SET007 Axioms: SET007+591.ax


%------------------------------------------------------------------------------
% File     : SET007+591 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Definition of the Riemann Definite Integral and Related Lemmas
% Version  : [Urb08] axioms.
% English  :

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : integra1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  117 (   2 unit)
%            Number of atoms       :  904 (  81 equality)
%            Maximal formula depth :   21 (   9 average)
%            Number of connectives :  892 ( 105 ~  ;   1  |; 394  &)
%                                         (  20 <=>; 372 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   36 (   1 propositional; 0-4 arity)
%            Number of functors    :   52 (   4 constant; 0-5 arity)
%            Number of variables   :  371 (   0 singleton; 360 !;  11 ?)
%            Maximal term depth    :    6 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(rc1_integra1,axiom,(
    ? [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & v1_membered(A)
      & v2_membered(A)
      & v1_integra1(A) ) )).

fof(cc1_integra1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v1_integra1(A)
       => ( ~ v1_xboole_0(A)
          & v1_membered(A)
          & v2_membered(A)
          & v1_rcomp_1(A) ) ) ) )).

fof(cc2_integra1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v1_integra1(A)
       => ( v1_membered(A)
          & v2_membered(A)
          & v3_seq_4(A) ) ) ) )).

fof(rc2_integra1,axiom,(
    ? [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_seq_4(A)
      & v1_rcomp_1(A)
      & v1_integra1(A) ) )).

fof(fc1_integra1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ~ v1_xboole_0(k1_integra1(A)) ) )).

fof(rc3_integra1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ? [B] :
          ( m2_integra1(B,A)
          & ~ v1_xboole_0(B) ) ) )).

fof(d1_integra1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v1_integra1(A)
      <=> ? [B] :
            ( m1_subset_1(B,k1_numbers)
            & ? [C] :
                ( m1_subset_1(C,k1_numbers)
                & r1_xreal_0(B,C)
                & A = k1_rcomp_1(B,C) ) ) ) ) )).

fof(t1_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => v1_rcomp_1(A) ) )).

fof(t2_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ~ v1_xboole_0(A) ) )).

fof(t3_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ( v2_seq_4(A)
        & v1_seq_4(A) ) ) )).

fof(t4_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ? [B] :
          ( m1_subset_1(B,k1_numbers)
          & ? [C] :
              ( m1_subset_1(C,k1_numbers)
              & r1_xreal_0(B,C)
              & B = k4_pscomp_1(A)
              & C = k3_pscomp_1(A) ) ) ) )).

fof(t5_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => A = k1_rcomp_1(k4_pscomp_1(A),k3_pscomp_1(A)) ) )).

fof(t6_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ! [E] :
                      ( v1_xreal_0(E)
                     => ( ( A = k1_rcomp_1(B,D)
                          & A = k1_rcomp_1(C,E) )
                       => ( B = C
                          & D = E ) ) ) ) ) ) ) )).

fof(d2_integra1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_goboard1(B)
            & m2_finseq_1(B,k1_numbers) )
         => ( m1_integra1(B,A)
          <=> ( r1_tarski(k5_relset_1(k5_numbers,k1_numbers,B),A)
              & k1_goboard1(B,k3_finseq_1(B)) = k3_pscomp_1(A) ) ) ) ) )).

fof(d3_integra1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( B = k1_integra1(A)
        <=> ! [C] :
              ( r2_hidden(C,B)
            <=> m1_integra1(C,A) ) ) ) )).

fof(d4_integra1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ( m2_integra1(B,A)
          <=> ! [C] :
                ( r2_hidden(C,B)
              <=> m1_integra1(C,A) ) ) ) ) )).

fof(t7_integra1,axiom,(
    $true )).

fof(t8_integra1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_integra1(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m2_integra1(C,B) )
             => ! [D] :
                  ( m3_integra1(D,B,C)
                 => ( r2_hidden(A,k4_finseq_1(D))
                   => r2_hidden(k1_goboard1(D,A),B) ) ) ) ) ) )).

fof(t9_integra1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_integra1(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m2_integra1(C,B) )
             => ! [D] :
                  ( m3_integra1(D,B,C)
                 => ( r2_hidden(A,k4_finseq_1(D))
                   => ( A = np__1
                      | ( r2_hidden(k10_binop_2(A,np__1),k4_finseq_1(D))
                        & r2_hidden(k2_seq_1(k5_numbers,k1_numbers,D,k10_binop_2(A,np__1)),B)
                        & r2_hidden(k10_binop_2(A,np__1),k5_numbers) ) ) ) ) ) ) ) )).

fof(d5_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m2_integra1(B,A) )
         => ! [C] :
              ( m3_integra1(C,A,B)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( r2_hidden(D,k4_finseq_1(C))
                   => ! [E] :
                        ( ( v1_integra1(E)
                          & m1_subset_1(E,k1_zfmisc_1(k1_numbers)) )
                       => ( ( D = np__1
                           => ( E = k2_integra1(A,B,C,D)
                            <=> ( k4_pscomp_1(E) = k4_pscomp_1(A)
                                & k3_pscomp_1(E) = k1_goboard1(C,D) ) ) )
                          & ( D != np__1
                           => ( E = k2_integra1(A,B,C,D)
                            <=> ( k4_pscomp_1(E) = k2_seq_1(k5_numbers,k1_numbers,C,k10_binop_2(D,np__1))
                                & k3_pscomp_1(E) = k1_goboard1(C,D) ) ) ) ) ) ) ) ) ) ) )).

fof(t10_integra1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_integra1(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m2_integra1(C,B) )
             => ! [D] :
                  ( m3_integra1(D,B,C)
                 => ( r2_hidden(A,k4_finseq_1(D))
                   => r1_tarski(k2_integra1(B,C,D,A),B) ) ) ) ) ) )).

fof(d6_integra1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => k3_integra1(A) = k10_binop_2(k3_pscomp_1(A),k4_pscomp_1(A)) ) )).

fof(t11_integra1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v3_seq_4(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => r1_xreal_0(np__0,k3_integra1(A)) ) )).

fof(d7_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m2_integra1(C,A) )
             => ! [D] :
                  ( m3_integra1(D,A,C)
                 => ! [E] :
                      ( m2_finseq_1(E,k1_numbers)
                     => ( E = k4_integra1(A,B,C,D)
                      <=> ( k3_finseq_1(E) = k3_finseq_1(D)
                          & ! [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ( r2_hidden(F,k2_finseq_1(k3_finseq_1(D)))
                               => k1_goboard1(E,F) = k11_binop_2(k3_pscomp_1(k5_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,k2_integra1(A,C,D,F)))),k3_integra1(k2_integra1(A,C,D,F))) ) ) ) ) ) ) ) ) ) )).

fof(d8_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m2_integra1(C,A) )
             => ! [D] :
                  ( m3_integra1(D,A,C)
                 => ! [E] :
                      ( m2_finseq_1(E,k1_numbers)
                     => ( E = k5_integra1(A,B,C,D)
                      <=> ( k3_finseq_1(E) = k3_finseq_1(D)
                          & ! [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ( r2_hidden(F,k2_finseq_1(k3_finseq_1(D)))
                               => k1_goboard1(E,F) = k11_binop_2(k4_pscomp_1(k5_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,k2_integra1(A,C,D,F)))),k3_integra1(k2_integra1(A,C,D,F))) ) ) ) ) ) ) ) ) ) )).

fof(d9_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m2_integra1(C,A) )
             => ! [D] :
                  ( m3_integra1(D,A,C)
                 => k6_integra1(A,B,C,D) = k15_rvsum_1(k4_integra1(A,B,C,D)) ) ) ) ) )).

fof(d10_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m2_integra1(C,A) )
             => ! [D] :
                  ( m3_integra1(D,A,C)
                 => k7_integra1(A,B,C,D) = k15_rvsum_1(k5_integra1(A,B,C,D)) ) ) ) ) )).

fof(d11_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k8_integra1(A),k1_numbers) )
             => ( C = k9_integra1(A,B)
              <=> ( k4_relset_1(k8_integra1(A),k1_numbers,C) = k8_integra1(A)
                  & ! [D] :
                      ( m3_integra1(D,A,k8_integra1(A))
                     => ( r2_hidden(D,k4_relset_1(k8_integra1(A),k1_numbers,C))
                       => k2_seq_1(k8_integra1(A),k1_numbers,C,D) = k6_integra1(A,B,k8_integra1(A),D) ) ) ) ) ) ) ) )).

fof(d12_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k8_integra1(A),k1_numbers) )
             => ( C = k10_integra1(A,B)
              <=> ( k4_relset_1(k8_integra1(A),k1_numbers,C) = k8_integra1(A)
                  & ! [D] :
                      ( m3_integra1(D,A,k8_integra1(A))
                     => ( r2_hidden(D,k4_relset_1(k8_integra1(A),k1_numbers,C))
                       => k2_seq_1(k8_integra1(A),k1_numbers,C,D) = k7_integra1(A,B,k8_integra1(A),D) ) ) ) ) ) ) ) )).

fof(d13_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ( r1_integra1(A,B)
          <=> v2_seq_4(k5_relset_1(k8_integra1(A),k1_numbers,k9_integra1(A,B))) ) ) ) )).

fof(d14_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ( r2_integra1(A,B)
          <=> v1_seq_4(k5_relset_1(k8_integra1(A),k1_numbers,k10_integra1(A,B))) ) ) ) )).

fof(d15_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => k11_integra1(A,B) = k4_pscomp_1(k5_relset_1(k8_integra1(A),k1_numbers,k9_integra1(A,B))) ) ) )).

fof(d16_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => k12_integra1(A,B) = k3_pscomp_1(k5_relset_1(k8_integra1(A),k1_numbers,k10_integra1(A,B))) ) ) )).

fof(d17_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ( r3_integra1(A,B)
          <=> ( r1_integra1(A,B)
              & r2_integra1(A,B)
              & k11_integra1(A,B) = k12_integra1(A,B) ) ) ) ) )).

fof(d18_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => k13_integra1(A,B) = k11_integra1(A,B) ) ) )).

fof(t12_integra1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k1_numbers) )
             => r1_tarski(k5_relset_1(A,k1_numbers,k6_seq_1(A,k1_numbers,B,C)),k21_complsp1(k5_relset_1(A,k1_numbers,B),k5_relset_1(A,k1_numbers,C))) ) ) ) )).

fof(t13_integra1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ( r2_rfunct_1(B,A)
           => v2_seq_4(k5_relset_1(A,k1_numbers,B)) ) ) ) )).

fof(t14_integra1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ( v2_seq_4(k5_relset_1(A,k1_numbers,B))
           => r2_rfunct_1(B,A) ) ) ) )).

fof(t15_integra1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ( r1_rfunct_1(B,A)
           => v1_seq_4(k5_relset_1(A,k1_numbers,B)) ) ) ) )).

fof(t16_integra1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ( v1_seq_4(k5_relset_1(A,k1_numbers,B))
           => r1_rfunct_1(B,A) ) ) ) )).

fof(t17_integra1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ( r3_rfunct_1(B,A)
           => v3_seq_4(k5_relset_1(A,k1_numbers,B)) ) ) ) )).

fof(t18_integra1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => r1_partfun2(A,k1_numbers,k5_rfunct_1(A,A),A) ) )).

fof(t19_integra1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(A)) )
         => k5_relset_1(B,k1_numbers,k5_rfunct_1(B,B)) = k1_seq_4(np__1) ) ) )).

fof(t20_integra1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(A)) )
         => ! [C] :
              ( ~ r1_xboole_0(C,k4_relset_1(B,k1_numbers,k5_rfunct_1(B,B)))
             => k5_relset_1(B,k1_numbers,k2_partfun1(B,k1_numbers,k5_rfunct_1(B,B),C)) = k1_seq_4(np__1) ) ) ) )).

fof(t21_integra1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_integra1(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m2_integra1(C,B) )
             => ! [D] :
                  ( m3_integra1(D,B,C)
                 => ( r2_hidden(A,k2_finseq_1(k3_finseq_1(D)))
                   => k3_integra1(k2_integra1(B,C,D,A)) = k1_goboard1(k5_integra1(B,k5_rfunct_1(B,B),C,D),A) ) ) ) ) ) )).

fof(t22_integra1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_integra1(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m2_integra1(C,B) )
             => ! [D] :
                  ( m3_integra1(D,B,C)
                 => ( r2_hidden(A,k2_finseq_1(k3_finseq_1(D)))
                   => k3_integra1(k2_integra1(B,C,D,A)) = k1_goboard1(k4_integra1(B,k5_rfunct_1(B,B),C,D),A) ) ) ) ) ) )).

fof(t23_integra1,axiom,(
    ! [A] :
      ( m2_finseq_1(A,k1_numbers)
     => ! [B] :
          ( m2_finseq_1(B,k1_numbers)
         => ! [C] :
              ( m2_finseq_1(C,k1_numbers)
             => ( ( k3_finseq_1(A) = k3_finseq_1(B)
                  & k3_finseq_1(A) = k3_finseq_1(C)
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( r2_hidden(D,k4_finseq_1(A))
                       => k1_goboard1(C,D) = k9_binop_2(k4_finseq_4(k5_numbers,k1_numbers,A,D),k4_finseq_4(k5_numbers,k1_numbers,B,D)) ) ) )
               => k15_rvsum_1(C) = k9_binop_2(k15_rvsum_1(A),k15_rvsum_1(B)) ) ) ) ) )).

fof(t24_integra1,axiom,(
    ! [A] :
      ( m2_finseq_1(A,k1_numbers)
     => ! [B] :
          ( m2_finseq_1(B,k1_numbers)
         => ! [C] :
              ( m2_finseq_1(C,k1_numbers)
             => ( ( k3_finseq_1(A) = k3_finseq_1(B)
                  & k3_finseq_1(A) = k3_finseq_1(C)
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( r2_hidden(D,k4_finseq_1(A))
                       => k1_goboard1(C,D) = k10_binop_2(k4_finseq_4(k5_numbers,k1_numbers,A,D),k4_finseq_4(k5_numbers,k1_numbers,B,D)) ) ) )
               => k15_rvsum_1(C) = k10_binop_2(k15_rvsum_1(A),k15_rvsum_1(B)) ) ) ) ) )).

fof(t25_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m2_integra1(B,A) )
         => ! [C] :
              ( m3_integra1(C,A,B)
             => k15_rvsum_1(k5_integra1(A,k5_rfunct_1(A,A),B,C)) = k3_integra1(A) ) ) ) )).

fof(t26_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m2_integra1(B,A) )
         => ! [C] :
              ( m3_integra1(C,A,B)
             => k15_rvsum_1(k4_integra1(A,k5_rfunct_1(A,A),B,C)) = k3_integra1(A) ) ) ) )).

fof(t27_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,k1_numbers)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m2_integra1(C,A) )
             => ! [D] :
                  ( m3_integra1(D,A,C)
                 => ( r2_rfunct_1(B,A)
                   => r1_xreal_0(k11_binop_2(k4_pscomp_1(k1_pscomp_1(A,k1_numbers,B)),k3_integra1(A)),k7_integra1(A,B,C,D)) ) ) ) ) ) )).

fof(t28_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,k1_numbers)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m2_integra1(C,A) )
             => ! [D] :
                  ( m3_integra1(D,A,C)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( ( r1_rfunct_1(B,A)
                          & r2_hidden(E,k2_finseq_1(k3_finseq_1(D))) )
                       => r1_xreal_0(k11_binop_2(k3_pscomp_1(k5_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,k2_integra1(A,C,D,E)))),k3_integra1(k2_integra1(A,C,D,E))),k11_binop_2(k3_pscomp_1(k1_pscomp_1(A,k1_numbers,B)),k3_integra1(k2_integra1(A,C,D,E)))) ) ) ) ) ) ) )).

fof(t29_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,k1_numbers)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m2_integra1(C,A) )
             => ! [D] :
                  ( m3_integra1(D,A,C)
                 => ( r1_rfunct_1(B,A)
                   => r1_xreal_0(k6_integra1(A,B,C,D),k11_binop_2(k3_pscomp_1(k1_pscomp_1(A,k1_numbers,B)),k3_integra1(A))) ) ) ) ) ) )).

fof(t30_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,k1_numbers)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m2_integra1(C,A) )
             => ! [D] :
                  ( m3_integra1(D,A,C)
                 => ( r3_rfunct_1(B,A)
                   => r1_xreal_0(k7_integra1(A,B,C,D),k6_integra1(A,B,C,D)) ) ) ) ) ) )).

fof(d19_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( m3_integra1(B,A,k8_integra1(A))
         => k17_integra1(A,B) = k2_seq_4(k16_integra1(k14_integra1(A,k5_rfunct_1(A,A),k8_integra1(A),B))) ) ) )).

fof(d20_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m2_integra1(B,A) )
         => ! [C] :
              ( m3_integra1(C,A,B)
             => ! [D] :
                  ( m3_integra1(D,A,B)
                 => ( r4_integra1(A,B,C,D)
                  <=> ( r1_xreal_0(k3_finseq_1(C),k3_finseq_1(D))
                      & r1_tarski(k16_integra1(C),k16_integra1(D)) ) ) ) ) ) ) )).

fof(t31_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m2_integra1(B,A) )
         => ! [C] :
              ( m3_integra1(C,A,B)
             => ! [D] :
                  ( m3_integra1(D,A,B)
                 => ( k3_finseq_1(C) = np__1
                   => r4_integra1(A,B,C,D) ) ) ) ) ) )).

fof(t32_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,k1_numbers)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m2_integra1(C,A) )
             => ! [D] :
                  ( m3_integra1(D,A,C)
                 => ! [E] :
                      ( m3_integra1(E,A,C)
                     => ( ( r1_rfunct_1(B,A)
                          & k3_finseq_1(D) = np__1 )
                       => r1_xreal_0(k6_integra1(A,B,C,E),k6_integra1(A,B,C,D)) ) ) ) ) ) ) )).

fof(t33_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,k1_numbers)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m2_integra1(C,A) )
             => ! [D] :
                  ( m3_integra1(D,A,C)
                 => ! [E] :
                      ( m3_integra1(E,A,C)
                     => ( ( r2_rfunct_1(B,A)
                          & k3_finseq_1(D) = np__1 )
                       => r1_xreal_0(k7_integra1(A,B,C,D),k7_integra1(A,B,C,E)) ) ) ) ) ) ) )).

fof(t34_integra1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_integra1(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m2_integra1(C,B) )
             => ! [D] :
                  ( m3_integra1(D,B,C)
                 => ~ ( r2_hidden(A,k4_finseq_1(D))
                      & ! [E] :
                          ( ( v1_integra1(E)
                            & m1_subset_1(E,k1_zfmisc_1(k1_numbers)) )
                         => ! [F] :
                              ( ( v1_integra1(F)
                                & m1_subset_1(F,k1_zfmisc_1(k1_numbers)) )
                             => ~ ( E = k1_rcomp_1(k4_pscomp_1(B),k1_goboard1(D,A))
                                  & F = k1_rcomp_1(k1_goboard1(D,A),k3_pscomp_1(B))
                                  & B = k4_subset_1(k1_numbers,E,F) ) ) ) ) ) ) ) ) )).

fof(t35_integra1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_integra1(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m2_integra1(C,B) )
             => ! [D] :
                  ( m3_integra1(D,B,C)
                 => ! [E] :
                      ( m3_integra1(E,B,C)
                     => ~ ( r2_hidden(A,k4_finseq_1(D))
                          & r4_integra1(B,C,D,E)
                          & ! [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ~ ( r2_hidden(F,k4_finseq_1(E))
                                  & k1_goboard1(D,A) = k1_goboard1(E,F) ) ) ) ) ) ) ) ) )).

fof(d21_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m2_integra1(B,A) )
         => ! [C] :
              ( m3_integra1(C,A,B)
             => ! [D] :
                  ( m3_integra1(D,A,B)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( r4_integra1(A,B,C,D)
                       => ! [F] :
                            ( m2_subset_1(F,k1_numbers,k5_numbers)
                           => ( ( r2_hidden(E,k4_finseq_1(C))
                               => ( F = k18_integra1(A,B,C,D,E)
                                <=> ( r2_hidden(F,k4_finseq_1(D))
                                    & k1_goboard1(C,E) = k1_goboard1(D,F) ) ) )
                              & ( ~ r2_hidden(E,k4_finseq_1(C))
                               => ( F = k18_integra1(A,B,C,D,E)
                                <=> F = np__0 ) ) ) ) ) ) ) ) ) ) )).

fof(t36_integra1,axiom,(
    ! [A] :
      ( ( v1_goboard1(A)
        & m2_finseq_1(A,k1_numbers) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_xreal_0(B,k3_finseq_1(A))
           => ( v1_goboard1(k1_rfinseq(k1_numbers,A,B))
              & m2_finseq_1(k1_rfinseq(k1_numbers,A,B),k1_numbers) ) ) ) ) )).

fof(t37_integra1,axiom,(
    ! [A] :
      ( ( v1_goboard1(A)
        & m2_finseq_1(A,k1_numbers) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( r2_hidden(C,k4_finseq_1(A))
                  & r1_xreal_0(B,C) )
               => ( v1_goboard1(k1_jordan3(k1_numbers,A,B,C))
                  & m2_finseq_1(k1_jordan3(k1_numbers,A,B,C),k1_numbers) ) ) ) ) ) )).

fof(t38_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m2_integra1(B,A) )
         => ! [C] :
              ( m3_integra1(C,A,B)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ~ ( r2_hidden(D,k4_finseq_1(C))
                          & r2_hidden(E,k4_finseq_1(C))
                          & r1_xreal_0(D,E)
                          & ! [F] :
                              ( ( v1_integra1(F)
                                & m1_subset_1(F,k1_zfmisc_1(k1_numbers)) )
                             => ~ ( k4_pscomp_1(F) = k1_goboard1(k1_jordan3(k1_numbers,C,D,E),np__1)
                                  & k3_pscomp_1(F) = k1_goboard1(k1_jordan3(k1_numbers,C,D,E),k3_finseq_1(k1_jordan3(k1_numbers,C,D,E)))
                                  & k3_finseq_1(k1_jordan3(k1_numbers,C,D,E)) = k9_binop_2(k10_binop_2(E,D),np__1)
                                  & m1_integra1(k1_jordan3(k1_numbers,C,D,E),F) ) ) ) ) ) ) ) ) )).

fof(t39_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_integra1(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m2_integra1(C,A) )
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & m2_integra1(D,B) )
                 => ! [E] :
                      ( m3_integra1(E,A,C)
                     => ! [F] :
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ! [G] :
                              ( m2_subset_1(G,k1_numbers,k5_numbers)
                             => ( ( r2_hidden(F,k4_finseq_1(E))
                                  & r2_hidden(G,k4_finseq_1(E))
                                  & r1_xreal_0(F,G)
                                  & r1_xreal_0(k4_pscomp_1(B),k1_goboard1(E,F))
                                  & k1_goboard1(E,G) = k3_pscomp_1(B) )
                               => m3_integra1(k1_jordan3(k1_numbers,E,F,G),B,D) ) ) ) ) ) ) ) ) )).

fof(d22_integra1,axiom,(
    ! [A] :
      ( m2_finseq_1(A,k1_numbers)
     => ! [B] :
          ( m2_finseq_1(B,k1_numbers)
         => ( B = k19_integra1(A)
          <=> ( k3_finseq_1(B) = k3_finseq_1(A)
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( r2_hidden(C,k2_finseq_1(k3_finseq_1(A)))
                   => k1_goboard1(B,C) = k15_rvsum_1(k16_finseq_1(k1_numbers,A,C)) ) ) ) ) ) ) )).

fof(t40_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,k1_numbers)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m2_integra1(C,A) )
             => ! [D] :
                  ( m3_integra1(D,A,C)
                 => ! [E] :
                      ( m3_integra1(E,A,C)
                     => ( ( r4_integra1(A,C,D,E)
                          & r1_rfunct_1(B,A) )
                       => ! [F] :
                            ( ( ~ v1_xboole_0(F)
                              & m2_subset_1(F,k1_numbers,k5_numbers) )
                           => ( r2_hidden(F,k4_finseq_1(D))
                             => r1_xreal_0(k15_rvsum_1(k16_finseq_1(k1_numbers,k14_integra1(A,B,C,E),k18_integra1(A,C,D,E,F))),k15_rvsum_1(k16_finseq_1(k1_numbers,k14_integra1(A,B,C,D),F))) ) ) ) ) ) ) ) ) )).

fof(t41_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,k1_numbers)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m2_integra1(C,A) )
             => ! [D] :
                  ( m3_integra1(D,A,C)
                 => ! [E] :
                      ( m3_integra1(E,A,C)
                     => ( ( r4_integra1(A,C,D,E)
                          & r2_rfunct_1(B,A) )
                       => ! [F] :
                            ( ( ~ v1_xboole_0(F)
                              & m2_subset_1(F,k1_numbers,k5_numbers) )
                           => ( r2_hidden(F,k4_finseq_1(D))
                             => r1_xreal_0(k15_rvsum_1(k16_finseq_1(k1_numbers,k15_integra1(A,B,C,D),F)),k15_rvsum_1(k16_finseq_1(k1_numbers,k15_integra1(A,B,C,E),k18_integra1(A,C,D,E,F)))) ) ) ) ) ) ) ) ) )).

fof(t42_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,k1_numbers)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m2_integra1(C,A) )
             => ! [D] :
                  ( m3_integra1(D,A,C)
                 => ! [E] :
                      ( m3_integra1(E,A,C)
                     => ! [F] :
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ( ( r4_integra1(A,C,D,E)
                              & r2_hidden(F,k4_finseq_1(D))
                              & r1_rfunct_1(B,A) )
                           => r1_xreal_0(k1_goboard1(k19_integra1(k14_integra1(A,B,C,E)),k18_integra1(A,C,D,E,F)),k1_goboard1(k19_integra1(k14_integra1(A,B,C,D)),F)) ) ) ) ) ) ) ) )).

fof(t43_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,k1_numbers)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m2_integra1(C,A) )
             => ! [D] :
                  ( m3_integra1(D,A,C)
                 => ! [E] :
                      ( m3_integra1(E,A,C)
                     => ! [F] :
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ( ( r4_integra1(A,C,D,E)
                              & r2_hidden(F,k4_finseq_1(D))
                              & r2_rfunct_1(B,A) )
                           => r1_xreal_0(k1_goboard1(k19_integra1(k15_integra1(A,B,C,D)),F),k1_goboard1(k19_integra1(k15_integra1(A,B,C,E)),k18_integra1(A,C,D,E,F))) ) ) ) ) ) ) ) )).

fof(t44_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m2_integra1(C,A) )
             => ! [D] :
                  ( m3_integra1(D,A,C)
                 => k1_goboard1(k19_integra1(k14_integra1(A,B,C,D)),k3_finseq_1(D)) = k6_integra1(A,B,C,D) ) ) ) ) )).

fof(t45_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m2_integra1(C,A) )
             => ! [D] :
                  ( m3_integra1(D,A,C)
                 => k1_goboard1(k19_integra1(k15_integra1(A,B,C,D)),k3_finseq_1(D)) = k7_integra1(A,B,C,D) ) ) ) ) )).

fof(t46_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m2_integra1(B,A) )
         => ! [C] :
              ( m3_integra1(C,A,B)
             => ! [D] :
                  ( m3_integra1(D,A,B)
                 => ( r4_integra1(A,B,C,D)
                   => k18_integra1(A,B,C,D,k3_finseq_1(C)) = k3_finseq_1(D) ) ) ) ) ) )).

fof(t47_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,k1_numbers)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m2_integra1(C,A) )
             => ! [D] :
                  ( m3_integra1(D,A,C)
                 => ! [E] :
                      ( m3_integra1(E,A,C)
                     => ( ( r4_integra1(A,C,D,E)
                          & r1_rfunct_1(B,A) )
                       => r1_xreal_0(k6_integra1(A,B,C,E),k6_integra1(A,B,C,D)) ) ) ) ) ) ) )).

fof(t48_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,k1_numbers)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m2_integra1(C,A) )
             => ! [D] :
                  ( m3_integra1(D,A,C)
                 => ! [E] :
                      ( m3_integra1(E,A,C)
                     => ( ( r4_integra1(A,C,D,E)
                          & r2_rfunct_1(B,A) )
                       => r1_xreal_0(k7_integra1(A,B,C,D),k7_integra1(A,B,C,E)) ) ) ) ) ) ) )).

fof(t49_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m2_integra1(B,A) )
         => ! [C] :
              ( m3_integra1(C,A,B)
             => ! [D] :
                  ( m3_integra1(D,A,B)
                 => ? [E] :
                      ( m3_integra1(E,A,B)
                      & r4_integra1(A,B,C,E)
                      & r4_integra1(A,B,D,E) ) ) ) ) ) )).

fof(t50_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,k1_numbers)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m2_integra1(C,A) )
             => ! [D] :
                  ( m3_integra1(D,A,C)
                 => ! [E] :
                      ( m3_integra1(E,A,C)
                     => ( r3_rfunct_1(B,A)
                       => r1_xreal_0(k7_integra1(A,B,C,D),k6_integra1(A,B,C,E)) ) ) ) ) ) ) )).

fof(t51_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,k1_numbers)
            & m2_relset_1(B,A,k1_numbers) )
         => ( r3_rfunct_1(B,A)
           => r1_xreal_0(k12_integra1(A,B),k11_integra1(A,B)) ) ) ) )).

fof(t52_integra1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
         => k21_complsp1(k5_pscomp_1(A),k5_pscomp_1(B)) = k5_pscomp_1(k21_complsp1(A,B)) ) ) )).

fof(t53_integra1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
         => ( ( v1_seq_4(A)
              & v1_seq_4(B) )
           => v1_seq_4(k21_complsp1(A,B)) ) ) ) )).

fof(t54_integra1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
         => ( ( v1_seq_4(A)
              & v1_seq_4(B) )
           => k3_pscomp_1(k21_complsp1(A,B)) = k9_binop_2(k3_pscomp_1(A),k3_pscomp_1(B)) ) ) ) )).

fof(t55_integra1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_integra1(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,B,k1_numbers)
                & m2_relset_1(C,B,k1_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,k1_numbers)
                    & m2_relset_1(D,B,k1_numbers) )
                 => ! [E] :
                      ( ( ~ v1_xboole_0(E)
                        & m2_integra1(E,B) )
                     => ! [F] :
                          ( m3_integra1(F,B,E)
                         => ( ( r2_hidden(A,k2_finseq_1(k3_finseq_1(F)))
                              & r1_rfunct_1(C,B)
                              & r1_rfunct_1(D,B) )
                           => r1_xreal_0(k1_goboard1(k14_integra1(B,k6_seq_1(B,k1_numbers,C,D),E,F),A),k9_binop_2(k1_goboard1(k14_integra1(B,C,E,F),A),k1_goboard1(k14_integra1(B,D,E,F),A))) ) ) ) ) ) ) ) )).

fof(t56_integra1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_integra1(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,B,k1_numbers)
                & m2_relset_1(C,B,k1_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,k1_numbers)
                    & m2_relset_1(D,B,k1_numbers) )
                 => ! [E] :
                      ( ( ~ v1_xboole_0(E)
                        & m2_integra1(E,B) )
                     => ! [F] :
                          ( m3_integra1(F,B,E)
                         => ( ( r2_hidden(A,k2_finseq_1(k3_finseq_1(F)))
                              & r2_rfunct_1(C,B)
                              & r2_rfunct_1(D,B) )
                           => r1_xreal_0(k9_binop_2(k1_goboard1(k15_integra1(B,C,E,F),A),k1_goboard1(k15_integra1(B,D,E,F),A)),k1_goboard1(k15_integra1(B,k6_seq_1(B,k1_numbers,C,D),E,F),A)) ) ) ) ) ) ) ) )).

fof(t57_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,k1_numbers)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,k1_numbers)
                & m2_relset_1(C,A,k1_numbers) )
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & m2_integra1(D,A) )
                 => ! [E] :
                      ( m3_integra1(E,A,D)
                     => ( ( r1_rfunct_1(B,A)
                          & r1_rfunct_1(C,A) )
                       => r1_xreal_0(k6_integra1(A,k6_seq_1(A,k1_numbers,B,C),D,E),k9_binop_2(k6_integra1(A,B,D,E),k6_integra1(A,C,D,E))) ) ) ) ) ) ) )).

fof(t58_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,k1_numbers)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,k1_numbers)
                & m2_relset_1(C,A,k1_numbers) )
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & m2_integra1(D,A) )
                 => ! [E] :
                      ( m3_integra1(E,A,D)
                     => ( ( r2_rfunct_1(B,A)
                          & r2_rfunct_1(C,A) )
                       => r1_xreal_0(k9_binop_2(k7_integra1(A,B,D,E),k7_integra1(A,C,D,E)),k7_integra1(A,k6_seq_1(A,k1_numbers,B,C),D,E)) ) ) ) ) ) ) )).

fof(t59_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,k1_numbers)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,k1_numbers)
                & m2_relset_1(C,A,k1_numbers) )
             => ( ( r3_rfunct_1(B,A)
                  & r3_rfunct_1(C,A)
                  & r3_integra1(A,B)
                  & r3_integra1(A,C) )
               => ( r3_integra1(A,k6_seq_1(A,k1_numbers,B,C))
                  & k13_integra1(A,k6_seq_1(A,k1_numbers,B,C)) = k9_binop_2(k13_integra1(A,B),k13_integra1(A,C)) ) ) ) ) ) )).

fof(dt_m1_integra1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( m1_integra1(B,A)
         => ( ~ v1_xboole_0(B)
            & v1_goboard1(B)
            & m2_finseq_1(B,k1_numbers) ) ) ) )).

fof(existence_m1_integra1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ? [B] : m1_integra1(B,A) ) )).

fof(dt_m2_integra1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( m2_integra1(B,A)
         => ~ v1_xboole_0(B) ) ) )).

fof(existence_m2_integra1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ? [B] : m2_integra1(B,A) ) )).

fof(dt_m3_integra1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers))
        & ~ v1_xboole_0(B)
        & m2_integra1(B,A) )
     => ! [C] :
          ( m3_integra1(C,A,B)
         => m1_integra1(C,A) ) ) )).

fof(existence_m3_integra1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers))
        & ~ v1_xboole_0(B)
        & m2_integra1(B,A) )
     => ? [C] : m3_integra1(C,A,B) ) )).

fof(redefinition_m3_integra1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers))
        & ~ v1_xboole_0(B)
        & m2_integra1(B,A) )
     => ! [C] :
          ( m3_integra1(C,A,B)
        <=> m1_subset_1(C,B) ) ) )).

fof(dt_k1_integra1,axiom,(
    $true )).

fof(dt_k2_integra1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers))
        & ~ v1_xboole_0(B)
        & m2_integra1(B,A)
        & m1_subset_1(C,B)
        & m1_subset_1(D,k5_numbers) )
     => ( v1_integra1(k2_integra1(A,B,C,D))
        & m1_subset_1(k2_integra1(A,B,C,D),k1_zfmisc_1(k1_numbers)) ) ) )).

fof(dt_k3_integra1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => m1_subset_1(k3_integra1(A),k1_numbers) ) )).

fof(dt_k4_integra1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers))
        & v1_funct_1(B)
        & m1_relset_1(B,A,k1_numbers)
        & ~ v1_xboole_0(C)
        & m2_integra1(C,A)
        & m1_subset_1(D,C) )
     => m2_finseq_1(k4_integra1(A,B,C,D),k1_numbers) ) )).

fof(dt_k5_integra1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers))
        & v1_funct_1(B)
        & m1_relset_1(B,A,k1_numbers)
        & ~ v1_xboole_0(C)
        & m2_integra1(C,A)
        & m1_subset_1(D,C) )
     => m2_finseq_1(k5_integra1(A,B,C,D),k1_numbers) ) )).

fof(dt_k6_integra1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers))
        & v1_funct_1(B)
        & m1_relset_1(B,A,k1_numbers)
        & ~ v1_xboole_0(C)
        & m2_integra1(C,A)
        & m1_subset_1(D,C) )
     => m1_subset_1(k6_integra1(A,B,C,D),k1_numbers) ) )).

fof(dt_k7_integra1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers))
        & v1_funct_1(B)
        & m1_relset_1(B,A,k1_numbers)
        & ~ v1_xboole_0(C)
        & m2_integra1(C,A)
        & m1_subset_1(D,C) )
     => m1_subset_1(k7_integra1(A,B,C,D),k1_numbers) ) )).

fof(dt_k8_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => m2_integra1(k8_integra1(A),A) ) )).

fof(redefinition_k8_integra1,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => k8_integra1(A) = k1_integra1(A) ) )).

fof(dt_k9_integra1,axiom,(
    ! [A,B] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers))
        & v1_funct_1(B)
        & m1_relset_1(B,A,k1_numbers) )
     => ( v1_funct_1(k9_integra1(A,B))
        & m2_relset_1(k9_integra1(A,B),k8_integra1(A),k1_numbers) ) ) )).

fof(dt_k10_integra1,axiom,(
    ! [A,B] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers))
        & v1_funct_1(B)
        & m1_relset_1(B,A,k1_numbers) )
     => ( v1_funct_1(k10_integra1(A,B))
        & m2_relset_1(k10_integra1(A,B),k8_integra1(A),k1_numbers) ) ) )).

fof(dt_k11_integra1,axiom,(
    ! [A,B] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers))
        & v1_funct_1(B)
        & m1_relset_1(B,A,k1_numbers) )
     => m1_subset_1(k11_integra1(A,B),k1_numbers) ) )).

fof(dt_k12_integra1,axiom,(
    ! [A,B] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers))
        & v1_funct_1(B)
        & m1_relset_1(B,A,k1_numbers) )
     => m1_subset_1(k12_integra1(A,B),k1_numbers) ) )).

fof(dt_k13_integra1,axiom,(
    ! [A,B] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers))
        & v1_funct_1(B)
        & m1_relset_1(B,A,k1_numbers) )
     => m1_subset_1(k13_integra1(A,B),k1_numbers) ) )).

fof(dt_k14_integra1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers))
        & v1_funct_1(B)
        & m1_relset_1(B,A,k1_numbers)
        & ~ v1_xboole_0(C)
        & m2_integra1(C,A)
        & m1_subset_1(D,C) )
     => ( ~ v1_xboole_0(k14_integra1(A,B,C,D))
        & m2_finseq_1(k14_integra1(A,B,C,D),k1_numbers) ) ) )).

fof(redefinition_k14_integra1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers))
        & v1_funct_1(B)
        & m1_relset_1(B,A,k1_numbers)
        & ~ v1_xboole_0(C)
        & m2_integra1(C,A)
        & m1_subset_1(D,C) )
     => k14_integra1(A,B,C,D) = k4_integra1(A,B,C,D) ) )).

fof(dt_k15_integra1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers))
        & v1_funct_1(B)
        & m1_relset_1(B,A,k1_numbers)
        & ~ v1_xboole_0(C)
        & m2_integra1(C,A)
        & m1_subset_1(D,C) )
     => ( ~ v1_xboole_0(k15_integra1(A,B,C,D))
        & m2_finseq_1(k15_integra1(A,B,C,D),k1_numbers) ) ) )).

fof(redefinition_k15_integra1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers))
        & v1_funct_1(B)
        & m1_relset_1(B,A,k1_numbers)
        & ~ v1_xboole_0(C)
        & m2_integra1(C,A)
        & m1_subset_1(D,C) )
     => k15_integra1(A,B,C,D) = k5_integra1(A,B,C,D) ) )).

fof(dt_k16_integra1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_finseq_1(A,k1_numbers) )
     => ( ~ v1_xboole_0(k16_integra1(A))
        & v1_finset_1(k16_integra1(A))
        & m1_subset_1(k16_integra1(A),k1_zfmisc_1(k1_numbers)) ) ) )).

fof(redefinition_k16_integra1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_finseq_1(A,k1_numbers) )
     => k16_integra1(A) = k2_relat_1(A) ) )).

fof(dt_k17_integra1,axiom,(
    ! [A,B] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers))
        & m1_subset_1(B,k8_integra1(A)) )
     => m1_subset_1(k17_integra1(A,B),k1_numbers) ) )).

fof(dt_k18_integra1,axiom,(
    ! [A,B,C,D,E] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers))
        & ~ v1_xboole_0(B)
        & m2_integra1(B,A)
        & m1_subset_1(C,B)
        & m1_subset_1(D,B)
        & m1_subset_1(E,k5_numbers) )
     => m2_subset_1(k18_integra1(A,B,C,D,E),k1_numbers,k5_numbers) ) )).

fof(dt_k19_integra1,axiom,(
    ! [A] :
      ( m1_finseq_1(A,k1_numbers)
     => m2_finseq_1(k19_integra1(A),k1_numbers) ) )).
%------------------------------------------------------------------------------