% Mizar problem: t8_multop_1,multop_1,290,15 
fof(t8_multop_1,conjecture,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( ~ v1_xboole_0(D)
                 => ! [E] : 
                      ( ~ v1_xboole_0(E)
                     => ! [F] : 
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k4_zfmisc_1(A,B,C,D),E)
                            & m2_relset_1(F,k4_zfmisc_1(A,B,C,D),E) )
                         => ! [G] : 
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,k4_zfmisc_1(A,B,C,D),E)
                                & m2_relset_1(G,k4_zfmisc_1(A,B,C,D),E) )
                             => ( ! [H] : 
                                    ( m1_subset_1(H,A)
                                   => ! [I] : 
                                        ( m1_subset_1(I,B)
                                       => ! [J] : 
                                            ( m1_subset_1(J,C)
                                           => ! [K] : 
                                                ( m1_subset_1(K,D)
                                               => k4_multop_1(A,B,C,D,E,F,H,I,J,K) = k4_multop_1(A,B,C,D,E,G,H,I,J,K) ) ) ) )
                               => F = G ) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_relset_1,d2_multop_1,dt_k1_funct_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k3_multop_1,dt_k4_mcart_1,dt_k4_multop_1,dt_k4_zfmisc_1,dt_k5_domain_1,dt_k8_funct_2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc1_subset_1,fc1_xboole_0,fc4_subset_1,fc6_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,redefinition_k4_multop_1,redefinition_k5_domain_1,redefinition_k8_funct_2,redefinition_m2_relset_1,reflexivity_r1_tarski,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t7_multop_1,t8_boole]),
    [file(multop_1,t8_multop_1)]).

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

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(d2_multop_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C,D,E] : k3_multop_1(A,B,C,D,E) = k1_funct_1(A,k4_mcart_1(B,C,D,E)) ) ),
    file(multop_1,d2_multop_1),
    []).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    []).

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_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

fof(dt_k3_multop_1,axiom,(
    $true ),
    file(multop_1,k3_multop_1),
    []).

fof(dt_k4_mcart_1,axiom,(
    $true ),
    file(mcart_1,k4_mcart_1),
    []).

fof(dt_k4_multop_1,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & ~ v1_xboole_0(D)
        & ~ v1_xboole_0(E)
        & v1_funct_1(F)
        & v1_funct_2(F,k4_zfmisc_1(A,B,C,D),E)
        & m1_relset_1(F,k4_zfmisc_1(A,B,C,D),E)
        & m1_subset_1(G,A)
        & m1_subset_1(H,B)
        & m1_subset_1(I,C)
        & m1_subset_1(J,D) )
     => m1_subset_1(k4_multop_1(A,B,C,D,E,F,G,H,I,J),E) ) ),
    file(multop_1,k4_multop_1),
    []).

fof(dt_k4_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k4_zfmisc_1),
    []).

fof(dt_k5_domain_1,axiom,(
    ! [A,B,C,D,E,F,G,H] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & ~ v1_xboole_0(D)
        & m1_subset_1(E,A)
        & m1_subset_1(F,B)
        & m1_subset_1(G,C)
        & m1_subset_1(H,D) )
     => m1_subset_1(k5_domain_1(A,B,C,D,E,F,G,H),k4_zfmisc_1(A,B,C,D)) ) ),
    file(domain_1,k5_domain_1),
    []).

fof(dt_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ),
    file(funct_2,k8_funct_2),
    []).

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(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(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(fc6_subset_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & ~ v1_xboole_0(D) )
     => ~ v1_xboole_0(k4_zfmisc_1(A,B,C,D)) ) ),
    file(subset_1,fc6_subset_1),
    []).

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_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(redefinition_k4_multop_1,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & ~ v1_xboole_0(D)
        & ~ v1_xboole_0(E)
        & v1_funct_1(F)
        & v1_funct_2(F,k4_zfmisc_1(A,B,C,D),E)
        & m1_relset_1(F,k4_zfmisc_1(A,B,C,D),E)
        & m1_subset_1(G,A)
        & m1_subset_1(H,B)
        & m1_subset_1(I,C)
        & m1_subset_1(J,D) )
     => k4_multop_1(A,B,C,D,E,F,G,H,I,J) = k3_multop_1(F,G,H,I,J) ) ),
    file(multop_1,k4_multop_1),
    []).

fof(redefinition_k5_domain_1,axiom,(
    ! [A,B,C,D,E,F,G,H] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & ~ v1_xboole_0(D)
        & m1_subset_1(E,A)
        & m1_subset_1(F,B)
        & m1_subset_1(G,C)
        & m1_subset_1(H,D) )
     => k5_domain_1(A,B,C,D,E,F,G,H) = k4_mcart_1(E,F,G,H) ) ),
    file(domain_1,k5_domain_1),
    []).

fof(redefinition_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(funct_2,k8_funct_2),
    []).

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

fof(t7_multop_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( ~ v1_xboole_0(D)
                 => ! [E] : 
                      ( ~ v1_xboole_0(E)
                     => ! [F] : 
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k4_zfmisc_1(A,B,C,D),E)
                            & m2_relset_1(F,k4_zfmisc_1(A,B,C,D),E) )
                         => ! [G] : 
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,k4_zfmisc_1(A,B,C,D),E)
                                & m2_relset_1(G,k4_zfmisc_1(A,B,C,D),E) )
                             => ( ! [H] : 
                                    ( m1_subset_1(H,A)
                                   => ! [I] : 
                                        ( m1_subset_1(I,B)
                                       => ! [J] : 
                                            ( m1_subset_1(J,C)
                                           => ! [K] : 
                                                ( m1_subset_1(K,D)
                                               => k8_funct_2(k4_zfmisc_1(A,B,C,D),E,F,k5_domain_1(A,B,C,D,H,I,J,K)) = k8_funct_2(k4_zfmisc_1(A,B,C,D),E,G,k5_domain_1(A,B,C,D,H,I,J,K)) ) ) ) )
                               => F = G ) ) ) ) ) ) ) ) ),
    file(multop_1,t7_multop_1),
    []).

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