% Mizar problem: t31_afproj,afproj,1229,5 
fof(t31_afproj, conjecture,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) & l1_analoaf(A)) )  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) =>  (! [D] :  (m1_subset_1(D, u1_incsp_1(k13_afproj(A))) =>  (! [E] :  (m1_subset_1(E, u2_incsp_1(k13_afproj(A))) =>  ( (v1_aff_1(B, A) &  (v1_aff_4(C, A) &  (r1_tarski(B, C) &  (D=k5_afproj(A, B) & E=k4_tarski(k6_afproj(A, C), 2)) ) ) )  => r1_incsp_1(k13_afproj(A), D, E)) ) ) ) ) ) ) ) ) ) ) ).
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))) ) ) ).
fof(antisymmetry_r2_hidden, axiom,  (! [A, B] :  (r2_hidden(A, B) =>  ~ (r2_hidden(B, A)) ) ) ).
fof(asymmetry_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) =>  ~ (r2_tarski(B, A)) ) ) ).
fof(cc10_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ( ~ (v2_struct_0(A))  & v7_struct_0(A))  => v13_struct_0(A, 1)) ) ) ).
fof(cc11_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, 1) =>  ( ~ (v2_struct_0(A))  & v7_struct_0(A)) ) ) ) ).
fof(cc17_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc1_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C)) ) ) ).
fof(cc1_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v7_struct_0(A)) ) ) ).
fof(cc1_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_xboole_0(B)) ) ) ) ).
fof(cc2_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ).
fof(cc2_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc2_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ( ~ (v1_subset_1(B, A))  =>  ~ (v1_xboole_0(B)) ) ) ) ) ) ).
fof(cc3_relset_1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_xboole_0(C)) ) ) ) ).
fof(cc3_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  (v1_xboole_0(B) => v1_subset_1(B, A)) ) ) ) ) ).
fof(cc4_relset_1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A))) => v1_xboole_0(C)) ) ) ) ).
fof(cc4_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) =>  (v2_struct_0(A) & v8_struct_0(A)) ) ) ) ).
fof(cc4_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ~ (v1_subset_1(B, A)) ) ) ) ) ).
fof(cc5_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ( ~ (v2_struct_0(A))  &  ~ (v8_struct_0(A)) ) ) ) ) ).
fof(cc5_subset_1, axiom,  (! [A] :  (v1_zfmisc_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_zfmisc_1(B)) ) ) ) ).
fof(cc6_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v7_struct_0(A) => v8_struct_0(A)) ) ) ).
fof(cc7_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ~ (v7_struct_0(A)) ) ) ) ).
fof(cc8_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v13_struct_0(A, k5_ordinal1)) ) ) ).
fof(cc9_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, k5_ordinal1) => v2_struct_0(A)) ) ) ).
fof(commutativity_k2_tarski, axiom,  (! [A, B] : k2_tarski(A, B)=k2_tarski(B, A)) ).
fof(commutativity_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, B)=k2_xboole_0(B, A)) ).
fof(d10_afproj, axiom,  (! [A] :  ( ( ~ (v7_struct_0(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)))) ) ).
fof(d13_afproj, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) & l1_analoaf(A)) )  => k13_afproj(A)=g1_incsp_1(k9_afproj(A), k10_afproj(A), k11_afproj(A))) ) ).
fof(d1_afproj, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) & l1_analoaf(A)) )  => k1_afproj(A)=a_1_0_afproj(A)) ) ).
fof(d2_afproj, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) & l1_analoaf(A)) )  => k2_afproj(A)=a_1_1_afproj(A)) ) ).
fof(d3_afproj, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) & l1_analoaf(A)) )  => k3_afproj(A)=a_1_2_afproj(A)) ) ).
fof(d3_tarski, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) <=>  (! [C] :  (r2_hidden(C, A) => r2_hidden(C, B)) ) ) ) ) ).
fof(d4_afproj, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) & l1_analoaf(A)) )  => k4_afproj(A)=a_1_3_afproj(A)) ) ).
fof(d5_afproj, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) & l1_analoaf(A)) )  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => k5_afproj(A, B)=k6_eqrel_1(k1_afproj(A), k1_afproj(A), k3_afproj(A), B)) ) ) ) ).
fof(d5_tarski, axiom,  (! [A] :  (! [B] : k4_tarski(A, B)=k2_tarski(k2_tarski(A, B), k1_tarski(A))) ) ).
fof(d6_afproj, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) & l1_analoaf(A)) )  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => k6_afproj(A, B)=k6_eqrel_1(k2_afproj(A), k2_afproj(A), k4_afproj(A), B)) ) ) ) ).
fof(d7_afproj, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) & l1_analoaf(A)) )  => k7_afproj(A)=k8_eqrel_1(k1_afproj(A), k3_afproj(A))) ) ).
fof(d8_afproj, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) & l1_analoaf(A)) )  => k8_afproj(A)=k8_eqrel_1(k2_afproj(A), k4_afproj(A))) ) ).
fof(d9_afproj, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) & l1_analoaf(A)) )  => k9_afproj(A)=k2_xboole_0(u1_struct_0(A), k7_afproj(A))) ) ).
fof(dt_g1_incsp_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  =>  (v1_incsp_1(g1_incsp_1(A, B, C)) & l1_incsp_1(g1_incsp_1(A, B, C))) ) ) ).
fof(dt_k10_afproj, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) & l1_analoaf(A)) )  =>  ~ (v1_xboole_0(k10_afproj(A))) ) ) ).
fof(dt_k11_afproj, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) & l1_analoaf(A)) )  => m1_subset_1(k11_afproj(A), k1_zfmisc_1(k2_zfmisc_1(k9_afproj(A), k10_afproj(A))))) ) ).
fof(dt_k13_afproj, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) & l1_analoaf(A)) )  =>  (v1_incsp_1(k13_afproj(A)) & l1_incsp_1(k13_afproj(A))) ) ) ).
fof(dt_k1_afproj, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) & l1_analoaf(A)) )  => m1_subset_1(k1_afproj(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))) ) ).
fof(dt_k1_domain_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  (m1_subset_1(C, A) & m1_subset_1(D, B)) ) )  => m1_subset_1(k1_domain_1(A, B, C, D), k2_zfmisc_1(A, B))) ) ).
fof(dt_k1_tarski, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_afproj, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) & l1_analoaf(A)) )  => m1_subset_1(k2_afproj(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))) ) ).
fof(dt_k2_tarski, axiom, $true).
fof(dt_k2_xboole_0, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_afproj, axiom,  (! [A] :  ( ( ~ (v7_struct_0(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)) & m1_subset_1(k3_afproj(A), k1_zfmisc_1(k2_zfmisc_1(k1_afproj(A), k1_afproj(A))))) ) ) ) ) ).
fof(dt_k4_afproj, axiom,  (! [A] :  ( ( ~ (v7_struct_0(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)) & m1_subset_1(k4_afproj(A), k1_zfmisc_1(k2_zfmisc_1(k2_afproj(A), k2_afproj(A))))) ) ) ) ) ).
fof(dt_k4_tarski, axiom, $true).
fof(dt_k5_afproj, axiom,  (! [A, B] :  ( ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) & l1_analoaf(A)) )  & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))  => m1_subset_1(k5_afproj(A, B), k1_zfmisc_1(k1_afproj(A)))) ) ).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k6_afproj, axiom,  (! [A, B] :  ( ( ( ~ (v7_struct_0(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)))) ) ).
fof(dt_k6_eqrel_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => m1_subset_1(k6_eqrel_1(A, B, C, D), k1_zfmisc_1(B))) ) ).
fof(dt_k7_afproj, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) & l1_analoaf(A)) )  =>  ~ (v1_xboole_0(k7_afproj(A))) ) ) ).
fof(dt_k7_eqrel_1, axiom,  (! [A, B] :  ( (v3_relat_2(B) &  (v8_relat_2(B) &  (v1_partfun1(B, A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, A)))) ) )  => m1_subset_1(k7_eqrel_1(A, B), k1_zfmisc_1(k1_zfmisc_1(A)))) ) ).
fof(dt_k8_afproj, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) & l1_analoaf(A)) )  =>  ~ (v1_xboole_0(k8_afproj(A))) ) ) ).
fof(dt_k8_eqrel_1, axiom,  (! [A, B] :  ( (v3_relat_2(B) &  (v8_relat_2(B) &  (v1_partfun1(B, A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, A)))) ) )  => m1_eqrel_1(k8_eqrel_1(A, B), A)) ) ).
fof(dt_k9_afproj, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) & l1_analoaf(A)) )  =>  ~ (v1_xboole_0(k9_afproj(A))) ) ) ).
fof(dt_k9_relat_1, axiom, $true).
fof(dt_l1_analoaf, axiom,  (! [A] :  (l1_analoaf(A) => l1_struct_0(A)) ) ).
fof(dt_l1_incsp_1, axiom, $true).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_m1_eqrel_1, axiom,  (! [A] :  (! [B] :  (m1_eqrel_1(B, A) => m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_u1_incsp_1, axiom,  (! [A] :  (l1_incsp_1(A) =>  ~ (v1_xboole_0(u1_incsp_1(A))) ) ) ).
fof(dt_u1_struct_0, axiom, $true).
fof(dt_u2_incsp_1, axiom,  (! [A] :  (l1_incsp_1(A) =>  ~ (v1_xboole_0(u2_incsp_1(A))) ) ) ).
fof(dt_u3_incsp_1, axiom,  (! [A] :  (l1_incsp_1(A) => m1_subset_1(u3_incsp_1(A), k1_zfmisc_1(k2_zfmisc_1(u1_incsp_1(A), u2_incsp_1(A))))) ) ).
fof(existence_l1_analoaf, axiom,  (? [A] : l1_analoaf(A)) ).
fof(existence_l1_incsp_1, axiom,  (? [A] : l1_incsp_1(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_m1_eqrel_1, axiom,  (! [A] :  (? [B] : m1_eqrel_1(B, A)) ) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc10_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_xboole_0(k2_zfmisc_1(A, B))) ) ) ).
fof(fc1_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v4_relat_1(B, A))  &  (v1_relat_1(C) & v4_relat_1(C, A)) )  => v4_relat_1(k2_xboole_0(B, C), A)) ) ).
fof(fc1_struct_0, axiom,  (! [A] :  ( (v2_struct_0(A) & l1_struct_0(A))  => v1_xboole_0(u1_struct_0(A))) ) ).
fof(fc1_subset_1, axiom,  (! [A] :  ~ (v1_xboole_0(k1_zfmisc_1(A))) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc1_xtuple_0, axiom,  (! [A, B] : v1_xtuple_0(k4_tarski(A, B))) ).
fof(fc2_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_xboole_0(u1_struct_0(A))) ) ) ).
fof(fc2_xboole_0, axiom,  (! [A] :  ~ (v1_xboole_0(k1_tarski(A))) ) ).
fof(fc3_xboole_0, axiom,  (! [A, B] :  ~ (v1_xboole_0(k2_tarski(A, B))) ) ).
fof(fc4_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v5_relat_1(B, A))  &  (v1_relat_1(C) & v5_relat_1(C, A)) )  => v5_relat_1(k2_xboole_0(B, C), A)) ) ).
fof(fc4_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(A, B))) ) ) ).
fof(fc5_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(B, A))) ) ) ).
fof(fc6_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(fc7_struct_0, axiom,  (! [A] :  ( (v7_struct_0(A) & l1_struct_0(A))  => v1_zfmisc_1(u1_struct_0(A))) ) ).
fof(fc8_struct_0, axiom,  (! [A] :  ( (v8_struct_0(A) & l1_struct_0(A))  => v1_finset_1(u1_struct_0(A))) ) ).
fof(fc9_struct_0, axiom,  (! [A] :  ( ( ~ (v8_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_finset_1(u1_struct_0(A))) ) ) ).
fof(fraenkel_a_1_0_afproj, axiom,  (! [A, B] :  ( ( ~ (v7_struct_0(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)) ) ) ) ) ) ).
fof(fraenkel_a_1_1_afproj, axiom,  (! [A, B] :  ( ( ~ (v7_struct_0(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)) ) ) ) ) ) ).
fof(fraenkel_a_1_2_afproj, axiom,  (! [A, B] :  ( ( ~ (v7_struct_0(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=k1_domain_1(k1_zfmisc_1(u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)), C, D) &  (v1_aff_1(C, B) &  (v1_aff_1(D, B) & r1_aff_4(B, C, D)) ) ) ) ) ) ) ) ).
fof(fraenkel_a_1_3_afproj, axiom,  (! [A, B] :  ( ( ~ (v7_struct_0(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=k1_domain_1(k1_zfmisc_1(u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)), C, D) &  (v1_aff_4(C, B) &  (v1_aff_4(D, B) & r1_aff_4(B, C, D)) ) ) ) ) ) ) ) ).
fof(free_g1_incsp_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  =>  (! [D, E, F] :  (g1_incsp_1(A, B, C)=g1_incsp_1(D, E, F) =>  (A=D &  (B=E & C=F) ) ) ) ) ) ).
fof(idempotence_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, A)=A) ).
fof(rc1_relset_1, axiom,  (! [A, B] :  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_xboole_0(C) &  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ) ) ).
fof(rc1_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc1_xtuple_0, axiom,  (? [A] : v1_xtuple_0(A)) ).
fof(rc21_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc22_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc2_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_xboole_0(B)) ) ) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc3_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_subset_1(B, A)) ) ) ) ).
fof(rc4_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc4_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_subset_1(B, A)) ) ) ) ).
fof(rc5_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc6_subset_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(redefinition_k1_domain_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  (m1_subset_1(C, A) & m1_subset_1(D, B)) ) )  => k1_domain_1(A, B, C, D)=k4_tarski(C, D)) ) ).
fof(redefinition_k6_eqrel_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => k6_eqrel_1(A, B, C, D)=k9_relat_1(C, D)) ) ).
fof(redefinition_k8_eqrel_1, axiom,  (! [A, B] :  ( (v3_relat_2(B) &  (v8_relat_2(B) &  (v1_partfun1(B, A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, A)))) ) )  => k8_eqrel_1(A, B)=k7_eqrel_1(A, B)) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(spc2_boole, axiom,  ~ (v1_xboole_0(2)) ).
fof(t1_boole, axiom,  (! [A] : k2_xboole_0(A, k1_xboole_0)=A) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t29_afproj, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) & l1_analoaf(A)) )  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) =>  (! [D] :  (m1_subset_1(D, u1_incsp_1(k13_afproj(A))) =>  (! [E] :  (m1_subset_1(E, u2_incsp_1(k13_afproj(A))) =>  ( (D=k5_afproj(A, C) &  (E=k4_tarski(k6_afproj(A, B), 2) &  (v1_aff_1(C, A) & v1_aff_4(B, A)) ) )  =>  (r1_incsp_1(k13_afproj(A), D, E) <=> r1_aff_4(A, C, B)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t2_tarski, axiom,  (! [A] :  (! [B] :  ( (! [C] :  (r2_hidden(C, A) <=> r2_hidden(C, B)) )  => A=B) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t42_aff_4, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) & l1_analoaf(A)) )  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) =>  ( (v1_aff_1(B, A) &  (v1_aff_4(C, A) & r1_tarski(B, C)) )  => r1_aff_4(A, B, C)) ) ) ) ) ) ) ).
fof(t4_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r2_tarski(A, B) & m1_subset_1(B, k1_zfmisc_1(C)))  => m1_subset_1(A, C)) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
