TSTP Solution File: KLE037+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : KLE037+1 : TPTP v5.0.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art09.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 11:58:26 EST 2010

% Result   : Theorem 0.27s
% Output   : CNFRefutation 0.27s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   39 (  34 unt;   0 def)
%            Number of atoms       :   48 (  27 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   20 (  11   ~;   6   |;   2   &)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    5 (   2 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   :   57 (   2 sgn  30   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1] : multiplication(one,X1) = X1,
    file('/tmp/tmpDjibyD/sel_KLE037+1.p_1',multiplicative_left_identity) ).

fof(2,axiom,
    ! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
    file('/tmp/tmpDjibyD/sel_KLE037+1.p_1',left_distributivity) ).

fof(3,axiom,
    ! [X1,X2] : addition(X1,X2) = addition(X2,X1),
    file('/tmp/tmpDjibyD/sel_KLE037+1.p_1',additive_commutativity) ).

fof(4,axiom,
    ! [X1] : addition(X1,X1) = X1,
    file('/tmp/tmpDjibyD/sel_KLE037+1.p_1',additive_idempotence) ).

fof(6,axiom,
    ! [X1,X2] :
      ( leq(X1,X2)
    <=> addition(X1,X2) = X2 ),
    file('/tmp/tmpDjibyD/sel_KLE037+1.p_1',order) ).

fof(7,axiom,
    ! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
    file('/tmp/tmpDjibyD/sel_KLE037+1.p_1',additive_associativity) ).

fof(9,axiom,
    ! [X1] : leq(addition(one,multiplication(X1,star(X1))),star(X1)),
    file('/tmp/tmpDjibyD/sel_KLE037+1.p_1',star_unfold_right) ).

fof(14,conjecture,
    ! [X4] : leq(one,star(X4)),
    file('/tmp/tmpDjibyD/sel_KLE037+1.p_1',goals) ).

fof(15,negated_conjecture,
    ~ ! [X4] : leq(one,star(X4)),
    inference(assume_negation,[status(cth)],[14]) ).

fof(16,plain,
    ! [X2] : multiplication(one,X2) = X2,
    inference(variable_rename,[status(thm)],[1]) ).

cnf(17,plain,
    multiplication(one,X1) = X1,
    inference(split_conjunct,[status(thm)],[16]) ).

fof(18,plain,
    ! [X4,X5,X6] : multiplication(addition(X4,X5),X6) = addition(multiplication(X4,X6),multiplication(X5,X6)),
    inference(variable_rename,[status(thm)],[2]) ).

cnf(19,plain,
    multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
    inference(split_conjunct,[status(thm)],[18]) ).

fof(20,plain,
    ! [X3,X4] : addition(X3,X4) = addition(X4,X3),
    inference(variable_rename,[status(thm)],[3]) ).

cnf(21,plain,
    addition(X1,X2) = addition(X2,X1),
    inference(split_conjunct,[status(thm)],[20]) ).

fof(22,plain,
    ! [X2] : addition(X2,X2) = X2,
    inference(variable_rename,[status(thm)],[4]) ).

cnf(23,plain,
    addition(X1,X1) = X1,
    inference(split_conjunct,[status(thm)],[22]) ).

fof(27,plain,
    ! [X1,X2] :
      ( ( ~ leq(X1,X2)
        | addition(X1,X2) = X2 )
      & ( addition(X1,X2) != X2
        | leq(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[6]) ).

fof(28,plain,
    ! [X3,X4] :
      ( ( ~ leq(X3,X4)
        | addition(X3,X4) = X4 )
      & ( addition(X3,X4) != X4
        | leq(X3,X4) ) ),
    inference(variable_rename,[status(thm)],[27]) ).

cnf(29,plain,
    ( leq(X1,X2)
    | addition(X1,X2) != X2 ),
    inference(split_conjunct,[status(thm)],[28]) ).

cnf(30,plain,
    ( addition(X1,X2) = X2
    | ~ leq(X1,X2) ),
    inference(split_conjunct,[status(thm)],[28]) ).

fof(31,plain,
    ! [X4,X5,X6] : addition(X6,addition(X5,X4)) = addition(addition(X6,X5),X4),
    inference(variable_rename,[status(thm)],[7]) ).

cnf(32,plain,
    addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[31]) ).

fof(35,plain,
    ! [X2] : leq(addition(one,multiplication(X2,star(X2))),star(X2)),
    inference(variable_rename,[status(thm)],[9]) ).

cnf(36,plain,
    leq(addition(one,multiplication(X1,star(X1))),star(X1)),
    inference(split_conjunct,[status(thm)],[35]) ).

fof(46,negated_conjecture,
    ? [X4] : ~ leq(one,star(X4)),
    inference(fof_nnf,[status(thm)],[15]) ).

fof(47,negated_conjecture,
    ? [X5] : ~ leq(one,star(X5)),
    inference(variable_rename,[status(thm)],[46]) ).

fof(48,negated_conjecture,
    ~ leq(one,star(esk1_0)),
    inference(skolemize,[status(esa)],[47]) ).

cnf(49,negated_conjecture,
    ~ leq(one,star(esk1_0)),
    inference(split_conjunct,[status(thm)],[48]) ).

cnf(70,plain,
    addition(X1,X2) = addition(X1,addition(X1,X2)),
    inference(spm,[status(thm)],[32,23,theory(equality)]) ).

cnf(81,plain,
    addition(addition(one,multiplication(X1,star(X1))),star(X1)) = star(X1),
    inference(spm,[status(thm)],[30,36,theory(equality)]) ).

cnf(83,plain,
    addition(one,addition(star(X1),multiplication(X1,star(X1)))) = star(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[81,32,theory(equality)]),21,theory(equality)]) ).

cnf(126,plain,
    addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
    inference(spm,[status(thm)],[19,17,theory(equality)]) ).

cnf(177,plain,
    leq(X1,addition(X1,X2)),
    inference(spm,[status(thm)],[29,70,theory(equality)]) ).

cnf(1802,plain,
    addition(one,multiplication(addition(one,X1),star(X1))) = star(X1),
    inference(rw,[status(thm)],[83,126,theory(equality)]) ).

cnf(1807,plain,
    leq(one,star(X1)),
    inference(spm,[status(thm)],[177,1802,theory(equality)]) ).

cnf(1933,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[49,1807,theory(equality)]) ).

cnf(1934,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[1933,theory(equality)]) ).

cnf(1935,negated_conjecture,
    $false,
    1934,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KLE/KLE037+1.p
% --creating new selector for [KLE002+0.ax]
% -running prover on /tmp/tmpDjibyD/sel_KLE037+1.p_1 with time limit 29
% -prover status Theorem
% Problem KLE037+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE037+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE037+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
% 
%------------------------------------------------------------------------------