Z3---4.15.1.UNS-Prf.s

%------------------------------------------------------------------------------
% File     : Z3---4.15.1
% Problem  : ALG375-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_E %s %d THM

% Computer : n006.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sat Jun 21 04:59:00 AM UTC 2025

% Result   : Unsatisfiable 3.21s 3.40s
% Output   : Proof 3.29s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   31
% Syntax   : Number of formulae    :   71 (  16 unt;   0 typ;   0 def)
%            Number of atoms       :  405 (   0 equ)
%            Maximal formula atoms :   12 (   5 avg)
%            Number of connectives :  542 ( 222   ~; 282   |;   0   &)
%                                         (  38 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of FOOLs       :   14 (  14 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   6 usr;   2 prp; 0-3 aty)
%            Number of functors    :   18 (  18 usr;   6 con; 0-3 aty)
%            Number of variables   :   80 (  72   !;   0   ?;  80   :)

% Comments : 
%------------------------------------------------------------------------------
tff(c_HOL_Oord__class_Oless_type,type,
    c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).

tff(tc_RealDef_Oreal_type,type,
    tc_RealDef_Oreal: $i ).

tff(c_RealVector_Onorm__class_Onorm_type,type,
    c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).

tff(tc_Complex_Ocomplex_type,type,
    tc_Complex_Ocomplex: $i ).

tff(c_HOL_Ominus__class_Ominus_type,type,
    c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).

tff(v_z_____type,type,
    v_z____: $i ).

tff(v_d_type,type,
    v_d: $i > $i ).

tff(v_sko__CHAINED__1_type,type,
    v_sko__CHAINED__1: ( $i * $i * $i ) > $i ).

tff(v_s_____type,type,
    v_s____: $i ).

tff(v_p_type,type,
    v_p: $i ).

tff(c_HOL_Ozero__class_Ozero_type,type,
    c_HOL_Ozero__class_Ozero: $i > $i ).

tff(v_thesis_____type,type,
    v_thesis____: $o ).

tff(c_HOL_Oinverse__class_Odivide_type,type,
    c_HOL_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).

tff(c_Int_Onumber__class_Onumber__of_type,type,
    c_Int_Onumber__class_Onumber__of: ( $i * $i ) > $i ).

tff(c_Int_OBit0_type,type,
    c_Int_OBit0: $i > $i ).

tff(c_Int_OBit1_type,type,
    c_Int_OBit1: $i > $i ).

tff(c_Int_OPls_type,type,
    c_Int_OPls: $i ).

tff(c_HOL_Oabs__class_Oabs_type,type,
    c_HOL_Oabs__class_Oabs: ( $i * $i ) > $i ).

tff(c_HOL_Ouminus__class_Ouminus_type,type,
    c_HOL_Ouminus__class_Ouminus: ( $i * $i ) > $i ).

tff(c_Polynomial_Opoly_type,type,
    c_Polynomial_Opoly: ( $i * $i * $i ) > $i ).

tff(1,plain,
    ^ [V_da: $i] :
      refl(( ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
          | v_thesis____
          | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),V_da,tc_RealDef_Oreal) )
      <=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
          | v_thesis____
          | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),V_da,tc_RealDef_Oreal) ) )),
    inference(bind,[status(th)],[]) ).

tff(2,plain,
    ( ! [V_da: $i] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
        | v_thesis____
        | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),V_da,tc_RealDef_Oreal) )
  <=> ! [V_da: $i] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
        | v_thesis____
        | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),V_da,tc_RealDef_Oreal) ) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [V_da: $i] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
        | v_thesis____
        | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),V_da,tc_RealDef_Oreal) )
  <=> ! [V_da: $i] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
        | v_thesis____
        | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),V_da,tc_RealDef_Oreal) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(4,plain,
    ^ [V_da: $i] :
      rewrite(( ( v_thesis____
          | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),V_da,tc_RealDef_Oreal)
          | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal) )
      <=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
          | v_thesis____
          | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),V_da,tc_RealDef_Oreal) ) )),
    inference(bind,[status(th)],[]) ).

tff(5,plain,
    ( ! [V_da: $i] :
        ( v_thesis____
        | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),V_da,tc_RealDef_Oreal)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal) )
  <=> ! [V_da: $i] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
        | v_thesis____
        | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),V_da,tc_RealDef_Oreal) ) ),
    inference(quant_intro,[status(thm)],[4]) ).

tff(6,axiom,
    ! [V_da: $i] :
      ( v_thesis____
      | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),V_da,tc_RealDef_Oreal)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).

tff(7,plain,
    ! [V_da: $i] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
      | v_thesis____
      | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),V_da,tc_RealDef_Oreal) ),
    inference(modus_ponens,[status(thm)],[6,5]) ).

tff(8,plain,
    ! [V_da: $i] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
      | v_thesis____
      | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),V_da,tc_RealDef_Oreal) ),
    inference(modus_ponens,[status(thm)],[7,3]) ).

tff(9,plain,
    ! [V_da: $i] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
      | v_thesis____
      | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),V_da,tc_RealDef_Oreal) ),
    inference(skolemize,[status(sab)],[8]) ).

tff(10,plain,
    ! [V_da: $i] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
      | v_thesis____
      | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),V_da,tc_RealDef_Oreal) ),
    inference(modus_ponens,[status(thm)],[9,2]) ).

tff(11,plain,
    ( ~ v_thesis____
  <=> ~ v_thesis____ ),
    inference(rewrite,[status(thm)],[]) ).

tff(12,axiom,
    ~ v_thesis____,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

tff(13,plain,
    ~ v_thesis____,
    inference(modus_ponens,[status(thm)],[12,11]) ).

tff(14,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
  <=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal) ),
    inference(rewrite,[status(thm)],[]) ).

tff(15,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).

tff(16,plain,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal),
    inference(modus_ponens,[status(thm)],[15,14]) ).

tff(17,plain,
    ( ( ~ ! [V_da: $i] :
            ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
            | v_thesis____
            | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),V_da,tc_RealDef_Oreal) )
      | v_thesis____
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
      | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal) )
  <=> ( ~ ! [V_da: $i] :
            ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
            | v_thesis____
            | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),V_da,tc_RealDef_Oreal) )
      | v_thesis____
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
      | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(18,plain,
    ( ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
      | v_thesis____
      | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal) )
  <=> ( v_thesis____
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
      | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(19,plain,
    ( ( ~ ! [V_da: $i] :
            ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
            | v_thesis____
            | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),V_da,tc_RealDef_Oreal) )
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
      | v_thesis____
      | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal) )
  <=> ( ~ ! [V_da: $i] :
            ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
            | v_thesis____
            | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),V_da,tc_RealDef_Oreal) )
      | v_thesis____
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
      | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal) ) ),
    inference(monotonicity,[status(thm)],[18]) ).

tff(20,plain,
    ( ( ~ ! [V_da: $i] :
            ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
            | v_thesis____
            | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),V_da,tc_RealDef_Oreal) )
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
      | v_thesis____
      | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal) )
  <=> ( ~ ! [V_da: $i] :
            ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
            | v_thesis____
            | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),V_da,tc_RealDef_Oreal) )
      | v_thesis____
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
      | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal) ) ),
    inference(transitivity,[status(thm)],[19,17]) ).

tff(21,plain,
    ( ~ ! [V_da: $i] :
          ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
          | v_thesis____
          | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),V_da,tc_RealDef_Oreal) )
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
    | v_thesis____
    | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(22,plain,
    ( ~ ! [V_da: $i] :
          ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
          | v_thesis____
          | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),V_da,tc_RealDef_Oreal) )
    | v_thesis____
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
    | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal) ),
    inference(modus_ponens,[status(thm)],[21,20]) ).

tff(23,plain,
    c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal),
    inference(unit_resolution,[status(thm)],[22,16,13,10]) ).

tff(24,plain,
    ^ [V_da: $i] :
      refl(( ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
          | v_thesis____
          | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_d(V_da),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )
      <=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
          | v_thesis____
          | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_d(V_da),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) )),
    inference(bind,[status(th)],[]) ).

tff(25,plain,
    ( ! [V_da: $i] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
        | v_thesis____
        | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_d(V_da),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )
  <=> ! [V_da: $i] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
        | v_thesis____
        | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_d(V_da),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
    inference(quant_intro,[status(thm)],[24]) ).

tff(26,plain,
    ( ! [V_da: $i] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
        | v_thesis____
        | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_d(V_da),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )
  <=> ! [V_da: $i] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
        | v_thesis____
        | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_d(V_da),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(27,plain,
    ^ [V_da: $i] :
      rewrite(( ( v_thesis____
          | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_d(V_da),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
          | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal) )
      <=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
          | v_thesis____
          | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_d(V_da),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) )),
    inference(bind,[status(th)],[]) ).

tff(28,plain,
    ( ! [V_da: $i] :
        ( v_thesis____
        | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_d(V_da),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal) )
  <=> ! [V_da: $i] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
        | v_thesis____
        | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_d(V_da),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
    inference(quant_intro,[status(thm)],[27]) ).

tff(29,axiom,
    ! [V_da: $i] :
      ( v_thesis____
      | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_d(V_da),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).

tff(30,plain,
    ! [V_da: $i] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
      | v_thesis____
      | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_d(V_da),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(modus_ponens,[status(thm)],[29,28]) ).

tff(31,plain,
    ! [V_da: $i] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
      | v_thesis____
      | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_d(V_da),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(modus_ponens,[status(thm)],[30,26]) ).

tff(32,plain,
    ! [V_da: $i] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
      | v_thesis____
      | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_d(V_da),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(skolemize,[status(sab)],[31]) ).

tff(33,plain,
    ! [V_da: $i] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
      | v_thesis____
      | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_d(V_da),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(modus_ponens,[status(thm)],[32,25]) ).

tff(34,plain,
    ( ( ~ ! [V_da: $i] :
            ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
            | v_thesis____
            | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_d(V_da),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )
      | v_thesis____
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
      | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )
  <=> ( ~ ! [V_da: $i] :
            ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
            | v_thesis____
            | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_d(V_da),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )
      | v_thesis____
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
      | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(35,plain,
    ( ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
      | v_thesis____
      | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )
  <=> ( v_thesis____
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
      | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(36,plain,
    ( ( ~ ! [V_da: $i] :
            ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
            | v_thesis____
            | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_d(V_da),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
      | v_thesis____
      | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )
  <=> ( ~ ! [V_da: $i] :
            ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
            | v_thesis____
            | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_d(V_da),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )
      | v_thesis____
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
      | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
    inference(monotonicity,[status(thm)],[35]) ).

tff(37,plain,
    ( ( ~ ! [V_da: $i] :
            ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
            | v_thesis____
            | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_d(V_da),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
      | v_thesis____
      | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )
  <=> ( ~ ! [V_da: $i] :
            ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
            | v_thesis____
            | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_d(V_da),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )
      | v_thesis____
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
      | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
    inference(transitivity,[status(thm)],[36,34]) ).

tff(38,plain,
    ( ~ ! [V_da: $i] :
          ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
          | v_thesis____
          | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_d(V_da),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
    | v_thesis____
    | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(39,plain,
    ( ~ ! [V_da: $i] :
          ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
          | v_thesis____
          | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_d(V_da),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )
    | v_thesis____
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(modus_ponens,[status(thm)],[38,37]) ).

tff(40,plain,
    ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(unit_resolution,[status(thm)],[39,16,13,33]) ).

tff(41,plain,
    ^ [V_w: $i] :
      refl(( ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
          | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
          | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,V_w,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )
      <=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
          | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
          | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,V_w,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) )),
    inference(bind,[status(th)],[]) ).

tff(42,plain,
    ( ! [V_w: $i] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
        | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
        | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,V_w,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )
  <=> ! [V_w: $i] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
        | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
        | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,V_w,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
    inference(quant_intro,[status(thm)],[41]) ).

tff(43,plain,
    ( ! [V_w: $i] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
        | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
        | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,V_w,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )
  <=> ! [V_w: $i] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
        | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
        | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,V_w,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(44,plain,
    ^ [V_w: $i] :
      trans(monotonicity(rewrite(( ( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,V_w,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
              | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal) )
          <=> ( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
              | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,V_w,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) )),
          ( ( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,V_w,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
            | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
            | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
        <=> ( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
            | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,V_w,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
            | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ) )),
        rewrite(( ( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
            | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,V_w,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
            | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
        <=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
            | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
            | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,V_w,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) )),
        ( ( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,V_w,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
          | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
          | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
      <=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
          | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
          | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,V_w,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) )),
    inference(bind,[status(th)],[]) ).

tff(45,plain,
    ( ! [V_w: $i] :
        ( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,V_w,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
        | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
  <=> ! [V_w: $i] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
        | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
        | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,V_w,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
    inference(quant_intro,[status(thm)],[44]) ).

tff(46,axiom,
    ! [V_w: $i] :
      ( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,V_w,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
      | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_1) ).

tff(47,plain,
    ! [V_w: $i] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
      | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
      | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,V_w,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(modus_ponens,[status(thm)],[46,45]) ).

tff(48,plain,
    ! [V_w: $i] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
      | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
      | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,V_w,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(modus_ponens,[status(thm)],[47,43]) ).

tff(49,plain,
    ! [V_w: $i] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
      | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
      | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,V_w,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(skolemize,[status(sab)],[48]) ).

tff(50,plain,
    ! [V_w: $i] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
      | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
      | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,V_w,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(modus_ponens,[status(thm)],[49,42]) ).

tff(51,plain,
    ( ( ~ ! [V_w: $i] :
            ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
            | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
            | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,V_w,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
      | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
      | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )
  <=> ( ~ ! [V_w: $i] :
            ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
            | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
            | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,V_w,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
      | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
      | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(52,plain,
    ( ~ ! [V_w: $i] :
          ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
          | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
          | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,V_w,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
    | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(53,plain,
    ( ~ ! [V_w: $i] :
          ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
          | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_w,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
          | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,V_w,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
    | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(modus_ponens,[status(thm)],[52,51]) ).

tff(54,plain,
    ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
    inference(unit_resolution,[status(thm)],[53,50,40,23]) ).

tff(55,plain,
    ^ [V_da: $i] :
      refl(( ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
          | v_thesis____
          | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
      <=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
          | v_thesis____
          | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ) )),
    inference(bind,[status(th)],[]) ).

tff(56,plain,
    ( ! [V_da: $i] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
        | v_thesis____
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
  <=> ! [V_da: $i] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
        | v_thesis____
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ) ),
    inference(quant_intro,[status(thm)],[55]) ).

tff(57,plain,
    ( ! [V_da: $i] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
        | v_thesis____
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
  <=> ! [V_da: $i] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
        | v_thesis____
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(58,plain,
    ^ [V_da: $i] :
      rewrite(( ( v_thesis____
          | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
          | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal) )
      <=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
          | v_thesis____
          | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ) )),
    inference(bind,[status(th)],[]) ).

tff(59,plain,
    ( ! [V_da: $i] :
        ( v_thesis____
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal) )
  <=> ! [V_da: $i] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
        | v_thesis____
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ) ),
    inference(quant_intro,[status(thm)],[58]) ).

tff(60,axiom,
    ! [V_da: $i] :
      ( v_thesis____
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

tff(61,plain,
    ! [V_da: $i] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
      | v_thesis____
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
    inference(modus_ponens,[status(thm)],[60,59]) ).

tff(62,plain,
    ! [V_da: $i] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
      | v_thesis____
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
    inference(modus_ponens,[status(thm)],[61,57]) ).

tff(63,plain,
    ! [V_da: $i] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
      | v_thesis____
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
    inference(skolemize,[status(sab)],[62]) ).

tff(64,plain,
    ! [V_da: $i] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
      | v_thesis____
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
    inference(modus_ponens,[status(thm)],[63,56]) ).

tff(65,plain,
    ( ( ~ ! [V_da: $i] :
            ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
            | v_thesis____
            | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
      | v_thesis____
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
  <=> ( ~ ! [V_da: $i] :
            ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
            | v_thesis____
            | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
      | v_thesis____
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(66,plain,
    ( ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
      | v_thesis____
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
  <=> ( v_thesis____
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(67,plain,
    ( ( ~ ! [V_da: $i] :
            ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
            | v_thesis____
            | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
      | v_thesis____
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
  <=> ( ~ ! [V_da: $i] :
            ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
            | v_thesis____
            | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
      | v_thesis____
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ) ),
    inference(monotonicity,[status(thm)],[66]) ).

tff(68,plain,
    ( ( ~ ! [V_da: $i] :
            ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
            | v_thesis____
            | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
      | v_thesis____
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
  <=> ( ~ ! [V_da: $i] :
            ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
            | v_thesis____
            | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
      | v_thesis____
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ) ),
    inference(transitivity,[status(thm)],[67,65]) ).

tff(69,plain,
    ( ~ ! [V_da: $i] :
          ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
          | v_thesis____
          | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
    | v_thesis____
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(70,plain,
    ( ~ ! [V_da: $i] :
          ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_da,tc_RealDef_Oreal)
          | v_thesis____
          | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(V_da),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
    | v_thesis____
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_p,v_s____,v_z____),tc_RealDef_Oreal)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_d(v_sko__CHAINED__1(v_p,v_s____,v_z____)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
    inference(modus_ponens,[status(thm)],[69,68]) ).

tff(71,plain,
    $false,
    inference(unit_resolution,[status(thm)],[70,16,13,64,54]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : ALG375-1 : TPTP v9.0.0. Released v4.1.0.
% 0.06/0.12  % Command    : run_E %s %d THM
% 0.11/0.32  % Computer : n006.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Thu Jun 19 11:09:35 EDT 2025
% 0.11/0.32  % CPUTime    : 
% 3.21/3.40  % SZS status Unsatisfiable
% 3.21/3.40  % SZS output start Proof
% See solution above
% 3.31/3.49  % E exiting
%------------------------------------------------------------------------------