TSTP Solution File: LAT291+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : LAT291+1 : TPTP v5.0.0. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art03.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 13:54:03 EST 2010

% Result   : Theorem 21.59s
% Output   : CNFRefutation 21.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   57 (  15 unt;   0 def)
%            Number of atoms       :  230 (  29 equ)
%            Maximal formula atoms :    7 (   4 avg)
%            Number of connectives :  275 ( 102   ~; 104   |;  55   &)
%                                         (   0 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   2 con; 0-4 aty)
%            Number of variables   :   43 (   0 sgn  31   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(6,axiom,
    ! [X1] :
      ( l3_lattices(X1)
     => ( l1_lattices(X1)
        & l2_lattices(X1) ) ),
    file('/tmp/tmpzSTGD2/sel_LAT291+1.p_1',dt_l3_lattices) ).

fof(8,axiom,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v10_lattices(X1)
        & v17_lattices(X1)
        & ~ v3_realset2(X1)
        & l3_lattices(X1) )
     => k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),k5_lattices(X1)) = k1_xboole_0 ),
    file('/tmp/tmpzSTGD2/sel_LAT291+1.p_1',t36_lopclset) ).

fof(37,axiom,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & l1_lattices(X1) )
     => m1_subset_1(k5_lattices(X1),u1_struct_0(X1)) ),
    file('/tmp/tmpzSTGD2/sel_LAT291+1.p_1',dt_k5_lattices) ).

fof(38,axiom,
    ! [X1] : k4_xboole_0(X1,k1_xboole_0) = X1,
    file('/tmp/tmpzSTGD2/sel_LAT291+1.p_1',t3_boole) ).

fof(64,conjecture,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v10_lattices(X1)
        & v17_lattices(X1)
        & ~ v3_realset2(X1)
        & l3_lattices(X1) )
     => k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),k6_lattices(X1)) = k7_lopclset(X1) ),
    file('/tmp/tmpzSTGD2/sel_LAT291+1.p_1',t37_lopclset) ).

fof(84,axiom,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v10_lattices(X1)
        & v17_lattices(X1)
        & l3_lattices(X1) )
     => k7_lattices(X1,k5_lattices(X1)) = k6_lattices(X1) ),
    file('/tmp/tmpzSTGD2/sel_LAT291+1.p_1',t37_lattice4) ).

fof(100,axiom,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v10_lattices(X1)
        & v17_lattices(X1)
        & ~ v3_realset2(X1)
        & l3_lattices(X1) )
     => ! [X2] :
          ( m1_subset_1(X2,u1_struct_0(X1))
         => k4_xboole_0(k7_lopclset(X1),k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),X2)) = k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),k7_lattices(X1,X2)) ) ),
    file('/tmp/tmpzSTGD2/sel_LAT291+1.p_1',t28_lopclset) ).

fof(102,negated_conjecture,
    ~ ! [X1] :
        ( ( ~ v3_struct_0(X1)
          & v10_lattices(X1)
          & v17_lattices(X1)
          & ~ v3_realset2(X1)
          & l3_lattices(X1) )
       => k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),k6_lattices(X1)) = k7_lopclset(X1) ),
    inference(assume_negation,[status(cth)],[64]) ).

fof(104,plain,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v10_lattices(X1)
        & v17_lattices(X1)
        & ~ v3_realset2(X1)
        & l3_lattices(X1) )
     => k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),k5_lattices(X1)) = k1_xboole_0 ),
    inference(fof_simplification,[status(thm)],[8,theory(equality)]) ).

fof(119,plain,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & l1_lattices(X1) )
     => m1_subset_1(k5_lattices(X1),u1_struct_0(X1)) ),
    inference(fof_simplification,[status(thm)],[37,theory(equality)]) ).

fof(128,negated_conjecture,
    ~ ! [X1] :
        ( ( ~ v3_struct_0(X1)
          & v10_lattices(X1)
          & v17_lattices(X1)
          & ~ v3_realset2(X1)
          & l3_lattices(X1) )
       => k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),k6_lattices(X1)) = k7_lopclset(X1) ),
    inference(fof_simplification,[status(thm)],[102,theory(equality)]) ).

fof(135,plain,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v10_lattices(X1)
        & v17_lattices(X1)
        & l3_lattices(X1) )
     => k7_lattices(X1,k5_lattices(X1)) = k6_lattices(X1) ),
    inference(fof_simplification,[status(thm)],[84,theory(equality)]) ).

fof(138,plain,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v10_lattices(X1)
        & v17_lattices(X1)
        & ~ v3_realset2(X1)
        & l3_lattices(X1) )
     => ! [X2] :
          ( m1_subset_1(X2,u1_struct_0(X1))
         => k4_xboole_0(k7_lopclset(X1),k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),X2)) = k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),k7_lattices(X1,X2)) ) ),
    inference(fof_simplification,[status(thm)],[100,theory(equality)]) ).

fof(166,plain,
    ! [X1] :
      ( ~ l3_lattices(X1)
      | ( l1_lattices(X1)
        & l2_lattices(X1) ) ),
    inference(fof_nnf,[status(thm)],[6]) ).

fof(167,plain,
    ! [X2] :
      ( ~ l3_lattices(X2)
      | ( l1_lattices(X2)
        & l2_lattices(X2) ) ),
    inference(variable_rename,[status(thm)],[166]) ).

fof(168,plain,
    ! [X2] :
      ( ( l1_lattices(X2)
        | ~ l3_lattices(X2) )
      & ( l2_lattices(X2)
        | ~ l3_lattices(X2) ) ),
    inference(distribute,[status(thm)],[167]) ).

cnf(170,plain,
    ( l1_lattices(X1)
    | ~ l3_lattices(X1) ),
    inference(split_conjunct,[status(thm)],[168]) ).

fof(173,plain,
    ! [X1] :
      ( v3_struct_0(X1)
      | ~ v10_lattices(X1)
      | ~ v17_lattices(X1)
      | v3_realset2(X1)
      | ~ l3_lattices(X1)
      | k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),k5_lattices(X1)) = k1_xboole_0 ),
    inference(fof_nnf,[status(thm)],[104]) ).

fof(174,plain,
    ! [X2] :
      ( v3_struct_0(X2)
      | ~ v10_lattices(X2)
      | ~ v17_lattices(X2)
      | v3_realset2(X2)
      | ~ l3_lattices(X2)
      | k8_funct_2(u1_struct_0(X2),k1_zfmisc_1(k7_lopclset(X2)),k9_lopclset(X2),k5_lattices(X2)) = k1_xboole_0 ),
    inference(variable_rename,[status(thm)],[173]) ).

cnf(175,plain,
    ( k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),k5_lattices(X1)) = k1_xboole_0
    | v3_realset2(X1)
    | v3_struct_0(X1)
    | ~ l3_lattices(X1)
    | ~ v17_lattices(X1)
    | ~ v10_lattices(X1) ),
    inference(split_conjunct,[status(thm)],[174]) ).

fof(312,plain,
    ! [X1] :
      ( v3_struct_0(X1)
      | ~ l1_lattices(X1)
      | m1_subset_1(k5_lattices(X1),u1_struct_0(X1)) ),
    inference(fof_nnf,[status(thm)],[119]) ).

fof(313,plain,
    ! [X2] :
      ( v3_struct_0(X2)
      | ~ l1_lattices(X2)
      | m1_subset_1(k5_lattices(X2),u1_struct_0(X2)) ),
    inference(variable_rename,[status(thm)],[312]) ).

cnf(314,plain,
    ( m1_subset_1(k5_lattices(X1),u1_struct_0(X1))
    | v3_struct_0(X1)
    | ~ l1_lattices(X1) ),
    inference(split_conjunct,[status(thm)],[313]) ).

fof(315,plain,
    ! [X2] : k4_xboole_0(X2,k1_xboole_0) = X2,
    inference(variable_rename,[status(thm)],[38]) ).

cnf(316,plain,
    k4_xboole_0(X1,k1_xboole_0) = X1,
    inference(split_conjunct,[status(thm)],[315]) ).

fof(408,negated_conjecture,
    ? [X1] :
      ( ~ v3_struct_0(X1)
      & v10_lattices(X1)
      & v17_lattices(X1)
      & ~ v3_realset2(X1)
      & l3_lattices(X1)
      & k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),k6_lattices(X1)) != k7_lopclset(X1) ),
    inference(fof_nnf,[status(thm)],[128]) ).

fof(409,negated_conjecture,
    ? [X2] :
      ( ~ v3_struct_0(X2)
      & v10_lattices(X2)
      & v17_lattices(X2)
      & ~ v3_realset2(X2)
      & l3_lattices(X2)
      & k8_funct_2(u1_struct_0(X2),k1_zfmisc_1(k7_lopclset(X2)),k9_lopclset(X2),k6_lattices(X2)) != k7_lopclset(X2) ),
    inference(variable_rename,[status(thm)],[408]) ).

fof(410,negated_conjecture,
    ( ~ v3_struct_0(esk15_0)
    & v10_lattices(esk15_0)
    & v17_lattices(esk15_0)
    & ~ v3_realset2(esk15_0)
    & l3_lattices(esk15_0)
    & k8_funct_2(u1_struct_0(esk15_0),k1_zfmisc_1(k7_lopclset(esk15_0)),k9_lopclset(esk15_0),k6_lattices(esk15_0)) != k7_lopclset(esk15_0) ),
    inference(skolemize,[status(esa)],[409]) ).

cnf(411,negated_conjecture,
    k8_funct_2(u1_struct_0(esk15_0),k1_zfmisc_1(k7_lopclset(esk15_0)),k9_lopclset(esk15_0),k6_lattices(esk15_0)) != k7_lopclset(esk15_0),
    inference(split_conjunct,[status(thm)],[410]) ).

cnf(412,negated_conjecture,
    l3_lattices(esk15_0),
    inference(split_conjunct,[status(thm)],[410]) ).

cnf(413,negated_conjecture,
    ~ v3_realset2(esk15_0),
    inference(split_conjunct,[status(thm)],[410]) ).

cnf(414,negated_conjecture,
    v17_lattices(esk15_0),
    inference(split_conjunct,[status(thm)],[410]) ).

cnf(415,negated_conjecture,
    v10_lattices(esk15_0),
    inference(split_conjunct,[status(thm)],[410]) ).

cnf(416,negated_conjecture,
    ~ v3_struct_0(esk15_0),
    inference(split_conjunct,[status(thm)],[410]) ).

fof(512,plain,
    ! [X1] :
      ( v3_struct_0(X1)
      | ~ v10_lattices(X1)
      | ~ v17_lattices(X1)
      | ~ l3_lattices(X1)
      | k7_lattices(X1,k5_lattices(X1)) = k6_lattices(X1) ),
    inference(fof_nnf,[status(thm)],[135]) ).

fof(513,plain,
    ! [X2] :
      ( v3_struct_0(X2)
      | ~ v10_lattices(X2)
      | ~ v17_lattices(X2)
      | ~ l3_lattices(X2)
      | k7_lattices(X2,k5_lattices(X2)) = k6_lattices(X2) ),
    inference(variable_rename,[status(thm)],[512]) ).

cnf(514,plain,
    ( k7_lattices(X1,k5_lattices(X1)) = k6_lattices(X1)
    | v3_struct_0(X1)
    | ~ l3_lattices(X1)
    | ~ v17_lattices(X1)
    | ~ v10_lattices(X1) ),
    inference(split_conjunct,[status(thm)],[513]) ).

fof(590,plain,
    ! [X1] :
      ( v3_struct_0(X1)
      | ~ v10_lattices(X1)
      | ~ v17_lattices(X1)
      | v3_realset2(X1)
      | ~ l3_lattices(X1)
      | ! [X2] :
          ( ~ m1_subset_1(X2,u1_struct_0(X1))
          | k4_xboole_0(k7_lopclset(X1),k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),X2)) = k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),k7_lattices(X1,X2)) ) ),
    inference(fof_nnf,[status(thm)],[138]) ).

fof(591,plain,
    ! [X3] :
      ( v3_struct_0(X3)
      | ~ v10_lattices(X3)
      | ~ v17_lattices(X3)
      | v3_realset2(X3)
      | ~ l3_lattices(X3)
      | ! [X4] :
          ( ~ m1_subset_1(X4,u1_struct_0(X3))
          | k4_xboole_0(k7_lopclset(X3),k8_funct_2(u1_struct_0(X3),k1_zfmisc_1(k7_lopclset(X3)),k9_lopclset(X3),X4)) = k8_funct_2(u1_struct_0(X3),k1_zfmisc_1(k7_lopclset(X3)),k9_lopclset(X3),k7_lattices(X3,X4)) ) ),
    inference(variable_rename,[status(thm)],[590]) ).

fof(592,plain,
    ! [X3,X4] :
      ( ~ m1_subset_1(X4,u1_struct_0(X3))
      | k4_xboole_0(k7_lopclset(X3),k8_funct_2(u1_struct_0(X3),k1_zfmisc_1(k7_lopclset(X3)),k9_lopclset(X3),X4)) = k8_funct_2(u1_struct_0(X3),k1_zfmisc_1(k7_lopclset(X3)),k9_lopclset(X3),k7_lattices(X3,X4))
      | v3_struct_0(X3)
      | ~ v10_lattices(X3)
      | ~ v17_lattices(X3)
      | v3_realset2(X3)
      | ~ l3_lattices(X3) ),
    inference(shift_quantors,[status(thm)],[591]) ).

cnf(593,plain,
    ( v3_realset2(X1)
    | v3_struct_0(X1)
    | k4_xboole_0(k7_lopclset(X1),k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),X2)) = k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),k7_lattices(X1,X2))
    | ~ l3_lattices(X1)
    | ~ v17_lattices(X1)
    | ~ v10_lattices(X1)
    | ~ m1_subset_1(X2,u1_struct_0(X1)) ),
    inference(split_conjunct,[status(thm)],[592]) ).

cnf(1060,plain,
    ( k4_xboole_0(k7_lopclset(X1),k1_xboole_0) = k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),k7_lattices(X1,k5_lattices(X1)))
    | v3_realset2(X1)
    | v3_struct_0(X1)
    | ~ m1_subset_1(k5_lattices(X1),u1_struct_0(X1))
    | ~ l3_lattices(X1)
    | ~ v17_lattices(X1)
    | ~ v10_lattices(X1) ),
    inference(spm,[status(thm)],[593,175,theory(equality)]) ).

cnf(1062,plain,
    ( k7_lopclset(X1) = k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),k7_lattices(X1,k5_lattices(X1)))
    | v3_realset2(X1)
    | v3_struct_0(X1)
    | ~ m1_subset_1(k5_lattices(X1),u1_struct_0(X1))
    | ~ l3_lattices(X1)
    | ~ v17_lattices(X1)
    | ~ v10_lattices(X1) ),
    inference(rw,[status(thm)],[1060,316,theory(equality)]) ).

cnf(5579,plain,
    ( k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),k6_lattices(X1)) = k7_lopclset(X1)
    | v3_realset2(X1)
    | v3_struct_0(X1)
    | ~ m1_subset_1(k5_lattices(X1),u1_struct_0(X1))
    | ~ l3_lattices(X1)
    | ~ v17_lattices(X1)
    | ~ v10_lattices(X1) ),
    inference(spm,[status(thm)],[1062,514,theory(equality)]) ).

cnf(134201,negated_conjecture,
    ( v3_realset2(esk15_0)
    | v3_struct_0(esk15_0)
    | ~ m1_subset_1(k5_lattices(esk15_0),u1_struct_0(esk15_0))
    | ~ l3_lattices(esk15_0)
    | ~ v17_lattices(esk15_0)
    | ~ v10_lattices(esk15_0) ),
    inference(spm,[status(thm)],[411,5579,theory(equality)]) ).

cnf(134274,negated_conjecture,
    ( v3_realset2(esk15_0)
    | v3_struct_0(esk15_0)
    | ~ m1_subset_1(k5_lattices(esk15_0),u1_struct_0(esk15_0))
    | $false
    | ~ v17_lattices(esk15_0)
    | ~ v10_lattices(esk15_0) ),
    inference(rw,[status(thm)],[134201,412,theory(equality)]) ).

cnf(134275,negated_conjecture,
    ( v3_realset2(esk15_0)
    | v3_struct_0(esk15_0)
    | ~ m1_subset_1(k5_lattices(esk15_0),u1_struct_0(esk15_0))
    | $false
    | $false
    | ~ v10_lattices(esk15_0) ),
    inference(rw,[status(thm)],[134274,414,theory(equality)]) ).

cnf(134276,negated_conjecture,
    ( v3_realset2(esk15_0)
    | v3_struct_0(esk15_0)
    | ~ m1_subset_1(k5_lattices(esk15_0),u1_struct_0(esk15_0))
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[134275,415,theory(equality)]) ).

cnf(134277,negated_conjecture,
    ( v3_realset2(esk15_0)
    | v3_struct_0(esk15_0)
    | ~ m1_subset_1(k5_lattices(esk15_0),u1_struct_0(esk15_0)) ),
    inference(cn,[status(thm)],[134276,theory(equality)]) ).

cnf(134278,negated_conjecture,
    ( v3_struct_0(esk15_0)
    | ~ m1_subset_1(k5_lattices(esk15_0),u1_struct_0(esk15_0)) ),
    inference(sr,[status(thm)],[134277,413,theory(equality)]) ).

cnf(134279,negated_conjecture,
    ~ m1_subset_1(k5_lattices(esk15_0),u1_struct_0(esk15_0)),
    inference(sr,[status(thm)],[134278,416,theory(equality)]) ).

cnf(134282,negated_conjecture,
    ( v3_struct_0(esk15_0)
    | ~ l1_lattices(esk15_0) ),
    inference(spm,[status(thm)],[134279,314,theory(equality)]) ).

cnf(134283,negated_conjecture,
    ~ l1_lattices(esk15_0),
    inference(sr,[status(thm)],[134282,416,theory(equality)]) ).

cnf(134284,negated_conjecture,
    ~ l3_lattices(esk15_0),
    inference(spm,[status(thm)],[134283,170,theory(equality)]) ).

cnf(134285,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[134284,412,theory(equality)]) ).

cnf(134286,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[134285,theory(equality)]) ).

cnf(134287,negated_conjecture,
    $false,
    134286,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/LAT/LAT291+1.p
% --creating new selector for []
% -running prover on /tmp/tmpzSTGD2/sel_LAT291+1.p_1 with time limit 29
% -prover status Theorem
% Problem LAT291+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/LAT/LAT291+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/LAT/LAT291+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
% 
%------------------------------------------------------------------------------