TSTP Solution File: KRS114+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : KRS114+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 13:00:29 EST 2010

% Result   : Unsatisfiable 0.17s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   63 (   5 unt;   0 def)
%            Number of atoms       :  293 (  15 equ)
%            Maximal formula atoms :   20 (   4 avg)
%            Number of connectives :  377 ( 147   ~; 143   |;  78   &)
%                                         (   7 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   13 (  11 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   1 con; 0-1 aty)
%            Number of variables   :  130 (   2 sgn  79   !;  21   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2] :
      ( rinvR(X1,X2)
    <=> rr(X2,X1) ),
    file('/tmp/tmpibZxSv/sel_KRS114+1.p_1',axiom_10) ).

fof(2,axiom,
    cUnsatisfiable(i2003_11_14_17_21_262),
    file('/tmp/tmpibZxSv/sel_KRS114+1.p_1',axiom_11) ).

fof(9,axiom,
    ! [X1] :
      ( cp(X1)
    <=> ~ ? [X2] : ra_Px1(X1,X2) ),
    file('/tmp/tmpibZxSv/sel_KRS114+1.p_1',axiom_3) ).

fof(13,axiom,
    ! [X1] :
      ( ca_Ax3(X1)
    <=> ( cqxcomp(X1)
        & cpxcomp(X1) ) ),
    file('/tmp/tmpibZxSv/sel_KRS114+1.p_1',axiom_7) ).

fof(14,axiom,
    ! [X1] :
      ( cpxcomp(X1)
    <=> ? [X6] : ra_Px1(X1,X6) ),
    file('/tmp/tmpibZxSv/sel_KRS114+1.p_1',axiom_4) ).

fof(16,axiom,
    ! [X1] :
      ( ca_Ax4(X1)
    <=> ( ! [X6,X7] :
            ( ( rinvR(X1,X6)
              & rinvR(X1,X7) )
           => X6 = X7 )
        & ? [X2] :
            ( rinvR(X1,X2)
            & ca_Vx5(X2) ) ) ),
    file('/tmp/tmpibZxSv/sel_KRS114+1.p_1',axiom_8) ).

fof(17,axiom,
    ! [X1] :
      ( ca_Vx5(X1)
    <=> ! [X2] :
          ( rs(X1,X2)
         => cp(X2) ) ),
    file('/tmp/tmpibZxSv/sel_KRS114+1.p_1',axiom_9) ).

fof(30,axiom,
    ! [X1] :
      ( cUnsatisfiable(X1)
    <=> ( ? [X2] :
            ( rr(X1,X2)
            & ca_Ax4(X2) )
        & ? [X2] :
            ( rs(X1,X2)
            & ca_Ax3(X2) ) ) ),
    file('/tmp/tmpibZxSv/sel_KRS114+1.p_1',axiom_2) ).

fof(37,plain,
    ! [X1,X2] :
      ( ( ~ rinvR(X1,X2)
        | rr(X2,X1) )
      & ( ~ rr(X2,X1)
        | rinvR(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[1]) ).

fof(38,plain,
    ! [X3,X4] :
      ( ( ~ rinvR(X3,X4)
        | rr(X4,X3) )
      & ( ~ rr(X4,X3)
        | rinvR(X3,X4) ) ),
    inference(variable_rename,[status(thm)],[37]) ).

cnf(39,plain,
    ( rinvR(X1,X2)
    | ~ rr(X2,X1) ),
    inference(split_conjunct,[status(thm)],[38]) ).

cnf(41,plain,
    cUnsatisfiable(i2003_11_14_17_21_262),
    inference(split_conjunct,[status(thm)],[2]) ).

fof(60,plain,
    ! [X1] :
      ( ( ~ cp(X1)
        | ! [X2] : ~ ra_Px1(X1,X2) )
      & ( ? [X2] : ra_Px1(X1,X2)
        | cp(X1) ) ),
    inference(fof_nnf,[status(thm)],[9]) ).

fof(61,plain,
    ! [X3] :
      ( ( ~ cp(X3)
        | ! [X4] : ~ ra_Px1(X3,X4) )
      & ( ? [X5] : ra_Px1(X3,X5)
        | cp(X3) ) ),
    inference(variable_rename,[status(thm)],[60]) ).

fof(62,plain,
    ! [X3] :
      ( ( ~ cp(X3)
        | ! [X4] : ~ ra_Px1(X3,X4) )
      & ( ra_Px1(X3,esk1_1(X3))
        | cp(X3) ) ),
    inference(skolemize,[status(esa)],[61]) ).

fof(63,plain,
    ! [X3,X4] :
      ( ( ~ ra_Px1(X3,X4)
        | ~ cp(X3) )
      & ( ra_Px1(X3,esk1_1(X3))
        | cp(X3) ) ),
    inference(shift_quantors,[status(thm)],[62]) ).

cnf(65,plain,
    ( ~ cp(X1)
    | ~ ra_Px1(X1,X2) ),
    inference(split_conjunct,[status(thm)],[63]) ).

fof(78,plain,
    ! [X1] :
      ( ( ~ ca_Ax3(X1)
        | ( cqxcomp(X1)
          & cpxcomp(X1) ) )
      & ( ~ cqxcomp(X1)
        | ~ cpxcomp(X1)
        | ca_Ax3(X1) ) ),
    inference(fof_nnf,[status(thm)],[13]) ).

fof(79,plain,
    ! [X2] :
      ( ( ~ ca_Ax3(X2)
        | ( cqxcomp(X2)
          & cpxcomp(X2) ) )
      & ( ~ cqxcomp(X2)
        | ~ cpxcomp(X2)
        | ca_Ax3(X2) ) ),
    inference(variable_rename,[status(thm)],[78]) ).

fof(80,plain,
    ! [X2] :
      ( ( cqxcomp(X2)
        | ~ ca_Ax3(X2) )
      & ( cpxcomp(X2)
        | ~ ca_Ax3(X2) )
      & ( ~ cqxcomp(X2)
        | ~ cpxcomp(X2)
        | ca_Ax3(X2) ) ),
    inference(distribute,[status(thm)],[79]) ).

cnf(82,plain,
    ( cpxcomp(X1)
    | ~ ca_Ax3(X1) ),
    inference(split_conjunct,[status(thm)],[80]) ).

fof(84,plain,
    ! [X1] :
      ( ( ~ cpxcomp(X1)
        | ? [X6] : ra_Px1(X1,X6) )
      & ( ! [X6] : ~ ra_Px1(X1,X6)
        | cpxcomp(X1) ) ),
    inference(fof_nnf,[status(thm)],[14]) ).

fof(85,plain,
    ! [X7] :
      ( ( ~ cpxcomp(X7)
        | ? [X8] : ra_Px1(X7,X8) )
      & ( ! [X9] : ~ ra_Px1(X7,X9)
        | cpxcomp(X7) ) ),
    inference(variable_rename,[status(thm)],[84]) ).

fof(86,plain,
    ! [X7] :
      ( ( ~ cpxcomp(X7)
        | ra_Px1(X7,esk3_1(X7)) )
      & ( ! [X9] : ~ ra_Px1(X7,X9)
        | cpxcomp(X7) ) ),
    inference(skolemize,[status(esa)],[85]) ).

fof(87,plain,
    ! [X7,X9] :
      ( ( ~ ra_Px1(X7,X9)
        | cpxcomp(X7) )
      & ( ~ cpxcomp(X7)
        | ra_Px1(X7,esk3_1(X7)) ) ),
    inference(shift_quantors,[status(thm)],[86]) ).

cnf(88,plain,
    ( ra_Px1(X1,esk3_1(X1))
    | ~ cpxcomp(X1) ),
    inference(split_conjunct,[status(thm)],[87]) ).

fof(96,plain,
    ! [X1] :
      ( ( ~ ca_Ax4(X1)
        | ( ! [X6,X7] :
              ( ~ rinvR(X1,X6)
              | ~ rinvR(X1,X7)
              | X6 = X7 )
          & ? [X2] :
              ( rinvR(X1,X2)
              & ca_Vx5(X2) ) ) )
      & ( ? [X6,X7] :
            ( rinvR(X1,X6)
            & rinvR(X1,X7)
            & X6 != X7 )
        | ! [X2] :
            ( ~ rinvR(X1,X2)
            | ~ ca_Vx5(X2) )
        | ca_Ax4(X1) ) ),
    inference(fof_nnf,[status(thm)],[16]) ).

fof(97,plain,
    ! [X8] :
      ( ( ~ ca_Ax4(X8)
        | ( ! [X9,X10] :
              ( ~ rinvR(X8,X9)
              | ~ rinvR(X8,X10)
              | X9 = X10 )
          & ? [X11] :
              ( rinvR(X8,X11)
              & ca_Vx5(X11) ) ) )
      & ( ? [X12,X13] :
            ( rinvR(X8,X12)
            & rinvR(X8,X13)
            & X12 != X13 )
        | ! [X14] :
            ( ~ rinvR(X8,X14)
            | ~ ca_Vx5(X14) )
        | ca_Ax4(X8) ) ),
    inference(variable_rename,[status(thm)],[96]) ).

fof(98,plain,
    ! [X8] :
      ( ( ~ ca_Ax4(X8)
        | ( ! [X9,X10] :
              ( ~ rinvR(X8,X9)
              | ~ rinvR(X8,X10)
              | X9 = X10 )
          & rinvR(X8,esk5_1(X8))
          & ca_Vx5(esk5_1(X8)) ) )
      & ( ( rinvR(X8,esk6_1(X8))
          & rinvR(X8,esk7_1(X8))
          & esk6_1(X8) != esk7_1(X8) )
        | ! [X14] :
            ( ~ rinvR(X8,X14)
            | ~ ca_Vx5(X14) )
        | ca_Ax4(X8) ) ),
    inference(skolemize,[status(esa)],[97]) ).

fof(99,plain,
    ! [X8,X9,X10,X14] :
      ( ( ~ rinvR(X8,X14)
        | ~ ca_Vx5(X14)
        | ( rinvR(X8,esk6_1(X8))
          & rinvR(X8,esk7_1(X8))
          & esk6_1(X8) != esk7_1(X8) )
        | ca_Ax4(X8) )
      & ( ( ( ~ rinvR(X8,X9)
            | ~ rinvR(X8,X10)
            | X9 = X10 )
          & rinvR(X8,esk5_1(X8))
          & ca_Vx5(esk5_1(X8)) )
        | ~ ca_Ax4(X8) ) ),
    inference(shift_quantors,[status(thm)],[98]) ).

fof(100,plain,
    ! [X8,X9,X10,X14] :
      ( ( rinvR(X8,esk6_1(X8))
        | ~ rinvR(X8,X14)
        | ~ ca_Vx5(X14)
        | ca_Ax4(X8) )
      & ( rinvR(X8,esk7_1(X8))
        | ~ rinvR(X8,X14)
        | ~ ca_Vx5(X14)
        | ca_Ax4(X8) )
      & ( esk6_1(X8) != esk7_1(X8)
        | ~ rinvR(X8,X14)
        | ~ ca_Vx5(X14)
        | ca_Ax4(X8) )
      & ( ~ rinvR(X8,X9)
        | ~ rinvR(X8,X10)
        | X9 = X10
        | ~ ca_Ax4(X8) )
      & ( rinvR(X8,esk5_1(X8))
        | ~ ca_Ax4(X8) )
      & ( ca_Vx5(esk5_1(X8))
        | ~ ca_Ax4(X8) ) ),
    inference(distribute,[status(thm)],[99]) ).

cnf(101,plain,
    ( ca_Vx5(esk5_1(X1))
    | ~ ca_Ax4(X1) ),
    inference(split_conjunct,[status(thm)],[100]) ).

cnf(102,plain,
    ( rinvR(X1,esk5_1(X1))
    | ~ ca_Ax4(X1) ),
    inference(split_conjunct,[status(thm)],[100]) ).

cnf(103,plain,
    ( X2 = X3
    | ~ ca_Ax4(X1)
    | ~ rinvR(X1,X3)
    | ~ rinvR(X1,X2) ),
    inference(split_conjunct,[status(thm)],[100]) ).

fof(107,plain,
    ! [X1] :
      ( ( ~ ca_Vx5(X1)
        | ! [X2] :
            ( ~ rs(X1,X2)
            | cp(X2) ) )
      & ( ? [X2] :
            ( rs(X1,X2)
            & ~ cp(X2) )
        | ca_Vx5(X1) ) ),
    inference(fof_nnf,[status(thm)],[17]) ).

fof(108,plain,
    ! [X3] :
      ( ( ~ ca_Vx5(X3)
        | ! [X4] :
            ( ~ rs(X3,X4)
            | cp(X4) ) )
      & ( ? [X5] :
            ( rs(X3,X5)
            & ~ cp(X5) )
        | ca_Vx5(X3) ) ),
    inference(variable_rename,[status(thm)],[107]) ).

fof(109,plain,
    ! [X3] :
      ( ( ~ ca_Vx5(X3)
        | ! [X4] :
            ( ~ rs(X3,X4)
            | cp(X4) ) )
      & ( ( rs(X3,esk8_1(X3))
          & ~ cp(esk8_1(X3)) )
        | ca_Vx5(X3) ) ),
    inference(skolemize,[status(esa)],[108]) ).

fof(110,plain,
    ! [X3,X4] :
      ( ( ~ rs(X3,X4)
        | cp(X4)
        | ~ ca_Vx5(X3) )
      & ( ( rs(X3,esk8_1(X3))
          & ~ cp(esk8_1(X3)) )
        | ca_Vx5(X3) ) ),
    inference(shift_quantors,[status(thm)],[109]) ).

fof(111,plain,
    ! [X3,X4] :
      ( ( ~ rs(X3,X4)
        | cp(X4)
        | ~ ca_Vx5(X3) )
      & ( rs(X3,esk8_1(X3))
        | ca_Vx5(X3) )
      & ( ~ cp(esk8_1(X3))
        | ca_Vx5(X3) ) ),
    inference(distribute,[status(thm)],[110]) ).

cnf(114,plain,
    ( cp(X2)
    | ~ ca_Vx5(X1)
    | ~ rs(X1,X2) ),
    inference(split_conjunct,[status(thm)],[111]) ).

fof(151,plain,
    ! [X1] :
      ( ( ~ cUnsatisfiable(X1)
        | ( ? [X2] :
              ( rr(X1,X2)
              & ca_Ax4(X2) )
          & ? [X2] :
              ( rs(X1,X2)
              & ca_Ax3(X2) ) ) )
      & ( ! [X2] :
            ( ~ rr(X1,X2)
            | ~ ca_Ax4(X2) )
        | ! [X2] :
            ( ~ rs(X1,X2)
            | ~ ca_Ax3(X2) )
        | cUnsatisfiable(X1) ) ),
    inference(fof_nnf,[status(thm)],[30]) ).

fof(152,plain,
    ! [X3] :
      ( ( ~ cUnsatisfiable(X3)
        | ( ? [X4] :
              ( rr(X3,X4)
              & ca_Ax4(X4) )
          & ? [X5] :
              ( rs(X3,X5)
              & ca_Ax3(X5) ) ) )
      & ( ! [X6] :
            ( ~ rr(X3,X6)
            | ~ ca_Ax4(X6) )
        | ! [X7] :
            ( ~ rs(X3,X7)
            | ~ ca_Ax3(X7) )
        | cUnsatisfiable(X3) ) ),
    inference(variable_rename,[status(thm)],[151]) ).

fof(153,plain,
    ! [X3] :
      ( ( ~ cUnsatisfiable(X3)
        | ( rr(X3,esk9_1(X3))
          & ca_Ax4(esk9_1(X3))
          & rs(X3,esk10_1(X3))
          & ca_Ax3(esk10_1(X3)) ) )
      & ( ! [X6] :
            ( ~ rr(X3,X6)
            | ~ ca_Ax4(X6) )
        | ! [X7] :
            ( ~ rs(X3,X7)
            | ~ ca_Ax3(X7) )
        | cUnsatisfiable(X3) ) ),
    inference(skolemize,[status(esa)],[152]) ).

fof(154,plain,
    ! [X3,X6,X7] :
      ( ( ~ rs(X3,X7)
        | ~ ca_Ax3(X7)
        | ~ rr(X3,X6)
        | ~ ca_Ax4(X6)
        | cUnsatisfiable(X3) )
      & ( ~ cUnsatisfiable(X3)
        | ( rr(X3,esk9_1(X3))
          & ca_Ax4(esk9_1(X3))
          & rs(X3,esk10_1(X3))
          & ca_Ax3(esk10_1(X3)) ) ) ),
    inference(shift_quantors,[status(thm)],[153]) ).

fof(155,plain,
    ! [X3,X6,X7] :
      ( ( ~ rs(X3,X7)
        | ~ ca_Ax3(X7)
        | ~ rr(X3,X6)
        | ~ ca_Ax4(X6)
        | cUnsatisfiable(X3) )
      & ( rr(X3,esk9_1(X3))
        | ~ cUnsatisfiable(X3) )
      & ( ca_Ax4(esk9_1(X3))
        | ~ cUnsatisfiable(X3) )
      & ( rs(X3,esk10_1(X3))
        | ~ cUnsatisfiable(X3) )
      & ( ca_Ax3(esk10_1(X3))
        | ~ cUnsatisfiable(X3) ) ),
    inference(distribute,[status(thm)],[154]) ).

cnf(156,plain,
    ( ca_Ax3(esk10_1(X1))
    | ~ cUnsatisfiable(X1) ),
    inference(split_conjunct,[status(thm)],[155]) ).

cnf(157,plain,
    ( rs(X1,esk10_1(X1))
    | ~ cUnsatisfiable(X1) ),
    inference(split_conjunct,[status(thm)],[155]) ).

cnf(158,plain,
    ( ca_Ax4(esk9_1(X1))
    | ~ cUnsatisfiable(X1) ),
    inference(split_conjunct,[status(thm)],[155]) ).

cnf(159,plain,
    ( rr(X1,esk9_1(X1))
    | ~ cUnsatisfiable(X1) ),
    inference(split_conjunct,[status(thm)],[155]) ).

cnf(181,plain,
    ( rinvR(esk9_1(X1),X1)
    | ~ cUnsatisfiable(X1) ),
    inference(spm,[status(thm)],[39,159,theory(equality)]) ).

cnf(185,plain,
    ( ~ cp(X1)
    | ~ cpxcomp(X1) ),
    inference(spm,[status(thm)],[65,88,theory(equality)]) ).

cnf(187,plain,
    ( cp(esk10_1(X1))
    | ~ ca_Vx5(X1)
    | ~ cUnsatisfiable(X1) ),
    inference(spm,[status(thm)],[114,157,theory(equality)]) ).

cnf(189,plain,
    ( X1 = esk5_1(X2)
    | ~ ca_Ax4(X2)
    | ~ rinvR(X2,X1) ),
    inference(spm,[status(thm)],[103,102,theory(equality)]) ).

cnf(201,plain,
    ( ~ cp(X1)
    | ~ ca_Ax3(X1) ),
    inference(spm,[status(thm)],[185,82,theory(equality)]) ).

cnf(203,plain,
    ( ~ ca_Ax3(esk10_1(X1))
    | ~ ca_Vx5(X1)
    | ~ cUnsatisfiable(X1) ),
    inference(spm,[status(thm)],[201,187,theory(equality)]) ).

cnf(204,plain,
    ( ~ ca_Vx5(X1)
    | ~ cUnsatisfiable(X1) ),
    inference(csr,[status(thm)],[203,156]) ).

cnf(206,plain,
    ( X1 = esk5_1(esk9_1(X1))
    | ~ ca_Ax4(esk9_1(X1))
    | ~ cUnsatisfiable(X1) ),
    inference(spm,[status(thm)],[189,181,theory(equality)]) ).

cnf(207,plain,
    ( esk5_1(esk9_1(X1)) = X1
    | ~ cUnsatisfiable(X1) ),
    inference(csr,[status(thm)],[206,158]) ).

cnf(208,plain,
    ( ca_Vx5(X1)
    | ~ ca_Ax4(esk9_1(X1))
    | ~ cUnsatisfiable(X1) ),
    inference(spm,[status(thm)],[101,207,theory(equality)]) ).

cnf(210,plain,
    ( ca_Vx5(X1)
    | ~ cUnsatisfiable(X1) ),
    inference(csr,[status(thm)],[208,158]) ).

cnf(211,plain,
    ~ cUnsatisfiable(X1),
    inference(csr,[status(thm)],[210,204]) ).

cnf(212,plain,
    $false,
    inference(sr,[status(thm)],[41,211,theory(equality)]) ).

cnf(213,plain,
    $false,
    212,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KRS/KRS114+1.p
% --creating new selector for []
% -running prover on /tmp/tmpibZxSv/sel_KRS114+1.p_1 with time limit 29
% -prover status Unsatisfiable
% Problem KRS114+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KRS/KRS114+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KRS/KRS114+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
% 
%------------------------------------------------------------------------------