TSTP Solution File: KRS106+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : KRS106+1 : TPTP v5.0.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art07.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 12:59:57 EST 2010

% Result   : Unsatisfiable 0.22s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   54 (   5 unt;   0 def)
%            Number of atoms       :  199 (  12 equ)
%            Maximal formula atoms :   19 (   3 avg)
%            Number of connectives :  243 (  98   ~;  93   |;  45   &)
%                                         (   3 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   1 con; 0-1 aty)
%            Number of variables   :  115 (   2 sgn  69   !;  15   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2] :
      ( rf3(X1,X2)
     => rf2(X1,X2) ),
    file('/tmp/tmp5S-neV/sel_KRS106+1.p_1',axiom_10) ).

fof(3,axiom,
    ! [X1] :
      ( cUnsatisfiable(X1)
    <=> ( ? [X2] :
            ( rf3(X1,X2)
            & cp2(X2) )
        & ? [X2] :
            ( rf1(X1,X2)
            & cp1(X2) )
        & ? [X2] :
            ( rf2(X1,X2)
            & cp1xcomp(X2) ) ) ),
    file('/tmp/tmp5S-neV/sel_KRS106+1.p_1',axiom_2) ).

fof(4,axiom,
    ! [X1] :
      ( cp1(X1)
    <=> ~ ? [X2] : ra_Px1(X1,X2) ),
    file('/tmp/tmp5S-neV/sel_KRS106+1.p_1',axiom_3) ).

fof(7,axiom,
    ! [X1,X2,X5] :
      ( ( rf2(X1,X2)
        & rf2(X1,X5) )
     => X2 = X5 ),
    file('/tmp/tmp5S-neV/sel_KRS106+1.p_1',axiom_6) ).

fof(9,axiom,
    ! [X1] :
      ( cp1xcomp(X1)
    <=> ? [X6] : ra_Px1(X1,X6) ),
    file('/tmp/tmp5S-neV/sel_KRS106+1.p_1',axiom_4) ).

fof(10,axiom,
    ! [X1,X2,X5] :
      ( ( rf1(X1,X2)
        & rf1(X1,X5) )
     => X2 = X5 ),
    file('/tmp/tmp5S-neV/sel_KRS106+1.p_1',axiom_5) ).

fof(11,axiom,
    cUnsatisfiable(i2003_11_14_17_20_57644),
    file('/tmp/tmp5S-neV/sel_KRS106+1.p_1',axiom_8) ).

fof(12,axiom,
    ! [X1,X2] :
      ( rf3(X1,X2)
     => rf1(X1,X2) ),
    file('/tmp/tmp5S-neV/sel_KRS106+1.p_1',axiom_9) ).

fof(30,plain,
    ! [X1,X2] :
      ( ~ rf3(X1,X2)
      | rf2(X1,X2) ),
    inference(fof_nnf,[status(thm)],[1]) ).

fof(31,plain,
    ! [X3,X4] :
      ( ~ rf3(X3,X4)
      | rf2(X3,X4) ),
    inference(variable_rename,[status(thm)],[30]) ).

cnf(32,plain,
    ( rf2(X1,X2)
    | ~ rf3(X1,X2) ),
    inference(split_conjunct,[status(thm)],[31]) ).

fof(36,plain,
    ! [X1] :
      ( ( ~ cUnsatisfiable(X1)
        | ( ? [X2] :
              ( rf3(X1,X2)
              & cp2(X2) )
          & ? [X2] :
              ( rf1(X1,X2)
              & cp1(X2) )
          & ? [X2] :
              ( rf2(X1,X2)
              & cp1xcomp(X2) ) ) )
      & ( ! [X2] :
            ( ~ rf3(X1,X2)
            | ~ cp2(X2) )
        | ! [X2] :
            ( ~ rf1(X1,X2)
            | ~ cp1(X2) )
        | ! [X2] :
            ( ~ rf2(X1,X2)
            | ~ cp1xcomp(X2) )
        | cUnsatisfiable(X1) ) ),
    inference(fof_nnf,[status(thm)],[3]) ).

fof(37,plain,
    ! [X3] :
      ( ( ~ cUnsatisfiable(X3)
        | ( ? [X4] :
              ( rf3(X3,X4)
              & cp2(X4) )
          & ? [X5] :
              ( rf1(X3,X5)
              & cp1(X5) )
          & ? [X6] :
              ( rf2(X3,X6)
              & cp1xcomp(X6) ) ) )
      & ( ! [X7] :
            ( ~ rf3(X3,X7)
            | ~ cp2(X7) )
        | ! [X8] :
            ( ~ rf1(X3,X8)
            | ~ cp1(X8) )
        | ! [X9] :
            ( ~ rf2(X3,X9)
            | ~ cp1xcomp(X9) )
        | cUnsatisfiable(X3) ) ),
    inference(variable_rename,[status(thm)],[36]) ).

fof(38,plain,
    ! [X3] :
      ( ( ~ cUnsatisfiable(X3)
        | ( rf3(X3,esk1_1(X3))
          & cp2(esk1_1(X3))
          & rf1(X3,esk2_1(X3))
          & cp1(esk2_1(X3))
          & rf2(X3,esk3_1(X3))
          & cp1xcomp(esk3_1(X3)) ) )
      & ( ! [X7] :
            ( ~ rf3(X3,X7)
            | ~ cp2(X7) )
        | ! [X8] :
            ( ~ rf1(X3,X8)
            | ~ cp1(X8) )
        | ! [X9] :
            ( ~ rf2(X3,X9)
            | ~ cp1xcomp(X9) )
        | cUnsatisfiable(X3) ) ),
    inference(skolemize,[status(esa)],[37]) ).

fof(39,plain,
    ! [X3,X7,X8,X9] :
      ( ( ~ rf2(X3,X9)
        | ~ cp1xcomp(X9)
        | ~ rf1(X3,X8)
        | ~ cp1(X8)
        | ~ rf3(X3,X7)
        | ~ cp2(X7)
        | cUnsatisfiable(X3) )
      & ( ~ cUnsatisfiable(X3)
        | ( rf3(X3,esk1_1(X3))
          & cp2(esk1_1(X3))
          & rf1(X3,esk2_1(X3))
          & cp1(esk2_1(X3))
          & rf2(X3,esk3_1(X3))
          & cp1xcomp(esk3_1(X3)) ) ) ),
    inference(shift_quantors,[status(thm)],[38]) ).

fof(40,plain,
    ! [X3,X7,X8,X9] :
      ( ( ~ rf2(X3,X9)
        | ~ cp1xcomp(X9)
        | ~ rf1(X3,X8)
        | ~ cp1(X8)
        | ~ rf3(X3,X7)
        | ~ cp2(X7)
        | cUnsatisfiable(X3) )
      & ( rf3(X3,esk1_1(X3))
        | ~ cUnsatisfiable(X3) )
      & ( cp2(esk1_1(X3))
        | ~ cUnsatisfiable(X3) )
      & ( rf1(X3,esk2_1(X3))
        | ~ cUnsatisfiable(X3) )
      & ( cp1(esk2_1(X3))
        | ~ cUnsatisfiable(X3) )
      & ( rf2(X3,esk3_1(X3))
        | ~ cUnsatisfiable(X3) )
      & ( cp1xcomp(esk3_1(X3))
        | ~ cUnsatisfiable(X3) ) ),
    inference(distribute,[status(thm)],[39]) ).

cnf(41,plain,
    ( cp1xcomp(esk3_1(X1))
    | ~ cUnsatisfiable(X1) ),
    inference(split_conjunct,[status(thm)],[40]) ).

cnf(42,plain,
    ( rf2(X1,esk3_1(X1))
    | ~ cUnsatisfiable(X1) ),
    inference(split_conjunct,[status(thm)],[40]) ).

cnf(43,plain,
    ( cp1(esk2_1(X1))
    | ~ cUnsatisfiable(X1) ),
    inference(split_conjunct,[status(thm)],[40]) ).

cnf(44,plain,
    ( rf1(X1,esk2_1(X1))
    | ~ cUnsatisfiable(X1) ),
    inference(split_conjunct,[status(thm)],[40]) ).

cnf(46,plain,
    ( rf3(X1,esk1_1(X1))
    | ~ cUnsatisfiable(X1) ),
    inference(split_conjunct,[status(thm)],[40]) ).

fof(48,plain,
    ! [X1] :
      ( ( ~ cp1(X1)
        | ! [X2] : ~ ra_Px1(X1,X2) )
      & ( ? [X2] : ra_Px1(X1,X2)
        | cp1(X1) ) ),
    inference(fof_nnf,[status(thm)],[4]) ).

fof(49,plain,
    ! [X3] :
      ( ( ~ cp1(X3)
        | ! [X4] : ~ ra_Px1(X3,X4) )
      & ( ? [X5] : ra_Px1(X3,X5)
        | cp1(X3) ) ),
    inference(variable_rename,[status(thm)],[48]) ).

fof(50,plain,
    ! [X3] :
      ( ( ~ cp1(X3)
        | ! [X4] : ~ ra_Px1(X3,X4) )
      & ( ra_Px1(X3,esk4_1(X3))
        | cp1(X3) ) ),
    inference(skolemize,[status(esa)],[49]) ).

fof(51,plain,
    ! [X3,X4] :
      ( ( ~ ra_Px1(X3,X4)
        | ~ cp1(X3) )
      & ( ra_Px1(X3,esk4_1(X3))
        | cp1(X3) ) ),
    inference(shift_quantors,[status(thm)],[50]) ).

cnf(53,plain,
    ( ~ cp1(X1)
    | ~ ra_Px1(X1,X2) ),
    inference(split_conjunct,[status(thm)],[51]) ).

fof(61,plain,
    ! [X1,X2,X5] :
      ( ~ rf2(X1,X2)
      | ~ rf2(X1,X5)
      | X2 = X5 ),
    inference(fof_nnf,[status(thm)],[7]) ).

fof(62,plain,
    ! [X6,X7,X8] :
      ( ~ rf2(X6,X7)
      | ~ rf2(X6,X8)
      | X7 = X8 ),
    inference(variable_rename,[status(thm)],[61]) ).

cnf(63,plain,
    ( X1 = X2
    | ~ rf2(X3,X2)
    | ~ rf2(X3,X1) ),
    inference(split_conjunct,[status(thm)],[62]) ).

fof(67,plain,
    ! [X1] :
      ( ( ~ cp1xcomp(X1)
        | ? [X6] : ra_Px1(X1,X6) )
      & ( ! [X6] : ~ ra_Px1(X1,X6)
        | cp1xcomp(X1) ) ),
    inference(fof_nnf,[status(thm)],[9]) ).

fof(68,plain,
    ! [X7] :
      ( ( ~ cp1xcomp(X7)
        | ? [X8] : ra_Px1(X7,X8) )
      & ( ! [X9] : ~ ra_Px1(X7,X9)
        | cp1xcomp(X7) ) ),
    inference(variable_rename,[status(thm)],[67]) ).

fof(69,plain,
    ! [X7] :
      ( ( ~ cp1xcomp(X7)
        | ra_Px1(X7,esk5_1(X7)) )
      & ( ! [X9] : ~ ra_Px1(X7,X9)
        | cp1xcomp(X7) ) ),
    inference(skolemize,[status(esa)],[68]) ).

fof(70,plain,
    ! [X7,X9] :
      ( ( ~ ra_Px1(X7,X9)
        | cp1xcomp(X7) )
      & ( ~ cp1xcomp(X7)
        | ra_Px1(X7,esk5_1(X7)) ) ),
    inference(shift_quantors,[status(thm)],[69]) ).

cnf(71,plain,
    ( ra_Px1(X1,esk5_1(X1))
    | ~ cp1xcomp(X1) ),
    inference(split_conjunct,[status(thm)],[70]) ).

fof(73,plain,
    ! [X1,X2,X5] :
      ( ~ rf1(X1,X2)
      | ~ rf1(X1,X5)
      | X2 = X5 ),
    inference(fof_nnf,[status(thm)],[10]) ).

fof(74,plain,
    ! [X6,X7,X8] :
      ( ~ rf1(X6,X7)
      | ~ rf1(X6,X8)
      | X7 = X8 ),
    inference(variable_rename,[status(thm)],[73]) ).

cnf(75,plain,
    ( X1 = X2
    | ~ rf1(X3,X2)
    | ~ rf1(X3,X1) ),
    inference(split_conjunct,[status(thm)],[74]) ).

cnf(76,plain,
    cUnsatisfiable(i2003_11_14_17_20_57644),
    inference(split_conjunct,[status(thm)],[11]) ).

fof(77,plain,
    ! [X1,X2] :
      ( ~ rf3(X1,X2)
      | rf1(X1,X2) ),
    inference(fof_nnf,[status(thm)],[12]) ).

fof(78,plain,
    ! [X3,X4] :
      ( ~ rf3(X3,X4)
      | rf1(X3,X4) ),
    inference(variable_rename,[status(thm)],[77]) ).

cnf(79,plain,
    ( rf1(X1,X2)
    | ~ rf3(X1,X2) ),
    inference(split_conjunct,[status(thm)],[78]) ).

cnf(128,plain,
    ( rf2(X1,esk1_1(X1))
    | ~ cUnsatisfiable(X1) ),
    inference(spm,[status(thm)],[32,46,theory(equality)]) ).

cnf(129,plain,
    ( rf1(X1,esk1_1(X1))
    | ~ cUnsatisfiable(X1) ),
    inference(spm,[status(thm)],[79,46,theory(equality)]) ).

cnf(131,plain,
    ( ~ cp1(X1)
    | ~ cp1xcomp(X1) ),
    inference(spm,[status(thm)],[53,71,theory(equality)]) ).

cnf(133,plain,
    ( X1 = esk3_1(X2)
    | ~ rf2(X2,X1)
    | ~ cUnsatisfiable(X2) ),
    inference(spm,[status(thm)],[63,42,theory(equality)]) ).

cnf(134,plain,
    ( X1 = esk2_1(X2)
    | ~ rf1(X2,X1)
    | ~ cUnsatisfiable(X2) ),
    inference(spm,[status(thm)],[75,44,theory(equality)]) ).

cnf(136,plain,
    ( ~ cp1(esk3_1(X1))
    | ~ cUnsatisfiable(X1) ),
    inference(spm,[status(thm)],[131,41,theory(equality)]) ).

cnf(141,plain,
    ( esk1_1(X1) = esk3_1(X1)
    | ~ cUnsatisfiable(X1) ),
    inference(spm,[status(thm)],[133,128,theory(equality)]) ).

cnf(145,plain,
    ( rf1(X1,esk3_1(X1))
    | ~ cUnsatisfiable(X1) ),
    inference(spm,[status(thm)],[129,141,theory(equality)]) ).

cnf(153,plain,
    ( esk3_1(X1) = esk2_1(X1)
    | ~ cUnsatisfiable(X1) ),
    inference(spm,[status(thm)],[134,145,theory(equality)]) ).

cnf(156,plain,
    ( cp1(esk3_1(X1))
    | ~ cUnsatisfiable(X1) ),
    inference(spm,[status(thm)],[43,153,theory(equality)]) ).

cnf(160,plain,
    ~ cUnsatisfiable(X1),
    inference(csr,[status(thm)],[156,136]) ).

cnf(161,plain,
    $false,
    inference(sr,[status(thm)],[76,160,theory(equality)]) ).

cnf(162,plain,
    $false,
    161,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KRS/KRS106+1.p
% --creating new selector for []
% -running prover on /tmp/tmp5S-neV/sel_KRS106+1.p_1 with time limit 29
% -prover status Unsatisfiable
% Problem KRS106+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KRS/KRS106+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KRS/KRS106+1.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Unsatisfiable
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
% 
%------------------------------------------------------------------------------