% Mizar problem: t25_afproj,afproj,583,31 
fof(t25_afproj,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u2_incsp_1(k14_afproj(A)))
         => m1_subset_1(k4_tarski(B,2),u2_incsp_1(k13_afproj(A))) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_incsp_1,antisymmetry_r2_hidden,cc1_partfun1,cc1_relset_1,commutativity_k2_tarski,commutativity_k2_xboole_0,d10_afproj,d13_afproj,d14_afproj,d1_afproj,d2_afproj,d3_afproj,d4_afproj,d5_tarski,d7_afproj,d8_afproj,d9_afproj,dt_g1_incsp_1,dt_k10_afproj,dt_k11_afproj,dt_k12_afproj,dt_k13_afproj,dt_k14_afproj,dt_k1_afproj,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_afproj,dt_k2_tarski,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_afproj,dt_k4_afproj,dt_k4_tarski,dt_k6_afproj,dt_k7_afproj,dt_k7_eqrel_1,dt_k8_afproj,dt_k8_eqrel_1,dt_k9_afproj,dt_l1_analoaf,dt_l1_incsp_1,dt_l1_struct_0,dt_m1_eqrel_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_incsp_1,dt_u1_struct_0,dt_u2_incsp_1,dt_u3_incsp_1,existence_l1_analoaf,existence_l1_incsp_1,existence_l1_struct_0,existence_m1_eqrel_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc1_struct_0,fc1_subset_1,fc1_xboole_0,fc2_subset_1,fc2_xboole_0,fc3_subset_1,fc3_xboole_0,fc4_subset_1,fraenkel_a_1_0_afproj,fraenkel_a_1_1_afproj,fraenkel_a_1_2_afproj,fraenkel_a_1_3_afproj,free_g1_incsp_1,idempotence_k2_xboole_0,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_struct_0,rc5_struct_0,redefinition_k8_eqrel_1,redefinition_m2_relset_1,reflexivity_r1_tarski,spc1_boole,spc2_boole,t1_boole,t1_subset,t23_afproj,t24_afproj,t2_subset,t2_tarski,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(afproj,t25_afproj)]).

fof(abstractness_v1_incsp_1,axiom,(
    ! [A] : 
      ( l1_incsp_1(A)
     => ( v1_incsp_1(A)
       => A = g1_incsp_1(u1_incsp_1(A),u2_incsp_1(A),u3_incsp_1(A)) ) ) ),
    file(incsp_1,v1_incsp_1),
    []).

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

fof(cc1_partfun1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v3_relat_2(A)
        & v8_relat_2(A) )
     => ( v1_relat_1(A)
        & v1_relat_2(A) ) ) ),
    file(partfun1,cc1_partfun1),
    []).

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(commutativity_k2_tarski,axiom,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    []).

fof(commutativity_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    []).

fof(d10_afproj,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => k10_afproj(A) = k2_xboole_0(k2_zfmisc_1(k1_afproj(A),k1_tarski(1)),k2_zfmisc_1(k8_afproj(A),k1_tarski(2))) ) ),
    file(afproj,d10_afproj),
    []).

fof(d13_afproj,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => k13_afproj(A) = g1_incsp_1(k9_afproj(A),k10_afproj(A),k11_afproj(A)) ) ),
    file(afproj,d13_afproj),
    []).

fof(d14_afproj,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => k14_afproj(A) = g1_incsp_1(k7_afproj(A),k8_afproj(A),k12_afproj(A)) ) ),
    file(afproj,d14_afproj),
    []).

fof(d1_afproj,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => k1_afproj(A) = a_1_0_afproj(A) ) ),
    file(afproj,d1_afproj),
    []).

fof(d2_afproj,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => k2_afproj(A) = a_1_1_afproj(A) ) ),
    file(afproj,d2_afproj),
    []).

fof(d3_afproj,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => k3_afproj(A) = a_1_2_afproj(A) ) ),
    file(afproj,d3_afproj),
    []).

fof(d4_afproj,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => k4_afproj(A) = a_1_3_afproj(A) ) ),
    file(afproj,d4_afproj),
    []).

fof(d5_tarski,axiom,(
    ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ),
    file(tarski,d5_tarski),
    []).

fof(d7_afproj,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => k7_afproj(A) = k8_eqrel_1(k1_afproj(A),k3_afproj(A)) ) ),
    file(afproj,d7_afproj),
    []).

fof(d8_afproj,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => k8_afproj(A) = k8_eqrel_1(k2_afproj(A),k4_afproj(A)) ) ),
    file(afproj,d8_afproj),
    []).

fof(d9_afproj,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => k9_afproj(A) = k2_xboole_0(u1_struct_0(A),k7_afproj(A)) ) ),
    file(afproj,d9_afproj),
    []).

fof(dt_g1_incsp_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_relset_1(C,A,B) )
     => ( v1_incsp_1(g1_incsp_1(A,B,C))
        & l1_incsp_1(g1_incsp_1(A,B,C)) ) ) ),
    file(incsp_1,g1_incsp_1),
    []).

fof(dt_k10_afproj,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ~ v1_xboole_0(k10_afproj(A)) ) ),
    file(afproj,k10_afproj),
    []).

fof(dt_k11_afproj,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => m2_relset_1(k11_afproj(A),k9_afproj(A),k10_afproj(A)) ) ),
    file(afproj,k11_afproj),
    []).

fof(dt_k12_afproj,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => m2_relset_1(k12_afproj(A),k7_afproj(A),k8_afproj(A)) ) ),
    file(afproj,k12_afproj),
    []).

fof(dt_k13_afproj,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ( v1_incsp_1(k13_afproj(A))
        & l1_incsp_1(k13_afproj(A)) ) ) ),
    file(afproj,k13_afproj),
    []).

fof(dt_k14_afproj,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ( v1_incsp_1(k14_afproj(A))
        & l1_incsp_1(k14_afproj(A)) ) ) ),
    file(afproj,k14_afproj),
    []).

fof(dt_k1_afproj,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => m1_subset_1(k1_afproj(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ),
    file(afproj,k1_afproj),
    []).

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_afproj,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => m1_subset_1(k2_afproj(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ),
    file(afproj,k2_afproj),
    []).

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    []).

fof(dt_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    []).

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

fof(dt_k3_afproj,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ( v3_relat_2(k3_afproj(A))
        & v8_relat_2(k3_afproj(A))
        & v1_partfun1(k3_afproj(A),k1_afproj(A),k1_afproj(A))
        & m2_relset_1(k3_afproj(A),k1_afproj(A),k1_afproj(A)) ) ) ),
    file(afproj,k3_afproj),
    []).

fof(dt_k4_afproj,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ( v3_relat_2(k4_afproj(A))
        & v8_relat_2(k4_afproj(A))
        & v1_partfun1(k4_afproj(A),k2_afproj(A),k2_afproj(A))
        & m2_relset_1(k4_afproj(A),k2_afproj(A),k2_afproj(A)) ) ) ),
    file(afproj,k4_afproj),
    []).

fof(dt_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    []).

fof(dt_k6_afproj,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k6_afproj(A,B),k1_zfmisc_1(k2_afproj(A))) ) ),
    file(afproj,k6_afproj),
    []).

fof(dt_k7_afproj,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ~ v1_xboole_0(k7_afproj(A)) ) ),
    file(afproj,k7_afproj),
    []).

fof(dt_k7_eqrel_1,axiom,(
    ! [A,B] : 
      ( ( v3_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m1_relset_1(B,A,A) )
     => m1_subset_1(k7_eqrel_1(A,B),k1_zfmisc_1(k1_zfmisc_1(A))) ) ),
    file(eqrel_1,k7_eqrel_1),
    []).

fof(dt_k8_afproj,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ~ v1_xboole_0(k8_afproj(A)) ) ),
    file(afproj,k8_afproj),
    []).

fof(dt_k8_eqrel_1,axiom,(
    ! [A,B] : 
      ( ( v3_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m1_relset_1(B,A,A) )
     => m1_eqrel_1(k8_eqrel_1(A,B),A) ) ),
    file(eqrel_1,k8_eqrel_1),
    []).

fof(dt_k9_afproj,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ~ v1_xboole_0(k9_afproj(A)) ) ),
    file(afproj,k9_afproj),
    []).

fof(dt_l1_analoaf,axiom,(
    ! [A] : 
      ( l1_analoaf(A)
     => l1_struct_0(A) ) ),
    file(analoaf,l1_analoaf),
    []).

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

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    []).

fof(dt_m1_eqrel_1,axiom,(
    ! [A,B] : 
      ( m1_eqrel_1(B,A)
     => m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) ),
    file(eqrel_1,m1_eqrel_1),
    []).

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(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_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    []).

fof(dt_u2_incsp_1,axiom,(
    ! [A] : 
      ( l1_incsp_1(A)
     => ~ v1_xboole_0(u2_incsp_1(A)) ) ),
    file(incsp_1,u2_incsp_1),
    []).

fof(dt_u3_incsp_1,axiom,(
    ! [A] : 
      ( l1_incsp_1(A)
     => m2_relset_1(u3_incsp_1(A),u1_incsp_1(A),u2_incsp_1(A)) ) ),
    file(incsp_1,u3_incsp_1),
    []).

fof(existence_l1_analoaf,axiom,(
    ? [A] : l1_analoaf(A) ),
    file(analoaf,l1_analoaf),
    []).

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

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    []).

fof(existence_m1_eqrel_1,axiom,(
    ! [A] : 
    ? [B] : m1_eqrel_1(B,A) ),
    file(eqrel_1,m1_eqrel_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_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(u1_struct_0(A)) ) ),
    file(struct_0,fc1_struct_0),
    []).

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_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    []).

fof(fc2_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(A,B)) ) ),
    file(xboole_0,fc2_xboole_0),
    []).

fof(fc3_subset_1,axiom,(
    ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ),
    file(subset_1,fc3_subset_1),
    []).

fof(fc3_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(B,A)) ) ),
    file(xboole_0,fc3_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(fraenkel_a_1_0_afproj,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & ~ v3_realset2(B)
        & v1_diraf(B)
        & l1_analoaf(B) )
     => ( r2_hidden(A,a_1_0_afproj(B))
      <=> ? [C] : 
            ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
            & A = C
            & v1_aff_1(C,B) ) ) ) ),
    file(afproj,a_1_0_afproj),
    []).

fof(fraenkel_a_1_1_afproj,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & ~ v3_realset2(B)
        & v1_diraf(B)
        & l1_analoaf(B) )
     => ( r2_hidden(A,a_1_1_afproj(B))
      <=> ? [C] : 
            ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
            & A = C
            & v1_aff_4(C,B) ) ) ) ),
    file(afproj,a_1_1_afproj),
    []).

fof(fraenkel_a_1_2_afproj,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & ~ v3_realset2(B)
        & v1_diraf(B)
        & l1_analoaf(B) )
     => ( r2_hidden(A,a_1_2_afproj(B))
      <=> ? [C,D] : 
            ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
            & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
            & A = k4_tarski(C,D)
            & v1_aff_1(C,B)
            & v1_aff_1(D,B)
            & r1_aff_4(B,C,D) ) ) ) ),
    file(afproj,a_1_2_afproj),
    []).

fof(fraenkel_a_1_3_afproj,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & ~ v3_realset2(B)
        & v1_diraf(B)
        & l1_analoaf(B) )
     => ( r2_hidden(A,a_1_3_afproj(B))
      <=> ? [C,D] : 
            ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
            & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
            & A = k4_tarski(C,D)
            & v1_aff_4(C,B)
            & v1_aff_4(D,B)
            & r1_aff_4(B,C,D) ) ) ) ),
    file(afproj,a_1_3_afproj),
    []).

fof(free_g1_incsp_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_relset_1(C,A,B) )
     => ! [D,E,F] : 
          ( g1_incsp_1(A,B,C) = g1_incsp_1(D,E,F)
         => ( A = D
            & B = E
            & C = F ) ) ) ),
    file(incsp_1,g1_incsp_1),
    []).

fof(idempotence_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_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(rc3_struct_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    []).

fof(rc5_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B) ) ) ),
    file(struct_0,rc5_struct_0),
    []).

fof(redefinition_k8_eqrel_1,axiom,(
    ! [A,B] : 
      ( ( v3_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m1_relset_1(B,A,A) )
     => k8_eqrel_1(A,B) = k7_eqrel_1(A,B) ) ),
    file(eqrel_1,k8_eqrel_1),
    []).

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(spc1_boole,axiom,(
    ~ v1_xboole_0(1) ),
    file(boole,spc1_boole),
    []).

fof(spc2_boole,axiom,(
    ~ v1_xboole_0(2) ),
    file(boole,spc2_boole),
    []).

fof(t1_boole,axiom,(
    ! [A] : k2_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t1_boole),
    []).

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

fof(t23_afproj,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u2_incsp_1(k13_afproj(A)))
        <=> ~ ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( ~ ( B = k4_tarski(C,1)
                      & v1_aff_1(C,A) )
                  & ~ ( B = k4_tarski(k6_afproj(A,C),2)
                      & v1_aff_4(C,A) ) ) ) ) ) ),
    file(afproj,t23_afproj),
    []).

fof(t24_afproj,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u2_incsp_1(k14_afproj(A)))
        <=> ? [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
              & B = k6_afproj(A,C)
              & v1_aff_4(C,A) ) ) ) ),
    file(afproj,t24_afproj),
    []).

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

fof(t2_tarski,axiom,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    []).

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