%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : MSC012+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art06.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 21:09:57 EST 2010

% Result   : Theorem 0.16s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   31 (  12 unt;   0 def)
%            Number of atoms       :   72 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   71 (  30   ~;  32   |;   7   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   2 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   0 con; 1-1 aty)
%            Number of variables   :   46 (   3 sgn  22   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2,X3] :
      ( ( less(X1,X2)
        & less(X2,X3) )
     => less(X1,X3) ),
    file('/tmp/tmpSMUfPt/sel_MSC012+1.p_1',transitive_less) ).

fof(2,conjecture,
    goal,
    file('/tmp/tmpSMUfPt/sel_MSC012+1.p_1',goal_to_be_proved) ).

fof(3,axiom,
    ! [X1,X2] :
      ( ( p(X1)
        & less(X1,X2)
        & p(X2) )
     => goal ),
    file('/tmp/tmpSMUfPt/sel_MSC012+1.p_1',left_to_right) ).

fof(4,axiom,
    ! [X1] :
    ? [X2] : less(X1,X2),
    file('/tmp/tmpSMUfPt/sel_MSC012+1.p_1',serial_less) ).

fof(5,axiom,
    ! [X1] :
      ( p(X1)
      | ? [X2] :
          ( less(X1,X2)
          & p(X2) ) ),
    file('/tmp/tmpSMUfPt/sel_MSC012+1.p_1',right_to_left) ).

fof(6,negated_conjecture,
    ~ goal,
    inference(assume_negation,[status(cth)],[2]) ).

fof(7,negated_conjecture,
    ~ goal,
    inference(fof_simplification,[status(thm)],[6,theory(equality)]) ).

fof(8,plain,
    ! [X1,X2,X3] :
      ( ~ less(X1,X2)
      | ~ less(X2,X3)
      | less(X1,X3) ),
    inference(fof_nnf,[status(thm)],[1]) ).

fof(9,plain,
    ! [X4,X5,X6] :
      ( ~ less(X4,X5)
      | ~ less(X5,X6)
      | less(X4,X6) ),
    inference(variable_rename,[status(thm)],[8]) ).

cnf(10,plain,
    ( less(X1,X2)
    | ~ less(X3,X2)
    | ~ less(X1,X3) ),
    inference(split_conjunct,[status(thm)],[9]) ).

cnf(11,negated_conjecture,
    ~ goal,
    inference(split_conjunct,[status(thm)],[7]) ).

fof(12,plain,
    ! [X1,X2] :
      ( ~ p(X1)
      | ~ less(X1,X2)
      | ~ p(X2)
      | goal ),
    inference(fof_nnf,[status(thm)],[3]) ).

fof(13,plain,
    ! [X3,X4] :
      ( ~ p(X3)
      | ~ less(X3,X4)
      | ~ p(X4)
      | goal ),
    inference(variable_rename,[status(thm)],[12]) ).

cnf(14,plain,
    ( goal
    | ~ p(X1)
    | ~ less(X2,X1)
    | ~ p(X2) ),
    inference(split_conjunct,[status(thm)],[13]) ).

fof(15,plain,
    ! [X3] :
    ? [X4] : less(X3,X4),
    inference(variable_rename,[status(thm)],[4]) ).

fof(16,plain,
    ! [X3] : less(X3,esk1_1(X3)),
    inference(skolemize,[status(esa)],[15]) ).

cnf(17,plain,
    less(X1,esk1_1(X1)),
    inference(split_conjunct,[status(thm)],[16]) ).

fof(18,plain,
    ! [X3] :
      ( p(X3)
      | ? [X4] :
          ( less(X3,X4)
          & p(X4) ) ),
    inference(variable_rename,[status(thm)],[5]) ).

fof(19,plain,
    ! [X3] :
      ( p(X3)
      | ( less(X3,esk2_1(X3))
        & p(esk2_1(X3)) ) ),
    inference(skolemize,[status(esa)],[18]) ).

fof(20,plain,
    ! [X3] :
      ( ( less(X3,esk2_1(X3))
        | p(X3) )
      & ( p(esk2_1(X3))
        | p(X3) ) ),
    inference(distribute,[status(thm)],[19]) ).

cnf(21,plain,
    ( p(X1)
    | p(esk2_1(X1)) ),
    inference(split_conjunct,[status(thm)],[20]) ).

cnf(22,plain,
    ( p(X1)
    | less(X1,esk2_1(X1)) ),
    inference(split_conjunct,[status(thm)],[20]) ).

cnf(23,plain,
    ( ~ p(X2)
    | ~ p(X1)
    | ~ less(X2,X1) ),
    inference(sr,[status(thm)],[14,11,theory(equality)]) ).

cnf(27,plain,
    ( less(X1,esk2_1(X2))
    | p(X2)
    | ~ less(X1,X2) ),
    inference(spm,[status(thm)],[10,22,theory(equality)]) ).

cnf(30,plain,
    ( p(X2)
    | ~ p(X1)
    | ~ p(esk2_1(X2))
    | ~ less(X1,X2) ),
    inference(spm,[status(thm)],[23,27,theory(equality)]) ).

cnf(32,plain,
    ( p(X2)
    | ~ p(X1)
    | ~ less(X1,X2) ),
    inference(csr,[status(thm)],[30,21]) ).

cnf(33,plain,
    ( ~ p(X1)
    | ~ less(X1,X2) ),
    inference(csr,[status(thm)],[32,23]) ).

cnf(34,plain,
    ~ p(X1),
    inference(spm,[status(thm)],[33,17,theory(equality)]) ).

cnf(38,plain,
    p(X1),
    inference(sr,[status(thm)],[21,34,theory(equality)]) ).

cnf(39,plain,
    $false,
    inference(sr,[status(thm)],[38,34,theory(equality)]) ).

cnf(40,plain,
    $false,
    39,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/MSC/MSC012+1.p
% --creating new selector for []
% -running prover on /tmp/tmpSMUfPt/sel_MSC012+1.p_1 with time limit 29
% -prover status Theorem
% Problem MSC012+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/MSC/MSC012+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/MSC/MSC012+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
% 
%------------------------------------------------------------------------------