TSTP Solution File: KRS084+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : KRS084+1 : TPTP v5.0.0. Released v3.1.0.
% 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 12:58:09 EST 2010

% Result   : Unsatisfiable 0.31s
% Output   : CNFRefutation 0.31s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   54 (   5 unt;   0 def)
%            Number of atoms       :  235 (   7 equ)
%            Maximal formula atoms :   23 (   4 avg)
%            Number of connectives :  296 ( 115   ~; 109   |;  62   &)
%                                         (   6 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   1 con; 0-2 aty)
%            Number of variables   :  109 (   1 sgn  63   !;  14   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(4,axiom,
    ! [X4] :
      ( cUnsatisfiable(X4)
    <=> ( ? [X5] :
            ( rinvF(X4,X5)
            & cd(X5) )
        & ! [X5] :
            ( rinvR(X4,X5)
           => ? [X6] :
                ( rinvF(X5,X6)
                & cd(X6) ) )
        & ~ cc(X4) ) ),
    file('/tmp/tmpx05ygd/sel_KRS084+1.p_1',axiom_2) ).

fof(5,axiom,
    ! [X4] :
      ( cd(X4)
    <=> ( ? [X5] :
            ( rf(X4,X5)
            & ~ cc(X5) )
        & cc(X4) ) ),
    file('/tmp/tmpx05ygd/sel_KRS084+1.p_1',axiom_3) ).

fof(8,axiom,
    ! [X4,X5] :
      ( rinvR(X4,X5)
    <=> rr(X5,X4) ),
    file('/tmp/tmpx05ygd/sel_KRS084+1.p_1',axiom_6) ).

fof(10,axiom,
    ! [X4,X5,X6] :
      ( ( rf(X4,X5)
        & rf(X4,X6) )
     => X5 = X6 ),
    file('/tmp/tmpx05ygd/sel_KRS084+1.p_1',axiom_4) ).

fof(11,axiom,
    ! [X4,X5] :
      ( rinvF(X4,X5)
    <=> rf(X5,X4) ),
    file('/tmp/tmpx05ygd/sel_KRS084+1.p_1',axiom_5) ).

fof(12,axiom,
    cUnsatisfiable(i2003_11_14_17_19_35232),
    file('/tmp/tmpx05ygd/sel_KRS084+1.p_1',axiom_8) ).

fof(13,axiom,
    ! [X4,X5] :
      ( rf(X4,X5)
     => rr(X4,X5) ),
    file('/tmp/tmpx05ygd/sel_KRS084+1.p_1',axiom_9) ).

fof(26,plain,
    ! [X4] :
      ( cUnsatisfiable(X4)
    <=> ( ? [X5] :
            ( rinvF(X4,X5)
            & cd(X5) )
        & ! [X5] :
            ( rinvR(X4,X5)
           => ? [X6] :
                ( rinvF(X5,X6)
                & cd(X6) ) )
        & ~ cc(X4) ) ),
    inference(fof_simplification,[status(thm)],[4,theory(equality)]) ).

fof(27,plain,
    ! [X4] :
      ( cd(X4)
    <=> ( ? [X5] :
            ( rf(X4,X5)
            & ~ cc(X5) )
        & cc(X4) ) ),
    inference(fof_simplification,[status(thm)],[5,theory(equality)]) ).

fof(39,plain,
    ! [X4] :
      ( ( ~ cUnsatisfiable(X4)
        | ( ? [X5] :
              ( rinvF(X4,X5)
              & cd(X5) )
          & ! [X5] :
              ( ~ rinvR(X4,X5)
              | ? [X6] :
                  ( rinvF(X5,X6)
                  & cd(X6) ) )
          & ~ cc(X4) ) )
      & ( ! [X5] :
            ( ~ rinvF(X4,X5)
            | ~ cd(X5) )
        | ? [X5] :
            ( rinvR(X4,X5)
            & ! [X6] :
                ( ~ rinvF(X5,X6)
                | ~ cd(X6) ) )
        | cc(X4)
        | cUnsatisfiable(X4) ) ),
    inference(fof_nnf,[status(thm)],[26]) ).

fof(40,plain,
    ! [X7] :
      ( ( ~ cUnsatisfiable(X7)
        | ( ? [X8] :
              ( rinvF(X7,X8)
              & cd(X8) )
          & ! [X9] :
              ( ~ rinvR(X7,X9)
              | ? [X10] :
                  ( rinvF(X9,X10)
                  & cd(X10) ) )
          & ~ cc(X7) ) )
      & ( ! [X11] :
            ( ~ rinvF(X7,X11)
            | ~ cd(X11) )
        | ? [X12] :
            ( rinvR(X7,X12)
            & ! [X13] :
                ( ~ rinvF(X12,X13)
                | ~ cd(X13) ) )
        | cc(X7)
        | cUnsatisfiable(X7) ) ),
    inference(variable_rename,[status(thm)],[39]) ).

fof(41,plain,
    ! [X7] :
      ( ( ~ cUnsatisfiable(X7)
        | ( rinvF(X7,esk1_1(X7))
          & cd(esk1_1(X7))
          & ! [X9] :
              ( ~ rinvR(X7,X9)
              | ( rinvF(X9,esk2_2(X7,X9))
                & cd(esk2_2(X7,X9)) ) )
          & ~ cc(X7) ) )
      & ( ! [X11] :
            ( ~ rinvF(X7,X11)
            | ~ cd(X11) )
        | ( rinvR(X7,esk3_1(X7))
          & ! [X13] :
              ( ~ rinvF(esk3_1(X7),X13)
              | ~ cd(X13) ) )
        | cc(X7)
        | cUnsatisfiable(X7) ) ),
    inference(skolemize,[status(esa)],[40]) ).

fof(42,plain,
    ! [X7,X9,X11,X13] :
      ( ( ( ( ~ rinvF(esk3_1(X7),X13)
            | ~ cd(X13) )
          & rinvR(X7,esk3_1(X7)) )
        | ~ rinvF(X7,X11)
        | ~ cd(X11)
        | cc(X7)
        | cUnsatisfiable(X7) )
      & ( ( ( ~ rinvR(X7,X9)
            | ( rinvF(X9,esk2_2(X7,X9))
              & cd(esk2_2(X7,X9)) ) )
          & rinvF(X7,esk1_1(X7))
          & cd(esk1_1(X7))
          & ~ cc(X7) )
        | ~ cUnsatisfiable(X7) ) ),
    inference(shift_quantors,[status(thm)],[41]) ).

fof(43,plain,
    ! [X7,X9,X11,X13] :
      ( ( ~ rinvF(esk3_1(X7),X13)
        | ~ cd(X13)
        | ~ rinvF(X7,X11)
        | ~ cd(X11)
        | cc(X7)
        | cUnsatisfiable(X7) )
      & ( rinvR(X7,esk3_1(X7))
        | ~ rinvF(X7,X11)
        | ~ cd(X11)
        | cc(X7)
        | cUnsatisfiable(X7) )
      & ( rinvF(X9,esk2_2(X7,X9))
        | ~ rinvR(X7,X9)
        | ~ cUnsatisfiable(X7) )
      & ( cd(esk2_2(X7,X9))
        | ~ rinvR(X7,X9)
        | ~ cUnsatisfiable(X7) )
      & ( rinvF(X7,esk1_1(X7))
        | ~ cUnsatisfiable(X7) )
      & ( cd(esk1_1(X7))
        | ~ cUnsatisfiable(X7) )
      & ( ~ cc(X7)
        | ~ cUnsatisfiable(X7) ) ),
    inference(distribute,[status(thm)],[42]) ).

cnf(45,plain,
    ( cd(esk1_1(X1))
    | ~ cUnsatisfiable(X1) ),
    inference(split_conjunct,[status(thm)],[43]) ).

cnf(46,plain,
    ( rinvF(X1,esk1_1(X1))
    | ~ cUnsatisfiable(X1) ),
    inference(split_conjunct,[status(thm)],[43]) ).

cnf(47,plain,
    ( cd(esk2_2(X1,X2))
    | ~ cUnsatisfiable(X1)
    | ~ rinvR(X1,X2) ),
    inference(split_conjunct,[status(thm)],[43]) ).

cnf(48,plain,
    ( rinvF(X2,esk2_2(X1,X2))
    | ~ cUnsatisfiable(X1)
    | ~ rinvR(X1,X2) ),
    inference(split_conjunct,[status(thm)],[43]) ).

fof(51,plain,
    ! [X4] :
      ( ( ~ cd(X4)
        | ( ? [X5] :
              ( rf(X4,X5)
              & ~ cc(X5) )
          & cc(X4) ) )
      & ( ! [X5] :
            ( ~ rf(X4,X5)
            | cc(X5) )
        | ~ cc(X4)
        | cd(X4) ) ),
    inference(fof_nnf,[status(thm)],[27]) ).

fof(52,plain,
    ! [X6] :
      ( ( ~ cd(X6)
        | ( ? [X7] :
              ( rf(X6,X7)
              & ~ cc(X7) )
          & cc(X6) ) )
      & ( ! [X8] :
            ( ~ rf(X6,X8)
            | cc(X8) )
        | ~ cc(X6)
        | cd(X6) ) ),
    inference(variable_rename,[status(thm)],[51]) ).

fof(53,plain,
    ! [X6] :
      ( ( ~ cd(X6)
        | ( rf(X6,esk4_1(X6))
          & ~ cc(esk4_1(X6))
          & cc(X6) ) )
      & ( ! [X8] :
            ( ~ rf(X6,X8)
            | cc(X8) )
        | ~ cc(X6)
        | cd(X6) ) ),
    inference(skolemize,[status(esa)],[52]) ).

fof(54,plain,
    ! [X6,X8] :
      ( ( ~ rf(X6,X8)
        | cc(X8)
        | ~ cc(X6)
        | cd(X6) )
      & ( ~ cd(X6)
        | ( rf(X6,esk4_1(X6))
          & ~ cc(esk4_1(X6))
          & cc(X6) ) ) ),
    inference(shift_quantors,[status(thm)],[53]) ).

fof(55,plain,
    ! [X6,X8] :
      ( ( ~ rf(X6,X8)
        | cc(X8)
        | ~ cc(X6)
        | cd(X6) )
      & ( rf(X6,esk4_1(X6))
        | ~ cd(X6) )
      & ( ~ cc(esk4_1(X6))
        | ~ cd(X6) )
      & ( cc(X6)
        | ~ cd(X6) ) ),
    inference(distribute,[status(thm)],[54]) ).

cnf(56,plain,
    ( cc(X1)
    | ~ cd(X1) ),
    inference(split_conjunct,[status(thm)],[55]) ).

cnf(57,plain,
    ( ~ cd(X1)
    | ~ cc(esk4_1(X1)) ),
    inference(split_conjunct,[status(thm)],[55]) ).

cnf(58,plain,
    ( rf(X1,esk4_1(X1))
    | ~ cd(X1) ),
    inference(split_conjunct,[status(thm)],[55]) ).

fof(67,plain,
    ! [X4,X5] :
      ( ( ~ rinvR(X4,X5)
        | rr(X5,X4) )
      & ( ~ rr(X5,X4)
        | rinvR(X4,X5) ) ),
    inference(fof_nnf,[status(thm)],[8]) ).

fof(68,plain,
    ! [X6,X7] :
      ( ( ~ rinvR(X6,X7)
        | rr(X7,X6) )
      & ( ~ rr(X7,X6)
        | rinvR(X6,X7) ) ),
    inference(variable_rename,[status(thm)],[67]) ).

cnf(69,plain,
    ( rinvR(X1,X2)
    | ~ rr(X2,X1) ),
    inference(split_conjunct,[status(thm)],[68]) ).

fof(74,plain,
    ! [X4,X5,X6] :
      ( ~ rf(X4,X5)
      | ~ rf(X4,X6)
      | X5 = X6 ),
    inference(fof_nnf,[status(thm)],[10]) ).

fof(75,plain,
    ! [X7,X8,X9] :
      ( ~ rf(X7,X8)
      | ~ rf(X7,X9)
      | X8 = X9 ),
    inference(variable_rename,[status(thm)],[74]) ).

cnf(76,plain,
    ( X1 = X2
    | ~ rf(X3,X2)
    | ~ rf(X3,X1) ),
    inference(split_conjunct,[status(thm)],[75]) ).

fof(77,plain,
    ! [X4,X5] :
      ( ( ~ rinvF(X4,X5)
        | rf(X5,X4) )
      & ( ~ rf(X5,X4)
        | rinvF(X4,X5) ) ),
    inference(fof_nnf,[status(thm)],[11]) ).

fof(78,plain,
    ! [X6,X7] :
      ( ( ~ rinvF(X6,X7)
        | rf(X7,X6) )
      & ( ~ rf(X7,X6)
        | rinvF(X6,X7) ) ),
    inference(variable_rename,[status(thm)],[77]) ).

cnf(80,plain,
    ( rf(X1,X2)
    | ~ rinvF(X2,X1) ),
    inference(split_conjunct,[status(thm)],[78]) ).

cnf(81,plain,
    cUnsatisfiable(i2003_11_14_17_19_35232),
    inference(split_conjunct,[status(thm)],[12]) ).

fof(82,plain,
    ! [X4,X5] :
      ( ~ rf(X4,X5)
      | rr(X4,X5) ),
    inference(fof_nnf,[status(thm)],[13]) ).

fof(83,plain,
    ! [X6,X7] :
      ( ~ rf(X6,X7)
      | rr(X6,X7) ),
    inference(variable_rename,[status(thm)],[82]) ).

cnf(84,plain,
    ( rr(X1,X2)
    | ~ rf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[83]) ).

cnf(122,plain,
    ( cc(esk1_1(X1))
    | ~ cUnsatisfiable(X1) ),
    inference(spm,[status(thm)],[56,45,theory(equality)]) ).

cnf(125,plain,
    ( rf(esk1_1(X1),X1)
    | ~ cUnsatisfiable(X1) ),
    inference(spm,[status(thm)],[80,46,theory(equality)]) ).

cnf(127,plain,
    ( X1 = esk4_1(X2)
    | ~ rf(X2,X1)
    | ~ cd(X2) ),
    inference(spm,[status(thm)],[76,58,theory(equality)]) ).

cnf(136,plain,
    ( rr(esk1_1(X1),X1)
    | ~ cUnsatisfiable(X1) ),
    inference(spm,[status(thm)],[84,125,theory(equality)]) ).

cnf(142,plain,
    ( rinvR(X1,esk1_1(X1))
    | ~ cUnsatisfiable(X1) ),
    inference(spm,[status(thm)],[69,136,theory(equality)]) ).

cnf(145,plain,
    ( cd(esk2_2(X1,esk1_1(X1)))
    | ~ cUnsatisfiable(X1) ),
    inference(spm,[status(thm)],[47,142,theory(equality)]) ).

cnf(146,plain,
    ( rinvF(esk1_1(X1),esk2_2(X1,esk1_1(X1)))
    | ~ cUnsatisfiable(X1) ),
    inference(spm,[status(thm)],[48,142,theory(equality)]) ).

cnf(166,plain,
    ( rf(esk2_2(X1,esk1_1(X1)),esk1_1(X1))
    | ~ cUnsatisfiable(X1) ),
    inference(spm,[status(thm)],[80,146,theory(equality)]) ).

cnf(176,plain,
    ( esk1_1(X1) = esk4_1(esk2_2(X1,esk1_1(X1)))
    | ~ cd(esk2_2(X1,esk1_1(X1)))
    | ~ cUnsatisfiable(X1) ),
    inference(spm,[status(thm)],[127,166,theory(equality)]) ).

cnf(304,plain,
    ( esk4_1(esk2_2(X1,esk1_1(X1))) = esk1_1(X1)
    | ~ cUnsatisfiable(X1) ),
    inference(csr,[status(thm)],[176,145]) ).

cnf(305,plain,
    ( ~ cd(esk2_2(X1,esk1_1(X1)))
    | ~ cc(esk1_1(X1))
    | ~ cUnsatisfiable(X1) ),
    inference(spm,[status(thm)],[57,304,theory(equality)]) ).

cnf(334,plain,
    ( ~ cd(esk2_2(X1,esk1_1(X1)))
    | ~ cUnsatisfiable(X1) ),
    inference(csr,[status(thm)],[305,122]) ).

cnf(335,plain,
    ~ cUnsatisfiable(X1),
    inference(csr,[status(thm)],[334,145]) ).

cnf(336,plain,
    $false,
    inference(sr,[status(thm)],[81,335,theory(equality)]) ).

cnf(337,plain,
    $false,
    336,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KRS/KRS084+1.p
% --creating new selector for []
% -running prover on /tmp/tmpx05ygd/sel_KRS084+1.p_1 with time limit 29
% -prover status Unsatisfiable
% Problem KRS084+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KRS/KRS084+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KRS/KRS084+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
% 
%------------------------------------------------------------------------------