TSTP Solution File: SWW258+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SWW258+1 : TPTP v5.2.0. Released v5.2.0.
% 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 : Sun Mar  6 15:26:46 EST 2011

% Result   : Theorem 104.54s
% Output   : CNFRefutation 104.54s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   63 (  27 unt;   0 def)
%            Number of atoms       :  159 (  16 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  168 (  72   ~;  70   |;  14   &)
%                                         (   4 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :   14 (  14 usr;   6 con; 0-3 aty)
%            Number of variables   :   65 (   1 sgn  50   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(408,axiom,
    ! [X18,X11,X4] :
      ( class_Orderings_Opreorder(X4)
     => ( c_Orderings_Oord__class_Oless(X4,X11,X18)
      <=> ( c_Orderings_Oord__class_Oless__eq(X4,X11,X18)
          & ~ c_Orderings_Oord__class_Oless__eq(X4,X18,X11) ) ) ),
    file('/tmp/tmphww_2b/sel_SWW258+1.p_2',fact_less__le__not__le) ).

fof(451,axiom,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    file('/tmp/tmphww_2b/sel_SWW258+1.p_2',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).

fof(456,axiom,
    v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
    file('/tmp/tmphww_2b/sel_SWW258+1.p_2',fact_w0) ).

fof(478,axiom,
    class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
    file('/tmp/tmphww_2b/sel_SWW258+1.p_2',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).

fof(578,axiom,
    class_Orderings_Opreorder(tc_RealDef_Oreal),
    file('/tmp/tmphww_2b/sel_SWW258+1.p_2',arity_RealDef__Oreal__Orderings_Opreorder) ).

fof(596,axiom,
    ! [X11,X4] :
      ( class_RealVector_Oreal__normed__vector(X4)
     => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4,X11),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
      <=> X11 = c_Groups_Ozero__class_Ozero(X4) ) ),
    file('/tmp/tmphww_2b/sel_SWW258+1.p_2',fact_norm__le__zero__iff) ).

fof(685,axiom,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
    file('/tmp/tmphww_2b/sel_SWW258+1.p_2',fact_m_I1_J) ).

fof(693,axiom,
    ! [X28,X24] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X24),X28) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X28),X24),
    file('/tmp/tmphww_2b/sel_SWW258+1.p_2',fact_real__mult__commute) ).

fof(703,axiom,
    ! [X25,X8] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X8)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X25)
       => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X8),X25)) ) ),
    file('/tmp/tmphww_2b/sel_SWW258+1.p_2',fact_real__mult__order) ).

fof(781,conjecture,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),
    file('/tmp/tmphww_2b/sel_SWW258+1.p_2',conj_0) ).

fof(833,axiom,
    ! [X5,X3,X4] :
      ( class_Rings_Olinordered__semidom(X4)
     => ( c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),X3)
       => c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X3),X5)) ) ),
    file('/tmp/tmphww_2b/sel_SWW258+1.p_2',fact_zero__less__power) ).

fof(1029,axiom,
    class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
    file('/tmp/tmphww_2b/sel_SWW258+1.p_2',arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero) ).

fof(1035,axiom,
    ! [X6,X4] :
      ( class_Fields_Olinordered__field__inverse__zero(X4)
     => ( c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),c_Rings_Oinverse__class_Oinverse(X4,X6))
      <=> c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),X6) ) ),
    file('/tmp/tmphww_2b/sel_SWW258+1.p_2',fact_inverse__positive__iff__positive) ).

fof(1272,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),
    file('/tmp/tmphww_2b/sel_SWW258+1.p_2',fact__0960_A_060_061_Acmod_Aw_096) ).

fof(1273,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),
    inference(assume_negation,[status(cth)],[781]) ).

fof(1297,plain,
    ! [X18,X11,X4] :
      ( class_Orderings_Opreorder(X4)
     => ( c_Orderings_Oord__class_Oless(X4,X11,X18)
      <=> ( c_Orderings_Oord__class_Oless__eq(X4,X11,X18)
          & ~ c_Orderings_Oord__class_Oless__eq(X4,X18,X11) ) ) ),
    inference(fof_simplification,[status(thm)],[408,theory(equality)]) ).

fof(1325,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),
    inference(fof_simplification,[status(thm)],[1273,theory(equality)]) ).

fof(2639,plain,
    ! [X18,X11,X4] :
      ( ~ class_Orderings_Opreorder(X4)
      | ( ( ~ c_Orderings_Oord__class_Oless(X4,X11,X18)
          | ( c_Orderings_Oord__class_Oless__eq(X4,X11,X18)
            & ~ c_Orderings_Oord__class_Oless__eq(X4,X18,X11) ) )
        & ( ~ c_Orderings_Oord__class_Oless__eq(X4,X11,X18)
          | c_Orderings_Oord__class_Oless__eq(X4,X18,X11)
          | c_Orderings_Oord__class_Oless(X4,X11,X18) ) ) ),
    inference(fof_nnf,[status(thm)],[1297]) ).

fof(2640,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Opreorder(X21)
      | ( ( ~ c_Orderings_Oord__class_Oless(X21,X20,X19)
          | ( c_Orderings_Oord__class_Oless__eq(X21,X20,X19)
            & ~ c_Orderings_Oord__class_Oless__eq(X21,X19,X20) ) )
        & ( ~ c_Orderings_Oord__class_Oless__eq(X21,X20,X19)
          | c_Orderings_Oord__class_Oless__eq(X21,X19,X20)
          | c_Orderings_Oord__class_Oless(X21,X20,X19) ) ) ),
    inference(variable_rename,[status(thm)],[2639]) ).

fof(2641,plain,
    ! [X19,X20,X21] :
      ( ( c_Orderings_Oord__class_Oless__eq(X21,X20,X19)
        | ~ c_Orderings_Oord__class_Oless(X21,X20,X19)
        | ~ class_Orderings_Opreorder(X21) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X21,X19,X20)
        | ~ c_Orderings_Oord__class_Oless(X21,X20,X19)
        | ~ class_Orderings_Opreorder(X21) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X21,X20,X19)
        | c_Orderings_Oord__class_Oless__eq(X21,X19,X20)
        | c_Orderings_Oord__class_Oless(X21,X20,X19)
        | ~ class_Orderings_Opreorder(X21) ) ),
    inference(distribute,[status(thm)],[2640]) ).

cnf(2642,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
    | ~ class_Orderings_Opreorder(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[2641]) ).

cnf(2771,plain,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[451]) ).

cnf(2783,plain,
    v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[456]) ).

cnf(2842,plain,
    class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[478]) ).

cnf(3132,plain,
    class_Orderings_Opreorder(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[578]) ).

fof(3176,plain,
    ! [X11,X4] :
      ( ~ class_RealVector_Oreal__normed__vector(X4)
      | ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4,X11),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
          | X11 = c_Groups_Ozero__class_Ozero(X4) )
        & ( X11 != c_Groups_Ozero__class_Ozero(X4)
          | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4,X11),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ) ),
    inference(fof_nnf,[status(thm)],[596]) ).

fof(3177,plain,
    ! [X12,X13] :
      ( ~ class_RealVector_Oreal__normed__vector(X13)
      | ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X13,X12),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
          | X12 = c_Groups_Ozero__class_Ozero(X13) )
        & ( X12 != c_Groups_Ozero__class_Ozero(X13)
          | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X13,X12),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ) ),
    inference(variable_rename,[status(thm)],[3176]) ).

fof(3178,plain,
    ! [X12,X13] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X13,X12),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | X12 = c_Groups_Ozero__class_Ozero(X13)
        | ~ class_RealVector_Oreal__normed__vector(X13) )
      & ( X12 != c_Groups_Ozero__class_Ozero(X13)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X13,X12),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | ~ class_RealVector_Oreal__normed__vector(X13) ) ),
    inference(distribute,[status(thm)],[3177]) ).

cnf(3180,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_RealVector_Oreal__normed__vector(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(split_conjunct,[status(thm)],[3178]) ).

cnf(3445,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
    inference(split_conjunct,[status(thm)],[685]) ).

fof(3477,plain,
    ! [X29,X30] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X30),X29) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X29),X30),
    inference(variable_rename,[status(thm)],[693]) ).

cnf(3478,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),
    inference(split_conjunct,[status(thm)],[3477]) ).

fof(3503,plain,
    ! [X25,X8] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X8)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X25)
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X8),X25)) ),
    inference(fof_nnf,[status(thm)],[703]) ).

fof(3504,plain,
    ! [X26,X27] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X27)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X26)
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X27),X26)) ),
    inference(variable_rename,[status(thm)],[3503]) ).

cnf(3505,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
    inference(split_conjunct,[status(thm)],[3504]) ).

cnf(3737,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),
    inference(split_conjunct,[status(thm)],[1325]) ).

fof(3902,plain,
    ! [X5,X3,X4] :
      ( ~ class_Rings_Olinordered__semidom(X4)
      | ~ c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),X3)
      | c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X3),X5)) ),
    inference(fof_nnf,[status(thm)],[833]) ).

fof(3903,plain,
    ! [X6,X7,X8] :
      ( ~ class_Rings_Olinordered__semidom(X8)
      | ~ c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
      | c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X6)) ),
    inference(variable_rename,[status(thm)],[3902]) ).

cnf(3904,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[3903]) ).

cnf(4491,plain,
    class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[1029]) ).

fof(4510,plain,
    ! [X6,X4] :
      ( ~ class_Fields_Olinordered__field__inverse__zero(X4)
      | ( ( ~ c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),c_Rings_Oinverse__class_Oinverse(X4,X6))
          | c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),X6) )
        & ( ~ c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),X6)
          | c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),c_Rings_Oinverse__class_Oinverse(X4,X6)) ) ) ),
    inference(fof_nnf,[status(thm)],[1035]) ).

fof(4511,plain,
    ! [X7,X8] :
      ( ~ class_Fields_Olinordered__field__inverse__zero(X8)
      | ( ( ~ c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),c_Rings_Oinverse__class_Oinverse(X8,X7))
          | c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7) )
        & ( ~ c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
          | c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),c_Rings_Oinverse__class_Oinverse(X8,X7)) ) ) ),
    inference(variable_rename,[status(thm)],[4510]) ).

fof(4512,plain,
    ! [X7,X8] :
      ( ( ~ c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),c_Rings_Oinverse__class_Oinverse(X8,X7))
        | c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
        | ~ class_Fields_Olinordered__field__inverse__zero(X8) )
      & ( ~ c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
        | c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),c_Rings_Oinverse__class_Oinverse(X8,X7))
        | ~ class_Fields_Olinordered__field__inverse__zero(X8) ) ),
    inference(distribute,[status(thm)],[4511]) ).

cnf(4513,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(split_conjunct,[status(thm)],[4512]) ).

cnf(5232,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),
    inference(split_conjunct,[status(thm)],[1272]) ).

cnf(6077,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
    inference(rw,[status(thm)],[3737,3478,theory(equality)]) ).

cnf(11826,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
    inference(spm,[status(thm)],[4513,4491,theory(equality)]) ).

cnf(25027,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
    | ~ class_Orderings_Opreorder(tc_RealDef_Oreal) ),
    inference(spm,[status(thm)],[2642,5232,theory(equality)]) ).

cnf(25093,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
    | $false ),
    inference(rw,[status(thm)],[25027,3132,theory(equality)]) ).

cnf(25094,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
    inference(cn,[status(thm)],[25093,theory(equality)]) ).

cnf(72352,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v_w____
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
    | ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
    inference(spm,[status(thm)],[3180,25094,theory(equality)]) ).

cnf(72370,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v_w____
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
    | $false ),
    inference(rw,[status(thm)],[72352,2771,theory(equality)]) ).

cnf(72371,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v_w____
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
    inference(cn,[status(thm)],[72370,theory(equality)]) ).

cnf(72372,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),
    inference(sr,[status(thm)],[72371,2783,theory(equality)]) ).

cnf(585840,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),
    inference(spm,[status(thm)],[6077,11826,theory(equality)]) ).

cnf(586480,negated_conjecture,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____) ),
    inference(spm,[status(thm)],[585840,3505,theory(equality)]) ).

cnf(586498,negated_conjecture,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | $false ),
    inference(rw,[status(thm)],[586480,3445,theory(equality)]) ).

cnf(586499,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
    inference(cn,[status(thm)],[586498,theory(equality)]) ).

cnf(586513,negated_conjecture,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
    | ~ class_Rings_Olinordered__semidom(tc_RealDef_Oreal) ),
    inference(spm,[status(thm)],[586499,3904,theory(equality)]) ).

cnf(586528,negated_conjecture,
    ( $false
    | ~ class_Rings_Olinordered__semidom(tc_RealDef_Oreal) ),
    inference(rw,[status(thm)],[586513,72372,theory(equality)]) ).

cnf(586529,negated_conjecture,
    ( $false
    | $false ),
    inference(rw,[status(thm)],[586528,2842,theory(equality)]) ).

cnf(586530,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[586529,theory(equality)]) ).

cnf(586531,negated_conjecture,
    $false,
    586530,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWW/SWW258+1.p
% --creating new selector for []
% eprover: CPU time limit exceeded, terminating
% -running prover on /tmp/tmphww_2b/sel_SWW258+1.p_1 with time limit 29
% -prover status ResourceOut
% -running prover on /tmp/tmphww_2b/sel_SWW258+1.p_2 with time limit 80
% -prover status Theorem
% Problem SWW258+1.p solved in phase 1.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWW/SWW258+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWW/SWW258+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
% 
%------------------------------------------------------------------------------