% Mizar problem: t77_incsp_1,incsp_1,1325,41 
fof(t77_incsp_1,conjecture,(
    ! [A] : 
      ( ( v5_incsp_1(A)
        & l2_incsp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_incsp_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_incsp_1(A))
             => ~ ( B != C
                  & ! [D] : 
                      ( m1_subset_1(D,u1_incsp_1(A))
                     => ! [E] : 
                          ( m1_subset_1(E,u1_incsp_1(A))
                         => v4_incsp_1(k9_domain_1(u1_incsp_1(A),B,C,D,E),A) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,dt_k1_enumset1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_enumset1,dt_k8_domain_1,dt_k9_domain_1,dt_l1_incsp_1,dt_l2_incsp_1,dt_m1_subset_1,dt_u1_incsp_1,dt_u4_incsp_1,existence_l1_incsp_1,existence_l2_incsp_1,existence_m1_subset_1,fc1_incsp_1,fc1_subset_1,fc1_xboole_0,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,redefinition_k8_domain_1,redefinition_k9_domain_1,reflexivity_r1_tarski,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t74_incsp_1,t75_incsp_1,t7_boole,t8_boole]),
    [file(incsp_1,t77_incsp_1)]).

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

fof(dt_k1_enumset1,axiom,(
    $true ),
    file(enumset1,k1_enumset1),
    []).

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_enumset1,axiom,(
    $true ),
    file(enumset1,k2_enumset1),
    []).

fof(dt_k8_domain_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A)
        & m1_subset_1(D,A) )
     => m1_subset_1(k8_domain_1(A,B,C,D),k1_zfmisc_1(A)) ) ),
    file(domain_1,k8_domain_1),
    []).

fof(dt_k9_domain_1,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A)
        & m1_subset_1(D,A)
        & m1_subset_1(E,A) )
     => m1_subset_1(k9_domain_1(A,B,C,D,E),k1_zfmisc_1(A)) ) ),
    file(domain_1,k9_domain_1),
    []).

fof(dt_l1_incsp_1,axiom,(
    $true ),
    file(incsp_1,l1_incsp_1),
    []).

fof(dt_l2_incsp_1,axiom,(
    ! [A] : 
      ( l2_incsp_1(A)
     => l1_incsp_1(A) ) ),
    file(incsp_1,l2_incsp_1),
    []).

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

fof(dt_u1_incsp_1,axiom,(
    ! [A] : 
      ( l1_incsp_1(A)
     => ~ v1_xboole_0(u1_incsp_1(A)) ) ),
    file(incsp_1,u1_incsp_1),
    []).

fof(dt_u4_incsp_1,axiom,(
    ! [A] : 
      ( l2_incsp_1(A)
     => ~ v1_xboole_0(u4_incsp_1(A)) ) ),
    file(incsp_1,u4_incsp_1),
    []).

fof(existence_l1_incsp_1,axiom,(
    ? [A] : l1_incsp_1(A) ),
    file(incsp_1,l1_incsp_1),
    []).

fof(existence_l2_incsp_1,axiom,(
    ? [A] : l2_incsp_1(A) ),
    file(incsp_1,l2_incsp_1),
    []).

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

fof(fc1_incsp_1,axiom,(
    ! [A,B,C,D] : ~ v1_xboole_0(k2_enumset1(A,B,C,D)) ),
    file(incsp_1,fc1_incsp_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(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_k8_domain_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A)
        & m1_subset_1(D,A) )
     => k8_domain_1(A,B,C,D) = k1_enumset1(B,C,D) ) ),
    file(domain_1,k8_domain_1),
    []).

fof(redefinition_k9_domain_1,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A)
        & m1_subset_1(D,A)
        & m1_subset_1(E,A) )
     => k9_domain_1(A,B,C,D,E) = k2_enumset1(B,C,D,E) ) ),
    file(domain_1,k9_domain_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(t74_incsp_1,axiom,(
    ! [A] : 
      ( ( v5_incsp_1(A)
        & l2_incsp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_incsp_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_incsp_1(A))
             => ! [D] : 
                  ( m1_subset_1(D,u4_incsp_1(A))
                 => ~ ( B != C
                      & ! [E] : 
                          ( m1_subset_1(E,u1_incsp_1(A))
                         => ~ ( r2_incsp_1(A,E,D)
                              & ~ v3_incsp_1(k8_domain_1(u1_incsp_1(A),B,C,E),A) ) ) ) ) ) ) ) ),
    file(incsp_1,t74_incsp_1),
    []).

fof(t75_incsp_1,axiom,(
    ! [A] : 
      ( ( v5_incsp_1(A)
        & l2_incsp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_incsp_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_incsp_1(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_incsp_1(A))
                 => ~ ( ~ v3_incsp_1(k8_domain_1(u1_incsp_1(A),B,C,D),A)
                      & ! [E] : 
                          ( m1_subset_1(E,u1_incsp_1(A))
                         => v4_incsp_1(k9_domain_1(u1_incsp_1(A),B,C,D,E),A) ) ) ) ) ) ) ),
    file(incsp_1,t75_incsp_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),
    []).