SET007 Axioms: SET007+551.ax


%------------------------------------------------------------------------------
% File     : SET007+551 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Another Times Macro Instruction
% 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    : sfmastr2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   37 (   0 unit)
%            Number of atoms       :  313 (  50 equality)
%            Maximal formula depth :   16 (  10 average)
%            Number of connectives :  306 (  30 ~  ;  10  |; 126  &)
%                                         (   4 <=>; 136 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   21 (   0 propositional; 1-3 arity)
%            Number of functors    :   50 (   8 constant; 0-4 arity)
%            Number of variables   :  111 (   0 singleton; 111 !;   0 ?)
%            Maximal term depth    :   12 (   2 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(fc1_sfmastr2,axiom,(
    ! [A,B] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(A)
        & v1_scmfsa7b(A)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_scmfsa_2(B) )
     => ( v1_relat_1(k1_sfmastr2(B,A))
        & v1_funct_1(k1_sfmastr2(B,A))
        & v1_ami_3(k1_sfmastr2(B,A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(k1_sfmastr2(B,A))
        & v1_scmfsa7b(k1_sfmastr2(B,A)) ) ) )).

fof(t1_sfmastr2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ( ( r5_scmfsa7b(C,k1_scmfsa6c(A))
                  & r6_scmfsa7b(C,k1_scmfsa6c(A)) )
               => ( r2_hidden(B,k2_sf_mastr(C))
                  | k20_scmfsa_2(k3_scmfsa6b(C,A),B) = k20_scmfsa_2(k1_scmfsa6c(A),B) ) ) ) ) ) )).

fof(t2_sfmastr2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( m2_scmfsa_2(B)
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ( ( r5_scmfsa7b(C,k1_scmfsa6c(A))
                  & r6_scmfsa7b(C,k1_scmfsa6c(A)) )
               => ( r2_hidden(B,k4_sf_mastr(C))
                  | k21_scmfsa_2(k3_scmfsa6b(C,A),B) = k21_scmfsa_2(k1_scmfsa6c(A),B) ) ) ) ) ) )).

fof(t3_sfmastr2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ~ ( ( ( r5_scmfsa7b(C,k1_scmfsa6c(A))
                      & r6_scmfsa7b(C,k1_scmfsa6c(A)) )
                    | v2_scmfsa6b(C) )
                  & ~ ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) != np__1
                      & v1_sf_mastr(B) )
                  & ~ r2_hidden(B,k2_sf_mastr(C))
                  & k20_scmfsa_2(k3_scmfsa6b(C,A),B) != k20_scmfsa_2(A,B) ) ) ) ) )).

fof(t4_sfmastr2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1
           => ( r5_scmfsa7b(B,A)
            <=> r5_scmfsa7b(B,k1_scmfsa6c(A)) ) ) ) ) )).

fof(t5_sfmastr2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1
           => ( ( ( r5_scmfsa7b(B,A)
                  & r6_scmfsa7b(B,A) )
               => ( r5_scmfsa7b(B,k1_scmfsa6c(A))
                  & r6_scmfsa7b(B,k1_scmfsa6c(A)) ) )
              & ( ( r5_scmfsa7b(B,k1_scmfsa6c(A))
                  & r6_scmfsa7b(B,k1_scmfsa6c(A)) )
               => ( r5_scmfsa7b(B,A)
                  & r6_scmfsa7b(B,A) ) ) ) ) ) ) )).

fof(t6_sfmastr2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k2_scmfsa_2))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(k3_scmfsa_2))
                 => ( k7_relat_1(A,k2_xboole_0(C,D)) = k7_relat_1(B,k2_xboole_0(C,D))
                  <=> ( ! [E] :
                          ( m1_scmfsa_2(E)
                         => ( r2_hidden(E,C)
                           => k20_scmfsa_2(A,E) = k20_scmfsa_2(B,E) ) )
                      & ! [E] :
                          ( m2_scmfsa_2(E)
                         => ( r2_hidden(E,D)
                           => k21_scmfsa_2(A,E) = k21_scmfsa_2(B,E) ) ) ) ) ) ) ) ) )).

fof(t7_sfmastr2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k2_scmfsa_2))
             => ( k7_relat_1(A,k2_xboole_0(C,k3_scmfsa_2)) = k7_relat_1(B,k2_xboole_0(C,k3_scmfsa_2))
              <=> ( ! [D] :
                      ( m1_scmfsa_2(D)
                     => ( r2_hidden(D,C)
                       => k20_scmfsa_2(A,D) = k20_scmfsa_2(B,D) ) )
                  & ! [D] :
                      ( m2_scmfsa_2(D)
                     => k21_scmfsa_2(A,D) = k21_scmfsa_2(B,D) ) ) ) ) ) ) )).

fof(d1_sfmastr2,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => k1_sfmastr2(A,B) = k5_scmfsa6a(k8_scmfsa_2(k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k1_sfmastr1(A),k2_sf_mastr(B))),A),k2_scmfsa_9(k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k1_sfmastr1(A),k2_sf_mastr(B))),k6_scmfsa6a(B,k10_scmfsa_2(k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k1_sfmastr1(A),k2_sf_mastr(B))),k4_scmfsa_2(np__0))))) ) ) )).

fof(t8_sfmastr2,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => r1_tarski(k4_subset_1(k2_scmfsa_2,k1_sfmastr1(A),k2_sf_mastr(B)),k2_sf_mastr(k1_sfmastr2(A,B))) ) ) )).

fof(t9_sfmastr2,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => k4_sf_mastr(k1_sfmastr2(A,B)) = k4_sf_mastr(B) ) ) )).

fof(d2_sfmastr2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ! [C] :
              ( m1_scmfsa_2(C)
             => k2_sfmastr2(A,B,C) = k5_scmfsa_9(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_scmfsa_2(k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k1_sfmastr1(C),k2_sf_mastr(B))),C),k1_scmfsa6c(A)),k6_scmfsa6a(B,k10_scmfsa_2(k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k1_sfmastr1(C),k2_sf_mastr(B))),k4_scmfsa_2(np__0))),k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k1_sfmastr1(C),k2_sf_mastr(B)))) ) ) ) )).

fof(t10_sfmastr2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & v1_scmfsa7b(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),np__0),k4_scmfsa_2(np__0)) = np__1 ) ) ) )).

fof(t11_sfmastr2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & v1_scmfsa7b(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ( ~ ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) != np__1
                    & v1_sf_mastr(B) )
               => k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),np__0),k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k1_sfmastr1(B),k2_sf_mastr(C)))) = k20_scmfsa_2(A,B) ) ) ) ) )).

fof(t12_sfmastr2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & v1_scmfsa7b(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( ( k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),D),k4_scmfsa_2(np__0)) = np__1
                      & r5_scmfsa7b(C,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),D))
                      & r6_scmfsa7b(C,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),D)) )
                   => ( k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),k1_nat_1(D,np__1)),k4_scmfsa_2(np__0)) = np__1
                      & ( ~ r1_xreal_0(k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),D),k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k1_sfmastr1(B),k2_sf_mastr(C)))),np__0)
                       => k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),k1_nat_1(D,np__1)),k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k1_sfmastr1(B),k2_sf_mastr(C)))) = k6_xcmplx_0(k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),D),k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k1_sfmastr1(B),k2_sf_mastr(C)))),np__1) ) ) ) ) ) ) ) )).

fof(t13_sfmastr2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ( ~ ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) != np__1
                    & v1_sf_mastr(B) )
               => k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),np__0),B) = k20_scmfsa_2(A,B) ) ) ) ) )).

fof(t14_sfmastr2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( m2_scmfsa_2(C)
             => ! [D] :
                  ( ( v1_ami_3(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                    & v1_scmfsa_4(D)
                    & m1_ami_1(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
                 => k21_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,D,B),np__0),C) = k21_scmfsa_2(A,C) ) ) ) ) )).

fof(d3_sfmastr2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ( r1_sfmastr2(A,B,C)
              <=> ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( ~ r1_xreal_0(k20_scmfsa_2(A,B),D)
                     => ( r5_scmfsa7b(C,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),D))
                        & r6_scmfsa7b(C,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),D)) ) ) ) ) ) ) ) )).

fof(t15_sfmastr2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ( v2_scmfsa6b(C)
               => r1_sfmastr2(A,B,C) ) ) ) ) )).

fof(t16_sfmastr2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & v1_scmfsa7b(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ( r1_sfmastr2(A,B,C)
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( r1_xreal_0(D,k20_scmfsa_2(A,B))
                     => k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),D),k4_scmfsa_2(np__0)) = np__1 ) ) ) ) ) ) )).

fof(t17_sfmastr2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & v1_scmfsa7b(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ( r1_sfmastr2(A,B,C)
               => ( ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) != np__1
                    & v1_sf_mastr(B) )
                  | ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( r1_xreal_0(D,k20_scmfsa_2(A,B))
                       => k2_xcmplx_0(k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),D),k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k1_sfmastr1(B),k2_sf_mastr(C)))),D) = k20_scmfsa_2(A,B) ) ) ) ) ) ) ) )).

fof(t18_sfmastr2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & v1_scmfsa7b(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ( ( r1_sfmastr2(A,B,C)
                  & r1_xreal_0(np__0,k20_scmfsa_2(A,B)) )
               => ( ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) != np__1
                    & v1_sf_mastr(B) )
                  | ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( r1_xreal_0(k20_scmfsa_2(A,B),D)
                       => ( k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),D),k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k1_sfmastr1(B),k2_sf_mastr(C)))) = np__0
                          & k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),D),k4_scmfsa_2(np__0)) = np__1 ) ) ) ) ) ) ) ) )).

fof(t19_sfmastr2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1
               => k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),np__0),k2_xboole_0(k2_sf_mastr(C),k3_scmfsa_2)) = k7_relat_1(A,k2_xboole_0(k2_sf_mastr(C),k3_scmfsa_2)) ) ) ) ) )).

fof(t20_sfmastr2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & v1_scmfsa7b(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( ( k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),D),k4_scmfsa_2(np__0)) = np__1
                      & r6_scmfsa7b(C,k1_scmfsa6c(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),D)))
                      & r5_scmfsa7b(C,k1_scmfsa6c(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),D))) )
                   => ( r1_xreal_0(k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),D),k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k1_sfmastr1(B),k2_sf_mastr(C)))),np__0)
                      | k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),k1_nat_1(D,np__1)),k2_xboole_0(k2_sf_mastr(C),k3_scmfsa_2)) = k7_relat_1(k3_scmfsa6b(C,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),D)),k2_xboole_0(k2_sf_mastr(C),k3_scmfsa_2)) ) ) ) ) ) ) )).

fof(t21_sfmastr2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & v1_scmfsa7b(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ~ ( ( r1_sfmastr2(A,B,C)
                        | v2_scmfsa6b(C) )
                      & ~ r1_xreal_0(k20_scmfsa_2(A,B),D)
                      & ~ ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) != np__1
                          & v1_sf_mastr(B) )
                      & k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),k1_nat_1(D,np__1)),k2_xboole_0(k2_sf_mastr(C),k3_scmfsa_2)) != k7_relat_1(k3_scmfsa6b(C,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),D)),k2_xboole_0(k2_sf_mastr(C),k3_scmfsa_2)) ) ) ) ) ) )).

fof(t22_sfmastr2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ( ( r1_xreal_0(k20_scmfsa_2(A,B),np__0)
                  & k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1 )
               => k7_relat_1(k3_scmfsa6b(k1_sfmastr2(B,C),A),k2_xboole_0(k2_sf_mastr(C),k3_scmfsa_2)) = k7_relat_1(A,k2_xboole_0(k2_sf_mastr(C),k3_scmfsa_2)) ) ) ) ) )).

fof(t23_sfmastr2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & v1_scmfsa7b(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( k20_scmfsa_2(A,B) = D
                   => ( ( ~ r1_sfmastr2(A,B,C)
                        & ~ v2_scmfsa6b(C) )
                      | ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) != np__1
                        & v1_sf_mastr(B) )
                      | k7_relat_1(k3_scmfsa6b(k1_sfmastr2(B,C),A),k4_subset_1(u1_struct_0(k1_scmfsa_2),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),D),k4_subset_1(u1_struct_0(k1_scmfsa_2),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) ) )).

fof(t24_sfmastr2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & v1_scmfsa7b(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1
               => ( ( ~ r1_sfmastr2(A,B,C)
                    & ~ v2_scmfsa6b(C) )
                  | ( r5_scmfsa7b(k1_sfmastr2(B,C),A)
                    & r6_scmfsa7b(k1_sfmastr2(B,C),A) ) ) ) ) ) ) )).

fof(d4_sfmastr2,axiom,(
    ! [A] :
      ( ( ~ v1_sf_mastr(A)
        & m1_scmfsa_2(A) )
     => k3_sfmastr2(A) = k1_sfmastr2(A,k6_scmfsa6a(k1_scmfsa_9(A,k2_scmfsa6a(k8_scmfsa_2(A,A))),k10_scmfsa_2(A,k4_scmfsa_2(np__0)))) ) )).

fof(t25_sfmastr2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( ~ v1_sf_mastr(B)
            & m1_scmfsa_2(B) )
         => ( r1_xreal_0(k20_scmfsa_2(A,B),np__0)
           => k20_scmfsa_2(k3_scmfsa6b(k3_sfmastr2(B),A),B) = k20_scmfsa_2(A,B) ) ) ) )).

fof(t26_sfmastr2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( ~ v1_sf_mastr(B)
            & m1_scmfsa_2(B) )
         => ( r1_xreal_0(np__0,k20_scmfsa_2(A,B))
           => k20_scmfsa_2(k3_scmfsa6b(k3_sfmastr2(B),A),B) = np__0 ) ) ) )).

fof(d5_sfmastr2,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_scmfsa_2(B)
         => k4_sfmastr2(A,B) = k6_scmfsa6a(k4_scmfsa6a(k6_scmfsa6a(k7_scmfsa6a(k8_scmfsa_2(k7_sfmastr1(np__1,k1_sfmastr2(A,k5_scmfsa6a(k9_scmfsa_2(B,k6_sfmastr1(np__1,k2_sfmastr1(A,B))),k2_scmfsa6c(B,k6_sfmastr1(np__1,k2_sfmastr1(A,B)))))),A),k10_scmfsa_2(B,B)),k8_scmfsa_2(k6_sfmastr1(np__1,k2_sfmastr1(A,B)),k4_scmfsa_2(np__0))),k1_sfmastr2(A,k5_scmfsa6a(k9_scmfsa_2(B,k6_sfmastr1(np__1,k2_sfmastr1(A,B))),k2_scmfsa6c(B,k6_sfmastr1(np__1,k2_sfmastr1(A,B)))))),k8_scmfsa_2(A,k7_sfmastr1(np__1,k1_sfmastr2(A,k5_scmfsa6a(k9_scmfsa_2(B,k6_sfmastr1(np__1,k2_sfmastr1(A,B))),k2_scmfsa6c(B,k6_sfmastr1(np__1,k2_sfmastr1(A,B)))))))) ) ) )).

fof(t27_sfmastr2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( ~ v1_sf_mastr(B)
            & m1_scmfsa_2(B) )
         => ! [C] :
              ( ( ~ v1_sf_mastr(C)
                & m1_scmfsa_2(C) )
             => ( B != C
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( D = k20_scmfsa_2(A,B)
                     => ( k20_scmfsa_2(k3_scmfsa6b(k4_sfmastr2(B,C),A),C) = k3_pre_ff(D)
                        & k20_scmfsa_2(k3_scmfsa6b(k4_sfmastr2(B,C),A),B) = k20_scmfsa_2(A,B) ) ) ) ) ) ) ) )).

fof(dt_k1_sfmastr2,axiom,(
    ! [A,B] :
      ( ( m1_scmfsa_2(A)
        & v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(B)
        & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ( v1_ami_3(k1_sfmastr2(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(k1_sfmastr2(A,B))
        & m1_ami_1(k1_sfmastr2(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) )).

fof(dt_k2_sfmastr2,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
        & v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(B)
        & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_scmfsa_2(C) )
     => ( v1_funct_1(k2_sfmastr2(A,B,C))
        & v1_funct_2(k2_sfmastr2(A,B,C),k5_numbers,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
        & m2_relset_1(k2_sfmastr2(A,B,C),k5_numbers,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) ) ) )).

fof(dt_k3_sfmastr2,axiom,(
    ! [A] :
      ( ( ~ v1_sf_mastr(A)
        & m1_scmfsa_2(A) )
     => ( v1_ami_3(k3_sfmastr2(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(k3_sfmastr2(A))
        & m1_ami_1(k3_sfmastr2(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) )).

fof(dt_k4_sfmastr2,axiom,(
    ! [A,B] :
      ( ( m1_scmfsa_2(A)
        & m1_scmfsa_2(B) )
     => ( v1_ami_3(k4_sfmastr2(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(k4_sfmastr2(A,B))
        & m1_ami_1(k4_sfmastr2(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) )).
%------------------------------------------------------------------------------