TSTP Solution File: ALG360-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : ALG360-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n004.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 : Tue Sep  6 16:09:56 EDT 2022

% Result   : Unsatisfiable 1.29s 1.14s
% Output   : Proof 1.33s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   83
% Syntax   : Number of formulae    :  161 (  49 unt;  21 typ;   0 def)
%            Number of atoms       :  635 ( 327 equ)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :  846 ( 372   ~; 410   |;   0   &)
%                                         (  64 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of FOOLs       :   21 (  21 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   28 (  16   >;  12   *;   0   +;   0  <<)
%            Number of predicates  :   14 (  12 usr;   1 prp; 0-3 aty)
%            Number of functors    :   13 (  13 usr;   5 con; 0-3 aty)
%            Number of variables   :  288 ( 265   !;   0   ?; 288   :)

% 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_HOL_Oone__class_Oone_type,type,
    c_HOL_Oone__class_Oone: $i > $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_Oplus__class_Oplus_type,type,
    c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).

tff(c_Power_Opower__class_Opower_type,type,
    c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).

tff(v_na_____type,type,
    v_na____: $i ).

tff(v_v_____type,type,
    v_v____: $i ).

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

tff(v_b_type,type,
    v_b: $i ).

tff(c_RealVector_Oof__real_type,type,
    c_RealVector_Oof__real: ( $i * $i ) > $i ).

tff(c_HOL_Otimes__class_Otimes_type,type,
    c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).

tff(class_OrderedGroup_Oab__semigroup__mult_type,type,
    class_OrderedGroup_Oab__semigroup__mult: $i > $o ).

tff(class_Ring__and__Field_Ofield_type,type,
    class_Ring__and__Field_Ofield: $i > $o ).

tff(class_Ring__and__Field_Odivision__by__zero_type,type,
    class_Ring__and__Field_Odivision__by__zero: $i > $o ).

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

tff(class_Ring__and__Field_Ocomm__semiring__1_type,type,
    class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).

tff(class_RealVector_Oreal__normed__vector_type,type,
    class_RealVector_Oreal__normed__vector: $i > $o ).

tff(class_RealVector_Oreal__algebra__1_type,type,
    class_RealVector_Oreal__algebra__1: $i > $o ).

tff(class_OrderedGroup_Omonoid__mult_type,type,
    class_OrderedGroup_Omonoid__mult: $i > $o ).

tff(1,plain,
    ( ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) )
  <=> ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__is__one_1) ).

tff(3,plain,
    c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
    inference(modus_ponens,[status(thm)],[2,1]) ).

tff(4,plain,
    c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(symmetry,[status(thm)],[3]) ).

tff(5,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex)
  <=> class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) ),
    inference(rewrite,[status(thm)],]) ).

tff(6,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).

tff(7,plain,
    class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
    inference(modus_ponens,[status(thm)],[6,5]) ).

tff(8,plain,
    ^ [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
      refl(
        ( ( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
          | ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) )
      <=> ( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
          | ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ) )),
    inference(bind,[status(th)],]) ).

tff(9,plain,
    ( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
        ( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
        | ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) )
  <=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
        ( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
        | ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ) ),
    inference(quant_intro,[status(thm)],[8]) ).

tff(10,plain,
    ( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
        ( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
        | ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) )
  <=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
        ( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
        | ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(11,axiom,
    ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
      ( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).

tff(12,plain,
    ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
      ( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ),
    inference(modus_ponens,[status(thm)],[11,10]) ).

tff(13,plain,
    ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
      ( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ),
    inference(skolemize,[status(sab)],[12]) ).

tff(14,plain,
    ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
      ( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ),
    inference(modus_ponens,[status(thm)],[13,9]) ).

tff(15,plain,
    ( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
            ( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
            | ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) )
      | ~ class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
  <=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
            ( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
            | ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) )
      | ~ class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(16,plain,
    ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
          ( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
          | ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) )
    | ~ class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex)
    | ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(17,plain,
    ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
          ( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
          | ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) )
    | ~ class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex)
    | ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
    inference(modus_ponens,[status(thm)],[16,15]) ).

tff(18,plain,
    c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    inference(unit_resolution,[status(thm)],[17,14,7]) ).

tff(19,plain,
    ( class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
  <=> class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) ),
    inference(rewrite,[status(thm)],]) ).

tff(20,axiom,
    class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).

tff(21,plain,
    class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
    inference(modus_ponens,[status(thm)],[20,19]) ).

tff(22,plain,
    ( class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
  <=> class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) ),
    inference(rewrite,[status(thm)],]) ).

tff(23,axiom,
    class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).

tff(24,plain,
    class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
    inference(modus_ponens,[status(thm)],[23,22]) ).

tff(25,plain,
    ( ( v_b != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
  <=> ( v_b != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(26,axiom,
    v_b != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).

tff(27,plain,
    v_b != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
    inference(modus_ponens,[status(thm)],[26,25]) ).

tff(28,plain,
    ^ [V_c: $i,V_b: $i,T_a: $i] :
      refl(
        ( ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
          | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
          | ~ class_Ring__and__Field_Ofield(T_a)
          | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) )
      <=> ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
          | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
          | ~ class_Ring__and__Field_Ofield(T_a)
          | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) ) )),
    inference(bind,[status(th)],]) ).

tff(29,plain,
    ( ! [V_c: $i,V_b: $i,T_a: $i] :
        ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
        | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
        | ~ class_Ring__and__Field_Ofield(T_a)
        | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) )
  <=> ! [V_c: $i,V_b: $i,T_a: $i] :
        ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
        | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
        | ~ class_Ring__and__Field_Ofield(T_a)
        | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) ) ),
    inference(quant_intro,[status(thm)],[28]) ).

tff(30,plain,
    ( ! [V_c: $i,V_b: $i,T_a: $i] :
        ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
        | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
        | ~ class_Ring__and__Field_Ofield(T_a)
        | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) )
  <=> ! [V_c: $i,V_b: $i,T_a: $i] :
        ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
        | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
        | ~ class_Ring__and__Field_Ofield(T_a)
        | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(31,plain,
    ^ [V_c: $i,V_b: $i,T_a: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              rewrite(
                ( ( ~ class_Ring__and__Field_Ofield(T_a)
                  | ~ class_Ring__and__Field_Odivision__by__zero(T_a) )
              <=> ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
                  | ~ class_Ring__and__Field_Ofield(T_a) ) )),
              ( ( ~ class_Ring__and__Field_Ofield(T_a)
                | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
                | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) )
            <=> ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
                | ~ class_Ring__and__Field_Ofield(T_a)
                | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) ) )),
            rewrite(
              ( ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
                | ~ class_Ring__and__Field_Ofield(T_a)
                | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) )
            <=> ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
                | ~ class_Ring__and__Field_Ofield(T_a)
                | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) ) )),
            ( ( ~ class_Ring__and__Field_Ofield(T_a)
              | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
              | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) )
          <=> ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
              | ~ class_Ring__and__Field_Ofield(T_a)
              | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) ) )),
          ( ( ~ class_Ring__and__Field_Ofield(T_a)
            | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
            | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b )
            | ( V_c = c_HOL_Ozero__class_Ozero(T_a) ) )
        <=> ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
            | ~ class_Ring__and__Field_Ofield(T_a)
            | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b )
            | ( V_c = c_HOL_Ozero__class_Ozero(T_a) ) ) )),
        rewrite(
          ( ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
            | ~ class_Ring__and__Field_Ofield(T_a)
            | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b )
            | ( V_c = c_HOL_Ozero__class_Ozero(T_a) ) )
        <=> ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
            | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
            | ~ class_Ring__and__Field_Ofield(T_a)
            | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) ) )),
        ( ( ~ class_Ring__and__Field_Ofield(T_a)
          | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
          | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b )
          | ( V_c = c_HOL_Ozero__class_Ozero(T_a) ) )
      <=> ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
          | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
          | ~ class_Ring__and__Field_Ofield(T_a)
          | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) ) )),
    inference(bind,[status(th)],]) ).

tff(32,plain,
    ( ! [V_c: $i,V_b: $i,T_a: $i] :
        ( ~ class_Ring__and__Field_Ofield(T_a)
        | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
        | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b )
        | ( V_c = c_HOL_Ozero__class_Ozero(T_a) ) )
  <=> ! [V_c: $i,V_b: $i,T_a: $i] :
        ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
        | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
        | ~ class_Ring__and__Field_Ofield(T_a)
        | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) ) ),
    inference(quant_intro,[status(thm)],[31]) ).

tff(33,axiom,
    ! [V_c: $i,V_b: $i,T_a: $i] :
      ( ~ class_Ring__and__Field_Ofield(T_a)
      | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b )
      | ( V_c = c_HOL_Ozero__class_Ozero(T_a) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_0) ).

tff(34,plain,
    ! [V_c: $i,V_b: $i,T_a: $i] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
      | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
      | ~ class_Ring__and__Field_Ofield(T_a)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) ),
    inference(modus_ponens,[status(thm)],[33,32]) ).

tff(35,plain,
    ! [V_c: $i,V_b: $i,T_a: $i] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
      | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
      | ~ class_Ring__and__Field_Ofield(T_a)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) ),
    inference(modus_ponens,[status(thm)],[34,30]) ).

tff(36,plain,
    ! [V_c: $i,V_b: $i,T_a: $i] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
      | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
      | ~ class_Ring__and__Field_Ofield(T_a)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) ),
    inference(skolemize,[status(sab)],[35]) ).

tff(37,plain,
    ! [V_c: $i,V_b: $i,T_a: $i] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
      | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
      | ~ class_Ring__and__Field_Ofield(T_a)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) ),
    inference(modus_ponens,[status(thm)],[36,29]) ).

tff(38,plain,
    ( ( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
            ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
            | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
            | ~ class_Ring__and__Field_Ofield(T_a)
            | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) )
      | ( v_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
      | ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
      | ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
  <=> ( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
            ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
            | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
            | ~ class_Ring__and__Field_Ofield(T_a)
            | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) )
      | ( v_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
      | ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
      | ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(39,plain,
    ( ( ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
      | ( v_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
      | ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
  <=> ( ( v_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
      | ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
      | ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(40,plain,
    ( ( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
            ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
            | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
            | ~ class_Ring__and__Field_Ofield(T_a)
            | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) )
      | ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
      | ( v_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
      | ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
  <=> ( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
            ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
            | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
            | ~ class_Ring__and__Field_Ofield(T_a)
            | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) )
      | ( v_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
      | ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
      | ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
    inference(monotonicity,[status(thm)],[39]) ).

tff(41,plain,
    ( ( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
            ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
            | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
            | ~ class_Ring__and__Field_Ofield(T_a)
            | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) )
      | ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
      | ( v_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
      | ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
  <=> ( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
            ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
            | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
            | ~ class_Ring__and__Field_Ofield(T_a)
            | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) )
      | ( v_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
      | ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
      | ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
    inference(transitivity,[status(thm)],[40,38]) ).

tff(42,plain,
    ( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
          ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
          | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
          | ~ class_Ring__and__Field_Ofield(T_a)
          | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) )
    | ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
    | ( v_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
    | ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
    | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(43,plain,
    ( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
          ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
          | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
          | ~ class_Ring__and__Field_Ofield(T_a)
          | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) )
    | ( v_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
    | ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
    | ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
    | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
    inference(modus_ponens,[status(thm)],[42,41]) ).

tff(44,plain,
    c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    inference(unit_resolution,[status(thm)],[43,37,27,24,21]) ).

tff(45,plain,
    c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),
    inference(symmetry,[status(thm)],[44]) ).

tff(46,plain,
    c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    inference(monotonicity,[status(thm)],[45]) ).

tff(47,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
  <=> class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
    inference(rewrite,[status(thm)],]) ).

tff(48,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).

tff(49,plain,
    class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
    inference(modus_ponens,[status(thm)],[48,47]) ).

tff(50,plain,
    ^ [V_b: $i,V_a: $i,T_a: $i] :
      refl(
        ( ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
          | ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) )
      <=> ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
          | ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ) )),
    inference(bind,[status(th)],]) ).

tff(51,plain,
    ( ! [V_b: $i,V_a: $i,T_a: $i] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
        | ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) )
  <=> ! [V_b: $i,V_a: $i,T_a: $i] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
        | ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ) ),
    inference(quant_intro,[status(thm)],[50]) ).

tff(52,plain,
    ( ! [V_b: $i,V_a: $i,T_a: $i] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
        | ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) )
  <=> ! [V_b: $i,V_a: $i,T_a: $i] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
        | ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(53,axiom,
    ! [V_b: $i,V_a: $i,T_a: $i] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
      | ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).

tff(54,plain,
    ! [V_b: $i,V_a: $i,T_a: $i] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
      | ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ),
    inference(modus_ponens,[status(thm)],[53,52]) ).

tff(55,plain,
    ! [V_b: $i,V_a: $i,T_a: $i] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
      | ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ),
    inference(skolemize,[status(sab)],[54]) ).

tff(56,plain,
    ! [V_b: $i,V_a: $i,T_a: $i] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
      | ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ),
    inference(modus_ponens,[status(thm)],[55,51]) ).

tff(57,plain,
    ( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
            ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
            | ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) )
      | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
  <=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
            ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
            | ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) )
      | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(58,plain,
    ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
          ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
          | ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) )
    | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
    | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(59,plain,
    ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
          ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
          | ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) )
    | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
    | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
    inference(modus_ponens,[status(thm)],[58,57]) ).

tff(60,plain,
    c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    inference(unit_resolution,[status(thm)],[59,56,49]) ).

tff(61,plain,
    ( class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
  <=> class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
    inference(rewrite,[status(thm)],]) ).

tff(62,axiom,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).

tff(63,plain,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    inference(modus_ponens,[status(thm)],[62,61]) ).

tff(64,plain,
    ^ [V_x: $i,T_a: $i] :
      refl(
        ( ( ~ class_RealVector_Oreal__normed__vector(T_a)
          | ( V_x = c_HOL_Ozero__class_Ozero(T_a) )
          | ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
      <=> ( ~ class_RealVector_Oreal__normed__vector(T_a)
          | ( V_x = c_HOL_Ozero__class_Ozero(T_a) )
          | ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) )),
    inference(bind,[status(th)],]) ).

tff(65,plain,
    ( ! [V_x: $i,T_a: $i] :
        ( ~ class_RealVector_Oreal__normed__vector(T_a)
        | ( V_x = c_HOL_Ozero__class_Ozero(T_a) )
        | ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
  <=> ! [V_x: $i,T_a: $i] :
        ( ~ class_RealVector_Oreal__normed__vector(T_a)
        | ( V_x = c_HOL_Ozero__class_Ozero(T_a) )
        | ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
    inference(quant_intro,[status(thm)],[64]) ).

tff(66,plain,
    ( ! [V_x: $i,T_a: $i] :
        ( ~ class_RealVector_Oreal__normed__vector(T_a)
        | ( V_x = c_HOL_Ozero__class_Ozero(T_a) )
        | ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
  <=> ! [V_x: $i,T_a: $i] :
        ( ~ class_RealVector_Oreal__normed__vector(T_a)
        | ( V_x = c_HOL_Ozero__class_Ozero(T_a) )
        | ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(67,plain,
    ^ [V_x: $i,T_a: $i] :
      rewrite(
        ( ( ~ class_RealVector_Oreal__normed__vector(T_a)
          | ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
          | ( V_x = c_HOL_Ozero__class_Ozero(T_a) ) )
      <=> ( ~ class_RealVector_Oreal__normed__vector(T_a)
          | ( V_x = c_HOL_Ozero__class_Ozero(T_a) )
          | ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) )),
    inference(bind,[status(th)],]) ).

tff(68,plain,
    ( ! [V_x: $i,T_a: $i] :
        ( ~ class_RealVector_Oreal__normed__vector(T_a)
        | ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
        | ( V_x = c_HOL_Ozero__class_Ozero(T_a) ) )
  <=> ! [V_x: $i,T_a: $i] :
        ( ~ class_RealVector_Oreal__normed__vector(T_a)
        | ( V_x = c_HOL_Ozero__class_Ozero(T_a) )
        | ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
    inference(quant_intro,[status(thm)],[67]) ).

tff(69,axiom,
    ! [V_x: $i,T_a: $i] :
      ( ~ class_RealVector_Oreal__normed__vector(T_a)
      | ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
      | ( V_x = c_HOL_Ozero__class_Ozero(T_a) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__eq__zero_0) ).

tff(70,plain,
    ! [V_x: $i,T_a: $i] :
      ( ~ class_RealVector_Oreal__normed__vector(T_a)
      | ( V_x = c_HOL_Ozero__class_Ozero(T_a) )
      | ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(modus_ponens,[status(thm)],[69,68]) ).

tff(71,plain,
    ! [V_x: $i,T_a: $i] :
      ( ~ class_RealVector_Oreal__normed__vector(T_a)
      | ( V_x = c_HOL_Ozero__class_Ozero(T_a) )
      | ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(modus_ponens,[status(thm)],[70,66]) ).

tff(72,plain,
    ! [V_x: $i,T_a: $i] :
      ( ~ class_RealVector_Oreal__normed__vector(T_a)
      | ( V_x = c_HOL_Ozero__class_Ozero(T_a) )
      | ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(skolemize,[status(sab)],[71]) ).

tff(73,plain,
    ! [V_x: $i,T_a: $i] :
      ( ~ class_RealVector_Oreal__normed__vector(T_a)
      | ( V_x = c_HOL_Ozero__class_Ozero(T_a) )
      | ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(modus_ponens,[status(thm)],[72,65]) ).

tff(74,plain,
    ( ( ~ ! [V_x: $i,T_a: $i] :
            ( ~ class_RealVector_Oreal__normed__vector(T_a)
            | ( V_x = c_HOL_Ozero__class_Ozero(T_a) )
            | ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
      | ( v_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
      | ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
      | ( c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
  <=> ( ~ ! [V_x: $i,T_a: $i] :
            ( ~ class_RealVector_Oreal__normed__vector(T_a)
            | ( V_x = c_HOL_Ozero__class_Ozero(T_a) )
            | ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
      | ( v_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
      | ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
      | ( c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(75,plain,
    ( ( ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
      | ( v_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
      | ( c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
  <=> ( ( v_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
      | ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
      | ( c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(76,plain,
    ( ( ~ ! [V_x: $i,T_a: $i] :
            ( ~ class_RealVector_Oreal__normed__vector(T_a)
            | ( V_x = c_HOL_Ozero__class_Ozero(T_a) )
            | ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
      | ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
      | ( v_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
      | ( c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
  <=> ( ~ ! [V_x: $i,T_a: $i] :
            ( ~ class_RealVector_Oreal__normed__vector(T_a)
            | ( V_x = c_HOL_Ozero__class_Ozero(T_a) )
            | ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
      | ( v_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
      | ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
      | ( c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
    inference(monotonicity,[status(thm)],[75]) ).

tff(77,plain,
    ( ( ~ ! [V_x: $i,T_a: $i] :
            ( ~ class_RealVector_Oreal__normed__vector(T_a)
            | ( V_x = c_HOL_Ozero__class_Ozero(T_a) )
            | ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
      | ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
      | ( v_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
      | ( c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
  <=> ( ~ ! [V_x: $i,T_a: $i] :
            ( ~ class_RealVector_Oreal__normed__vector(T_a)
            | ( V_x = c_HOL_Ozero__class_Ozero(T_a) )
            | ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
      | ( v_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
      | ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
      | ( c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
    inference(transitivity,[status(thm)],[76,74]) ).

tff(78,plain,
    ( ~ ! [V_x: $i,T_a: $i] :
          ( ~ class_RealVector_Oreal__normed__vector(T_a)
          | ( V_x = c_HOL_Ozero__class_Ozero(T_a) )
          | ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
    | ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
    | ( v_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
    | ( c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(79,plain,
    ( ~ ! [V_x: $i,T_a: $i] :
          ( ~ class_RealVector_Oreal__normed__vector(T_a)
          | ( V_x = c_HOL_Ozero__class_Ozero(T_a) )
          | ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
    | ( v_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
    | ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
    | ( c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(modus_ponens,[status(thm)],[78,77]) ).

tff(80,plain,
    c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
    inference(unit_resolution,[status(thm)],[79,73,27,63]) ).

tff(81,plain,
    ( class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)
  <=> class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex) ),
    inference(rewrite,[status(thm)],]) ).

tff(82,axiom,
    class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__algebra__1) ).

tff(83,plain,
    class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
    inference(modus_ponens,[status(thm)],[82,81]) ).

tff(84,plain,
    ^ [V_x: $i,T_a: $i] :
      refl(
        ( ( ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
          | ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
          | ~ class_RealVector_Oreal__algebra__1(T_a) )
      <=> ( ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
          | ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
          | ~ class_RealVector_Oreal__algebra__1(T_a) ) )),
    inference(bind,[status(th)],]) ).

tff(85,plain,
    ( ! [V_x: $i,T_a: $i] :
        ( ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
        | ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
        | ~ class_RealVector_Oreal__algebra__1(T_a) )
  <=> ! [V_x: $i,T_a: $i] :
        ( ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
        | ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
        | ~ class_RealVector_Oreal__algebra__1(T_a) ) ),
    inference(quant_intro,[status(thm)],[84]) ).

tff(86,plain,
    ( ! [V_x: $i,T_a: $i] :
        ( ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
        | ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
        | ~ class_RealVector_Oreal__algebra__1(T_a) )
  <=> ! [V_x: $i,T_a: $i] :
        ( ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
        | ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
        | ~ class_RealVector_Oreal__algebra__1(T_a) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(87,plain,
    ^ [V_x: $i,T_a: $i] :
      rewrite(
        ( ( ~ class_RealVector_Oreal__algebra__1(T_a)
          | ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
          | ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
      <=> ( ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
          | ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
          | ~ class_RealVector_Oreal__algebra__1(T_a) ) )),
    inference(bind,[status(th)],]) ).

tff(88,plain,
    ( ! [V_x: $i,T_a: $i] :
        ( ~ class_RealVector_Oreal__algebra__1(T_a)
        | ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
        | ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
  <=> ! [V_x: $i,T_a: $i] :
        ( ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
        | ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
        | ~ class_RealVector_Oreal__algebra__1(T_a) ) ),
    inference(quant_intro,[status(thm)],[87]) ).

tff(89,axiom,
    ! [V_x: $i,T_a: $i] :
      ( ~ class_RealVector_Oreal__algebra__1(T_a)
      | ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
      | ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real__eq__0__iff_0) ).

tff(90,plain,
    ! [V_x: $i,T_a: $i] :
      ( ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
      | ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
      | ~ class_RealVector_Oreal__algebra__1(T_a) ),
    inference(modus_ponens,[status(thm)],[89,88]) ).

tff(91,plain,
    ! [V_x: $i,T_a: $i] :
      ( ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
      | ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
      | ~ class_RealVector_Oreal__algebra__1(T_a) ),
    inference(modus_ponens,[status(thm)],[90,86]) ).

tff(92,plain,
    ! [V_x: $i,T_a: $i] :
      ( ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
      | ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
      | ~ class_RealVector_Oreal__algebra__1(T_a) ),
    inference(skolemize,[status(sab)],[91]) ).

tff(93,plain,
    ! [V_x: $i,T_a: $i] :
      ( ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
      | ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
      | ~ class_RealVector_Oreal__algebra__1(T_a) ),
    inference(modus_ponens,[status(thm)],[92,85]) ).

tff(94,plain,
    ( ( ~ ! [V_x: $i,T_a: $i] :
            ( ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
            | ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
            | ~ class_RealVector_Oreal__algebra__1(T_a) )
      | ( c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
      | ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)
      | ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) )
  <=> ( ~ ! [V_x: $i,T_a: $i] :
            ( ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
            | ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
            | ~ class_RealVector_Oreal__algebra__1(T_a) )
      | ( c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
      | ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)
      | ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(95,plain,
    ( ( ( c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
      | ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
      | ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex) )
  <=> ( ( c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
      | ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)
      | ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(96,plain,
    ( ( ~ ! [V_x: $i,T_a: $i] :
            ( ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
            | ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
            | ~ class_RealVector_Oreal__algebra__1(T_a) )
      | ( c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
      | ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
      | ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex) )
  <=> ( ~ ! [V_x: $i,T_a: $i] :
            ( ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
            | ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
            | ~ class_RealVector_Oreal__algebra__1(T_a) )
      | ( c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
      | ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)
      | ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ) ),
    inference(monotonicity,[status(thm)],[95]) ).

tff(97,plain,
    ( ( ~ ! [V_x: $i,T_a: $i] :
            ( ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
            | ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
            | ~ class_RealVector_Oreal__algebra__1(T_a) )
      | ( c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
      | ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
      | ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex) )
  <=> ( ~ ! [V_x: $i,T_a: $i] :
            ( ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
            | ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
            | ~ class_RealVector_Oreal__algebra__1(T_a) )
      | ( c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
      | ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)
      | ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ) ),
    inference(transitivity,[status(thm)],[96,94]) ).

tff(98,plain,
    ( ~ ! [V_x: $i,T_a: $i] :
          ( ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
          | ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
          | ~ class_RealVector_Oreal__algebra__1(T_a) )
    | ( c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
    | ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
    | ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex) ),
    inference(quant_inst,[status(thm)],]) ).

tff(99,plain,
    ( ~ ! [V_x: $i,T_a: $i] :
          ( ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
          | ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
          | ~ class_RealVector_Oreal__algebra__1(T_a) )
    | ( c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
    | ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)
    | ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
    inference(modus_ponens,[status(thm)],[98,97]) ).

tff(100,plain,
    c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
    inference(unit_resolution,[status(thm)],[99,93,83,80]) ).

tff(101,plain,
    ( ( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
            ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
            | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
            | ~ class_Ring__and__Field_Ofield(T_a)
            | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) )
      | ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
      | ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
      | ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex) ) )
  <=> ( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
            ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
            | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
            | ~ class_Ring__and__Field_Ofield(T_a)
            | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) )
      | ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
      | ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
      | ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(102,plain,
    ( ( ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
      | ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
      | ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex) ) )
  <=> ( ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
      | ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
      | ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(103,plain,
    ( ( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
            ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
            | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
            | ~ class_Ring__and__Field_Ofield(T_a)
            | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) )
      | ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
      | ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
      | ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex) ) )
  <=> ( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
            ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
            | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
            | ~ class_Ring__and__Field_Ofield(T_a)
            | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) )
      | ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
      | ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
      | ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex) ) ) ),
    inference(monotonicity,[status(thm)],[102]) ).

tff(104,plain,
    ( ( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
            ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
            | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
            | ~ class_Ring__and__Field_Ofield(T_a)
            | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) )
      | ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
      | ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
      | ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex) ) )
  <=> ( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
            ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
            | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
            | ~ class_Ring__and__Field_Ofield(T_a)
            | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) )
      | ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
      | ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
      | ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex) ) ) ),
    inference(transitivity,[status(thm)],[103,101]) ).

tff(105,plain,
    ( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
          ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
          | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
          | ~ class_Ring__and__Field_Ofield(T_a)
          | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) )
    | ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
    | ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
    | ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
    | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(106,plain,
    ( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
          ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
          | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
          | ~ class_Ring__and__Field_Ofield(T_a)
          | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) )
    | ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
    | ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
    | ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
    | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex) ) ),
    inference(modus_ponens,[status(thm)],[105,104]) ).

tff(107,plain,
    ( ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
    | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex) ) ),
    inference(unit_resolution,[status(thm)],[106,37,24,21]) ).

tff(108,plain,
    c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),
    inference(unit_resolution,[status(thm)],[107,100]) ).

tff(109,plain,
    c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    inference(symmetry,[status(thm)],[108]) ).

tff(110,plain,
    c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    inference(transitivity,[status(thm)],[109,60,46,18]) ).

tff(111,plain,
    ( class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
  <=> class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) ),
    inference(rewrite,[status(thm)],]) ).

tff(112,axiom,
    class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).

tff(113,plain,
    class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
    inference(modus_ponens,[status(thm)],[112,111]) ).

tff(114,plain,
    ^ [V_a: $i,T_a: $i] :
      refl(
        ( ( ~ class_OrderedGroup_Omonoid__mult(T_a)
          | ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) )
      <=> ( ~ class_OrderedGroup_Omonoid__mult(T_a)
          | ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ) )),
    inference(bind,[status(th)],]) ).

tff(115,plain,
    ( ! [V_a: $i,T_a: $i] :
        ( ~ class_OrderedGroup_Omonoid__mult(T_a)
        | ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) )
  <=> ! [V_a: $i,T_a: $i] :
        ( ~ class_OrderedGroup_Omonoid__mult(T_a)
        | ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ) ),
    inference(quant_intro,[status(thm)],[114]) ).

tff(116,plain,
    ( ! [V_a: $i,T_a: $i] :
        ( ~ class_OrderedGroup_Omonoid__mult(T_a)
        | ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) )
  <=> ! [V_a: $i,T_a: $i] :
        ( ~ class_OrderedGroup_Omonoid__mult(T_a)
        | ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(117,axiom,
    ! [V_a: $i,T_a: $i] :
      ( ~ class_OrderedGroup_Omonoid__mult(T_a)
      | ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1__right_0) ).

tff(118,plain,
    ! [V_a: $i,T_a: $i] :
      ( ~ class_OrderedGroup_Omonoid__mult(T_a)
      | ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ),
    inference(modus_ponens,[status(thm)],[117,116]) ).

tff(119,plain,
    ! [V_a: $i,T_a: $i] :
      ( ~ class_OrderedGroup_Omonoid__mult(T_a)
      | ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ),
    inference(skolemize,[status(sab)],[118]) ).

tff(120,plain,
    ! [V_a: $i,T_a: $i] :
      ( ~ class_OrderedGroup_Omonoid__mult(T_a)
      | ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ),
    inference(modus_ponens,[status(thm)],[119,115]) ).

tff(121,plain,
    ( ( ~ ! [V_a: $i,T_a: $i] :
            ( ~ class_OrderedGroup_Omonoid__mult(T_a)
            | ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) )
      | ~ class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex) ) )
  <=> ( ~ ! [V_a: $i,T_a: $i] :
            ( ~ class_OrderedGroup_Omonoid__mult(T_a)
            | ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) )
      | ~ class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(122,plain,
    ( ~ ! [V_a: $i,T_a: $i] :
          ( ~ class_OrderedGroup_Omonoid__mult(T_a)
          | ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) )
    | ~ class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
    | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(123,plain,
    ( ~ ! [V_a: $i,T_a: $i] :
          ( ~ class_OrderedGroup_Omonoid__mult(T_a)
          | ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) )
    | ~ class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
    | ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex) ) ),
    inference(modus_ponens,[status(thm)],[122,121]) ).

tff(124,plain,
    c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),
    inference(unit_resolution,[status(thm)],[123,120,113]) ).

tff(125,plain,
    c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    inference(symmetry,[status(thm)],[124]) ).

tff(126,plain,
    c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    inference(monotonicity,[status(thm)],[125,110]) ).

tff(127,plain,
    c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    inference(monotonicity,[status(thm)],[126]) ).

tff(128,plain,
    ( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
  <=> c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(monotonicity,[status(thm)],[127,4]) ).

tff(129,plain,
    ( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
  <=> c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(symmetry,[status(thm)],[128]) ).

tff(130,plain,
    ( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
  <=> ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(monotonicity,[status(thm)],[129]) ).

tff(131,plain,
    ( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
  <=> ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(rewrite,[status(thm)],]) ).

tff(132,plain,
    ( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
  <=> ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(rewrite,[status(thm)],]) ).

tff(133,axiom,
    ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

tff(134,plain,
    ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(modus_ponens,[status(thm)],[133,132]) ).

tff(135,plain,
    ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(modus_ponens,[status(thm)],[134,131]) ).

tff(136,plain,
    ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(modus_ponens,[status(thm)],[135,130]) ).

tff(137,plain,
    ( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
  <=> c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(rewrite,[status(thm)],]) ).

tff(138,axiom,
    c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_v_0) ).

tff(139,plain,
    c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(modus_ponens,[status(thm)],[138,137]) ).

tff(140,plain,
    $false,
    inference(unit_resolution,[status(thm)],[139,136]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ALG360-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n004.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Mon Aug 29 16:00:50 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35  Usage: tptp [options] [-file:]file
% 0.13/0.35    -h, -?       prints this message.
% 0.13/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.35    -m, -model   generate model.
% 0.13/0.35    -p, -proof   generate proof.
% 0.13/0.35    -c, -core    generate unsat core of named formulas.
% 0.13/0.35    -st, -statistics display statistics.
% 0.13/0.35    -t:timeout   set timeout (in second).
% 0.13/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35    -<param>:<value> configuration parameter and value.
% 0.13/0.35    -o:<output-file> file to place output in.
% 1.29/1.14  % SZS status Unsatisfiable
% 1.29/1.14  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------