%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : KLE146+1 : TPTP v5.0.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art03.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 12:37:34 EST 2010

% Result   : Theorem 0.28s
% Output   : CNFRefutation 0.28s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   29 (  25 unt;   0 def)
%            Number of atoms       :   37 (  20 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   18 (  10   ~;   5   |;   2   &)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   39 (   2 sgn  22   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(4,axiom,
    ! [X1,X2] : addition(X1,X2) = addition(X2,X1),
    file('/tmp/tmpC9lHwP/sel_KLE146+1.p_1',additive_commutativity) ).

fof(7,axiom,
    ! [X1] : addition(X1,X1) = X1,
    file('/tmp/tmpC9lHwP/sel_KLE146+1.p_1',idempotence) ).

fof(10,axiom,
    ! [X1] : strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
    file('/tmp/tmpC9lHwP/sel_KLE146+1.p_1',infty_unfold1) ).

fof(11,axiom,
    ! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
    file('/tmp/tmpC9lHwP/sel_KLE146+1.p_1',additive_associativity) ).

fof(16,axiom,
    ! [X1,X2] :
      ( leq(X1,X2)
    <=> addition(X1,X2) = X2 ),
    file('/tmp/tmpC9lHwP/sel_KLE146+1.p_1',order) ).

fof(19,conjecture,
    ! [X4] : leq(one,strong_iteration(X4)),
    file('/tmp/tmpC9lHwP/sel_KLE146+1.p_1',goals) ).

fof(20,negated_conjecture,
    ~ ! [X4] : leq(one,strong_iteration(X4)),
    inference(assume_negation,[status(cth)],[19]) ).

fof(27,plain,
    ! [X3,X4] : addition(X3,X4) = addition(X4,X3),
    inference(variable_rename,[status(thm)],[4]) ).

cnf(28,plain,
    addition(X1,X2) = addition(X2,X1),
    inference(split_conjunct,[status(thm)],[27]) ).

fof(33,plain,
    ! [X2] : addition(X2,X2) = X2,
    inference(variable_rename,[status(thm)],[7]) ).

cnf(34,plain,
    addition(X1,X1) = X1,
    inference(split_conjunct,[status(thm)],[33]) ).

fof(41,plain,
    ! [X2] : strong_iteration(X2) = addition(multiplication(X2,strong_iteration(X2)),one),
    inference(variable_rename,[status(thm)],[10]) ).

cnf(42,plain,
    strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
    inference(split_conjunct,[status(thm)],[41]) ).

fof(43,plain,
    ! [X4,X5,X6] : addition(X6,addition(X5,X4)) = addition(addition(X6,X5),X4),
    inference(variable_rename,[status(thm)],[11]) ).

cnf(44,plain,
    addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[43]) ).

fof(54,plain,
    ! [X1,X2] :
      ( ( ~ leq(X1,X2)
        | addition(X1,X2) = X2 )
      & ( addition(X1,X2) != X2
        | leq(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[16]) ).

fof(55,plain,
    ! [X3,X4] :
      ( ( ~ leq(X3,X4)
        | addition(X3,X4) = X4 )
      & ( addition(X3,X4) != X4
        | leq(X3,X4) ) ),
    inference(variable_rename,[status(thm)],[54]) ).

cnf(56,plain,
    ( leq(X1,X2)
    | addition(X1,X2) != X2 ),
    inference(split_conjunct,[status(thm)],[55]) ).

fof(62,negated_conjecture,
    ? [X4] : ~ leq(one,strong_iteration(X4)),
    inference(fof_nnf,[status(thm)],[20]) ).

fof(63,negated_conjecture,
    ? [X5] : ~ leq(one,strong_iteration(X5)),
    inference(variable_rename,[status(thm)],[62]) ).

fof(64,negated_conjecture,
    ~ leq(one,strong_iteration(esk1_0)),
    inference(skolemize,[status(esa)],[63]) ).

cnf(65,negated_conjecture,
    ~ leq(one,strong_iteration(esk1_0)),
    inference(split_conjunct,[status(thm)],[64]) ).

cnf(91,plain,
    addition(X1,X2) = addition(X1,addition(X1,X2)),
    inference(spm,[status(thm)],[44,34,theory(equality)]) ).

cnf(112,plain,
    addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
    inference(rw,[status(thm)],[42,28,theory(equality)]) ).

cnf(252,plain,
    leq(X1,addition(X1,X2)),
    inference(spm,[status(thm)],[56,91,theory(equality)]) ).

cnf(272,plain,
    leq(one,strong_iteration(X1)),
    inference(spm,[status(thm)],[252,112,theory(equality)]) ).

cnf(292,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[65,272,theory(equality)]) ).

cnf(293,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[292,theory(equality)]) ).

cnf(294,negated_conjecture,
    $false,
    293,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KLE/KLE146+1.p
% --creating new selector for [KLE004+0.ax]
% -running prover on /tmp/tmpC9lHwP/sel_KLE146+1.p_1 with time limit 29
% -prover status Theorem
% Problem KLE146+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE146+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE146+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
% 
%------------------------------------------------------------------------------