TSTP Solution File: ALG177+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : ALG177+1 : TPTP v5.0.0. Released v2.7.0.
% 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 04:13:04 EST 2010

% Result   : Theorem 0.30s
% Output   : CNFRefutation 0.30s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   42 (   6 unt;   0 def)
%            Number of atoms       :  161 (  42 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  201 (  82   ~;  64   |;  33   &)
%                                         (   0 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   5 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   1 con; 0-2 aty)
%            Number of variables   :   84 (   0 sgn  58   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(2,axiom,
    ? [X1] :
      ( sorti1(X1)
      & ! [X2] :
          ( sorti1(X2)
         => op1(X1,X2) != X2 ) ),
    file('/tmp/tmptovbKj/sel_ALG177+1.p_1',ax3) ).

fof(3,conjecture,
    ( ( ! [X1] :
          ( sorti1(X1)
         => sorti2(h(X1)) )
      & ! [X2] :
          ( sorti2(X2)
         => sorti1(j(X2)) ) )
   => ~ ( ! [X3] :
            ( sorti1(X3)
           => ! [X4] :
                ( sorti1(X4)
               => h(op1(X3,X4)) = op2(h(X3),h(X4)) ) )
        & ! [X5] :
            ( sorti2(X5)
           => ! [X6] :
                ( sorti2(X6)
               => j(op2(X5,X6)) = op1(j(X5),j(X6)) ) )
        & ! [X7] :
            ( sorti2(X7)
           => h(j(X7)) = X7 )
        & ! [X8] :
            ( sorti1(X8)
           => j(h(X8)) = X8 ) ) ),
    file('/tmp/tmptovbKj/sel_ALG177+1.p_1',co1) ).

fof(4,axiom,
    ! [X1] :
      ( sorti1(X1)
     => ! [X2] :
          ( sorti1(X2)
         => sorti1(op1(X1,X2)) ) ),
    file('/tmp/tmptovbKj/sel_ALG177+1.p_1',ax1) ).

fof(5,axiom,
    ~ ? [X1] :
        ( sorti2(X1)
        & ! [X2] :
            ( sorti2(X2)
           => op2(X1,X2) != X2 ) ),
    file('/tmp/tmptovbKj/sel_ALG177+1.p_1',ax4) ).

fof(6,negated_conjecture,
    ~ ( ( ! [X1] :
            ( sorti1(X1)
           => sorti2(h(X1)) )
        & ! [X2] :
            ( sorti2(X2)
           => sorti1(j(X2)) ) )
     => ~ ( ! [X3] :
              ( sorti1(X3)
             => ! [X4] :
                  ( sorti1(X4)
                 => h(op1(X3,X4)) = op2(h(X3),h(X4)) ) )
          & ! [X5] :
              ( sorti2(X5)
             => ! [X6] :
                  ( sorti2(X6)
                 => j(op2(X5,X6)) = op1(j(X5),j(X6)) ) )
          & ! [X7] :
              ( sorti2(X7)
             => h(j(X7)) = X7 )
          & ! [X8] :
              ( sorti1(X8)
             => j(h(X8)) = X8 ) ) ),
    inference(assume_negation,[status(cth)],[3]) ).

fof(11,plain,
    ? [X1] :
      ( sorti1(X1)
      & ! [X2] :
          ( ~ sorti1(X2)
          | op1(X1,X2) != X2 ) ),
    inference(fof_nnf,[status(thm)],[2]) ).

fof(12,plain,
    ? [X3] :
      ( sorti1(X3)
      & ! [X4] :
          ( ~ sorti1(X4)
          | op1(X3,X4) != X4 ) ),
    inference(variable_rename,[status(thm)],[11]) ).

fof(13,plain,
    ( sorti1(esk1_0)
    & ! [X4] :
        ( ~ sorti1(X4)
        | op1(esk1_0,X4) != X4 ) ),
    inference(skolemize,[status(esa)],[12]) ).

fof(14,plain,
    ! [X4] :
      ( ( ~ sorti1(X4)
        | op1(esk1_0,X4) != X4 )
      & sorti1(esk1_0) ),
    inference(shift_quantors,[status(thm)],[13]) ).

cnf(15,plain,
    sorti1(esk1_0),
    inference(split_conjunct,[status(thm)],[14]) ).

cnf(16,plain,
    ( op1(esk1_0,X1) != X1
    | ~ sorti1(X1) ),
    inference(split_conjunct,[status(thm)],[14]) ).

fof(17,negated_conjecture,
    ( ! [X1] :
        ( ~ sorti1(X1)
        | sorti2(h(X1)) )
    & ! [X2] :
        ( ~ sorti2(X2)
        | sorti1(j(X2)) )
    & ! [X3] :
        ( ~ sorti1(X3)
        | ! [X4] :
            ( ~ sorti1(X4)
            | h(op1(X3,X4)) = op2(h(X3),h(X4)) ) )
    & ! [X5] :
        ( ~ sorti2(X5)
        | ! [X6] :
            ( ~ sorti2(X6)
            | j(op2(X5,X6)) = op1(j(X5),j(X6)) ) )
    & ! [X7] :
        ( ~ sorti2(X7)
        | h(j(X7)) = X7 )
    & ! [X8] :
        ( ~ sorti1(X8)
        | j(h(X8)) = X8 ) ),
    inference(fof_nnf,[status(thm)],[6]) ).

fof(18,negated_conjecture,
    ( ! [X9] :
        ( ~ sorti1(X9)
        | sorti2(h(X9)) )
    & ! [X10] :
        ( ~ sorti2(X10)
        | sorti1(j(X10)) )
    & ! [X11] :
        ( ~ sorti1(X11)
        | ! [X12] :
            ( ~ sorti1(X12)
            | h(op1(X11,X12)) = op2(h(X11),h(X12)) ) )
    & ! [X13] :
        ( ~ sorti2(X13)
        | ! [X14] :
            ( ~ sorti2(X14)
            | j(op2(X13,X14)) = op1(j(X13),j(X14)) ) )
    & ! [X15] :
        ( ~ sorti2(X15)
        | h(j(X15)) = X15 )
    & ! [X16] :
        ( ~ sorti1(X16)
        | j(h(X16)) = X16 ) ),
    inference(variable_rename,[status(thm)],[17]) ).

fof(19,negated_conjecture,
    ! [X9,X10,X11,X12,X13,X14,X15,X16] :
      ( ( ~ sorti1(X16)
        | j(h(X16)) = X16 )
      & ( ~ sorti2(X15)
        | h(j(X15)) = X15 )
      & ( ~ sorti2(X14)
        | j(op2(X13,X14)) = op1(j(X13),j(X14))
        | ~ sorti2(X13) )
      & ( ~ sorti1(X12)
        | h(op1(X11,X12)) = op2(h(X11),h(X12))
        | ~ sorti1(X11) )
      & ( ~ sorti2(X10)
        | sorti1(j(X10)) )
      & ( ~ sorti1(X9)
        | sorti2(h(X9)) ) ),
    inference(shift_quantors,[status(thm)],[18]) ).

cnf(20,negated_conjecture,
    ( sorti2(h(X1))
    | ~ sorti1(X1) ),
    inference(split_conjunct,[status(thm)],[19]) ).

cnf(21,negated_conjecture,
    ( sorti1(j(X1))
    | ~ sorti2(X1) ),
    inference(split_conjunct,[status(thm)],[19]) ).

cnf(22,negated_conjecture,
    ( h(op1(X1,X2)) = op2(h(X1),h(X2))
    | ~ sorti1(X1)
    | ~ sorti1(X2) ),
    inference(split_conjunct,[status(thm)],[19]) ).

cnf(24,negated_conjecture,
    ( h(j(X1)) = X1
    | ~ sorti2(X1) ),
    inference(split_conjunct,[status(thm)],[19]) ).

cnf(25,negated_conjecture,
    ( j(h(X1)) = X1
    | ~ sorti1(X1) ),
    inference(split_conjunct,[status(thm)],[19]) ).

fof(26,plain,
    ! [X1] :
      ( ~ sorti1(X1)
      | ! [X2] :
          ( ~ sorti1(X2)
          | sorti1(op1(X1,X2)) ) ),
    inference(fof_nnf,[status(thm)],[4]) ).

fof(27,plain,
    ! [X3] :
      ( ~ sorti1(X3)
      | ! [X4] :
          ( ~ sorti1(X4)
          | sorti1(op1(X3,X4)) ) ),
    inference(variable_rename,[status(thm)],[26]) ).

fof(28,plain,
    ! [X3,X4] :
      ( ~ sorti1(X4)
      | sorti1(op1(X3,X4))
      | ~ sorti1(X3) ),
    inference(shift_quantors,[status(thm)],[27]) ).

cnf(29,plain,
    ( sorti1(op1(X1,X2))
    | ~ sorti1(X1)
    | ~ sorti1(X2) ),
    inference(split_conjunct,[status(thm)],[28]) ).

fof(30,plain,
    ! [X1] :
      ( ~ sorti2(X1)
      | ? [X2] :
          ( sorti2(X2)
          & op2(X1,X2) = X2 ) ),
    inference(fof_nnf,[status(thm)],[5]) ).

fof(31,plain,
    ! [X3] :
      ( ~ sorti2(X3)
      | ? [X4] :
          ( sorti2(X4)
          & op2(X3,X4) = X4 ) ),
    inference(variable_rename,[status(thm)],[30]) ).

fof(32,plain,
    ! [X3] :
      ( ~ sorti2(X3)
      | ( sorti2(esk2_1(X3))
        & op2(X3,esk2_1(X3)) = esk2_1(X3) ) ),
    inference(skolemize,[status(esa)],[31]) ).

fof(33,plain,
    ! [X3] :
      ( ( sorti2(esk2_1(X3))
        | ~ sorti2(X3) )
      & ( op2(X3,esk2_1(X3)) = esk2_1(X3)
        | ~ sorti2(X3) ) ),
    inference(distribute,[status(thm)],[32]) ).

cnf(34,plain,
    ( op2(X1,esk2_1(X1)) = esk2_1(X1)
    | ~ sorti2(X1) ),
    inference(split_conjunct,[status(thm)],[33]) ).

cnf(35,plain,
    ( sorti2(esk2_1(X1))
    | ~ sorti2(X1) ),
    inference(split_conjunct,[status(thm)],[33]) ).

cnf(40,negated_conjecture,
    ( j(op2(h(X1),h(X2))) = op1(X1,X2)
    | ~ sorti1(op1(X1,X2))
    | ~ sorti1(X2)
    | ~ sorti1(X1) ),
    inference(spm,[status(thm)],[25,22,theory(equality)]) ).

cnf(63,negated_conjecture,
    ( op1(X1,X2) = j(op2(h(X1),h(X2)))
    | ~ sorti1(X2)
    | ~ sorti1(X1) ),
    inference(csr,[status(thm)],[40,29]) ).

cnf(64,negated_conjecture,
    ( j(op2(h(esk1_0),h(X1))) != X1
    | ~ sorti1(X1)
    | ~ sorti1(esk1_0) ),
    inference(spm,[status(thm)],[16,63,theory(equality)]) ).

cnf(68,negated_conjecture,
    ( j(op2(h(esk1_0),h(X1))) != X1
    | ~ sorti1(X1)
    | $false ),
    inference(rw,[status(thm)],[64,15,theory(equality)]) ).

cnf(69,negated_conjecture,
    ( j(op2(h(esk1_0),h(X1))) != X1
    | ~ sorti1(X1) ),
    inference(cn,[status(thm)],[68,theory(equality)]) ).

cnf(70,negated_conjecture,
    ( j(op2(h(esk1_0),X1)) != j(X1)
    | ~ sorti1(j(X1))
    | ~ sorti2(X1) ),
    inference(spm,[status(thm)],[69,24,theory(equality)]) ).

cnf(72,negated_conjecture,
    ( j(op2(h(esk1_0),X1)) != j(X1)
    | ~ sorti2(X1) ),
    inference(csr,[status(thm)],[70,21]) ).

cnf(73,negated_conjecture,
    ( ~ sorti2(esk2_1(h(esk1_0)))
    | ~ sorti2(h(esk1_0)) ),
    inference(spm,[status(thm)],[72,34,theory(equality)]) ).

cnf(74,negated_conjecture,
    ~ sorti2(h(esk1_0)),
    inference(csr,[status(thm)],[73,35]) ).

cnf(75,negated_conjecture,
    ~ sorti1(esk1_0),
    inference(spm,[status(thm)],[74,20,theory(equality)]) ).

cnf(76,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[75,15,theory(equality)]) ).

cnf(77,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[76,theory(equality)]) ).

cnf(78,negated_conjecture,
    $false,
    77,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/ALG/ALG177+1.p
% --creating new selector for []
% -running prover on /tmp/tmptovbKj/sel_ALG177+1.p_1 with time limit 29
% -prover status Theorem
% Problem ALG177+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/ALG/ALG177+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/ALG/ALG177+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
% 
%------------------------------------------------------------------------------