TSTP Solution File: SWW229+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SWW229+1 : TPTP v5.2.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art02.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 : Sun Mar  6 15:12:05 EST 2011

% Result   : Theorem 5.87s
% Output   : CNFRefutation 5.87s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   33 (  24 unt;   0 def)
%            Number of atoms       :   42 (  16 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   22 (  13   ~;   7   |;   0   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :   16 (  16 usr;   8 con; 0-3 aty)
%            Number of variables   :   48 (   0 sgn  28   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(148,axiom,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    file('/tmp/tmpKgqQNY/sel_SWW229+1.p_1',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).

fof(346,axiom,
    ! [X65,X33] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X33,X65) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X33,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X65)),
    file('/tmp/tmpKgqQNY/sel_SWW229+1.p_1',fact_real__diff__def) ).

fof(378,axiom,
    ! [X16,X17,X4] :
      ( class_RealVector_Oreal__normed__vector(X4)
     => c_RealVector_Onorm__class_Onorm(X4,c_Groups_Ominus__class_Ominus(X4,X17,X16)) = c_RealVector_Onorm__class_Onorm(X4,c_Groups_Ominus__class_Ominus(X4,X16,X17)) ),
    file('/tmp/tmpKgqQNY/sel_SWW229+1.p_1',fact_norm__minus__commute) ).

fof(459,axiom,
    ! [X16,X17,X4] :
      ( class_RealVector_Oreal__normed__vector(X4)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4,X17),c_RealVector_Onorm__class_Onorm(X4,X16))),c_RealVector_Onorm__class_Onorm(X4,c_Groups_Ominus__class_Ominus(X4,X17,X16))) ),
    file('/tmp/tmpKgqQNY/sel_SWW229+1.p_1',fact_norm__triangle__ineq3) ).

fof(604,axiom,
    ! [X33] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X33) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X33),
    file('/tmp/tmpKgqQNY/sel_SWW229+1.p_1',fact_real__norm__def) ).

fof(755,conjecture,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),
    file('/tmp/tmpKgqQNY/sel_SWW229+1.p_1',conj_0) ).

fof(1186,axiom,
    ! [X2,X3] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3))),
    file('/tmp/tmpKgqQNY/sel_SWW229+1.p_1',fact_abs__minus__add__cancel) ).

fof(1255,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),
    inference(assume_negation,[status(cth)],[755]) ).

fof(1295,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),
    inference(fof_simplification,[status(thm)],[1255,theory(equality)]) ).

cnf(1758,plain,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[148]) ).

fof(2389,plain,
    ! [X66,X67] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X67,X66) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X67,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X66)),
    inference(variable_rename,[status(thm)],[346]) ).

cnf(2390,plain,
    c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)),
    inference(split_conjunct,[status(thm)],[2389]) ).

fof(2480,plain,
    ! [X16,X17,X4] :
      ( ~ class_RealVector_Oreal__normed__vector(X4)
      | c_RealVector_Onorm__class_Onorm(X4,c_Groups_Ominus__class_Ominus(X4,X17,X16)) = c_RealVector_Onorm__class_Onorm(X4,c_Groups_Ominus__class_Ominus(X4,X16,X17)) ),
    inference(fof_nnf,[status(thm)],[378]) ).

fof(2481,plain,
    ! [X18,X19,X20] :
      ( ~ class_RealVector_Oreal__normed__vector(X20)
      | c_RealVector_Onorm__class_Onorm(X20,c_Groups_Ominus__class_Ominus(X20,X19,X18)) = c_RealVector_Onorm__class_Onorm(X20,c_Groups_Ominus__class_Ominus(X20,X18,X19)) ),
    inference(variable_rename,[status(thm)],[2480]) ).

cnf(2482,plain,
    ( c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)) = c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X3,X2))
    | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(split_conjunct,[status(thm)],[2481]) ).

fof(2719,plain,
    ! [X16,X17,X4] :
      ( ~ class_RealVector_Oreal__normed__vector(X4)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4,X17),c_RealVector_Onorm__class_Onorm(X4,X16))),c_RealVector_Onorm__class_Onorm(X4,c_Groups_Ominus__class_Ominus(X4,X17,X16))) ),
    inference(fof_nnf,[status(thm)],[459]) ).

fof(2720,plain,
    ! [X18,X19,X20] :
      ( ~ class_RealVector_Oreal__normed__vector(X20)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X20,X19),c_RealVector_Onorm__class_Onorm(X20,X18))),c_RealVector_Onorm__class_Onorm(X20,c_Groups_Ominus__class_Ominus(X20,X19,X18))) ),
    inference(variable_rename,[status(thm)],[2719]) ).

cnf(2721,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3))),c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)))
    | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(split_conjunct,[status(thm)],[2720]) ).

fof(3143,plain,
    ! [X34] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X34) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X34),
    inference(variable_rename,[status(thm)],[604]) ).

cnf(3144,plain,
    c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
    inference(split_conjunct,[status(thm)],[3143]) ).

cnf(3583,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),
    inference(split_conjunct,[status(thm)],[1295]) ).

fof(4895,plain,
    ! [X4,X5] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X5))),
    inference(variable_rename,[status(thm)],[1186]) ).

cnf(4896,plain,
    c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))),
    inference(split_conjunct,[status(thm)],[4895]) ).

cnf(12328,plain,
    c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X1)),
    inference(spm,[status(thm)],[2482,1758,theory(equality)]) ).

cnf(12973,plain,
    c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[4896,2390,theory(equality)]),3144,theory(equality)]) ).

cnf(12974,plain,
    c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2)) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[12973,2390,theory(equality)]),3144,theory(equality)]) ).

cnf(19390,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3))),c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)))
    | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(rw,[status(thm)],[2721,3144,theory(equality)]) ).

cnf(42356,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[3583,3144,theory(equality)]),12974,theory(equality)]) ).

cnf(89321,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),
    inference(rw,[status(thm)],[42356,12328,theory(equality)]) ).

cnf(89741,negated_conjecture,
    ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    inference(spm,[status(thm)],[89321,19390,theory(equality)]) ).

cnf(89755,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[89741,1758,theory(equality)]) ).

cnf(89756,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[89755,theory(equality)]) ).

cnf(89757,negated_conjecture,
    $false,
    89756,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWW/SWW229+1.p
% --creating new selector for []
% -running prover on /tmp/tmpKgqQNY/sel_SWW229+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWW229+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWW/SWW229+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWW/SWW229+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
% 
%------------------------------------------------------------------------------