TSTP Solution File: KRS105+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : KRS105+1 : TPTP v5.0.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art04.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 12:59:53 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    :   50 (   8 unt;   0 def)
%            Number of atoms       :  136 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  149 (  63   ~;  59   |;  18   &)
%                                         (   3 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    8 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   1 con; 0-1 aty)
%            Number of variables   :   70 (   1 sgn  47   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1] :
      ( cUnsatisfiable(X1)
     => cdxcomp(X1) ),
    file('/tmp/tmpqLJ1fB/sel_KRS105+1.p_1',axiom_2) ).

fof(2,axiom,
    ! [X1] :
      ( cUnsatisfiable(X1)
     => cc(X1) ),
    file('/tmp/tmpqLJ1fB/sel_KRS105+1.p_1',axiom_3) ).

fof(5,axiom,
    ! [X1] :
      ( cdxcomp(X1)
    <=> ? [X2] : ra_Px1(X1,X2) ),
    file('/tmp/tmpqLJ1fB/sel_KRS105+1.p_1',axiom_6) ).

fof(6,axiom,
    ! [X1] :
      ( ca_Ax2(X1)
    <=> ! [X3] :
          ( rr(X1,X3)
         => cc(X3) ) ),
    file('/tmp/tmpqLJ1fB/sel_KRS105+1.p_1',axiom_7) ).

fof(7,axiom,
    ! [X1] :
      ( cc(X1)
     => ! [X3] :
          ( rr(X1,X3)
         => cc(X3) ) ),
    file('/tmp/tmpqLJ1fB/sel_KRS105+1.p_1',axiom_4) ).

fof(8,axiom,
    ! [X1] :
      ( cd(X1)
    <=> ~ ? [X3] : ra_Px1(X1,X3) ),
    file('/tmp/tmpqLJ1fB/sel_KRS105+1.p_1',axiom_5) ).

fof(9,axiom,
    ! [X1] :
      ( ca_Ax2(X1)
     => cd(X1) ),
    file('/tmp/tmpqLJ1fB/sel_KRS105+1.p_1',axiom_8) ).

fof(10,axiom,
    cUnsatisfiable(i2003_11_14_17_20_53634),
    file('/tmp/tmpqLJ1fB/sel_KRS105+1.p_1',axiom_9) ).

fof(13,plain,
    ! [X1] :
      ( ~ cUnsatisfiable(X1)
      | cdxcomp(X1) ),
    inference(fof_nnf,[status(thm)],[1]) ).

fof(14,plain,
    ! [X2] :
      ( ~ cUnsatisfiable(X2)
      | cdxcomp(X2) ),
    inference(variable_rename,[status(thm)],[13]) ).

cnf(15,plain,
    ( cdxcomp(X1)
    | ~ cUnsatisfiable(X1) ),
    inference(split_conjunct,[status(thm)],[14]) ).

fof(16,plain,
    ! [X1] :
      ( ~ cUnsatisfiable(X1)
      | cc(X1) ),
    inference(fof_nnf,[status(thm)],[2]) ).

fof(17,plain,
    ! [X2] :
      ( ~ cUnsatisfiable(X2)
      | cc(X2) ),
    inference(variable_rename,[status(thm)],[16]) ).

cnf(18,plain,
    ( cc(X1)
    | ~ cUnsatisfiable(X1) ),
    inference(split_conjunct,[status(thm)],[17]) ).

fof(26,plain,
    ! [X1] :
      ( ( ~ cdxcomp(X1)
        | ? [X2] : ra_Px1(X1,X2) )
      & ( ! [X2] : ~ ra_Px1(X1,X2)
        | cdxcomp(X1) ) ),
    inference(fof_nnf,[status(thm)],[5]) ).

fof(27,plain,
    ! [X3] :
      ( ( ~ cdxcomp(X3)
        | ? [X4] : ra_Px1(X3,X4) )
      & ( ! [X5] : ~ ra_Px1(X3,X5)
        | cdxcomp(X3) ) ),
    inference(variable_rename,[status(thm)],[26]) ).

fof(28,plain,
    ! [X3] :
      ( ( ~ cdxcomp(X3)
        | ra_Px1(X3,esk1_1(X3)) )
      & ( ! [X5] : ~ ra_Px1(X3,X5)
        | cdxcomp(X3) ) ),
    inference(skolemize,[status(esa)],[27]) ).

fof(29,plain,
    ! [X3,X5] :
      ( ( ~ ra_Px1(X3,X5)
        | cdxcomp(X3) )
      & ( ~ cdxcomp(X3)
        | ra_Px1(X3,esk1_1(X3)) ) ),
    inference(shift_quantors,[status(thm)],[28]) ).

cnf(30,plain,
    ( ra_Px1(X1,esk1_1(X1))
    | ~ cdxcomp(X1) ),
    inference(split_conjunct,[status(thm)],[29]) ).

fof(32,plain,
    ! [X1] :
      ( ( ~ ca_Ax2(X1)
        | ! [X3] :
            ( ~ rr(X1,X3)
            | cc(X3) ) )
      & ( ? [X3] :
            ( rr(X1,X3)
            & ~ cc(X3) )
        | ca_Ax2(X1) ) ),
    inference(fof_nnf,[status(thm)],[6]) ).

fof(33,plain,
    ! [X4] :
      ( ( ~ ca_Ax2(X4)
        | ! [X5] :
            ( ~ rr(X4,X5)
            | cc(X5) ) )
      & ( ? [X6] :
            ( rr(X4,X6)
            & ~ cc(X6) )
        | ca_Ax2(X4) ) ),
    inference(variable_rename,[status(thm)],[32]) ).

fof(34,plain,
    ! [X4] :
      ( ( ~ ca_Ax2(X4)
        | ! [X5] :
            ( ~ rr(X4,X5)
            | cc(X5) ) )
      & ( ( rr(X4,esk2_1(X4))
          & ~ cc(esk2_1(X4)) )
        | ca_Ax2(X4) ) ),
    inference(skolemize,[status(esa)],[33]) ).

fof(35,plain,
    ! [X4,X5] :
      ( ( ~ rr(X4,X5)
        | cc(X5)
        | ~ ca_Ax2(X4) )
      & ( ( rr(X4,esk2_1(X4))
          & ~ cc(esk2_1(X4)) )
        | ca_Ax2(X4) ) ),
    inference(shift_quantors,[status(thm)],[34]) ).

fof(36,plain,
    ! [X4,X5] :
      ( ( ~ rr(X4,X5)
        | cc(X5)
        | ~ ca_Ax2(X4) )
      & ( rr(X4,esk2_1(X4))
        | ca_Ax2(X4) )
      & ( ~ cc(esk2_1(X4))
        | ca_Ax2(X4) ) ),
    inference(distribute,[status(thm)],[35]) ).

cnf(37,plain,
    ( ca_Ax2(X1)
    | ~ cc(esk2_1(X1)) ),
    inference(split_conjunct,[status(thm)],[36]) ).

cnf(38,plain,
    ( ca_Ax2(X1)
    | rr(X1,esk2_1(X1)) ),
    inference(split_conjunct,[status(thm)],[36]) ).

fof(40,plain,
    ! [X1] :
      ( ~ cc(X1)
      | ! [X3] :
          ( ~ rr(X1,X3)
          | cc(X3) ) ),
    inference(fof_nnf,[status(thm)],[7]) ).

fof(41,plain,
    ! [X4] :
      ( ~ cc(X4)
      | ! [X5] :
          ( ~ rr(X4,X5)
          | cc(X5) ) ),
    inference(variable_rename,[status(thm)],[40]) ).

fof(42,plain,
    ! [X4,X5] :
      ( ~ rr(X4,X5)
      | cc(X5)
      | ~ cc(X4) ),
    inference(shift_quantors,[status(thm)],[41]) ).

cnf(43,plain,
    ( cc(X2)
    | ~ cc(X1)
    | ~ rr(X1,X2) ),
    inference(split_conjunct,[status(thm)],[42]) ).

fof(44,plain,
    ! [X1] :
      ( ( ~ cd(X1)
        | ! [X3] : ~ ra_Px1(X1,X3) )
      & ( ? [X3] : ra_Px1(X1,X3)
        | cd(X1) ) ),
    inference(fof_nnf,[status(thm)],[8]) ).

fof(45,plain,
    ! [X4] :
      ( ( ~ cd(X4)
        | ! [X5] : ~ ra_Px1(X4,X5) )
      & ( ? [X6] : ra_Px1(X4,X6)
        | cd(X4) ) ),
    inference(variable_rename,[status(thm)],[44]) ).

fof(46,plain,
    ! [X4] :
      ( ( ~ cd(X4)
        | ! [X5] : ~ ra_Px1(X4,X5) )
      & ( ra_Px1(X4,esk3_1(X4))
        | cd(X4) ) ),
    inference(skolemize,[status(esa)],[45]) ).

fof(47,plain,
    ! [X4,X5] :
      ( ( ~ ra_Px1(X4,X5)
        | ~ cd(X4) )
      & ( ra_Px1(X4,esk3_1(X4))
        | cd(X4) ) ),
    inference(shift_quantors,[status(thm)],[46]) ).

cnf(49,plain,
    ( ~ cd(X1)
    | ~ ra_Px1(X1,X2) ),
    inference(split_conjunct,[status(thm)],[47]) ).

fof(50,plain,
    ! [X1] :
      ( ~ ca_Ax2(X1)
      | cd(X1) ),
    inference(fof_nnf,[status(thm)],[9]) ).

fof(51,plain,
    ! [X2] :
      ( ~ ca_Ax2(X2)
      | cd(X2) ),
    inference(variable_rename,[status(thm)],[50]) ).

cnf(52,plain,
    ( cd(X1)
    | ~ ca_Ax2(X1) ),
    inference(split_conjunct,[status(thm)],[51]) ).

cnf(53,plain,
    cUnsatisfiable(i2003_11_14_17_20_53634),
    inference(split_conjunct,[status(thm)],[10]) ).

cnf(54,plain,
    cc(i2003_11_14_17_20_53634),
    inference(spm,[status(thm)],[18,53,theory(equality)]) ).

cnf(59,plain,
    ( ~ cd(X1)
    | ~ cdxcomp(X1) ),
    inference(spm,[status(thm)],[49,30,theory(equality)]) ).

cnf(60,plain,
    ( cc(esk2_1(X1))
    | ca_Ax2(X1)
    | ~ cc(X1) ),
    inference(spm,[status(thm)],[43,38,theory(equality)]) ).

cnf(62,plain,
    ( ~ cd(X1)
    | ~ cUnsatisfiable(X1) ),
    inference(spm,[status(thm)],[59,15,theory(equality)]) ).

cnf(64,plain,
    ( ~ cUnsatisfiable(X1)
    | ~ ca_Ax2(X1) ),
    inference(spm,[status(thm)],[62,52,theory(equality)]) ).

cnf(65,plain,
    ~ ca_Ax2(i2003_11_14_17_20_53634),
    inference(spm,[status(thm)],[64,53,theory(equality)]) ).

cnf(66,plain,
    ( ca_Ax2(X1)
    | ~ cc(X1) ),
    inference(csr,[status(thm)],[60,37]) ).

cnf(67,plain,
    ~ cc(i2003_11_14_17_20_53634),
    inference(spm,[status(thm)],[65,66,theory(equality)]) ).

cnf(68,plain,
    $false,
    inference(rw,[status(thm)],[67,54,theory(equality)]) ).

cnf(69,plain,
    $false,
    inference(cn,[status(thm)],[68,theory(equality)]) ).

cnf(70,plain,
    $false,
    69,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KRS/KRS105+1.p
% --creating new selector for []
% -running prover on /tmp/tmpqLJ1fB/sel_KRS105+1.p_1 with time limit 29
% -prover status Unsatisfiable
% Problem KRS105+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KRS/KRS105+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KRS/KRS105+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
% 
%------------------------------------------------------------------------------