TSTP Solution File: COM017+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : COM017+1 : TPTP v5.0.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art01.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 05:47:54 EST 2010

% Result   : Theorem 0.29s
% Output   : CNFRefutation 0.29s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   52 (   8 unt;   0 def)
%            Number of atoms       :  319 (   0 equ)
%            Maximal formula atoms :   44 (   6 avg)
%            Number of connectives :  473 ( 206   ~; 204   |;  58   &)
%                                         (   1 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-4 aty)
%            Number of variables   :  110 (   0 sgn  43   !;  11   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(4,axiom,
    aRewritingSystem0(xR),
    file('/tmp/tmpvZwfpk/sel_COM017+1.p_1',m__656) ).

fof(5,axiom,
    ! [X1,X2] :
      ( ( aElement0(X1)
        & aRewritingSystem0(X2) )
     => ! [X3] :
          ( aReductOfIn0(X3,X1,X2)
         => aElement0(X3) ) ),
    file('/tmp/tmpvZwfpk/sel_COM017+1.p_1',mReduct) ).

fof(8,axiom,
    ! [X1] :
      ( aRewritingSystem0(X1)
     => ( isLocallyConfluent0(X1)
      <=> ! [X2,X3,X4] :
            ( ( aElement0(X2)
              & aElement0(X3)
              & aElement0(X4)
              & aReductOfIn0(X3,X2,X1)
              & aReductOfIn0(X4,X2,X1) )
           => ? [X5] :
                ( aElement0(X5)
                & sdtmndtasgtdt0(X3,X1,X5)
                & sdtmndtasgtdt0(X4,X1,X5) ) ) ) ),
    file('/tmp/tmpvZwfpk/sel_COM017+1.p_1',mWCRDef) ).

fof(11,conjecture,
    ? [X1] :
      ( aElement0(X1)
      & sdtmndtasgtdt0(xu,xR,X1)
      & sdtmndtasgtdt0(xv,xR,X1) ),
    file('/tmp/tmpvZwfpk/sel_COM017+1.p_1',m__) ).

fof(12,axiom,
    ( aElement0(xa)
    & aElement0(xb)
    & aElement0(xc) ),
    file('/tmp/tmpvZwfpk/sel_COM017+1.p_1',m__731) ).

fof(13,axiom,
    ( aElement0(xu)
    & aReductOfIn0(xu,xa,xR)
    & sdtmndtasgtdt0(xu,xR,xb) ),
    file('/tmp/tmpvZwfpk/sel_COM017+1.p_1',m__755) ).

fof(14,axiom,
    ( aElement0(xv)
    & aReductOfIn0(xv,xa,xR)
    & sdtmndtasgtdt0(xv,xR,xc) ),
    file('/tmp/tmpvZwfpk/sel_COM017+1.p_1',m__779) ).

fof(20,axiom,
    ( isLocallyConfluent0(xR)
    & isTerminating0(xR) ),
    file('/tmp/tmpvZwfpk/sel_COM017+1.p_1',m__656_01) ).

fof(23,negated_conjecture,
    ~ ? [X1] :
        ( aElement0(X1)
        & sdtmndtasgtdt0(xu,xR,X1)
        & sdtmndtasgtdt0(xv,xR,X1) ),
    inference(assume_negation,[status(cth)],[11]) ).

cnf(48,plain,
    aRewritingSystem0(xR),
    inference(split_conjunct,[status(thm)],[4]) ).

fof(49,plain,
    ! [X1,X2] :
      ( ~ aElement0(X1)
      | ~ aRewritingSystem0(X2)
      | ! [X3] :
          ( ~ aReductOfIn0(X3,X1,X2)
          | aElement0(X3) ) ),
    inference(fof_nnf,[status(thm)],[5]) ).

fof(50,plain,
    ! [X4,X5] :
      ( ~ aElement0(X4)
      | ~ aRewritingSystem0(X5)
      | ! [X6] :
          ( ~ aReductOfIn0(X6,X4,X5)
          | aElement0(X6) ) ),
    inference(variable_rename,[status(thm)],[49]) ).

fof(51,plain,
    ! [X4,X5,X6] :
      ( ~ aReductOfIn0(X6,X4,X5)
      | aElement0(X6)
      | ~ aElement0(X4)
      | ~ aRewritingSystem0(X5) ),
    inference(shift_quantors,[status(thm)],[50]) ).

cnf(52,plain,
    ( aElement0(X3)
    | ~ aRewritingSystem0(X1)
    | ~ aElement0(X2)
    | ~ aReductOfIn0(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[51]) ).

fof(64,plain,
    ! [X1] :
      ( ~ aRewritingSystem0(X1)
      | ( ( ~ isLocallyConfluent0(X1)
          | ! [X2,X3,X4] :
              ( ~ aElement0(X2)
              | ~ aElement0(X3)
              | ~ aElement0(X4)
              | ~ aReductOfIn0(X3,X2,X1)
              | ~ aReductOfIn0(X4,X2,X1)
              | ? [X5] :
                  ( aElement0(X5)
                  & sdtmndtasgtdt0(X3,X1,X5)
                  & sdtmndtasgtdt0(X4,X1,X5) ) ) )
        & ( ? [X2,X3,X4] :
              ( aElement0(X2)
              & aElement0(X3)
              & aElement0(X4)
              & aReductOfIn0(X3,X2,X1)
              & aReductOfIn0(X4,X2,X1)
              & ! [X5] :
                  ( ~ aElement0(X5)
                  | ~ sdtmndtasgtdt0(X3,X1,X5)
                  | ~ sdtmndtasgtdt0(X4,X1,X5) ) )
          | isLocallyConfluent0(X1) ) ) ),
    inference(fof_nnf,[status(thm)],[8]) ).

fof(65,plain,
    ! [X6] :
      ( ~ aRewritingSystem0(X6)
      | ( ( ~ isLocallyConfluent0(X6)
          | ! [X7,X8,X9] :
              ( ~ aElement0(X7)
              | ~ aElement0(X8)
              | ~ aElement0(X9)
              | ~ aReductOfIn0(X8,X7,X6)
              | ~ aReductOfIn0(X9,X7,X6)
              | ? [X10] :
                  ( aElement0(X10)
                  & sdtmndtasgtdt0(X8,X6,X10)
                  & sdtmndtasgtdt0(X9,X6,X10) ) ) )
        & ( ? [X11,X12,X13] :
              ( aElement0(X11)
              & aElement0(X12)
              & aElement0(X13)
              & aReductOfIn0(X12,X11,X6)
              & aReductOfIn0(X13,X11,X6)
              & ! [X14] :
                  ( ~ aElement0(X14)
                  | ~ sdtmndtasgtdt0(X12,X6,X14)
                  | ~ sdtmndtasgtdt0(X13,X6,X14) ) )
          | isLocallyConfluent0(X6) ) ) ),
    inference(variable_rename,[status(thm)],[64]) ).

fof(66,plain,
    ! [X6] :
      ( ~ aRewritingSystem0(X6)
      | ( ( ~ isLocallyConfluent0(X6)
          | ! [X7,X8,X9] :
              ( ~ aElement0(X7)
              | ~ aElement0(X8)
              | ~ aElement0(X9)
              | ~ aReductOfIn0(X8,X7,X6)
              | ~ aReductOfIn0(X9,X7,X6)
              | ( aElement0(esk7_4(X6,X7,X8,X9))
                & sdtmndtasgtdt0(X8,X6,esk7_4(X6,X7,X8,X9))
                & sdtmndtasgtdt0(X9,X6,esk7_4(X6,X7,X8,X9)) ) ) )
        & ( ( aElement0(esk8_1(X6))
            & aElement0(esk9_1(X6))
            & aElement0(esk10_1(X6))
            & aReductOfIn0(esk9_1(X6),esk8_1(X6),X6)
            & aReductOfIn0(esk10_1(X6),esk8_1(X6),X6)
            & ! [X14] :
                ( ~ aElement0(X14)
                | ~ sdtmndtasgtdt0(esk9_1(X6),X6,X14)
                | ~ sdtmndtasgtdt0(esk10_1(X6),X6,X14) ) )
          | isLocallyConfluent0(X6) ) ) ),
    inference(skolemize,[status(esa)],[65]) ).

fof(67,plain,
    ! [X6,X7,X8,X9,X14] :
      ( ( ( ( ( ~ aElement0(X14)
              | ~ sdtmndtasgtdt0(esk9_1(X6),X6,X14)
              | ~ sdtmndtasgtdt0(esk10_1(X6),X6,X14) )
            & aElement0(esk8_1(X6))
            & aElement0(esk9_1(X6))
            & aElement0(esk10_1(X6))
            & aReductOfIn0(esk9_1(X6),esk8_1(X6),X6)
            & aReductOfIn0(esk10_1(X6),esk8_1(X6),X6) )
          | isLocallyConfluent0(X6) )
        & ( ~ aElement0(X7)
          | ~ aElement0(X8)
          | ~ aElement0(X9)
          | ~ aReductOfIn0(X8,X7,X6)
          | ~ aReductOfIn0(X9,X7,X6)
          | ( aElement0(esk7_4(X6,X7,X8,X9))
            & sdtmndtasgtdt0(X8,X6,esk7_4(X6,X7,X8,X9))
            & sdtmndtasgtdt0(X9,X6,esk7_4(X6,X7,X8,X9)) )
          | ~ isLocallyConfluent0(X6) ) )
      | ~ aRewritingSystem0(X6) ),
    inference(shift_quantors,[status(thm)],[66]) ).

fof(68,plain,
    ! [X6,X7,X8,X9,X14] :
      ( ( ~ aElement0(X14)
        | ~ sdtmndtasgtdt0(esk9_1(X6),X6,X14)
        | ~ sdtmndtasgtdt0(esk10_1(X6),X6,X14)
        | isLocallyConfluent0(X6)
        | ~ aRewritingSystem0(X6) )
      & ( aElement0(esk8_1(X6))
        | isLocallyConfluent0(X6)
        | ~ aRewritingSystem0(X6) )
      & ( aElement0(esk9_1(X6))
        | isLocallyConfluent0(X6)
        | ~ aRewritingSystem0(X6) )
      & ( aElement0(esk10_1(X6))
        | isLocallyConfluent0(X6)
        | ~ aRewritingSystem0(X6) )
      & ( aReductOfIn0(esk9_1(X6),esk8_1(X6),X6)
        | isLocallyConfluent0(X6)
        | ~ aRewritingSystem0(X6) )
      & ( aReductOfIn0(esk10_1(X6),esk8_1(X6),X6)
        | isLocallyConfluent0(X6)
        | ~ aRewritingSystem0(X6) )
      & ( aElement0(esk7_4(X6,X7,X8,X9))
        | ~ aElement0(X7)
        | ~ aElement0(X8)
        | ~ aElement0(X9)
        | ~ aReductOfIn0(X8,X7,X6)
        | ~ aReductOfIn0(X9,X7,X6)
        | ~ isLocallyConfluent0(X6)
        | ~ aRewritingSystem0(X6) )
      & ( sdtmndtasgtdt0(X8,X6,esk7_4(X6,X7,X8,X9))
        | ~ aElement0(X7)
        | ~ aElement0(X8)
        | ~ aElement0(X9)
        | ~ aReductOfIn0(X8,X7,X6)
        | ~ aReductOfIn0(X9,X7,X6)
        | ~ isLocallyConfluent0(X6)
        | ~ aRewritingSystem0(X6) )
      & ( sdtmndtasgtdt0(X9,X6,esk7_4(X6,X7,X8,X9))
        | ~ aElement0(X7)
        | ~ aElement0(X8)
        | ~ aElement0(X9)
        | ~ aReductOfIn0(X8,X7,X6)
        | ~ aReductOfIn0(X9,X7,X6)
        | ~ isLocallyConfluent0(X6)
        | ~ aRewritingSystem0(X6) ) ),
    inference(distribute,[status(thm)],[67]) ).

cnf(69,plain,
    ( sdtmndtasgtdt0(X2,X1,esk7_4(X1,X3,X4,X2))
    | ~ aRewritingSystem0(X1)
    | ~ isLocallyConfluent0(X1)
    | ~ aReductOfIn0(X2,X3,X1)
    | ~ aReductOfIn0(X4,X3,X1)
    | ~ aElement0(X2)
    | ~ aElement0(X4)
    | ~ aElement0(X3) ),
    inference(split_conjunct,[status(thm)],[68]) ).

cnf(70,plain,
    ( sdtmndtasgtdt0(X4,X1,esk7_4(X1,X3,X4,X2))
    | ~ aRewritingSystem0(X1)
    | ~ isLocallyConfluent0(X1)
    | ~ aReductOfIn0(X2,X3,X1)
    | ~ aReductOfIn0(X4,X3,X1)
    | ~ aElement0(X2)
    | ~ aElement0(X4)
    | ~ aElement0(X3) ),
    inference(split_conjunct,[status(thm)],[68]) ).

cnf(71,plain,
    ( aElement0(esk7_4(X1,X3,X4,X2))
    | ~ aRewritingSystem0(X1)
    | ~ isLocallyConfluent0(X1)
    | ~ aReductOfIn0(X2,X3,X1)
    | ~ aReductOfIn0(X4,X3,X1)
    | ~ aElement0(X2)
    | ~ aElement0(X4)
    | ~ aElement0(X3) ),
    inference(split_conjunct,[status(thm)],[68]) ).

fof(83,negated_conjecture,
    ! [X1] :
      ( ~ aElement0(X1)
      | ~ sdtmndtasgtdt0(xu,xR,X1)
      | ~ sdtmndtasgtdt0(xv,xR,X1) ),
    inference(fof_nnf,[status(thm)],[23]) ).

fof(84,negated_conjecture,
    ! [X2] :
      ( ~ aElement0(X2)
      | ~ sdtmndtasgtdt0(xu,xR,X2)
      | ~ sdtmndtasgtdt0(xv,xR,X2) ),
    inference(variable_rename,[status(thm)],[83]) ).

cnf(85,negated_conjecture,
    ( ~ sdtmndtasgtdt0(xv,xR,X1)
    | ~ sdtmndtasgtdt0(xu,xR,X1)
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[84]) ).

cnf(88,plain,
    aElement0(xa),
    inference(split_conjunct,[status(thm)],[12]) ).

cnf(90,plain,
    aReductOfIn0(xu,xa,xR),
    inference(split_conjunct,[status(thm)],[13]) ).

cnf(93,plain,
    aReductOfIn0(xv,xa,xR),
    inference(split_conjunct,[status(thm)],[14]) ).

cnf(131,plain,
    isLocallyConfluent0(xR),
    inference(split_conjunct,[status(thm)],[20]) ).

cnf(248,plain,
    ( aElement0(esk7_4(X1,X3,X4,X2))
    | ~ isLocallyConfluent0(X1)
    | ~ aReductOfIn0(X4,X3,X1)
    | ~ aReductOfIn0(X2,X3,X1)
    | ~ aElement0(X4)
    | ~ aElement0(X3)
    | ~ aRewritingSystem0(X1) ),
    inference(csr,[status(thm)],[71,52]) ).

cnf(249,plain,
    ( aElement0(esk7_4(X1,X3,X4,X2))
    | ~ isLocallyConfluent0(X1)
    | ~ aReductOfIn0(X4,X3,X1)
    | ~ aReductOfIn0(X2,X3,X1)
    | ~ aElement0(X3)
    | ~ aRewritingSystem0(X1) ),
    inference(csr,[status(thm)],[248,52]) ).

cnf(271,plain,
    ( sdtmndtasgtdt0(X4,X1,esk7_4(X1,X3,X4,X2))
    | ~ isLocallyConfluent0(X1)
    | ~ aReductOfIn0(X4,X3,X1)
    | ~ aReductOfIn0(X2,X3,X1)
    | ~ aElement0(X4)
    | ~ aElement0(X3)
    | ~ aRewritingSystem0(X1) ),
    inference(csr,[status(thm)],[70,52]) ).

cnf(272,plain,
    ( sdtmndtasgtdt0(X4,X1,esk7_4(X1,X3,X4,X2))
    | ~ isLocallyConfluent0(X1)
    | ~ aReductOfIn0(X4,X3,X1)
    | ~ aReductOfIn0(X2,X3,X1)
    | ~ aElement0(X3)
    | ~ aRewritingSystem0(X1) ),
    inference(csr,[status(thm)],[271,52]) ).

cnf(273,negated_conjecture,
    ( ~ sdtmndtasgtdt0(xu,xR,esk7_4(xR,X1,xv,X2))
    | ~ aElement0(esk7_4(xR,X1,xv,X2))
    | ~ isLocallyConfluent0(xR)
    | ~ aReductOfIn0(xv,X1,xR)
    | ~ aReductOfIn0(X2,X1,xR)
    | ~ aElement0(X1)
    | ~ aRewritingSystem0(xR) ),
    inference(spm,[status(thm)],[85,272,theory(equality)]) ).

cnf(277,negated_conjecture,
    ( ~ sdtmndtasgtdt0(xu,xR,esk7_4(xR,X1,xv,X2))
    | ~ aElement0(esk7_4(xR,X1,xv,X2))
    | $false
    | ~ aReductOfIn0(xv,X1,xR)
    | ~ aReductOfIn0(X2,X1,xR)
    | ~ aElement0(X1)
    | ~ aRewritingSystem0(xR) ),
    inference(rw,[status(thm)],[273,131,theory(equality)]) ).

cnf(278,negated_conjecture,
    ( ~ sdtmndtasgtdt0(xu,xR,esk7_4(xR,X1,xv,X2))
    | ~ aElement0(esk7_4(xR,X1,xv,X2))
    | $false
    | ~ aReductOfIn0(xv,X1,xR)
    | ~ aReductOfIn0(X2,X1,xR)
    | ~ aElement0(X1)
    | $false ),
    inference(rw,[status(thm)],[277,48,theory(equality)]) ).

cnf(279,negated_conjecture,
    ( ~ sdtmndtasgtdt0(xu,xR,esk7_4(xR,X1,xv,X2))
    | ~ aElement0(esk7_4(xR,X1,xv,X2))
    | ~ aReductOfIn0(xv,X1,xR)
    | ~ aReductOfIn0(X2,X1,xR)
    | ~ aElement0(X1) ),
    inference(cn,[status(thm)],[278,theory(equality)]) ).

cnf(280,plain,
    ( sdtmndtasgtdt0(X2,X1,esk7_4(X1,X3,X4,X2))
    | ~ isLocallyConfluent0(X1)
    | ~ aReductOfIn0(X4,X3,X1)
    | ~ aReductOfIn0(X2,X3,X1)
    | ~ aElement0(X4)
    | ~ aElement0(X3)
    | ~ aRewritingSystem0(X1) ),
    inference(csr,[status(thm)],[69,52]) ).

cnf(281,plain,
    ( sdtmndtasgtdt0(X2,X1,esk7_4(X1,X3,X4,X2))
    | ~ isLocallyConfluent0(X1)
    | ~ aReductOfIn0(X4,X3,X1)
    | ~ aReductOfIn0(X2,X3,X1)
    | ~ aElement0(X3)
    | ~ aRewritingSystem0(X1) ),
    inference(csr,[status(thm)],[280,52]) ).

cnf(989,negated_conjecture,
    ( ~ aReductOfIn0(xv,X1,xR)
    | ~ aReductOfIn0(xu,X1,xR)
    | ~ aElement0(esk7_4(xR,X1,xv,xu))
    | ~ aElement0(X1)
    | ~ isLocallyConfluent0(xR)
    | ~ aRewritingSystem0(xR) ),
    inference(spm,[status(thm)],[279,281,theory(equality)]) ).

cnf(990,negated_conjecture,
    ( ~ aReductOfIn0(xv,X1,xR)
    | ~ aReductOfIn0(xu,X1,xR)
    | ~ aElement0(esk7_4(xR,X1,xv,xu))
    | ~ aElement0(X1)
    | $false
    | ~ aRewritingSystem0(xR) ),
    inference(rw,[status(thm)],[989,131,theory(equality)]) ).

cnf(991,negated_conjecture,
    ( ~ aReductOfIn0(xv,X1,xR)
    | ~ aReductOfIn0(xu,X1,xR)
    | ~ aElement0(esk7_4(xR,X1,xv,xu))
    | ~ aElement0(X1)
    | $false
    | $false ),
    inference(rw,[status(thm)],[990,48,theory(equality)]) ).

cnf(992,negated_conjecture,
    ( ~ aReductOfIn0(xv,X1,xR)
    | ~ aReductOfIn0(xu,X1,xR)
    | ~ aElement0(esk7_4(xR,X1,xv,xu))
    | ~ aElement0(X1) ),
    inference(cn,[status(thm)],[991,theory(equality)]) ).

cnf(993,negated_conjecture,
    ( ~ aReductOfIn0(xv,X1,xR)
    | ~ aReductOfIn0(xu,X1,xR)
    | ~ aElement0(X1)
    | ~ isLocallyConfluent0(xR)
    | ~ aRewritingSystem0(xR) ),
    inference(spm,[status(thm)],[992,249,theory(equality)]) ).

cnf(994,negated_conjecture,
    ( ~ aReductOfIn0(xv,X1,xR)
    | ~ aReductOfIn0(xu,X1,xR)
    | ~ aElement0(X1)
    | $false
    | ~ aRewritingSystem0(xR) ),
    inference(rw,[status(thm)],[993,131,theory(equality)]) ).

cnf(995,negated_conjecture,
    ( ~ aReductOfIn0(xv,X1,xR)
    | ~ aReductOfIn0(xu,X1,xR)
    | ~ aElement0(X1)
    | $false
    | $false ),
    inference(rw,[status(thm)],[994,48,theory(equality)]) ).

cnf(996,negated_conjecture,
    ( ~ aReductOfIn0(xv,X1,xR)
    | ~ aReductOfIn0(xu,X1,xR)
    | ~ aElement0(X1) ),
    inference(cn,[status(thm)],[995,theory(equality)]) ).

cnf(997,plain,
    ( ~ aReductOfIn0(xu,xa,xR)
    | ~ aElement0(xa) ),
    inference(spm,[status(thm)],[996,93,theory(equality)]) ).

cnf(998,plain,
    ( $false
    | ~ aElement0(xa) ),
    inference(rw,[status(thm)],[997,90,theory(equality)]) ).

cnf(999,plain,
    ( $false
    | $false ),
    inference(rw,[status(thm)],[998,88,theory(equality)]) ).

cnf(1000,plain,
    $false,
    inference(cn,[status(thm)],[999,theory(equality)]) ).

cnf(1001,plain,
    $false,
    1000,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/COM/COM017+1.p
% --creating new selector for []
% -running prover on /tmp/tmpvZwfpk/sel_COM017+1.p_1 with time limit 29
% -prover status Theorem
% Problem COM017+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/COM/COM017+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/COM/COM017+1.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
% 
%------------------------------------------------------------------------------