% Mizar problem: t29_matrix_3,matrix_3,1338,49 
fof(t29_matrix_3,conjecture,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(A,A),A)
                    & m2_relset_1(D,k2_zfmisc_1(A,A),A) )
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(A,A),A)
                        & m2_relset_1(E,k2_zfmisc_1(A,A),A) )
                     => ! [F] : 
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,B,A)
                            & m2_relset_1(F,B,A) )
                         => ! [G] : 
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,C,A)
                                & m2_relset_1(G,C,A) )
                             => ( ( v1_binop_1(D,A)
                                  & v2_binop_1(D,A)
                                  & v1_setwiseo(D,A)
                                  & v1_binop_1(E,A) )
                               => ! [H] : 
                                    ( m1_subset_1(H,B)
                                   => ! [I] : 
                                        ( m1_subset_1(I,C)
                                       => k7_setwiseo(k2_zfmisc_1(B,C),A,D,k8_matrix_3(B,C,k2_setwiseo(B,H),k2_setwiseo(C,I)),k9_matrix_3(B,C,A,E,F,G)) = k7_setwiseo(C,A,D,k2_setwiseo(C,I),k8_funcop_1(A,C,E,k7_setwiseo(B,A,D,k2_setwiseo(B,H),F),G)) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_finset_1,cc1_finsub_1,cc1_funct_1,cc1_funct_2,cc1_relset_1,cc2_finset_1,cc2_finsub_1,cc2_funct_1,cc3_finsub_1,cc5_funct_2,cc6_funct_2,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_setwiseo,dt_k2_zfmisc_1,dt_k4_funcop_1,dt_k5_finsub_1,dt_k5_funcop_1,dt_k7_finseqop,dt_k7_funcop_1,dt_k7_setwiseo,dt_k8_funcop_1,dt_k8_matrix_3,dt_k9_matrix_3,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc14_finset_1,fc1_finset_1,fc1_finsub_1,fc1_subset_1,fc1_xboole_0,fc2_finsub_1,fc2_subset_1,fc4_subset_1,fc5_funcop_1,fc6_funcop_1,rc1_finset_1,rc1_funct_1,rc1_funct_2,rc1_partfun1,rc1_subset_1,rc1_xboole_0,rc2_funct_1,rc2_partfun1,rc2_subset_1,rc2_xboole_0,rc3_finset_1,rc3_funct_1,rc4_finset_1,redefinition_k2_setwiseo,redefinition_k7_funcop_1,redefinition_k8_funcop_1,redefinition_k8_matrix_3,redefinition_k9_matrix_3,redefinition_m2_relset_1,reflexivity_r1_tarski,t1_subset,t25_matrix_3,t26_matrix_3,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t79_funcop_1,t7_boole,t8_boole]),
    [file(matrix_3,t29_matrix_3)]).

fof(antisymmetry_r2_hidden,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    []).

fof(cc1_finset_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_finset_1(A) ) ),
    file(finset_1,cc1_finset_1),
    []).

fof(cc1_finsub_1,axiom,(
    ! [A] : 
      ( v4_finsub_1(A)
     => ( v1_finsub_1(A)
        & v3_finsub_1(A) ) ) ),
    file(finsub_1,cc1_finsub_1),
    []).

fof(cc1_funct_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    []).

fof(cc1_funct_2,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v1_partfun1(C,A,B) )
       => ( v1_funct_1(C)
          & v1_funct_2(C,A,B) ) ) ) ),
    file(funct_2,cc1_funct_2),
    []).

fof(cc1_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    []).

fof(cc2_finset_1,axiom,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_finset_1(B) ) ) ),
    file(finset_1,cc2_finset_1),
    []).

fof(cc2_finsub_1,axiom,(
    ! [A] : 
      ( ( v1_finsub_1(A)
        & v3_finsub_1(A) )
     => v4_finsub_1(A) ) ),
    file(finsub_1,cc2_finsub_1),
    []).

fof(cc2_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_xboole_0(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A) ) ) ),
    file(funct_1,cc2_funct_1),
    []).

fof(cc3_finsub_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k5_finsub_1(A))
     => v1_finset_1(B) ) ),
    file(finsub_1,cc3_finsub_1),
    []).

fof(cc5_funct_2,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc5_funct_2),
    []).

fof(cc6_funct_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & ~ v1_xboole_0(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc6_funct_2),
    []).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    []).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    []).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    []).

fof(dt_k2_setwiseo,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => m1_subset_1(k2_setwiseo(A,B),k5_finsub_1(A)) ) ),
    file(setwiseo,k2_setwiseo),
    []).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

fof(dt_k4_funcop_1,axiom,(
    $true ),
    file(funcop_1,k4_funcop_1),
    []).

fof(dt_k5_finsub_1,axiom,(
    ! [A] : v4_finsub_1(k5_finsub_1(A)) ),
    file(finsub_1,k5_finsub_1),
    []).

fof(dt_k5_funcop_1,axiom,(
    $true ),
    file(funcop_1,k5_funcop_1),
    []).

fof(dt_k7_finseqop,axiom,(
    ! [A,B,C] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_relat_1(C)
        & v1_funct_1(C) )
     => ( v1_relat_1(k7_finseqop(A,B,C))
        & v1_funct_1(k7_finseqop(A,B,C)) ) ) ),
    file(finseqop,k7_finseqop),
    []).

fof(dt_k7_funcop_1,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & v1_funct_1(D)
        & v1_funct_2(D,B,A)
        & m1_relset_1(D,B,A)
        & m1_subset_1(E,A) )
     => ( v1_funct_1(k7_funcop_1(A,B,C,D,E))
        & v1_funct_2(k7_funcop_1(A,B,C,D,E),B,A)
        & m2_relset_1(k7_funcop_1(A,B,C,D,E),B,A) ) ) ),
    file(funcop_1,k7_funcop_1),
    []).

fof(dt_k7_setwiseo,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(B,B),B)
        & m1_relset_1(C,k2_zfmisc_1(B,B),B)
        & m1_subset_1(D,k5_finsub_1(A))
        & v1_funct_1(E)
        & v1_funct_2(E,A,B)
        & m1_relset_1(E,A,B) )
     => m1_subset_1(k7_setwiseo(A,B,C,D,E),B) ) ),
    file(setwiseo,k7_setwiseo),
    []).

fof(dt_k8_funcop_1,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & m1_subset_1(D,A)
        & v1_funct_1(E)
        & v1_funct_2(E,B,A)
        & m1_relset_1(E,B,A) )
     => ( v1_funct_1(k8_funcop_1(A,B,C,D,E))
        & v1_funct_2(k8_funcop_1(A,B,C,D,E),B,A)
        & m2_relset_1(k8_funcop_1(A,B,C,D,E),B,A) ) ) ),
    file(funcop_1,k8_funcop_1),
    []).

fof(dt_k8_matrix_3,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,k5_finsub_1(A))
        & m1_subset_1(D,k5_finsub_1(B)) )
     => m1_subset_1(k8_matrix_3(A,B,C,D),k5_finsub_1(k2_zfmisc_1(A,B))) ) ),
    file(matrix_3,k8_matrix_3),
    []).

fof(dt_k9_matrix_3,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(C,C),C)
        & m1_relset_1(D,k2_zfmisc_1(C,C),C)
        & v1_funct_1(E)
        & v1_funct_2(E,A,C)
        & m1_relset_1(E,A,C)
        & v1_funct_1(F)
        & v1_funct_2(F,B,C)
        & m1_relset_1(F,B,C) )
     => ( v1_funct_1(k9_matrix_3(A,B,C,D,E,F))
        & v1_funct_2(k9_matrix_3(A,B,C,D,E,F),k2_zfmisc_1(A,B),C)
        & m2_relset_1(k9_matrix_3(A,B,C,D,E,F),k2_zfmisc_1(A,B),C) ) ) ),
    file(matrix_3,k9_matrix_3),
    []).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    []).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    []).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    []).

fof(fc14_finset_1,axiom,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_zfmisc_1(A,B)) ) ),
    file(finset_1,fc14_finset_1),
    []).

fof(fc1_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_finset_1(k1_tarski(A)) ) ),
    file(finset_1,fc1_finset_1),
    []).

fof(fc1_finsub_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_zfmisc_1(A))
      & v1_finsub_1(k1_zfmisc_1(A))
      & v3_finsub_1(k1_zfmisc_1(A))
      & v4_finsub_1(k1_zfmisc_1(A)) ) ),
    file(finsub_1,fc1_finsub_1),
    []).

fof(fc1_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    []).

fof(fc1_xboole_0,axiom,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    []).

fof(fc2_finsub_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k5_finsub_1(A))
      & v1_finsub_1(k5_finsub_1(A))
      & v3_finsub_1(k5_finsub_1(A))
      & v4_finsub_1(k5_finsub_1(A)) ) ),
    file(finsub_1,fc2_finsub_1),
    []).

fof(fc2_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    []).

fof(fc4_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    []).

fof(fc5_funcop_1,axiom,(
    ! [A,B,C] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k4_funcop_1(A,B,C))
        & v1_funct_1(k4_funcop_1(A,B,C)) ) ) ),
    file(funcop_1,fc5_funcop_1),
    []).

fof(fc6_funcop_1,axiom,(
    ! [A,B,C] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(C)
        & v1_funct_1(C) )
     => ( v1_relat_1(k5_funcop_1(A,B,C))
        & v1_funct_1(k5_funcop_1(A,B,C)) ) ) ),
    file(funcop_1,fc6_funcop_1),
    []).

fof(rc1_finset_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A) ) ),
    file(finset_1,rc1_finset_1),
    []).

fof(rc1_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    []).

fof(rc1_funct_2,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C)
      & v1_funct_2(C,A,B) ) ),
    file(funct_2,rc1_funct_2),
    []).

fof(rc1_partfun1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A) ) ),
    file(partfun1,rc1_partfun1),
    []).

fof(rc1_subset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    []).

fof(rc1_xboole_0,axiom,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    []).

fof(rc2_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_1),
    []).

fof(rc2_partfun1,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C) ) ),
    file(partfun1,rc2_partfun1),
    []).

fof(rc2_subset_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    []).

fof(rc2_xboole_0,axiom,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    []).

fof(rc3_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc3_finset_1),
    []).

fof(rc3_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_1),
    []).

fof(rc4_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc4_finset_1),
    []).

fof(redefinition_k2_setwiseo,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => k2_setwiseo(A,B) = k1_tarski(B) ) ),
    file(setwiseo,k2_setwiseo),
    []).

fof(redefinition_k7_funcop_1,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & v1_funct_1(D)
        & v1_funct_2(D,B,A)
        & m1_relset_1(D,B,A)
        & m1_subset_1(E,A) )
     => k7_funcop_1(A,B,C,D,E) = k4_funcop_1(C,D,E) ) ),
    file(funcop_1,k7_funcop_1),
    []).

fof(redefinition_k8_funcop_1,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & m1_subset_1(D,A)
        & v1_funct_1(E)
        & v1_funct_2(E,B,A)
        & m1_relset_1(E,B,A) )
     => k8_funcop_1(A,B,C,D,E) = k5_funcop_1(C,D,E) ) ),
    file(funcop_1,k8_funcop_1),
    []).

fof(redefinition_k8_matrix_3,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,k5_finsub_1(A))
        & m1_subset_1(D,k5_finsub_1(B)) )
     => k8_matrix_3(A,B,C,D) = k2_zfmisc_1(C,D) ) ),
    file(matrix_3,k8_matrix_3),
    []).

fof(redefinition_k9_matrix_3,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(C,C),C)
        & m1_relset_1(D,k2_zfmisc_1(C,C),C)
        & v1_funct_1(E)
        & v1_funct_2(E,A,C)
        & m1_relset_1(E,A,C)
        & v1_funct_1(F)
        & v1_funct_2(F,B,C)
        & m1_relset_1(F,B,C) )
     => k9_matrix_3(A,B,C,D,E,F) = k7_finseqop(D,E,F) ) ),
    file(matrix_3,k9_matrix_3),
    []).

fof(redefinition_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(reflexivity_r1_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

fof(t1_subset,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    []).

fof(t25_matrix_3,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(C,C),C)
                    & m2_relset_1(D,k2_zfmisc_1(C,C),C) )
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(C,C),C)
                        & m2_relset_1(E,k2_zfmisc_1(C,C),C) )
                     => ! [F] : 
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,A,C)
                            & m2_relset_1(F,A,C) )
                         => ! [G] : 
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,B,C)
                                & m2_relset_1(G,B,C) )
                             => ! [H] : 
                                  ( m1_subset_1(H,k5_finsub_1(A))
                                 => ! [I] : 
                                      ( m1_subset_1(I,k5_finsub_1(B))
                                     => ( ( v1_binop_1(D,C)
                                          & v2_binop_1(D,C)
                                          & v1_binop_1(E,C) )
                                       => ( ( k8_matrix_3(B,A,I,H) = k1_xboole_0
                                            & ~ v1_setwiseo(D,C) )
                                          | k7_setwiseo(k2_zfmisc_1(A,B),C,D,k8_matrix_3(A,B,H,I),k9_matrix_3(A,B,C,E,F,G)) = k7_setwiseo(k2_zfmisc_1(B,A),C,D,k8_matrix_3(B,A,I,H),k9_matrix_3(B,A,C,E,G,F)) ) ) ) ) ) ) ) ) ) ) ) ),
    file(matrix_3,t25_matrix_3),
    []).

fof(t26_matrix_3,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(A,A),A)
                    & m2_relset_1(D,k2_zfmisc_1(A,A),A) )
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(A,A),A)
                        & m2_relset_1(E,k2_zfmisc_1(A,A),A) )
                     => ! [F] : 
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,B,A)
                            & m2_relset_1(F,B,A) )
                         => ! [G] : 
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,C,A)
                                & m2_relset_1(G,C,A) )
                             => ( ( v1_binop_1(D,A)
                                  & v2_binop_1(D,A)
                                  & v1_setwiseo(D,A) )
                               => ! [H] : 
                                    ( m1_subset_1(H,B)
                                   => ! [I] : 
                                        ( m1_subset_1(I,C)
                                       => k7_setwiseo(k2_zfmisc_1(B,C),A,D,k8_matrix_3(B,C,k2_setwiseo(B,H),k2_setwiseo(C,I)),k9_matrix_3(B,C,A,E,F,G)) = k7_setwiseo(B,A,D,k2_setwiseo(B,H),k7_funcop_1(A,B,E,F,k7_setwiseo(C,A,D,k2_setwiseo(C,I),G))) ) ) ) ) ) ) ) ) ) ) ),
    file(matrix_3,t26_matrix_3),
    []).

fof(t2_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    []).

fof(t3_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    []).

fof(t4_subset,axiom,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    []).

fof(t5_subset,axiom,(
    ! [A,B,C] : ~ ( r2_hidden(A,B)
      & m1_subset_1(B,k1_zfmisc_1(C))
      & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    []).

fof(t6_boole,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    []).

fof(t79_funcop_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] : 
                      ( m1_subset_1(E,B)
                     => ( v1_binop_1(C,B)
                       => k8_funcop_1(B,A,C,E,D) = k7_funcop_1(B,A,C,D,E) ) ) ) ) ) ) ),
    file(funcop_1,t79_funcop_1),
    []).

fof(t7_boole,axiom,(
    ! [A,B] : ~ ( r2_hidden(A,B)
      & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    []).

fof(t8_boole,axiom,(
    ! [A,B] : ~ ( v1_xboole_0(A)
      & A != B
      & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    []).