TSTP Solution File: KRS111+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : KRS111+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 13:00:16 EST 2010

% Result   : Unsatisfiable 0.23s
% Output   : CNFRefutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   54 (   5 unt;   0 def)
%            Number of atoms       :  199 (  13 equ)
%            Maximal formula atoms :   19 (   3 avg)
%            Number of connectives :  244 (  99   ~;  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(2,axiom,
    cUnsatisfiable(i2003_11_14_17_21_15425),
    file('/tmp/tmpnVa08V/sel_KRS111+1.p_1',axiom_11) ).

fof(3,axiom,
    ! [X1,X2] :
      ( rs(X1,X2)
     => rf(X1,X2) ),
    file('/tmp/tmpnVa08V/sel_KRS111+1.p_1',axiom_12) ).

fof(4,axiom,
    ! [X1,X2] :
      ( rs(X1,X2)
     => rf1(X1,X2) ),
    file('/tmp/tmpnVa08V/sel_KRS111+1.p_1',axiom_13) ).

fof(7,axiom,
    ! [X1] :
      ( cp(X1)
    <=> ~ ? [X2] : ra_Px1(X1,X2) ),
    file('/tmp/tmpnVa08V/sel_KRS111+1.p_1',axiom_3) ).

fof(10,axiom,
    ! [X1,X2,X3] :
      ( ( rf1(X1,X2)
        & rf1(X1,X3) )
     => X2 = X3 ),
    file('/tmp/tmpnVa08V/sel_KRS111+1.p_1',axiom_6) ).

fof(12,axiom,
    ! [X1] :
      ( cpxcomp(X1)
    <=> ? [X7] : ra_Px1(X1,X7) ),
    file('/tmp/tmpnVa08V/sel_KRS111+1.p_1',axiom_4) ).

fof(13,axiom,
    ! [X1,X2,X3] :
      ( ( rf(X1,X2)
        & rf(X1,X3) )
     => X2 = X3 ),
    file('/tmp/tmpnVa08V/sel_KRS111+1.p_1',axiom_5) ).

fof(28,axiom,
    ! [X1] :
      ( cUnsatisfiable(X1)
    <=> ( ? [X2] :
            ( rf1(X1,X2)
            & cpxcomp(X2) )
        & ? [X2] :
            ( rs(X1,X2)
            & cowlThing(X2) )
        & ? [X2] :
            ( rf(X1,X2)
            & cp(X2) ) ) ),
    file('/tmp/tmpnVa08V/sel_KRS111+1.p_1',axiom_2) ).

cnf(41,plain,
    cUnsatisfiable(i2003_11_14_17_21_15425),
    inference(split_conjunct,[status(thm)],[2]) ).

fof(42,plain,
    ! [X1,X2] :
      ( ~ rs(X1,X2)
      | rf(X1,X2) ),
    inference(fof_nnf,[status(thm)],[3]) ).

fof(43,plain,
    ! [X3,X4] :
      ( ~ rs(X3,X4)
      | rf(X3,X4) ),
    inference(variable_rename,[status(thm)],[42]) ).

cnf(44,plain,
    ( rf(X1,X2)
    | ~ rs(X1,X2) ),
    inference(split_conjunct,[status(thm)],[43]) ).

fof(45,plain,
    ! [X1,X2] :
      ( ~ rs(X1,X2)
      | rf1(X1,X2) ),
    inference(fof_nnf,[status(thm)],[4]) ).

fof(46,plain,
    ! [X3,X4] :
      ( ~ rs(X3,X4)
      | rf1(X3,X4) ),
    inference(variable_rename,[status(thm)],[45]) ).

cnf(47,plain,
    ( rf1(X1,X2)
    | ~ rs(X1,X2) ),
    inference(split_conjunct,[status(thm)],[46]) ).

fof(54,plain,
    ! [X1] :
      ( ( ~ cp(X1)
        | ! [X2] : ~ ra_Px1(X1,X2) )
      & ( ? [X2] : ra_Px1(X1,X2)
        | cp(X1) ) ),
    inference(fof_nnf,[status(thm)],[7]) ).

fof(55,plain,
    ! [X3] :
      ( ( ~ cp(X3)
        | ! [X4] : ~ ra_Px1(X3,X4) )
      & ( ? [X5] : ra_Px1(X3,X5)
        | cp(X3) ) ),
    inference(variable_rename,[status(thm)],[54]) ).

fof(56,plain,
    ! [X3] :
      ( ( ~ cp(X3)
        | ! [X4] : ~ ra_Px1(X3,X4) )
      & ( ra_Px1(X3,esk1_1(X3))
        | cp(X3) ) ),
    inference(skolemize,[status(esa)],[55]) ).

fof(57,plain,
    ! [X3,X4] :
      ( ( ~ ra_Px1(X3,X4)
        | ~ cp(X3) )
      & ( ra_Px1(X3,esk1_1(X3))
        | cp(X3) ) ),
    inference(shift_quantors,[status(thm)],[56]) ).

cnf(59,plain,
    ( ~ cp(X1)
    | ~ ra_Px1(X1,X2) ),
    inference(split_conjunct,[status(thm)],[57]) ).

fof(66,plain,
    ! [X1,X2,X3] :
      ( ~ rf1(X1,X2)
      | ~ rf1(X1,X3)
      | X2 = X3 ),
    inference(fof_nnf,[status(thm)],[10]) ).

fof(67,plain,
    ! [X4,X5,X6] :
      ( ~ rf1(X4,X5)
      | ~ rf1(X4,X6)
      | X5 = X6 ),
    inference(variable_rename,[status(thm)],[66]) ).

cnf(68,plain,
    ( X1 = X2
    | ~ rf1(X3,X2)
    | ~ rf1(X3,X1) ),
    inference(split_conjunct,[status(thm)],[67]) ).

fof(73,plain,
    ! [X1] :
      ( ( ~ cpxcomp(X1)
        | ? [X7] : ra_Px1(X1,X7) )
      & ( ! [X7] : ~ ra_Px1(X1,X7)
        | cpxcomp(X1) ) ),
    inference(fof_nnf,[status(thm)],[12]) ).

fof(74,plain,
    ! [X8] :
      ( ( ~ cpxcomp(X8)
        | ? [X9] : ra_Px1(X8,X9) )
      & ( ! [X10] : ~ ra_Px1(X8,X10)
        | cpxcomp(X8) ) ),
    inference(variable_rename,[status(thm)],[73]) ).

fof(75,plain,
    ! [X8] :
      ( ( ~ cpxcomp(X8)
        | ra_Px1(X8,esk2_1(X8)) )
      & ( ! [X10] : ~ ra_Px1(X8,X10)
        | cpxcomp(X8) ) ),
    inference(skolemize,[status(esa)],[74]) ).

fof(76,plain,
    ! [X8,X10] :
      ( ( ~ ra_Px1(X8,X10)
        | cpxcomp(X8) )
      & ( ~ cpxcomp(X8)
        | ra_Px1(X8,esk2_1(X8)) ) ),
    inference(shift_quantors,[status(thm)],[75]) ).

cnf(77,plain,
    ( ra_Px1(X1,esk2_1(X1))
    | ~ cpxcomp(X1) ),
    inference(split_conjunct,[status(thm)],[76]) ).

fof(79,plain,
    ! [X1,X2,X3] :
      ( ~ rf(X1,X2)
      | ~ rf(X1,X3)
      | X2 = X3 ),
    inference(fof_nnf,[status(thm)],[13]) ).

fof(80,plain,
    ! [X4,X5,X6] :
      ( ~ rf(X4,X5)
      | ~ rf(X4,X6)
      | X5 = X6 ),
    inference(variable_rename,[status(thm)],[79]) ).

cnf(81,plain,
    ( X1 = X2
    | ~ rf(X3,X2)
    | ~ rf(X3,X1) ),
    inference(split_conjunct,[status(thm)],[80]) ).

fof(126,plain,
    ! [X1] :
      ( ( ~ cUnsatisfiable(X1)
        | ( ? [X2] :
              ( rf1(X1,X2)
              & cpxcomp(X2) )
          & ? [X2] :
              ( rs(X1,X2)
              & cowlThing(X2) )
          & ? [X2] :
              ( rf(X1,X2)
              & cp(X2) ) ) )
      & ( ! [X2] :
            ( ~ rf1(X1,X2)
            | ~ cpxcomp(X2) )
        | ! [X2] :
            ( ~ rs(X1,X2)
            | ~ cowlThing(X2) )
        | ! [X2] :
            ( ~ rf(X1,X2)
            | ~ cp(X2) )
        | cUnsatisfiable(X1) ) ),
    inference(fof_nnf,[status(thm)],[28]) ).

fof(127,plain,
    ! [X3] :
      ( ( ~ cUnsatisfiable(X3)
        | ( ? [X4] :
              ( rf1(X3,X4)
              & cpxcomp(X4) )
          & ? [X5] :
              ( rs(X3,X5)
              & cowlThing(X5) )
          & ? [X6] :
              ( rf(X3,X6)
              & cp(X6) ) ) )
      & ( ! [X7] :
            ( ~ rf1(X3,X7)
            | ~ cpxcomp(X7) )
        | ! [X8] :
            ( ~ rs(X3,X8)
            | ~ cowlThing(X8) )
        | ! [X9] :
            ( ~ rf(X3,X9)
            | ~ cp(X9) )
        | cUnsatisfiable(X3) ) ),
    inference(variable_rename,[status(thm)],[126]) ).

fof(128,plain,
    ! [X3] :
      ( ( ~ cUnsatisfiable(X3)
        | ( rf1(X3,esk3_1(X3))
          & cpxcomp(esk3_1(X3))
          & rs(X3,esk4_1(X3))
          & cowlThing(esk4_1(X3))
          & rf(X3,esk5_1(X3))
          & cp(esk5_1(X3)) ) )
      & ( ! [X7] :
            ( ~ rf1(X3,X7)
            | ~ cpxcomp(X7) )
        | ! [X8] :
            ( ~ rs(X3,X8)
            | ~ cowlThing(X8) )
        | ! [X9] :
            ( ~ rf(X3,X9)
            | ~ cp(X9) )
        | cUnsatisfiable(X3) ) ),
    inference(skolemize,[status(esa)],[127]) ).

fof(129,plain,
    ! [X3,X7,X8,X9] :
      ( ( ~ rf(X3,X9)
        | ~ cp(X9)
        | ~ rs(X3,X8)
        | ~ cowlThing(X8)
        | ~ rf1(X3,X7)
        | ~ cpxcomp(X7)
        | cUnsatisfiable(X3) )
      & ( ~ cUnsatisfiable(X3)
        | ( rf1(X3,esk3_1(X3))
          & cpxcomp(esk3_1(X3))
          & rs(X3,esk4_1(X3))
          & cowlThing(esk4_1(X3))
          & rf(X3,esk5_1(X3))
          & cp(esk5_1(X3)) ) ) ),
    inference(shift_quantors,[status(thm)],[128]) ).

fof(130,plain,
    ! [X3,X7,X8,X9] :
      ( ( ~ rf(X3,X9)
        | ~ cp(X9)
        | ~ rs(X3,X8)
        | ~ cowlThing(X8)
        | ~ rf1(X3,X7)
        | ~ cpxcomp(X7)
        | cUnsatisfiable(X3) )
      & ( rf1(X3,esk3_1(X3))
        | ~ cUnsatisfiable(X3) )
      & ( cpxcomp(esk3_1(X3))
        | ~ cUnsatisfiable(X3) )
      & ( rs(X3,esk4_1(X3))
        | ~ cUnsatisfiable(X3) )
      & ( cowlThing(esk4_1(X3))
        | ~ cUnsatisfiable(X3) )
      & ( rf(X3,esk5_1(X3))
        | ~ cUnsatisfiable(X3) )
      & ( cp(esk5_1(X3))
        | ~ cUnsatisfiable(X3) ) ),
    inference(distribute,[status(thm)],[129]) ).

cnf(131,plain,
    ( cp(esk5_1(X1))
    | ~ cUnsatisfiable(X1) ),
    inference(split_conjunct,[status(thm)],[130]) ).

cnf(132,plain,
    ( rf(X1,esk5_1(X1))
    | ~ cUnsatisfiable(X1) ),
    inference(split_conjunct,[status(thm)],[130]) ).

cnf(134,plain,
    ( rs(X1,esk4_1(X1))
    | ~ cUnsatisfiable(X1) ),
    inference(split_conjunct,[status(thm)],[130]) ).

cnf(135,plain,
    ( cpxcomp(esk3_1(X1))
    | ~ cUnsatisfiable(X1) ),
    inference(split_conjunct,[status(thm)],[130]) ).

cnf(136,plain,
    ( rf1(X1,esk3_1(X1))
    | ~ cUnsatisfiable(X1) ),
    inference(split_conjunct,[status(thm)],[130]) ).

cnf(165,plain,
    ( rf(X1,esk4_1(X1))
    | ~ cUnsatisfiable(X1) ),
    inference(spm,[status(thm)],[44,134,theory(equality)]) ).

cnf(166,plain,
    ( rf1(X1,esk4_1(X1))
    | ~ cUnsatisfiable(X1) ),
    inference(spm,[status(thm)],[47,134,theory(equality)]) ).

cnf(171,plain,
    ( ~ cp(X1)
    | ~ cpxcomp(X1) ),
    inference(spm,[status(thm)],[59,77,theory(equality)]) ).

cnf(173,plain,
    ( X1 = esk5_1(X2)
    | ~ rf(X2,X1)
    | ~ cUnsatisfiable(X2) ),
    inference(spm,[status(thm)],[81,132,theory(equality)]) ).

cnf(174,plain,
    ( X1 = esk3_1(X2)
    | ~ rf1(X2,X1)
    | ~ cUnsatisfiable(X2) ),
    inference(spm,[status(thm)],[68,136,theory(equality)]) ).

cnf(178,plain,
    ( ~ cp(esk3_1(X1))
    | ~ cUnsatisfiable(X1) ),
    inference(spm,[status(thm)],[171,135,theory(equality)]) ).

cnf(188,plain,
    ( esk4_1(X1) = esk5_1(X1)
    | ~ cUnsatisfiable(X1) ),
    inference(spm,[status(thm)],[173,165,theory(equality)]) ).

cnf(200,plain,
    ( esk4_1(X1) = esk3_1(X1)
    | ~ cUnsatisfiable(X1) ),
    inference(spm,[status(thm)],[174,166,theory(equality)]) ).

cnf(207,plain,
    ( esk3_1(X1) = esk5_1(X1)
    | ~ cUnsatisfiable(X1) ),
    inference(spm,[status(thm)],[188,200,theory(equality)]) ).

cnf(210,plain,
    ( ~ cp(esk5_1(X1))
    | ~ cUnsatisfiable(X1) ),
    inference(spm,[status(thm)],[178,207,theory(equality)]) ).

cnf(212,plain,
    ~ cUnsatisfiable(X1),
    inference(csr,[status(thm)],[210,131]) ).

cnf(213,plain,
    $false,
    inference(sr,[status(thm)],[41,212,theory(equality)]) ).

cnf(214,plain,
    $false,
    213,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KRS/KRS111+1.p
% --creating new selector for []
% -running prover on /tmp/tmpnVa08V/sel_KRS111+1.p_1 with time limit 29
% -prover status Unsatisfiable
% Problem KRS111+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KRS/KRS111+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KRS/KRS111+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
% 
%------------------------------------------------------------------------------