(X1)
        & v4_group_1(X1)
        & l1_group_1(X1) )
     => m1_fraenkel(k4_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1)) ),
    file('/tmp/tmp-YGLCg/sel_GRP622+1.p_1',dt_k4_autgroup) ).

fof(20,axiom,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & l1_struct_0(X1) )
     => ~ v1_xboole_0(u1_struct_0(X1)) ),
    file('/tmp/tmp-YGLCg/sel_GRP622+1.p_1',fc1_struct_0) ).

fof(41,conjecture,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v1_group_1(X1)
        & v3_group_1(X1)
        & v4_group_1(X1)
        & l1_group_1(X1) )
     => r1_tarski(k4_autgroup(X1),k1_fraenkel(u1_struct_0(X1),u1_struct_0(X1))) ),
    file('/tmp/tmp-YGLCg/sel_GRP622+1.p_1',t12_autgroup) ).

fof(44,axiom,
    ! [X1,X2,X3] :
      ( ( ~ v1_xboole_0(X2)
        & m1_fraenkel(X3,X1,X2) )
     => ! [X4] :
          ( m2_fraenkel(X4,X1,X2,X3)
         => ( v1_funct_1(X4)
            & v1_funct_2(X4,X1,X2)
            & m2_relset_1(X4,X1,X2) ) ) ),
    file('/tmp/tmp-YGLCg/sel_GRP622+1.p_1',dt_m2_fraenkel) ).

fof(50,axiom,
    ! [X1,X2] :
      ( ( ~ v1_xboole_0(X1)
        & v1_funct_1(X2)
        & v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)
        & m1_relset_1(X2,k2_zfmisc_1(X1,X1),X1) )
     => ( ~ v3_struct_0(g1_group_1(X1,X2))
        & v1_group_1(g1_group_1(X1,X2)) ) ),
    file('/tmp/tmp-YGLCg/sel_GRP622+1.p_1',fc1_group_1) ).

fof(51,axiom,
    ! [X1,X2] :
      ( ~ v1_xboole_0(X2)
     => k1_fraenkel(X1,X2) = k1_funct_2(X1,X2) ),
    file('/tmp/tmp-YGLCg/sel_GRP622+1.p_1',redefinition_k1_fraenkel) ).

fof(52,axiom,
    ! [X1] :
      ( l1_group_1(X1)
     => l1_struct_0(X1) ),
    file('/tmp/tmp-YGLCg/sel_GRP622+1.p_1',dt_l1_group_1) ).

fof(58,axiom,
    ! [X1] :
      ( l1_group_1(X1)
     => ( v1_group_1(X1)
       => X1 = g1_group_1(u1_struct_0(X1),u1_group_1(X1)) ) ),
    file('/tmp/tmp-YGLCg/sel_GRP622+1.p_1',abstractness_v1_group_1) ).

fof(61,axiom,
    ! [X1,X2,X3] :
      ( ( ~ v1_xboole_0(X2)
        & m1_fraenkel(X3,X1,X2) )
     => ! [X4] :
          ( m2_fraenkel(X4,X1,X2,X3)
        <=> m1_subset_1(X4,X3) ) ),
    file('/tmp/tmp-YGLCg/sel_GRP622+1.p_1',redefinition_m2_fraenkel) ).

fof(62,axiom,
    ! [X1,X2] :
      ( ( v1_funct_1(X2)
        & v1_funct_2(X2,X1,X1)
        & m2_relset_1(X2,X1,X1) )
     => r2_hidden(X2,k1_funct_2(X1,X1)) ),
    file('/tmp/tmp-YGLCg/sel_GRP622+1.p_1',t12_funct_2) ).

fof(64,axiom,
    ! [X1] :
      ( l1_group_1(X1)
     => ( v1_funct_1(u1_group_1(X1))
        & v1_funct_2(u1_group_1(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
        & m2_relset_1(u1_group_1(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1)) ) ),
    file('/tmp/tmp-YGLCg/sel_GRP622+1.p_1',dt_u1_group_1) ).

fof(66,axiom,
    ! [X1,X2] :
      ( r1_tarski(X1,X2)
    <=> ! [X3] :
          ( r2_hidden(X3,X1)
         => r2_hidden(X3,X2) ) ),
    file('/tmp/tmp-YGLCg/sel_GRP622+1.p_1',d3_tarski) ).

fof(70,negated_conjecture,
    ~ ! [X1] :
        ( ( ~ v3_struct_0(X1)
          & v1_group_1(X1)
          & v3_group_1(X1)
          & v4_group_1(X1)
          & l1_group_1(X1) )
       => r1_tarski(k4_autgroup(X1),k1_fraenkel(u1_struct_0(X1),u1_struct_0(X1))) ),
    inference(assume_negation,[status(cth)],[41]) ).

fof(73,plain,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v1_group_1(X1)
        & v3_group_1(X1)
        & v4_group_1(X1)
        & l1_group_1(X1) )
     => m1_fraenkel(k4_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1)) ),
    inference(fof_simplification,[status(thm)],[13,theory(equality)]) ).

fof(76,plain,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & l1_struct_0(X1) )
     => ~ v1_xboole_0(u1_struct_0(X1)) ),
    inference(fof_simplification,[status(thm)],[20,theory(equality)]) ).

fof(83,negated_conjecture,
    ~ ! [X1] :
        ( ( ~ v3_struct_0(X1)
          & v1_group_1(X1)
          & v3_group_1(X1)
          & v4_group_1(X1)
          & l1_group_1(X1) )
       => r1_tarski(k4_autgroup(X1),k1_fraenkel(u1_struct_0(X1),u1_struct_0(X1))) ),
    inference(fof_simplification,[status(thm)],[70,theory(equality)]) ).

fof(84,plain,
    ! [X1,X2,X3] :
      ( ( ~ v1_xboole_0(X2)
        & m1_fraenkel(X3,X1,X2) )
     => ! [X4] :
          ( m2_fraenkel(X4,X1,X2,X3)
         => ( v1_funct_1(X4)
            & v1_funct_2(X4,X1,X2)
            & m2_relset_1(X4,X1,X2) ) ) ),
    inference(fof_simplification,[status(thm)],[44,theory(equality)]) ).

fof(87,plain,
    ! [X1,X2] :
      ( ( ~ v1_xboole_0(X1)
        & v1_funct_1(X2)
        & v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)
        & m1_relset_1(X2,k2_zfmisc_1(X1,X1),X1) )
     => ( ~ v3_struct_0(g1_group_1(X1,X2))
        & v1_group_1(g1_group_1(X1,X2)) ) ),
    inference(fof_simplification,[status(thm)],[50,theory(equality)]) ).

fof(88,plain,
    ! [X1,X2] :
      ( ~ v1_xboole_0(X2)
     => k1_fraenkel(X1,X2) = k1_funct_2(X1,X2) ),
    inference(fof_simplification,[status(thm)],[51,theory(equality)]) ).

fof(90,plain,
    ! [X1,X2,X3] :
      ( ( ~ v1_xboole_0(X2)
        & m1_fraenkel(X3,X1,X2) )
     => ! [X4] :
          ( m2_fraenkel(X4,X1,X2,X3)
        <=> m1_subset_1(X4,X3) ) ),
    inference(fof_simplification,[status(thm)],[61,theory(equality)]) ).

fof(114,plain,
    ! [X1,X2,X3] :
      ( ( ~ m2_relset_1(X3,X1,X2)
        | m1_relset_1(X3,X1,X2) )
      & ( ~ m1_relset_1(X3,X1,X2)
        | m2_relset_1(X3,X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[7]) ).

fof(115,plain,
    ! [X4,X5,X6] :
      ( ( ~ m2_relset_1(X6,X4,X5)
        | m1_relset_1(X6,X4,X5) )
      & ( ~ m1_relset_1(X6,X4,X5)
        | m2_relset_1(X6,X4,X5) ) ),
    inference(variable_rename,[status(thm)],[114]) ).

cnf(117,plain,
    ( m1_relset_1(X1,X2,X3)
    | ~ m2_relset_1(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[115]) ).

fof(131,plain,
    ! [X1,X2] :
      ( ~ r2_hidden(X1,X2)
      | m1_subset_1(X1,X2) ),
    inference(fof_nnf,[status(thm)],[12]) ).

fof(132,plain,
    ! [X3,X4] :
      ( ~ r2_hidden(X3,X4)
      | m1_subset_1(X3,X4) ),
    inference(variable_rename,[status(thm)],[131]) ).

cnf(133,plain,
    ( m1_subset_1(X1,X2)
    | ~ r2_hidden(X1,X2) ),
    inference(split_conjunct,[status(thm)],[132]) ).

fof(134,plain,
    ! [X1] :
      ( v3_struct_0(X1)
      | ~ v1_group_1(X1)
      | ~ v3_group_1(X1)
      | ~ v4_group_1(X1)
      | ~ l1_group_1(X1)
      | m1_fraenkel(k4_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1)) ),
    inference(fof_nnf,[status(thm)],[73]) ).

fof(135,plain,
    ! [X2] :
      ( v3_struct_0(X2)
      | ~ v1_group_1(X2)
      | ~ v3_group_1(X2)
      | ~ v4_group_1(X2)
      | ~ l1_group_1(X2)
      | m1_fraenkel(k4_autgroup(X2),u1_struct_0(X2),u1_struct_0(X2)) ),
    inference(variable_rename,[status(thm)],[134]) ).

cnf(136,plain,
    ( m1_fraenkel(k4_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1))
    | v3_struct_0(X1)
    | ~ l1_group_1(X1)
    | ~ v4_group_1(X1)
    | ~ v3_group_1(X1)
    | ~ v1_group_1(X1) ),
    inference(split_conjunct,[status(thm)],[135]) ).

fof(160,plain,
    ! [X1] :
      ( v3_struct_0(X1)
      | ~ l1_struct_0(X1)
      | ~ v1_xboole_0(u1_struct_0(X1)) ),
    inference(fof_nnf,[status(thm)],[76]) ).

fof(161,plain,
    ! [X2] :
      ( v3_struct_0(X2)
      | ~ l1_struct_0(X2)
      | ~ v1_xboole_0(u1_struct_0(X2)) ),
    inference(variable_rename,[status(thm)],[160]) ).

cnf(162,plain,
    ( v3_struct_0(X1)
    | ~ v1_xboole_0(u1_struct_0(X1))
    | ~ l1_struct_0(X1) ),
    inference(split_conjunct,[status(thm)],[161]) ).

fof(243,negated_conjecture,
    ? [X1] :
      ( ~ v3_struct_0(X1)
      & v1_group_1(X1)
      & v3_group_1(X1)
      & v4_group_1(X1)
      & l1_group_1(X1)
      & ~ r1_tarski(k4_autgroup(X1),k1_fraenkel(u1_struct_0(X1),u1_struct_0(X1))) ),
    inference(fof_nnf,[status(thm)],[83]) ).

fof(244,negated_conjecture,
    ? [X2] :
      ( ~ v3_struct_0(X2)
      & v1_group_1(X2)
      & v3_group_1(X2)
      & v4_group_1(X2)
      & l1_group_1(X2)
      & ~ r1_tarski(k4_autgroup(X2),k1_fraenkel(u1_struct_0(X2),u1_struct_0(X2))) ),
    inference(variable_rename,[status(thm)],[243]) ).

fof(245,negated_conjecture,
    ( ~ v3_struct_0(esk15_0)
    & v1_group_1(esk15_0)
    & v3_group_1(esk15_0)
    & v4_group_1(esk15_0)
    & l1_group_1(esk15_0)
    & ~ r1_tarski(k4_autgroup(esk15_0),k1_fraenkel(u1_struct_0(esk15_0),u1_struct_0(esk15_0))) ),
    inference(skolemize,[status(esa)],[244]) ).

cnf(246,negated_conjecture,
    ~ r1_tarski(k4_autgroup(esk15_0),k1_fraenkel(u1_struct_0(esk15_0),u1_struct_0(esk15_0))),
    inference(split_conjunct,[status(thm)],[245]) ).

cnf(247,negated_conjecture,
    l1_group_1(esk15_0),
    inference(split_conjunct,[status(thm)],[245]) ).

cnf(248,negated_conjecture,
    v4_group_1(esk15_0),
    inference(split_conjunct,[status(thm)],[245]) ).

cnf(249,negated_conjecture,
    v3_group_1(esk15_0),
    inference(split_conjunct,[status(thm)],[245]) ).

cnf(250,negated_conjecture,
    v1_group_1(esk15_0),
    inference(split_conjunct,[status(thm)],[245]) ).

cnf(251,negated_conjecture,
    ~ v3_struct_0(esk15_0),
    inference(split_conjunct,[status(thm)],[245]) ).

fof(258,plain,
    ! [X1,X2,X3] :
      ( v1_xboole_0(X2)
      | ~ m1_fraenkel(X3,X1,X2)
      | ! [X4] :
          ( ~ m2_fraenkel(X4,X1,X2,X3)
          | ( v1_funct_1(X4)
            & v1_funct_2(X4,X1,X2)
            & m2_relset_1(X4,X1,X2) ) ) ),
    inference(fof_nnf,[status(thm)],[84]) ).

fof(259,plain,
    ! [X5,X6,X7] :
      ( v1_xboole_0(X6)
      | ~ m1_fraenkel(X7,X5,X6)
      | ! [X8] :
          ( ~ m2_fraenkel(X8,X5,X6,X7)
          | ( v1_funct_1(X8)
            & v1_funct_2(X8,X5,X6)
            & m2_relset_1(X8,X5,X6) ) ) ),
    inference(variable_rename,[status(thm)],[258]) ).

fof(260,plain,
    ! [X5,X6,X7,X8] :
      ( ~ m2_fraenkel(X8,X5,X6,X7)
      | ( v1_funct_1(X8)
        & v1_funct_2(X8,X5,X6)
        & m2_relset_1(X8,X5,X6) )
      | v1_xboole_0(X6)
      | ~ m1_fraenkel(X7,X5,X6) ),
    inference(shift_quantors,[status(thm)],[259]) ).

fof(261,plain,
    ! [X5,X6,X7,X8] :
      ( ( v1_funct_1(X8)
        | ~ m2_fraenkel(X8,X5,X6,X7)
        | v1_xboole_0(X6)
        | ~ m1_fraenkel(X7,X5,X6) )
      & ( v1_funct_2(X8,X5,X6)
        | ~ m2_fraenkel(X8,X5,X6,X7)
        | v1_xboole_0(X6)
        | ~ m1_fraenkel(X7,X5,X6) )
      & ( m2_relset_1(X8,X5,X6)
        | ~ m2_fraenkel(X8,X5,X6,X7)
        | v1_xboole_0(X6)
        | ~ m1_fraenkel(X7,X5,X6) ) ),
    inference(distribute,[status(thm)],[260]) ).

cnf(262,plain,
    ( v1_xboole_0(X3)
    | m2_relset_1(X4,X2,X3)
    | ~ m1_fraenkel(X1,X2,X3)
    | ~ m2_fraenkel(X4,X2,X3,X1) ),
    inference(split_conjunct,[status(thm)],[261]) ).

cnf(263,plain,
    ( v1_xboole_0(X3)
    | v1_funct_2(X4,X2,X3)
    | ~ m1_fraenkel(X1,X2,X3)
    | ~ m2_fraenkel(X4,X2,X3,X1) ),
    inference(split_conjunct,[status(thm)],[261]) ).

cnf(264,plain,
    ( v1_xboole_0(X3)
    | v1_funct_1(X4)
    | ~ m1_fraenkel(X1,X2,X3)
    | ~ m2_fraenkel(X4,X2,X3,X1) ),
    inference(split_conjunct,[status(thm)],[261]) ).

fof(280,plain,
    ! [X1,X2] :
      ( v1_xboole_0(X1)
      | ~ v1_funct_1(X2)
      | ~ v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)
      | ~ m1_relset_1(X2,k2_zfmisc_1(X1,X1),X1)
      | ( ~ v3_struct_0(g1_group_1(X1,X2))
        & v1_group_1(g1_group_1(X1,X2)) ) ),
    inference(fof_nnf,[status(thm)],[87]) ).

fof(281,plain,
    ! [X3,X4] :
      ( v1_xboole_0(X3)
      | ~ v1_funct_1(X4)
      | ~ v1_funct_2(X4,k2_zfmisc_1(X3,X3),X3)
      | ~ m1_relset_1(X4,k2_zfmisc_1(X3,X3),X3)
      | ( ~ v3_struct_0(g1_group_1(X3,X4))
        & v1_group_1(g1_group_1(X3,X4)) ) ),
    inference(variable_rename,[status(thm)],[280]) ).

fof(282,plain,
    ! [X3,X4] :
      ( ( ~ v3_struct_0(g1_group_1(X3,X4))
        | v1_xboole_0(X3)
        | ~ v1_funct_1(X4)
        | ~ v1_funct_2(X4,k2_zfmisc_1(X3,X3),X3)
        | ~ m1_relset_1(X4,k2_zfmisc_1(X3,X3),X3) )
      & ( v1_group_1(g1_group_1(X3,X4))
        | v1_xboole_0(X3)
        | ~ v1_funct_1(X4)
        | ~ v1_funct_2(X4,k2_zfmisc_1(X3,X3),X3)
        | ~ m1_relset_1(X4,k2_zfmisc_1(X3,X3),X3) ) ),
    inference(distribute,[status(thm)],[281]) ).

cnf(284,plain,
    ( v1_xboole_0(X2)
    | ~ m1_relset_1(X1,k2_zfmisc_1(X2,X2),X2)
    | ~ v1_funct_2(X1,k2_zfmisc_1(X2,X2),X2)
    | ~ v1_funct_1(X1)
    | ~ v3_struct_0(g1_group_1(X2,X1)) ),
    inference(split_conjunct,[status(thm)],[282]) ).

fof(285,plain,
    ! [X1,X2] :
      ( v1_xboole_0(X2)
      | k1_fraenkel(X1,X2) = k1_funct_2(X1,X2) ),
    inference(fof_nnf,[status(thm)],[88]) ).

fof(286,plain,
    ! [X3,X4] :
      ( v1_xboole_0(X4)
      | k1_fraenkel(X3,X4) = k1_funct_2(X3,X4) ),
    inference(variable_rename,[status(thm)],[285]) ).

cnf(287,plain,
    ( k1_fraenkel(X1,X2) = k1_funct_2(X1,X2)
    | v1_xboole_0(X2) ),
    inference(split_conjunct,[status(thm)],[286]) ).

fof(288,plain,
    ! [X1] :
      ( ~ l1_group_1(X1)
      | l1_struct_0(X1) ),
    inference(fof_nnf,[status(thm)],[52]) ).

fof(289,plain,
    ! [X2] :
      ( ~ l1_group_1(X2)
      | l1_struct_0(X2) ),
    inference(variable_rename,[status(thm)],[288]) ).

cnf(290,plain,
    ( l1_struct_0(X1)
    | ~ l1_group_1(X1) ),
    inference(split_conjunct,[status(thm)],[289]) ).

fof(303,plain,
    ! [X1] :
      ( ~ l1_group_1(X1)
      | ~ v1_group_1(X1)
      | X1 = g1_group_1(u1_struct_0(X1),u1_group_1(X1)) ),
    inference(fof_nnf,[status(thm)],[58]) ).

fof(304,plain,
    ! [X2] :
      ( ~ l1_group_1(X2)
      | ~ v1_group_1(X2)
      | X2 = g1_group_1(u1_struct_0(X2),u1_group_1(X2)) ),
    inference(variable_rename,[status(thm)],[303]) ).

cnf(305,plain,
    ( X1 = g1_group_1(u1_struct_0(X1),u1_group_1(X1))
    | ~ v1_group_1(X1)
    | ~ l1_group_1(X1) ),
    inference(split_conjunct,[status(thm)],[304]) ).

fof(308,plain,
    ! [X1,X2,X3] :
      ( v1_xboole_0(X2)
      | ~ m1_fraenkel(X3,X1,X2)
      | ! [X4] :
          ( ( ~ m2_fraenkel(X4,X1,X2,X3)
            | m1_subset_1(X4,X3) )
          & ( ~ m1_subset_1(X4,X3)
            | m2_fraenkel(X4,X1,X2,X3) ) ) ),
    inference(fof_nnf,[status(thm)],[90]) ).

fof(309,plain,
    ! [X5,X6,X7] :
      ( v1_xboole_0(X6)
      | ~ m1_fraenkel(X7,X5,X6)
      | ! [X8] :
          ( ( ~ m2_fraenkel(X8,X5,X6,X7)
            | m1_subset_1(X8,X7) )
          & ( ~ m1_subset_1(X8,X7)
            | m2_fraenkel(X8,X5,X6,X7) ) ) ),
    inference(variable_rename,[status(thm)],[308]) ).

fof(310,plain,
    ! [X5,X6,X7,X8] :
      ( ( ( ~ m2_fraenkel(X8,X5,X6,X7)
          | m1_subset_1(X8,X7) )
        & ( ~ m1_subset_1(X8,X7)
          | m2_fraenkel(X8,X5,X6,X7) ) )
      | v1_xboole_0(X6)
      | ~ m1_fraenkel(X7,X5,X6) ),
    inference(shift_quantors,[status(thm)],[309]) ).

fof(311,plain,
    ! [X5,X6,X7,X8] :
      ( ( ~ m2_fraenkel(X8,X5,X6,X7)
        | m1_subset_1(X8,X7)
        | v1_xboole_0(X6)
        | ~ m1_fraenkel(X7,X5,X6) )
      & ( ~ m1_subset_1(X8,X7)
        | m2_fraenkel(X8,X5,X6,X7)
        | v1_xboole_0(X6)
        | ~ m1_fraenkel(X7,X5,X6) ) ),
    inference(distribute,[status(thm)],[310]) ).

cnf(312,plain,
    ( v1_xboole_0(X3)
    | m2_fraenkel(X4,X2,X3,X1)
    | ~ m1_fraenkel(X1,X2,X3)
    | ~ m1_subset_1(X4,X1) ),
    inference(split_conjunct,[status(thm)],[311]) ).

fof(314,plain,
    ! [X1,X2] :
      ( ~ v1_funct_1(X2)
      | ~ v1_funct_2(X2,X1,X1)
      | ~ m2_relset_1(X2,X1,X1)
      | r2_hidden(X2,k1_funct_2(X1,X1)) ),
    inference(fof_nnf,[status(thm)],[62]) ).

fof(315,plain,
    ! [X3,X4] :
      ( ~ v1_funct_1(X4)
      | ~ v1_funct_2(X4,X3,X3)
      | ~ m2_relset_1(X4,X3,X3)
      | r2_hidden(X4,k1_funct_2(X3,X3)) ),
    inference(variable_rename,[status(thm)],[314]) ).

cnf(316,plain,
    ( r2_hidden(X1,k1_funct_2(X2,X2))
    | ~ m2_relset_1(X1,X2,X2)
    | ~ v1_funct_2(X1,X2,X2)
    | ~ v1_funct_1(X1) ),
    inference(split_conjunct,[status(thm)],[315]) ).

fof(323,plain,
    ! [X1] :
      ( ~ l1_group_1(X1)
      | ( v1_funct_1(u1_group_1(X1))
        & v1_funct_2(u1_group_1(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
        & m2_relset_1(u1_group_1(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1)) ) ),
    inference(fof_nnf,[status(thm)],[64]) ).

fof(324,plain,
    ! [X2] :
      ( ~ l1_group_1(X2)
      | ( v1_funct_1(u1_group_1(X2))
        & v1_funct_2(u1_group_1(X2),k2_zfmisc_1(u1_struct_0(X2),u1_struct_0(X2)),u1_struct_0(X2))
        & m2_relset_1(u1_group_1(X2),k2_zfmisc_1(u1_struct_0(X2),u1_struct_0(X2)),u1_struct_0(X2)) ) ),
    inference(variable_rename,[status(thm)],[323]) ).

fof(325,plain,
    ! [X2] :
      ( ( v1_funct_1(u1_group_1(X2))
        | ~ l1_group_1(X2) )
      & ( v1_funct_2(u1_group_1(X2),k2_zfmisc_1(u1_struct_0(X2),u1_struct_0(X2)),u1_struct_0(X2))
        | ~ l1_group_1(X2) )
      & ( m2_relset_1(u1_group_1(X2),k2_zfmisc_1(u1_struct_0(X2),u1_struct_0(X2)),u1_struct_0(X2))
        | ~ l1_group_1(X2) ) ),
    inference(distribute,[status(thm)],[324]) ).

cnf(326,plain,
    ( m2_relset_1(u1_group_1(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
    | ~ l1_group_1(X1) ),
    inference(split_conjunct,[status(thm)],[325]) ).

cnf(327,plain,
    ( v1_funct_2(u1_group_1(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
    | ~ l1_group_1(X1) ),
    inference(split_conjunct,[status(thm)],[325]) ).

cnf(328,plain,
    ( v1_funct_1(u1_group_1(X1))
    | ~ l1_group_1(X1) ),
    inference(split_conjunct,[status(thm)],[325]) ).

fof(331,plain,
    ! [X1,X2] :
      ( ( ~ r1_tarski(X1,X2)
        | ! [X3] :
            ( ~ r2_hidden(X3,X1)
            | r2_hidden(X3,X2) ) )
      & ( ? [X3] :
            ( r2_hidden(X3,X1)
            & ~ r2_hidden(X3,X2) )
        | r1_tarski(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[66]) ).

fof(332,plain,
    ! [X4,X5] :
      ( ( ~ r1_tarski(X4,X5)
        | ! [X6] :
            ( ~ r2_hidden(X6,X4)
            | r2_hidden(X6,X5) ) )
      & ( ? [X7] :
            ( r2_hidden(X7,X4)
            & ~ r2_hidden(X7,X5) )
        | r1_tarski(X4,X5) ) ),
    inference(variable_rename,[status(thm)],[331]) ).

fof(333,plain,
    ! [X4,X5] :
      ( ( ~ r1_tarski(X4,X5)
        | ! [X6] :
            ( ~ r2_hidden(X6,X4)
            | r2_hidden(X6,X5) ) )
      & ( ( r2_hidden(esk21_2(X4,X5),X4)
          & ~ r2_hidden(esk21_2(X4,X5),X5) )
        | r1_tarski(X4,X5) ) ),
    inference(skolemize,[status(esa)],[332]) ).

fof(334,plain,
    ! [X4,X5,X6] :
      ( ( ~ r2_hidden(X6,X4)
        | r2_hidden(X6,X5)
        | ~ r1_tarski(X4,X5) )
      & ( ( r2_hidden(esk21_2(X4,X5),X4)
          & ~ r2_hidden(esk21_2(X4,X5),X5) )
        | r1_tarski(X4,X5) ) ),
    inference(shift_quantors,[status(thm)],[333]) ).

fof(335,plain,
    ! [X4,X5,X6] :
      ( ( ~ r2_hidden(X6,X4)
        | r2_hidden(X6,X5)
        | ~ r1_tarski(X4,X5) )
      & ( r2_hidden(esk21_2(X4,X5),X4)
        | r1_tarski(X4,X5) )
      & ( ~ r2_hidden(esk21_2(X4,X5),X5)
        | r1_tarski(X4,X5) ) ),
    inference(distribute,[status(thm)],[334]) ).

cnf(336,plain,
    ( r1_tarski(X1,X2)
    | ~ r2_hidden(esk21_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[335]) ).

cnf(337,plain,
    ( r1_tarski(X1,X2)
    | r2_hidden(esk21_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[335]) ).

cnf(366,plain,
    ( v3_struct_0(X1)
    | ~ v1_xboole_0(u1_struct_0(X1))
    | ~ l1_group_1(X1) ),
    inference(spm,[status(thm)],[162,290,theory(equality)]) ).

cnf(374,plain,
    ( m1_subset_1(esk21_2(X1,X2),X1)
    | r1_tarski(X1,X2) ),
    inference(spm,[status(thm)],[133,337,theory(equality)]) ).

cnf(378,negated_conjecture,
    ( v1_xboole_0(u1_struct_0(esk15_0))
    | ~ r1_tarski(k4_autgroup(esk15_0),k1_funct_2(u1_struct_0(esk15_0),u1_struct_0(esk15_0))) ),
    inference(spm,[status(thm)],[246,287,theory(equality)]) ).

cnf(412,plain,
    ( m1_relset_1(u1_group_1(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
    | ~ l1_group_1(X1) ),
    inference(spm,[status(thm)],[117,326,theory(equality)]) ).

cnf(419,plain,
    ( v1_xboole_0(X1)
    | v1_funct_1(X2)
    | ~ m1_fraenkel(X4,X3,X1)
    | ~ m1_subset_1(X2,X4) ),
    inference(spm,[status(thm)],[264,312,theory(equality)]) ).

cnf(423,plain,
    ( m2_relset_1(X1,X2,X3)
    | v1_xboole_0(X3)
    | ~ m1_fraenkel(X4,X2,X3)
    | ~ m1_subset_1(X1,X4) ),
    inference(spm,[status(thm)],[262,312,theory(equality)]) ).

cnf(425,plain,
    ( v1_funct_2(X1,X2,X3)
    | v1_xboole_0(X3)
    | ~ m1_fraenkel(X4,X2,X3)
    | ~ m1_subset_1(X1,X4) ),
    inference(spm,[status(thm)],[263,312,theory(equality)]) ).

cnf(429,plain,
    ( r1_tarski(X1,k1_funct_2(X2,X2))
    | ~ v1_funct_2(esk21_2(X1,k1_funct_2(X2,X2)),X2,X2)
    | ~ m2_relset_1(esk21_2(X1,k1_funct_2(X2,X2)),X2,X2)
    | ~ v1_funct_1(esk21_2(X1,k1_funct_2(X2,X2))) ),
    inference(spm,[status(thm)],[336,316,theory(equality)]) ).

cnf(444,plain,
    ( v1_xboole_0(u1_struct_0(X1))
    | ~ v3_struct_0(g1_group_1(u1_struct_0(X1),u1_group_1(X1)))
    | ~ m1_relset_1(u1_group_1(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
    | ~ v1_funct_1(u1_group_1(X1))
    | ~ l1_group_1(X1) ),
    inference(spm,[status(thm)],[284,327,theory(equality)]) ).

cnf(486,negated_conjecture,
    ( ~ l1_group_1(esk15_0)
    | ~ v1_xboole_0(u1_struct_0(esk15_0)) ),
    inference(spm,[status(thm)],[251,366,theory(equality)]) ).

cnf(490,negated_conjecture,
    ( $false
    | ~ v1_xboole_0(u1_struct_0(esk15_0)) ),
    inference(rw,[status(thm)],[486,247,theory(equality)]) ).

cnf(491,negated_conjecture,
    ~ v1_xboole_0(u1_struct_0(esk15_0)),
    inference(cn,[status(thm)],[490,theory(equality)]) ).

cnf(517,negated_conjecture,
    ~ r1_tarski(k4_autgroup(esk15_0),k1_funct_2(u1_struct_0(esk15_0),u1_struct_0(esk15_0))),
    inference(sr,[status(thm)],[378,491,theory(equality)]) ).

cnf(753,plain,
    ( v1_xboole_0(u1_struct_0(X1))
    | v1_funct_1(X2)
    | v3_struct_0(X1)
    | ~ m1_subset_1(X2,k4_autgroup(X1))
    | ~ l1_group_1(X1)
    | ~ v4_group_1(X1)
    | ~ v3_group_1(X1)
    | ~ v1_group_1(X1) ),
    inference(spm,[status(thm)],[419,136,theory(equality)]) ).

cnf(831,plain,
    ( m2_relset_1(X1,u1_struct_0(X2),u1_struct_0(X2))
    | v1_xboole_0(u1_struct_0(X2))
    | v3_struct_0(X2)
    | ~ m1_subset_1(X1,k4_autgroup(X2))
    | ~ l1_group_1(X2)
    | ~ v4_group_1(X2)
    | ~ v3_group_1(X2)
    | ~ v1_group_1(X2) ),
    inference(spm,[status(thm)],[423,136,theory(equality)]) ).

cnf(885,plain,
    ( v1_funct_2(X1,u1_struct_0(X2),u1_struct_0(X2))
    | v1_xboole_0(u1_struct_0(X2))
    | v3_struct_0(X2)
    | ~ m1_subset_1(X1,k4_autgroup(X2))
    | ~ l1_group_1(X2)
    | ~ v4_group_1(X2)
    | ~ v3_group_1(X2)
    | ~ v1_group_1(X2) ),
    inference(spm,[status(thm)],[425,136,theory(equality)]) ).

cnf(1156,plain,
    ( v1_xboole_0(u1_struct_0(X1))
    | ~ l1_group_1(X1)
    | ~ v3_struct_0(g1_group_1(u1_struct_0(X1),u1_group_1(X1)))
    | ~ m1_relset_1(u1_group_1(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1)) ),
    inference(csr,[status(thm)],[444,328]) ).

cnf(1157,plain,
    ( v1_xboole_0(u1_struct_0(X1))
    | ~ l1_group_1(X1)
    | ~ v3_struct_0(g1_group_1(u1_struct_0(X1),u1_group_1(X1))) ),
    inference(csr,[status(thm)],[1156,412]) ).

cnf(1158,plain,
    ( v1_xboole_0(u1_struct_0(X1))
    | ~ l1_group_1(X1)
    | ~ v3_struct_0(X1)
    | ~ v1_group_1(X1) ),
    inference(spm,[status(thm)],[1157,305,theory(equality)]) ).

cnf(1499,plain,
    ( v1_xboole_0(u1_struct_0(X1))
    | v1_funct_1(X2)
    | ~ l1_group_1(X1)
    | ~ v4_group_1(X1)
    | ~ v3_group_1(X1)
    | ~ v1_group_1(X1)
    | ~ m1_subset_1(X2,k4_autgroup(X1)) ),
    inference(csr,[status(thm)],[753,1158]) ).

cnf(3416,plain,
    ( m2_relset_1(X1,u1_struct_0(X2),u1_struct_0(X2))
    | v1_xboole_0(u1_struct_0(X2))
    | ~ l1_group_1(X2)
    | ~ v4_group_1(X2)
    | ~ v3_group_1(X2)
    | ~ v1_group_1(X2)
    | ~ m1_subset_1(X1,k4_autgroup(X2)) ),
    inference(csr,[status(thm)],[831,1158]) ).

cnf(3422,plain,
    ( r1_tarski(X1,k1_funct_2(u1_struct_0(X2),u1_struct_0(X2)))
    | v1_xboole_0(u1_struct_0(X2))
    | ~ v1_funct_2(esk21_2(X1,k1_funct_2(u1_struct_0(X2),u1_struct_0(X2))),u1_struct_0(X2),u1_struct_0(X2))
    | ~ v1_funct_1(esk21_2(X1,k1_funct_2(u1_struct_0(X2),u1_struct_0(X2))))
    | ~ l1_group_1(X2)
    | ~ v4_group_1(X2)
    | ~ v3_group_1(X2)
    | ~ v1_group_1(X2)
    | ~ m1_subset_1(esk21_2(X1,k1_funct_2(u1_struct_0(X2),u1_struct_0(X2))),k4_autgroup(X2)) ),
    inference(spm,[status(thm)],[429,3416,theory(equality)]) ).

cnf(5793,plain,
    ( v1_funct_2(X1,u1_struct_0(X2),u1_struct_0(X2))
    | v1_xboole_0(u1_struct_0(X2))
    | ~ l1_group_1(X2)
    | ~ v4_group_1(X2)
    | ~ v3_group_1(X2)
    | ~ v1_group_1(X2)
    | ~ m1_subset_1(X1,k4_autgroup(X2)) ),
    inference(csr,[status(thm)],[885,1158]) ).

cnf(72071,plain,
    ( r1_tarski(X1,k1_funct_2(u1_struct_0(X2),u1_struct_0(X2)))
    | v1_xboole_0(u1_struct_0(X2))
    | ~ l1_group_1(X2)
    | ~ v4_group_1(X2)
    | ~ v3_group_1(X2)
    | ~ v1_group_1(X2)
    | ~ v1_funct_2(esk21_2(X1,k1_funct_2(u1_struct_0(X2),u1_struct_0(X2))),u1_struct_0(X2),u1_struct_0(X2))
    | ~ m1_subset_1(esk21_2(X1,k1_funct_2(u1_struct_0(X2),u1_struct_0(X2))),k4_autgroup(X2)) ),
    inference(csr,[status(thm)],[3422,1499]) ).

cnf(72072,plain,
    ( r1_tarski(X1,k1_funct_2(u1_struct_0(X2),u1_struct_0(X2)))
    | v1_xboole_0(u1_struct_0(X2))
    | ~ l1_group_1(X2)
    | ~ v4_group_1(X2)
    | ~ v3_group_1(X2)
    | ~ v1_group_1(X2)
    | ~ m1_subset_1(esk21_2(X1,k1_funct_2(u1_struct_0(X2),u1_struct_0(X2))),k4_autgroup(X2)) ),
    inference(csr,[status(thm)],[72071,5793]) ).

cnf(72074,plain,
    ( r1_tarski(k4_autgroup(X1),k1_funct_2(u1_struct_0(X1),u1_struct_0(X1)))
    | v1_xboole_0(u1_struct_0(X1))
    | ~ l1_group_1(X1)
    | ~ v4_group_1(X1)
    | ~ v3_group_1(X1)
    | ~ v1_group_1(X1) ),
    inference(spm,[status(thm)],[72072,374,theory(equality)]) ).

cnf(72174,negated_conjecture,
    ( v1_xboole_0(u1_struct_0(esk15_0))
    | ~ l1_group_1(esk15_0)
    | ~ v4_group_1(esk15_0)
    | ~ v3_group_1(esk15_0)
    | ~ v1_group_1(esk15_0) ),
    inference(spm,[status(thm)],[517,72074,theory(equality)]) ).

cnf(72187,negated_conjecture,
    ( v1_xboole_0(u1_struct_0(esk15_0))
    | $false
    | ~ v4_group_1(esk15_0)
    | ~ v3_group_1(esk15_0)
    | ~ v1_group_1(esk15_0) ),
    inference(rw,[status(thm)],[72174,247,theory(equality)]) ).

cnf(72188,negated_conjecture,
    ( v1_xboole_0(u1_struct_0(esk15_0))
    | $false
    | $false
    | ~ v3_group_1(esk15_0)
    | ~ v1_group_1(esk15_0) ),
    inference(rw,[status(thm)],[72187,248,theory(equality)]) ).

cnf(72189,negated_conjecture,
    ( v1_xboole_0(u1_struct_0(esk15_0))
    | $false
    | $false
    | $false
    | ~ v1_group_1(esk15_0) ),
    inference(rw,[status(thm)],[72188,249,theory(equality)]) ).

cnf(72190,negated_conjecture,
    ( v1_xboole_0(u1_struct_0(esk15_0))
    | $false
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[72189,250,theory(equality)]) ).

cnf(72191,negated_conjecture,
    v1_xboole_0(u1_struct_0(esk15_0)),
    inference(cn,[status(thm)],[72190,theory(equality)]) ).

cnf(72192,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[72191,491,theory(equality)]) ).

cnf(72193,negated_conjecture,
    $false,
    72192,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GRP/GRP622+1.p
% --creating new selector for []
% -running prover on /tmp/tmp-YGLCg/sel_GRP622+1.p_1 with time limit 29
% -prover status Theorem
% Problem GRP622+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GRP/GRP622+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GRP/GRP622+1.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
% 
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