SET007 Axioms: SET007+753.ax


%------------------------------------------------------------------------------
% File     : SET007+753 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Processes in Petri nets
% 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    : pnproc_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  147 (   7 unit)
%            Number of atoms       :  763 ( 106 equality)
%            Maximal formula depth :   22 (   8 average)
%            Number of connectives :  645 (  29 ~  ;   0  |; 255  &)
%                                         (  18 <=>; 343 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   23 (   1 propositional; 0-3 arity)
%            Number of functors    :   67 (   7 constant; 0-5 arity)
%            Number of variables   :  475 (   0 singleton; 459 !;  16 ?)
%            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(cc1_pnproc_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_finseq_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A)
        & v2_finseq_1(A) ) ) )).

fof(cc2_pnproc_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A)
        & v2_finseq_1(A) ) ) )).

fof(fc1_pnproc_1,axiom,(
    ! [A,B,C,D] :
      ( ( m3_pnproc_1(B,A)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(k3_finseq_2(B)))
        & ~ v1_xboole_0(D)
        & m1_subset_1(D,k1_zfmisc_1(k3_finseq_2(B))) )
     => ~ v1_xboole_0(k12_pnproc_1(A,B,C,D)) ) )).

fof(fc2_pnproc_1,axiom,(
    ! [A,B,C,D] :
      ( ( m3_pnproc_1(B,A)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(k3_finseq_2(B)))
        & ~ v1_xboole_0(D)
        & m1_subset_1(D,k1_zfmisc_1(k3_finseq_2(B))) )
     => ~ v1_xboole_0(k13_pnproc_1(A,B,C,D)) ) )).

fof(t1_pnproc_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ r1_xreal_0(A,np__0)
         => ( v1_relat_1(k1_tarski(k4_tarski(A,B)))
            & v1_funct_1(k1_tarski(k4_tarski(A,B)))
            & v2_finseq_1(k1_tarski(k4_tarski(A,B))) ) ) ) )).

fof(t2_pnproc_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_finseq_1(A) )
     => ( A = k1_xboole_0
      <=> k15_finseq_1(A) = k1_xboole_0 ) ) )).

fof(t3_pnproc_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B,C] :
          ( ( v1_relat_1(C)
            & v1_funct_1(C)
            & v2_finseq_1(C) )
         => ( C = k1_tarski(k4_tarski(A,B))
           => k15_finseq_1(C) = k9_finseq_1(B) ) ) ) )).

fof(t4_pnproc_1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v2_finseq_1(B) )
     => ~ ( k15_finseq_1(B) = k9_finseq_1(A)
          & ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => B != k1_tarski(k4_tarski(C,A)) ) ) ) )).

fof(t5_pnproc_1,axiom,(
    ! [A,B,C,D] :
      ~ ( v1_relat_1(k2_tarski(k4_tarski(A,B),k4_tarski(C,D)))
        & v1_funct_1(k2_tarski(k4_tarski(A,B),k4_tarski(C,D)))
        & v1_finseq_1(k2_tarski(k4_tarski(A,B),k4_tarski(C,D)))
        & ~ ( A = np__1
            & C = np__1
            & B = D )
        & ~ ( A = np__1
            & C = np__2 )
        & ~ ( A = np__2
            & C = np__1 ) ) )).

fof(t6_pnproc_1,axiom,(
    ! [A,B] : k10_finseq_1(A,B) = k2_tarski(k4_tarski(np__1,A),k4_tarski(np__2,B)) )).

fof(t7_pnproc_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_finseq_1(A) )
     => k1_card_1(A) = k3_finseq_1(k15_finseq_1(A)) ) )).

fof(t8_pnproc_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v1_relat_1(B)
         => ( r1_xboole_0(k1_relat_1(A),k1_relat_1(B))
           => r1_xboole_0(A,B) ) ) ) )).

fof(t9_pnproc_1,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => ! [D] :
          ( v1_relat_1(D)
         => ( r1_xboole_0(A,B)
           => r1_xboole_0(k7_relat_1(C,A),k7_relat_1(D,B)) ) ) ) )).

fof(t10_pnproc_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( ( r1_tarski(A,C)
                  & r1_tarski(B,C)
                  & r1_xboole_0(A,B) )
               => r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) ) ) ) ) )).

fof(t11_pnproc_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => r1_tarski(k8_relat_1(A,B),k7_relat_1(B,k10_relat_1(B,A))) ) )).

fof(t12_pnproc_1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => k8_relat_1(A,B) = k7_relat_1(B,k10_relat_1(B,A)) ) )).

fof(d1_pnproc_1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( m1_pnproc_1(B,A)
      <=> ( k1_relat_1(B) = A
          & r1_tarski(k2_relat_1(B),k5_numbers) ) ) ) )).

fof(d2_pnproc_1,axiom,(
    ! [A,B] :
      ( m1_pnproc_1(B,A)
     => ! [C] :
          ( m1_pnproc_1(C,A)
         => ( r1_pnproc_1(A,B,C)
          <=> ! [D] :
                ( r2_hidden(D,A)
               => k1_pnproc_1(A,B,D) = k1_pnproc_1(A,C,D) ) ) ) ) )).

fof(d3_pnproc_1,axiom,(
    ! [A] : k3_pnproc_1(A) = k2_funcop_1(A,np__0) )).

fof(d4_pnproc_1,axiom,(
    ! [A,B] :
      ( m1_pnproc_1(B,A)
     => ! [C] :
          ( m1_pnproc_1(C,A)
         => ( r2_pnproc_1(A,B,C)
          <=> ! [D] :
                ( r2_hidden(D,A)
               => r1_xreal_0(k1_pnproc_1(A,B,D),k1_pnproc_1(A,C,D)) ) ) ) ) )).

fof(t13_pnproc_1,axiom,(
    ! [A,B] :
      ( m1_pnproc_1(B,A)
     => r2_pnproc_1(A,k3_pnproc_1(A),B) ) )).

fof(t14_pnproc_1,axiom,(
    ! [A,B] :
      ( m1_pnproc_1(B,A)
     => ! [C] :
          ( m1_pnproc_1(C,A)
         => ! [D] :
              ( m1_pnproc_1(D,A)
             => ( ( r2_pnproc_1(A,B,C)
                  & r2_pnproc_1(A,C,D) )
               => r2_pnproc_1(A,B,D) ) ) ) ) )).

fof(d5_pnproc_1,axiom,(
    ! [A,B] :
      ( m1_pnproc_1(B,A)
     => ! [C] :
          ( m1_pnproc_1(C,A)
         => ! [D] :
              ( m1_pnproc_1(D,A)
             => ( D = k4_pnproc_1(A,B,C)
              <=> ! [E] :
                    ( r2_hidden(E,A)
                   => k1_pnproc_1(A,D,E) = k1_nat_1(k1_pnproc_1(A,B,E),k1_pnproc_1(A,C,E)) ) ) ) ) ) )).

fof(t15_pnproc_1,axiom,(
    ! [A,B] :
      ( m1_pnproc_1(B,A)
     => r1_pnproc_1(A,k4_pnproc_1(A,B,k3_pnproc_1(A)),B) ) )).

fof(d6_pnproc_1,axiom,(
    ! [A,B] :
      ( m1_pnproc_1(B,A)
     => ! [C] :
          ( m1_pnproc_1(C,A)
         => ( r2_pnproc_1(A,C,B)
           => ! [D] :
                ( m1_pnproc_1(D,A)
               => ( D = k5_pnproc_1(A,B,C)
                <=> ! [E] :
                      ( r2_hidden(E,A)
                     => k1_pnproc_1(A,D,E) = k6_xcmplx_0(k1_pnproc_1(A,B,E),k1_pnproc_1(A,C,E)) ) ) ) ) ) ) )).

fof(t16_pnproc_1,axiom,(
    ! [A,B] :
      ( m1_pnproc_1(B,A)
     => ! [C] :
          ( m1_pnproc_1(C,A)
         => r2_pnproc_1(A,B,k4_pnproc_1(A,B,C)) ) ) )).

fof(t17_pnproc_1,axiom,(
    ! [A,B] :
      ( m1_pnproc_1(B,A)
     => r1_pnproc_1(A,k5_pnproc_1(A,B,k3_pnproc_1(A)),B) ) )).

fof(t18_pnproc_1,axiom,(
    ! [A,B] :
      ( m1_pnproc_1(B,A)
     => ! [C] :
          ( m1_pnproc_1(C,A)
         => ! [D] :
              ( m1_pnproc_1(D,A)
             => ( ( r2_pnproc_1(A,B,C)
                  & r2_pnproc_1(A,C,D) )
               => r2_pnproc_1(A,k5_pnproc_1(A,D,C),k5_pnproc_1(A,D,B)) ) ) ) ) )).

fof(t19_pnproc_1,axiom,(
    ! [A,B] :
      ( m1_pnproc_1(B,A)
     => ! [C] :
          ( m1_pnproc_1(C,A)
         => r1_pnproc_1(A,k5_pnproc_1(A,k4_pnproc_1(A,B,C),C),B) ) ) )).

fof(t20_pnproc_1,axiom,(
    ! [A,B] :
      ( m1_pnproc_1(B,A)
     => ! [C] :
          ( m1_pnproc_1(C,A)
         => ! [D] :
              ( m1_pnproc_1(D,A)
             => ( ( r2_pnproc_1(A,B,C)
                  & r2_pnproc_1(A,C,D) )
               => r2_pnproc_1(A,k5_pnproc_1(A,C,B),k5_pnproc_1(A,D,B)) ) ) ) ) )).

fof(t21_pnproc_1,axiom,(
    ! [A,B] :
      ( m1_pnproc_1(B,A)
     => ! [C] :
          ( m1_pnproc_1(C,A)
         => ! [D] :
              ( m1_pnproc_1(D,A)
             => ( r2_pnproc_1(A,B,C)
               => r1_pnproc_1(A,k5_pnproc_1(A,k4_pnproc_1(A,C,D),B),k4_pnproc_1(A,k5_pnproc_1(A,C,B),D)) ) ) ) ) )).

fof(t22_pnproc_1,axiom,(
    ! [A,B] :
      ( m1_pnproc_1(B,A)
     => ! [C] :
          ( m1_pnproc_1(C,A)
         => ( ( r2_pnproc_1(A,B,C)
              & r2_pnproc_1(A,C,B) )
           => r1_pnproc_1(A,B,C) ) ) ) )).

fof(t23_pnproc_1,axiom,(
    ! [A,B] :
      ( m1_pnproc_1(B,A)
     => ! [C] :
          ( m1_pnproc_1(C,A)
         => ! [D] :
              ( m1_pnproc_1(D,A)
             => r1_pnproc_1(A,k4_pnproc_1(A,k4_pnproc_1(A,B,C),D),k4_pnproc_1(A,B,k4_pnproc_1(A,C,D))) ) ) ) )).

fof(t24_pnproc_1,axiom,(
    ! [A,B] :
      ( m1_pnproc_1(B,A)
     => ! [C] :
          ( m1_pnproc_1(C,A)
         => ! [D] :
              ( m1_pnproc_1(D,A)
             => ! [E] :
                  ( m1_pnproc_1(E,A)
                 => ( ( r2_pnproc_1(A,B,C)
                      & r2_pnproc_1(A,D,E) )
                   => r2_pnproc_1(A,k4_pnproc_1(A,B,D),k4_pnproc_1(A,C,E)) ) ) ) ) ) )).

fof(t25_pnproc_1,axiom,(
    ! [A,B] :
      ( m1_pnproc_1(B,A)
     => ! [C] :
          ( m1_pnproc_1(C,A)
         => ( r2_pnproc_1(A,B,C)
           => r2_pnproc_1(A,k5_pnproc_1(A,C,B),C) ) ) ) )).

fof(t26_pnproc_1,axiom,(
    ! [A,B] :
      ( m1_pnproc_1(B,A)
     => ! [C] :
          ( m1_pnproc_1(C,A)
         => ! [D] :
              ( m1_pnproc_1(D,A)
             => ! [E] :
                  ( m1_pnproc_1(E,A)
                 => ( ( r2_pnproc_1(A,B,C)
                      & r2_pnproc_1(A,D,E)
                      & r2_pnproc_1(A,E,B) )
                   => r2_pnproc_1(A,k5_pnproc_1(A,B,E),k5_pnproc_1(A,C,D)) ) ) ) ) ) )).

fof(t27_pnproc_1,axiom,(
    ! [A,B] :
      ( m1_pnproc_1(B,A)
     => ! [C] :
          ( m1_pnproc_1(C,A)
         => ( r2_pnproc_1(A,B,C)
           => r1_pnproc_1(A,C,k4_pnproc_1(A,k5_pnproc_1(A,C,B),B)) ) ) ) )).

fof(t28_pnproc_1,axiom,(
    ! [A,B] :
      ( m1_pnproc_1(B,A)
     => ! [C] :
          ( m1_pnproc_1(C,A)
         => r1_pnproc_1(A,k5_pnproc_1(A,k4_pnproc_1(A,B,C),B),C) ) ) )).

fof(t29_pnproc_1,axiom,(
    ! [A,B] :
      ( m1_pnproc_1(B,A)
     => ! [C] :
          ( m1_pnproc_1(C,A)
         => ! [D] :
              ( m1_pnproc_1(D,A)
             => ( r2_pnproc_1(A,k4_pnproc_1(A,B,C),D)
               => r1_pnproc_1(A,k5_pnproc_1(A,k5_pnproc_1(A,D,B),C),k5_pnproc_1(A,D,k4_pnproc_1(A,B,C))) ) ) ) ) )).

fof(t30_pnproc_1,axiom,(
    ! [A,B] :
      ( m1_pnproc_1(B,A)
     => ! [C] :
          ( m1_pnproc_1(C,A)
         => ! [D] :
              ( m1_pnproc_1(D,A)
             => ( ( r2_pnproc_1(A,B,C)
                  & r2_pnproc_1(A,C,D) )
               => r1_pnproc_1(A,k5_pnproc_1(A,D,k5_pnproc_1(A,C,B)),k4_pnproc_1(A,k5_pnproc_1(A,D,C),B)) ) ) ) ) )).

fof(t31_pnproc_1,axiom,(
    ! [A,B] :
      ( m1_pnproc_1(B,A)
     => r2_hidden(B,k1_funct_2(A,k5_numbers)) ) )).

fof(t32_pnproc_1,axiom,(
    ! [A,B] :
      ( r2_hidden(A,k1_funct_2(B,k5_numbers))
     => m1_pnproc_1(A,B) ) )).

fof(d7_pnproc_1,axiom,(
    ! [A,B] :
      ( m2_pnproc_1(B,A)
    <=> ? [C] :
          ( m1_pnproc_1(C,A)
          & ? [D] :
              ( m1_pnproc_1(D,A)
              & B = k4_tarski(C,D) ) ) ) )).

fof(d8_pnproc_1,axiom,(
    ! [A,B] :
      ( m1_pnproc_1(B,A)
     => ! [C] :
          ( m2_pnproc_1(C,A)
         => ( ( r2_pnproc_1(A,k6_pnproc_1(A,C),B)
             => k8_pnproc_1(A,B,C) = k4_pnproc_1(A,k5_pnproc_1(A,B,k6_pnproc_1(A,C)),k7_pnproc_1(A,C)) )
            & ( ~ r2_pnproc_1(A,k6_pnproc_1(A,C),B)
             => k8_pnproc_1(A,B,C) = B ) ) ) ) )).

fof(t33_pnproc_1,axiom,(
    ! [A,B] :
      ( m1_pnproc_1(B,A)
     => ! [C] :
          ( m2_pnproc_1(C,A)
         => ! [D] :
              ( m2_pnproc_1(D,A)
             => ( r2_pnproc_1(A,k4_pnproc_1(A,k6_pnproc_1(A,C),k6_pnproc_1(A,D)),B)
               => r1_pnproc_1(A,k8_pnproc_1(A,k8_pnproc_1(A,B,C),D),k4_pnproc_1(A,k4_pnproc_1(A,k5_pnproc_1(A,k5_pnproc_1(A,B,k6_pnproc_1(A,C)),k6_pnproc_1(A,D)),k7_pnproc_1(A,C)),k7_pnproc_1(A,D))) ) ) ) ) )).

fof(d9_pnproc_1,axiom,(
    ! [A,B] :
      ( m2_pnproc_1(B,A)
     => ! [C] :
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( C = k9_pnproc_1(A,B)
          <=> ( k1_relat_1(C) = k1_funct_2(A,k5_numbers)
              & ! [D] :
                  ( m1_pnproc_1(D,A)
                 => k1_funct_1(C,D) = k8_pnproc_1(A,D,B) ) ) ) ) ) )).

fof(t34_pnproc_1,axiom,(
    ! [A,B] :
      ( m2_pnproc_1(B,A)
     => r1_tarski(k2_relat_1(k9_pnproc_1(A,B)),k1_funct_2(A,k5_numbers)) ) )).

fof(t35_pnproc_1,axiom,(
    ! [A,B] :
      ( m1_pnproc_1(B,A)
     => ! [C] :
          ( m2_pnproc_1(C,A)
         => ! [D] :
              ( m2_pnproc_1(D,A)
             => k8_pnproc_1(A,k8_pnproc_1(A,B,D),C) = k1_funct_1(k5_relat_1(k9_pnproc_1(A,D),k9_pnproc_1(A,C)),B) ) ) ) )).

fof(d10_pnproc_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ( m3_pnproc_1(B,A)
      <=> ! [C] :
            ( r2_hidden(C,B)
           => m2_pnproc_1(C,A) ) ) ) )).

fof(d11_pnproc_1,axiom,(
    ! [A,B] :
      ( m3_pnproc_1(B,A)
     => ! [C] :
          ( m2_finseq_2(C,B,k3_finseq_2(B))
         => ! [D] :
              ( ( v1_relat_1(D)
                & v1_funct_1(D) )
             => ( D = k10_pnproc_1(A,B,C)
              <=> ? [E] :
                    ( v1_relat_1(E)
                    & v1_funct_1(E)
                    & v1_finseq_1(E)
                    & v1_funcop_1(E)
                    & D = k4_funct_7(k1_funct_2(A,k5_numbers),E)
                    & k3_finseq_1(E) = k3_finseq_1(C)
                    & ! [F] :
                        ( m2_subset_1(F,k1_numbers,k5_numbers)
                       => ( r2_hidden(F,k4_finseq_1(C))
                         => k1_funct_1(E,F) = k9_pnproc_1(A,k4_finseq_4(k5_numbers,B,C,F)) ) ) ) ) ) ) ) )).

fof(t36_pnproc_1,axiom,(
    ! [A,B] :
      ( m3_pnproc_1(B,A)
     => k10_pnproc_1(A,B,k2_lang1(B)) = k6_relat_1(k1_funct_2(A,k5_numbers)) ) )).

fof(t37_pnproc_1,axiom,(
    ! [A,B] :
      ( m3_pnproc_1(B,A)
     => ! [C] :
          ( m4_pnproc_1(C,A,B)
         => k10_pnproc_1(A,B,k3_lang1(B,C)) = k9_pnproc_1(A,C) ) ) )).

fof(t38_pnproc_1,axiom,(
    ! [A,B] :
      ( m3_pnproc_1(B,A)
     => ! [C] :
          ( m4_pnproc_1(C,A,B)
         => k5_relat_1(k6_relat_1(k1_funct_2(A,k5_numbers)),k9_pnproc_1(A,C)) = k9_pnproc_1(A,C) ) ) )).

fof(t39_pnproc_1,axiom,(
    ! [A,B] :
      ( m3_pnproc_1(B,A)
     => ! [C] :
          ( m4_pnproc_1(C,A,B)
         => ! [D] :
              ( m4_pnproc_1(D,A,B)
             => k10_pnproc_1(A,B,k4_lang1(B,C,D)) = k5_relat_1(k9_pnproc_1(A,C),k9_pnproc_1(A,D)) ) ) ) )).

fof(t40_pnproc_1,axiom,(
    ! [A,B] :
      ( m3_pnproc_1(B,A)
     => ! [C] :
          ( m2_finseq_2(C,B,k3_finseq_2(B))
         => ( k1_relat_1(k10_pnproc_1(A,B,C)) = k1_funct_2(A,k5_numbers)
            & r1_tarski(k2_relat_1(k10_pnproc_1(A,B,C)),k1_funct_2(A,k5_numbers)) ) ) ) )).

fof(t41_pnproc_1,axiom,(
    ! [A,B] :
      ( m3_pnproc_1(B,A)
     => ! [C] :
          ( m2_finseq_2(C,B,k3_finseq_2(B))
         => ! [D] :
              ( m2_finseq_2(D,B,k3_finseq_2(B))
             => k10_pnproc_1(A,B,k1_lang1(B,C,D)) = k5_relat_1(k10_pnproc_1(A,B,C),k10_pnproc_1(A,B,D)) ) ) ) )).

fof(t42_pnproc_1,axiom,(
    ! [A,B] :
      ( m3_pnproc_1(B,A)
     => ! [C] :
          ( m4_pnproc_1(C,A,B)
         => ! [D] :
              ( m2_finseq_2(D,B,k3_finseq_2(B))
             => k10_pnproc_1(A,B,k1_lang1(B,D,k3_lang1(B,C))) = k5_relat_1(k10_pnproc_1(A,B,D),k9_pnproc_1(A,C)) ) ) ) )).

fof(d12_pnproc_1,axiom,(
    ! [A,B] :
      ( m3_pnproc_1(B,A)
     => ! [C] :
          ( m2_finseq_2(C,B,k3_finseq_2(B))
         => ! [D] :
              ( m1_pnproc_1(D,A)
             => k11_pnproc_1(A,B,C,D) = k1_funct_1(k10_pnproc_1(A,B,C),D) ) ) ) )).

fof(t43_pnproc_1,axiom,(
    ! [A,B] :
      ( m3_pnproc_1(B,A)
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(k3_finseq_2(B)))
         => ! [D] :
              ( m1_subset_1(D,k1_zfmisc_1(k3_finseq_2(B)))
             => ! [E] :
                  ( m1_subset_1(E,k1_zfmisc_1(k3_finseq_2(B)))
                 => k12_pnproc_1(A,B,k4_subset_1(k3_finseq_2(B),C,D),E) = k4_subset_1(k3_finseq_2(B),k12_pnproc_1(A,B,C,E),k12_pnproc_1(A,B,D,E)) ) ) ) ) )).

fof(t44_pnproc_1,axiom,(
    ! [A,B] :
      ( m3_pnproc_1(B,A)
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(k3_finseq_2(B)))
         => ! [D] :
              ( m1_subset_1(D,k1_zfmisc_1(k3_finseq_2(B)))
             => ! [E] :
                  ( m1_subset_1(E,k1_zfmisc_1(k3_finseq_2(B)))
                 => k12_pnproc_1(A,B,C,k4_subset_1(k3_finseq_2(B),D,E)) = k4_subset_1(k3_finseq_2(B),k12_pnproc_1(A,B,C,D),k12_pnproc_1(A,B,C,E)) ) ) ) ) )).

fof(t45_pnproc_1,axiom,(
    ! [A,B] :
      ( m3_pnproc_1(B,A)
     => ! [C] :
          ( m2_finseq_2(C,B,k3_finseq_2(B))
         => ! [D] :
              ( m2_finseq_2(D,B,k3_finseq_2(B))
             => k12_pnproc_1(A,B,k6_domain_1(k3_finseq_2(B),C),k6_domain_1(k3_finseq_2(B),D)) = k6_domain_1(k3_finseq_2(B),k1_lang1(B,C,D)) ) ) ) )).

fof(t46_pnproc_1,axiom,(
    ! [A,B] :
      ( m3_pnproc_1(B,A)
     => ! [C] :
          ( m2_finseq_2(C,B,k3_finseq_2(B))
         => ! [D] :
              ( m2_finseq_2(D,B,k3_finseq_2(B))
             => ! [E] :
                  ( m2_finseq_2(E,B,k3_finseq_2(B))
                 => k12_pnproc_1(A,B,k7_domain_1(k3_finseq_2(B),C,D),k6_domain_1(k3_finseq_2(B),E)) = k7_domain_1(k3_finseq_2(B),k1_lang1(B,C,E),k1_lang1(B,D,E)) ) ) ) ) )).

fof(t47_pnproc_1,axiom,(
    ! [A,B] :
      ( m3_pnproc_1(B,A)
     => ! [C] :
          ( m2_finseq_2(C,B,k3_finseq_2(B))
         => ! [D] :
              ( m2_finseq_2(D,B,k3_finseq_2(B))
             => ! [E] :
                  ( m2_finseq_2(E,B,k3_finseq_2(B))
                 => k12_pnproc_1(A,B,k6_domain_1(k3_finseq_2(B),C),k7_domain_1(k3_finseq_2(B),D,E)) = k7_domain_1(k3_finseq_2(B),k1_lang1(B,C,D),k1_lang1(B,C,E)) ) ) ) ) )).

fof(t48_pnproc_1,axiom,(
    ! [A,B] :
      ( m3_pnproc_1(B,A)
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(k3_finseq_2(B)))
         => ! [D] :
              ( m1_subset_1(D,k1_zfmisc_1(k3_finseq_2(B)))
             => ! [E] :
                  ( m1_subset_1(E,k1_zfmisc_1(k3_finseq_2(B)))
                 => k13_pnproc_1(A,B,k4_subset_1(k3_finseq_2(B),C,D),E) = k4_subset_1(k3_finseq_2(B),k13_pnproc_1(A,B,C,E),k13_pnproc_1(A,B,D,E)) ) ) ) ) )).

fof(t49_pnproc_1,axiom,(
    ! [A,B] :
      ( m3_pnproc_1(B,A)
     => ! [C] :
          ( m4_pnproc_1(C,A,B)
         => ! [D] :
              ( m4_pnproc_1(D,A,B)
             => k13_pnproc_1(A,B,k6_domain_1(k3_finseq_2(B),k3_lang1(B,C)),k6_domain_1(k3_finseq_2(B),k3_lang1(B,D))) = k7_domain_1(k3_finseq_2(B),k4_lang1(B,C,D),k4_lang1(B,D,C)) ) ) ) )).

fof(t50_pnproc_1,axiom,(
    ! [A,B] :
      ( m3_pnproc_1(B,A)
     => ! [C] :
          ( m4_pnproc_1(C,A,B)
         => ! [D] :
              ( m4_pnproc_1(D,A,B)
             => ! [E] :
                  ( m4_pnproc_1(E,A,B)
                 => k13_pnproc_1(A,B,k7_domain_1(k3_finseq_2(B),k3_lang1(B,C),k3_lang1(B,D)),k6_domain_1(k3_finseq_2(B),k3_lang1(B,E))) = k9_domain_1(k3_finseq_2(B),k4_lang1(B,C,E),k4_lang1(B,D,E),k4_lang1(B,E,C),k4_lang1(B,E,D)) ) ) ) ) )).

fof(t51_pnproc_1,axiom,(
    ! [A,B] :
      ( m3_pnproc_1(B,A)
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(k3_finseq_2(B)))
         => ! [D] :
              ( m1_subset_1(D,k1_zfmisc_1(k3_finseq_2(B)))
             => ! [E] :
                  ( m1_subset_1(E,k1_zfmisc_1(k3_finseq_2(B)))
                 => k12_pnproc_1(A,B,k12_pnproc_1(A,B,C,D),E) = k12_pnproc_1(A,B,C,k12_pnproc_1(A,B,D,E)) ) ) ) ) )).

fof(t52_pnproc_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_finseq_1(A) )
     => k14_pnproc_1(A,np__0) = A ) )).

fof(t53_pnproc_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v2_finseq_1(C) )
             => k14_pnproc_1(C,k1_nat_1(A,B)) = k14_pnproc_1(k14_pnproc_1(C,B),A) ) ) ) )).

fof(t55_pnproc_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v2_finseq_1(B) )
         => ( B = k1_xboole_0
          <=> k14_pnproc_1(B,A) = k1_xboole_0 ) ) ) )).

fof(t56_pnproc_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v2_finseq_1(B) )
         => ? [C] :
              ( v1_relat_1(C)
              & v1_funct_1(C)
              & v2_finseq_1(C)
              & k1_relat_1(C) = k1_relat_1(B)
              & k2_relat_1(C) = k1_relat_1(k14_pnproc_1(B,A))
              & ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( r2_hidden(D,k1_relat_1(B))
                   => k1_funct_1(C,D) = k1_nat_1(A,D) ) )
              & v2_funct_1(C) ) ) ) )).

fof(t57_pnproc_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v2_finseq_1(B) )
         => k1_card_1(B) = k1_card_1(k14_pnproc_1(B,A)) ) ) )).

fof(t58_pnproc_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => k4_finseq_1(B) = k4_finseq_1(k15_finseq_1(k14_pnproc_1(B,A))) ) ) )).

fof(t59_pnproc_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( r2_hidden(A,k4_finseq_1(C))
               => k1_funct_1(k14_finseq_1(k1_relat_1(k14_pnproc_1(C,B))),A) = k1_nat_1(B,A) ) ) ) ) )).

fof(t60_pnproc_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( r2_hidden(A,k4_finseq_1(C))
               => k1_funct_1(k15_finseq_1(k14_pnproc_1(C,B)),A) = k1_funct_1(C,A) ) ) ) ) )).

fof(t61_pnproc_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => k15_finseq_1(k14_pnproc_1(B,A)) = B ) ) )).

fof(t62_pnproc_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => k1_relat_1(k2_xboole_0(A,k14_pnproc_1(B,k3_finseq_1(A)))) = k2_finseq_1(k1_nat_1(k3_finseq_1(A),k3_finseq_1(B))) ) ) )).

fof(t63_pnproc_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v2_finseq_1(C) )
             => ( r1_xreal_0(k3_finseq_1(B),A)
               => r1_xboole_0(k4_finseq_1(B),k1_relat_1(k14_pnproc_1(C,A))) ) ) ) ) )).

fof(t64_pnproc_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => k7_finseq_1(A,B) = k2_xboole_0(A,k14_pnproc_1(B,k3_finseq_1(A))) ) ) )).

fof(t65_pnproc_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v2_finseq_1(C) )
             => ( r1_xreal_0(k3_finseq_1(B),A)
               => r1_xboole_0(B,k14_pnproc_1(C,A)) ) ) ) ) )).

fof(t66_pnproc_1,axiom,(
    ! [A,B] :
      ( m3_pnproc_1(B,A)
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(k3_finseq_2(B)))
         => ! [D] :
              ( m1_subset_1(D,k1_zfmisc_1(k3_finseq_2(B)))
             => ! [E] :
                  ( m1_subset_1(E,k1_zfmisc_1(k3_finseq_2(B)))
                 => k13_pnproc_1(A,B,k13_pnproc_1(A,B,C,D),E) = k13_pnproc_1(A,B,C,k13_pnproc_1(A,B,D,E)) ) ) ) ) )).

fof(t67_pnproc_1,axiom,(
    ! [A,B] :
      ( m3_pnproc_1(B,A)
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(k3_finseq_2(B)))
         => ! [D] :
              ( m1_subset_1(D,k1_zfmisc_1(k3_finseq_2(B)))
             => r1_tarski(k12_pnproc_1(A,B,C,D),k13_pnproc_1(A,B,C,D)) ) ) ) )).

fof(t68_pnproc_1,axiom,(
    ! [A,B] :
      ( m3_pnproc_1(B,A)
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(k3_finseq_2(B)))
         => ! [D] :
              ( m1_subset_1(D,k1_zfmisc_1(k3_finseq_2(B)))
             => ! [E] :
                  ( m1_subset_1(E,k1_zfmisc_1(k3_finseq_2(B)))
                 => ! [F] :
                      ( m1_subset_1(F,k1_zfmisc_1(k3_finseq_2(B)))
                     => ( ( r1_tarski(C,D)
                          & r1_tarski(E,F) )
                       => r1_tarski(k12_pnproc_1(A,B,C,E),k12_pnproc_1(A,B,D,F)) ) ) ) ) ) ) )).

fof(t69_pnproc_1,axiom,(
    ! [A,B] :
      ( m3_pnproc_1(B,A)
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(k3_finseq_2(B)))
         => ! [D] :
              ( m1_subset_1(D,k1_zfmisc_1(k3_finseq_2(B)))
             => ! [E] :
                  ( m1_subset_1(E,k1_zfmisc_1(k3_finseq_2(B)))
                 => ! [F] :
                      ( m1_subset_1(F,k1_zfmisc_1(k3_finseq_2(B)))
                     => ( ( r1_tarski(C,D)
                          & r1_tarski(E,F) )
                       => r1_tarski(k13_pnproc_1(A,B,C,E),k13_pnproc_1(A,B,D,F)) ) ) ) ) ) ) )).

fof(t70_pnproc_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v2_finseq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v2_finseq_1(C) )
             => ( r1_tarski(C,B)
               => r1_tarski(k14_pnproc_1(C,A),k14_pnproc_1(B,A)) ) ) ) ) )).

fof(t71_pnproc_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => r1_tarski(k14_pnproc_1(B,k3_finseq_1(A)),k7_finseq_1(A,B)) ) ) )).

fof(t72_pnproc_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v2_finseq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v2_finseq_1(C) )
             => ( r1_xboole_0(k1_relat_1(B),k1_relat_1(C))
               => r1_xboole_0(k1_relat_1(k14_pnproc_1(B,A)),k1_relat_1(k14_pnproc_1(C,A))) ) ) ) ) )).

fof(t73_pnproc_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v2_finseq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v2_finseq_1(C) )
             => ! [D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D)
                    & v2_finseq_1(D) )
                 => ( ( B = k2_xboole_0(C,D)
                      & r1_xboole_0(C,D) )
                   => k2_xboole_0(k14_pnproc_1(C,A),k14_pnproc_1(D,A)) = k14_pnproc_1(B,A) ) ) ) ) ) )).

fof(t74_pnproc_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v2_finseq_1(B) )
         => k4_finseq_1(k15_finseq_1(B)) = k4_finseq_1(k15_finseq_1(k14_pnproc_1(B,A))) ) ) )).

fof(t75_pnproc_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v2_finseq_1(C) )
             => ~ ( r2_hidden(A,k4_finseq_1(k15_finseq_1(C)))
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ~ ( D = k1_funct_1(k14_finseq_1(k1_relat_1(C)),A)
                          & k1_funct_1(k14_finseq_1(k1_relat_1(k14_pnproc_1(C,B))),A) = k1_nat_1(B,D) ) ) ) ) ) ) )).

fof(t76_pnproc_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v2_finseq_1(C) )
             => ( r2_hidden(A,k4_finseq_1(k15_finseq_1(C)))
               => k1_funct_1(k15_finseq_1(k14_pnproc_1(C,B)),A) = k1_funct_1(k15_finseq_1(C),A) ) ) ) ) )).

fof(t77_pnproc_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v2_finseq_1(B) )
         => k15_finseq_1(B) = k15_finseq_1(k14_pnproc_1(B,A)) ) ) )).

fof(t78_pnproc_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v2_finseq_1(C) )
             => ( r1_tarski(k1_relat_1(C),k2_finseq_1(A))
               => r1_tarski(k1_relat_1(k14_pnproc_1(C,B)),k2_finseq_1(k1_nat_1(B,A))) ) ) ) ) )).

fof(t79_pnproc_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v2_finseq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v2_finseq_1(C) )
             => ~ ( r1_tarski(B,A)
                  & ! [D] :
                      ( ( v1_relat_1(D)
                        & v1_funct_1(D)
                        & v2_finseq_1(D) )
                     => D != k2_xboole_0(B,k14_pnproc_1(C,k3_finseq_1(A))) ) ) ) ) ) )).

fof(t80_pnproc_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v2_finseq_1(C) )
             => ! [D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D)
                    & v2_finseq_1(D) )
                 => ~ ( r1_tarski(C,A)
                      & r1_tarski(D,B)
                      & ! [E] :
                          ( ( v1_relat_1(E)
                            & v1_funct_1(E)
                            & v2_finseq_1(E) )
                         => ~ ( E = k2_xboole_0(C,k14_pnproc_1(D,k3_finseq_1(A)))
                              & k4_finseq_1(k15_finseq_1(E)) = k2_finseq_1(k1_nat_1(k3_finseq_1(k15_finseq_1(C)),k3_finseq_1(k15_finseq_1(D)))) ) ) ) ) ) ) ) )).

fof(t81_pnproc_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v2_finseq_1(C) )
             => ! [D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D)
                    & v2_finseq_1(D) )
                 => ~ ( r1_tarski(C,A)
                      & r1_tarski(D,B)
                      & ! [E] :
                          ( ( v1_relat_1(E)
                            & v1_funct_1(E)
                            & v2_finseq_1(E) )
                         => ~ ( E = k2_xboole_0(C,k14_pnproc_1(D,k3_finseq_1(A)))
                              & k4_finseq_1(k15_finseq_1(E)) = k2_finseq_1(k1_nat_1(k3_finseq_1(k15_finseq_1(C)),k3_finseq_1(k15_finseq_1(D))))
                              & k15_finseq_1(E) = k2_xboole_0(k15_finseq_1(C),k14_pnproc_1(k15_finseq_1(D),k3_finseq_1(k15_finseq_1(C)))) ) ) ) ) ) ) ) )).

fof(t82_pnproc_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v2_finseq_1(C) )
             => ! [D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D)
                    & v2_finseq_1(D) )
                 => ~ ( r1_tarski(C,A)
                      & r1_tarski(D,B)
                      & ! [E] :
                          ( ( v1_relat_1(E)
                            & v1_funct_1(E)
                            & v2_finseq_1(E) )
                         => ~ ( E = k2_xboole_0(C,k14_pnproc_1(D,k3_finseq_1(A)))
                              & k7_finseq_1(k15_finseq_1(C),k15_finseq_1(D)) = k15_finseq_1(E) ) ) ) ) ) ) ) )).

fof(t83_pnproc_1,axiom,(
    ! [A,B] :
      ( m3_pnproc_1(B,A)
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(k3_finseq_2(B)))
         => ! [D] :
              ( m1_subset_1(D,k1_zfmisc_1(k3_finseq_2(B)))
             => ! [E] :
                  ( m1_subset_1(E,k1_zfmisc_1(k3_finseq_2(B)))
                 => ! [F] :
                      ( m1_subset_1(F,k1_zfmisc_1(k3_finseq_2(B)))
                     => r1_tarski(k12_pnproc_1(A,B,k13_pnproc_1(A,B,C,D),k13_pnproc_1(A,B,E,F)),k13_pnproc_1(A,B,k12_pnproc_1(A,B,C,E),k12_pnproc_1(A,B,D,F))) ) ) ) ) ) )).

fof(d16_pnproc_1,axiom,(
    ! [A,B] :
      ( m3_pnproc_1(B,A)
     => k15_pnproc_1(A,B) = k6_domain_1(k3_finseq_2(B),k2_lang1(B)) ) )).

fof(d17_pnproc_1,axiom,(
    ! [A,B] :
      ( m3_pnproc_1(B,A)
     => ! [C] :
          ( m4_pnproc_1(C,A,B)
         => k16_pnproc_1(A,B,C) = k6_domain_1(k3_finseq_2(B),k3_lang1(B,C)) ) ) )).

fof(t84_pnproc_1,axiom,(
    ! [A,B] :
      ( m3_pnproc_1(B,A)
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(k3_finseq_2(B)))
         => k12_pnproc_1(A,B,k15_pnproc_1(A,B),C) = C ) ) )).

fof(t85_pnproc_1,axiom,(
    ! [A,B] :
      ( m3_pnproc_1(B,A)
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(k3_finseq_2(B)))
         => k12_pnproc_1(A,B,C,k15_pnproc_1(A,B)) = C ) ) )).

fof(t86_pnproc_1,axiom,(
    ! [A,B] :
      ( m3_pnproc_1(B,A)
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(k3_finseq_2(B)))
         => k13_pnproc_1(A,B,k15_pnproc_1(A,B),C) = C ) ) )).

fof(s1_pnproc_1,axiom,(
    ? [A] :
      ( m1_pnproc_1(A,f1_s1_pnproc_1)
      & ! [B] :
          ( r2_hidden(B,f1_s1_pnproc_1)
         => k1_pnproc_1(f1_s1_pnproc_1,A,B) = f2_s1_pnproc_1(B) ) ) )).

fof(dt_m1_pnproc_1,axiom,(
    ! [A,B] :
      ( m1_pnproc_1(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B) ) ) )).

fof(existence_m1_pnproc_1,axiom,(
    ! [A] :
    ? [B] : m1_pnproc_1(B,A) )).

fof(dt_m2_pnproc_1,axiom,(
    $true )).

fof(existence_m2_pnproc_1,axiom,(
    ! [A] :
    ? [B] : m2_pnproc_1(B,A) )).

fof(dt_m3_pnproc_1,axiom,(
    ! [A,B] :
      ( m3_pnproc_1(B,A)
     => ~ v1_xboole_0(B) ) )).

fof(existence_m3_pnproc_1,axiom,(
    ! [A] :
    ? [B] : m3_pnproc_1(B,A) )).

fof(dt_m4_pnproc_1,axiom,(
    ! [A,B] :
      ( m3_pnproc_1(B,A)
     => ! [C] :
          ( m4_pnproc_1(C,A,B)
         => m2_pnproc_1(C,A) ) ) )).

fof(existence_m4_pnproc_1,axiom,(
    ! [A,B] :
      ( m3_pnproc_1(B,A)
     => ? [C] : m4_pnproc_1(C,A,B) ) )).

fof(redefinition_m4_pnproc_1,axiom,(
    ! [A,B] :
      ( m3_pnproc_1(B,A)
     => ! [C] :
          ( m4_pnproc_1(C,A,B)
        <=> m1_subset_1(C,B) ) ) )).

fof(symmetry_r1_pnproc_1,axiom,(
    ! [A,B,C] :
      ( ( m1_pnproc_1(B,A)
        & m1_pnproc_1(C,A) )
     => ( r1_pnproc_1(A,B,C)
       => r1_pnproc_1(A,C,B) ) ) )).

fof(reflexivity_r1_pnproc_1,axiom,(
    ! [A,B,C] :
      ( ( m1_pnproc_1(B,A)
        & m1_pnproc_1(C,A) )
     => r1_pnproc_1(A,B,B) ) )).

fof(redefinition_r1_pnproc_1,axiom,(
    ! [A,B,C] :
      ( ( m1_pnproc_1(B,A)
        & m1_pnproc_1(C,A) )
     => ( r1_pnproc_1(A,B,C)
      <=> B = C ) ) )).

fof(reflexivity_r2_pnproc_1,axiom,(
    ! [A,B,C] :
      ( ( m1_pnproc_1(B,A)
        & m1_pnproc_1(C,A) )
     => r2_pnproc_1(A,B,B) ) )).

fof(dt_k1_pnproc_1,axiom,(
    ! [A,B,C] :
      ( m1_pnproc_1(B,A)
     => m2_subset_1(k1_pnproc_1(A,B,C),k1_numbers,k5_numbers) ) )).

fof(redefinition_k1_pnproc_1,axiom,(
    ! [A,B,C] :
      ( m1_pnproc_1(B,A)
     => k1_pnproc_1(A,B,C) = k1_funct_1(B,C) ) )).

fof(dt_k2_pnproc_1,axiom,(
    ! [A,B,C] :
      ( m1_pnproc_1(B,A)
     => m2_subset_1(k2_pnproc_1(A,B,C),k1_numbers,k5_numbers) ) )).

fof(redefinition_k2_pnproc_1,axiom,(
    ! [A,B,C] :
      ( m1_pnproc_1(B,A)
     => k2_pnproc_1(A,B,C) = k1_funct_1(B,C) ) )).

fof(dt_k3_pnproc_1,axiom,(
    ! [A] : m1_pnproc_1(k3_pnproc_1(A),A) )).

fof(dt_k4_pnproc_1,axiom,(
    ! [A,B,C] :
      ( ( m1_pnproc_1(B,A)
        & m1_pnproc_1(C,A) )
     => m1_pnproc_1(k4_pnproc_1(A,B,C),A) ) )).

fof(commutativity_k4_pnproc_1,axiom,(
    ! [A,B,C] :
      ( ( m1_pnproc_1(B,A)
        & m1_pnproc_1(C,A) )
     => k4_pnproc_1(A,B,C) = k4_pnproc_1(A,C,B) ) )).

fof(dt_k5_pnproc_1,axiom,(
    ! [A,B,C] :
      ( ( m1_pnproc_1(B,A)
        & m1_pnproc_1(C,A) )
     => m1_pnproc_1(k5_pnproc_1(A,B,C),A) ) )).

fof(dt_k6_pnproc_1,axiom,(
    ! [A,B] :
      ( m2_pnproc_1(B,A)
     => m1_pnproc_1(k6_pnproc_1(A,B),A) ) )).

fof(redefinition_k6_pnproc_1,axiom,(
    ! [A,B] :
      ( m2_pnproc_1(B,A)
     => k6_pnproc_1(A,B) = k1_mcart_1(B) ) )).

fof(dt_k7_pnproc_1,axiom,(
    ! [A,B] :
      ( m2_pnproc_1(B,A)
     => m1_pnproc_1(k7_pnproc_1(A,B),A) ) )).

fof(redefinition_k7_pnproc_1,axiom,(
    ! [A,B] :
      ( m2_pnproc_1(B,A)
     => k7_pnproc_1(A,B) = k2_mcart_1(B) ) )).

fof(dt_k8_pnproc_1,axiom,(
    ! [A,B,C] :
      ( ( m1_pnproc_1(B,A)
        & m2_pnproc_1(C,A) )
     => m1_pnproc_1(k8_pnproc_1(A,B,C),A) ) )).

fof(dt_k9_pnproc_1,axiom,(
    ! [A,B] :
      ( m2_pnproc_1(B,A)
     => ( v1_relat_1(k9_pnproc_1(A,B))
        & v1_funct_1(k9_pnproc_1(A,B)) ) ) )).

fof(dt_k10_pnproc_1,axiom,(
    ! [A,B,C] :
      ( ( m3_pnproc_1(B,A)
        & m1_subset_1(C,k3_finseq_2(B)) )
     => ( v1_relat_1(k10_pnproc_1(A,B,C))
        & v1_funct_1(k10_pnproc_1(A,B,C)) ) ) )).

fof(dt_k11_pnproc_1,axiom,(
    ! [A,B,C,D] :
      ( ( m3_pnproc_1(B,A)
        & m1_subset_1(C,k3_finseq_2(B))
        & m1_pnproc_1(D,A) )
     => m1_pnproc_1(k11_pnproc_1(A,B,C,D),A) ) )).

fof(dt_k12_pnproc_1,axiom,(
    ! [A,B,C,D] :
      ( ( m3_pnproc_1(B,A)
        & m1_subset_1(C,k1_zfmisc_1(k3_finseq_2(B)))
        & m1_subset_1(D,k1_zfmisc_1(k3_finseq_2(B))) )
     => m1_subset_1(k12_pnproc_1(A,B,C,D),k1_zfmisc_1(k3_finseq_2(B))) ) )).

fof(dt_k13_pnproc_1,axiom,(
    ! [A,B,C,D] :
      ( ( m3_pnproc_1(B,A)
        & m1_subset_1(C,k1_zfmisc_1(k3_finseq_2(B)))
        & m1_subset_1(D,k1_zfmisc_1(k3_finseq_2(B))) )
     => m1_subset_1(k13_pnproc_1(A,B,C,D),k1_zfmisc_1(k3_finseq_2(B))) ) )).

fof(commutativity_k13_pnproc_1,axiom,(
    ! [A,B,C,D] :
      ( ( m3_pnproc_1(B,A)
        & m1_subset_1(C,k1_zfmisc_1(k3_finseq_2(B)))
        & m1_subset_1(D,k1_zfmisc_1(k3_finseq_2(B))) )
     => k13_pnproc_1(A,B,C,D) = k13_pnproc_1(A,B,D,C) ) )).

fof(dt_k14_pnproc_1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_finseq_1(A)
        & m1_subset_1(B,k5_numbers) )
     => ( v1_relat_1(k14_pnproc_1(A,B))
        & v1_funct_1(k14_pnproc_1(A,B))
        & v2_finseq_1(k14_pnproc_1(A,B)) ) ) )).

fof(dt_k15_pnproc_1,axiom,(
    ! [A,B] :
      ( m3_pnproc_1(B,A)
     => ( ~ v1_xboole_0(k15_pnproc_1(A,B))
        & m1_subset_1(k15_pnproc_1(A,B),k1_zfmisc_1(k3_finseq_2(B))) ) ) )).

fof(dt_k16_pnproc_1,axiom,(
    ! [A,B,C] :
      ( ( m3_pnproc_1(B,A)
        & m1_subset_1(C,B) )
     => ( ~ v1_xboole_0(k16_pnproc_1(A,B,C))
        & m1_subset_1(k16_pnproc_1(A,B,C),k1_zfmisc_1(k3_finseq_2(B))) ) ) )).

fof(d13_pnproc_1,axiom,(
    ! [A,B] :
      ( m3_pnproc_1(B,A)
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(k3_finseq_2(B)))
         => ! [D] :
              ( m1_subset_1(D,k1_zfmisc_1(k3_finseq_2(B)))
             => k12_pnproc_1(A,B,C,D) = a_4_0_pnproc_1(A,B,C,D) ) ) ) )).

fof(d14_pnproc_1,axiom,(
    ! [A,B] :
      ( m3_pnproc_1(B,A)
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(k3_finseq_2(B)))
         => ! [D] :
              ( m1_subset_1(D,k1_zfmisc_1(k3_finseq_2(B)))
             => k13_pnproc_1(A,B,C,D) = a_4_1_pnproc_1(A,B,C,D) ) ) ) )).

fof(d15_pnproc_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_finseq_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v2_finseq_1(C) )
             => ( C = k14_pnproc_1(A,B)
              <=> ( k1_relat_1(C) = a_2_0_pnproc_1(A,B)
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( r2_hidden(D,k1_relat_1(A))
                       => k1_funct_1(C,k1_nat_1(B,D)) = k1_funct_1(A,D) ) ) ) ) ) ) ) )).

fof(t54_pnproc_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( B != k1_xboole_0
           => k1_relat_1(k14_pnproc_1(B,A)) = a_2_1_pnproc_1(A,B) ) ) ) )).

fof(fraenkel_a_4_0_pnproc_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( m3_pnproc_1(C,B)
        & m1_subset_1(D,k1_zfmisc_1(k3_finseq_2(C)))
        & m1_subset_1(E,k1_zfmisc_1(k3_finseq_2(C))) )
     => ( r2_hidden(A,a_4_0_pnproc_1(B,C,D,E))
      <=> ? [F,G] :
            ( m2_finseq_2(F,C,k3_finseq_2(C))
            & m2_finseq_2(G,C,k3_finseq_2(C))
            & A = k1_lang1(C,F,G)
            & r2_hidden(F,D)
            & r2_hidden(G,E) ) ) ) )).

fof(fraenkel_a_4_1_pnproc_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( m3_pnproc_1(C,B)
        & m1_subset_1(D,k1_zfmisc_1(k3_finseq_2(C)))
        & m1_subset_1(E,k1_zfmisc_1(k3_finseq_2(C))) )
     => ( r2_hidden(A,a_4_1_pnproc_1(B,C,D,E))
      <=> ? [F] :
            ( m2_finseq_2(F,C,k3_finseq_2(C))
            & A = F
            & ? [G] :
                ( v1_relat_1(G)
                & v1_funct_1(G)
                & v2_finseq_1(G)
                & ? [H] :
                    ( v1_relat_1(H)
                    & v1_funct_1(H)
                    & v2_finseq_1(H)
                    & F = k2_xboole_0(G,H)
                    & r1_xboole_0(G,H)
                    & r2_hidden(k15_finseq_1(G),D)
                    & r2_hidden(k15_finseq_1(H),E) ) ) ) ) ) )).

fof(fraenkel_a_2_0_pnproc_1,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v2_finseq_1(B)
        & m2_subset_1(C,k1_numbers,k5_numbers) )
     => ( r2_hidden(A,a_2_0_pnproc_1(B,C))
      <=> ? [D] :
            ( m2_subset_1(D,k1_numbers,k5_numbers)
            & A = k1_nat_1(C,D)
            & r2_hidden(D,k1_relat_1(B)) ) ) ) )).

fof(fraenkel_a_2_1_pnproc_1,axiom,(
    ! [A,B,C] :
      ( ( m2_subset_1(B,k1_numbers,k5_numbers)
        & v1_relat_1(C)
        & v1_funct_1(C)
        & v1_finseq_1(C) )
     => ( r2_hidden(A,a_2_1_pnproc_1(B,C))
      <=> ? [D] :
            ( m2_subset_1(D,k1_numbers,k5_numbers)
            & A = D
            & r1_xreal_0(k1_nat_1(B,np__1),D)
            & r1_xreal_0(D,k1_nat_1(B,k3_finseq_1(C))) ) ) ) )).
%------------------------------------------------------------------------------