% Mizar problem: t15_projred2,projred2,438,5 
fof(t15_projred2, conjecture,  (! [A] :  ( (v6_incsp_1(A) &  (v1_incproj(A) &  (v2_incproj(A) &  (v3_incproj(A) &  (v4_incproj(A) &  (v5_incproj(A) &  (v9_incproj(A) & l1_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)) =>  (! [E] :  (m1_subset_1(E, u1_incsp_1(A)) =>  (! [F] :  (m1_subset_1(F, u1_incsp_1(A)) =>  (! [G] :  (m1_subset_1(G, u1_incsp_1(A)) =>  (! [H] :  (m1_subset_1(H, u1_incsp_1(A)) =>  (! [I] :  (m1_subset_1(I, u1_incsp_1(A)) =>  (! [J] :  (m1_subset_1(J, u1_incsp_1(A)) =>  (! [K] :  (m1_subset_1(K, u2_incsp_1(A)) =>  (! [L] :  (m1_subset_1(L, u2_incsp_1(A)) =>  (! [M] :  (m1_subset_1(M, u2_incsp_1(A)) =>  (! [N] :  (m1_subset_1(N, u2_incsp_1(A)) =>  (! [O] :  (m1_subset_1(O, u2_incsp_1(A)) =>  (! [P] :  (m1_subset_1(P, u2_incsp_1(A)) =>  (! [Q] :  (m1_subset_1(Q, u2_incsp_1(A)) =>  (! [R] :  (m1_subset_1(R, u2_incsp_1(A)) =>  ( (r4_incsp_1(A, k7_domain_1(u1_incsp_1(A), D, G), N) &  (r4_incsp_1(A, k8_domain_1(u1_incsp_1(A), G, I, E), O) &  (r4_incsp_1(A, k8_domain_1(u1_incsp_1(A), D, E, H), P) &  (r4_incsp_1(A, k8_domain_1(u1_incsp_1(A), B, C, E), Q) &  (r4_incsp_1(A, k7_domain_1(u1_incsp_1(A), D, J), R) &  (r4_incsp_1(A, k8_domain_1(u1_incsp_1(A), B, G, H), K) &  (r4_incsp_1(A, k8_domain_1(u1_incsp_1(A), C, H, J), L) &  (r4_incsp_1(A, k8_domain_1(u1_incsp_1(A), G, J, F), M) & r1_incsp_1(A, F, Q)) ) ) ) ) ) ) )  =>  (r1_incsp_1(A, B, N) |  (r1_incsp_1(A, B, P) |  (r1_incsp_1(A, C, O) |  (r1_incsp_1(A, C, P) |  (r1_incsp_1(A, C, R) |  (r1_projred2(A, N, O, P) |  (B=C |  (C=F |  (N=R | k3_relat_1(k1_projred1(A, N, P, B), k1_projred1(A, P, O, C))=k3_relat_1(k1_projred1(A, N, R, F), k1_projred1(A, R, O, C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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(cc1_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_funct_1(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(cc2_funct_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ) ).
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(cc3_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_funct_1(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(cc4_funct_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(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(cc5_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) )  =>  ( ~ (v1_zfmisc_1(A))  &  (v1_relat_1(A) & v1_funct_1(A)) ) ) ) ).
fof(cc6_funct_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) ) ) ) ).
fof(cc7_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_funct_1(A)) ) ).
fof(cc8_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, A) =>  (v1_relat_1(B) & v1_funct_1(B)) ) ) ) ) ).
fof(cc9_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_funct_1(B)) ) ) ) ).
fof(commutativity_k2_tarski, axiom,  (! [A, B] : k2_tarski(A, B)=k2_tarski(B, A)) ).
fof(commutativity_k7_domain_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  (m1_subset_1(B, A) & m1_subset_1(C, A)) )  => k7_domain_1(A, B, C)=k7_domain_1(A, C, B)) ) ).
fof(d1_projred1, axiom,  (! [A] :  ( (v6_incsp_1(A) &  (v1_incproj(A) &  (v2_incproj(A) &  (v3_incproj(A) &  (v4_incproj(A) &  (v5_incproj(A) &  (v9_incproj(A) & l1_incsp_1(A)) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u2_incsp_1(A)) =>  (! [C] :  (m1_subset_1(C, u2_incsp_1(A)) =>  (! [D] :  (m1_subset_1(D, u1_incsp_1(A)) =>  ~ ( ( ~ (r1_incsp_1(A, D, B))  &  ( ~ (r1_incsp_1(A, D, C))  &  ~ ( (! [E] :  ( (v1_funct_1(E) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(u1_incsp_1(A), u1_incsp_1(A)))))  =>  (E=k1_projred1(A, B, C, D) <=>  (r1_tarski(k1_relset_1(u1_incsp_1(A), E), u1_incsp_1(A)) &  ( (! [F] :  (m1_subset_1(F, u1_incsp_1(A)) =>  (r2_tarski(F, k1_relset_1(u1_incsp_1(A), E)) <=> r1_incsp_1(A, F, B)) ) )  &  (! [F] :  (m1_subset_1(F, u1_incsp_1(A)) =>  (! [G] :  (m1_subset_1(G, u1_incsp_1(A)) =>  ( (r1_incsp_1(A, F, B) & r1_incsp_1(A, G, C))  =>  (k1_funct_1(E, F)=G <=>  (? [H] :  (m1_subset_1(H, u2_incsp_1(A)) &  (r1_incsp_1(A, D, H) &  (r1_incsp_1(A, F, H) & r1_incsp_1(A, G, H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d1_projred2, axiom,  (! [A] :  ( (v6_incsp_1(A) &  (v1_incproj(A) &  (v2_incproj(A) &  (v3_incproj(A) &  (v4_incproj(A) & l1_incsp_1(A)) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u2_incsp_1(A)) =>  (! [C] :  (m1_subset_1(C, u2_incsp_1(A)) =>  (! [D] :  (m1_subset_1(D, u2_incsp_1(A)) =>  (r1_projred2(A, B, C, D) <=>  (? [E] :  (m1_subset_1(E, u1_incsp_1(A)) &  (r1_incsp_1(A, E, B) &  (r1_incsp_1(A, E, C) & r1_incsp_1(A, E, D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d2_projred2, axiom,  (! [A] :  ( (v6_incsp_1(A) &  (v1_incproj(A) &  (v2_incproj(A) &  (v3_incproj(A) &  (v4_incproj(A) & l1_incsp_1(A)) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u2_incsp_1(A)) => k1_projred2(A, B)=a_2_0_projred2(A, B)) ) ) ) ).
fof(d4_incproj, axiom,  (! [A] :  (l1_incsp_1(A) =>  (v1_incproj(A) <=>  (! [B] :  (m1_subset_1(B, u1_incsp_1(A)) =>  (! [C] :  (m1_subset_1(C, u1_incsp_1(A)) =>  (! [D] :  (m1_subset_1(D, u2_incsp_1(A)) =>  (! [E] :  (m1_subset_1(E, u2_incsp_1(A)) =>  ~ ( (r1_incsp_1(A, B, D) &  (r1_incsp_1(A, C, D) &  (r1_incsp_1(A, B, E) &  (r1_incsp_1(A, C, E) &  ( ~ (B=C)  &  ~ (D=E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d5_incproj, axiom,  (! [A] :  (l1_incsp_1(A) =>  (v6_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, u2_incsp_1(A)) &  (r1_incsp_1(A, B, D) & r1_incsp_1(A, C, D)) ) ) ) ) ) ) ) ) ) ).
fof(d5_zfmisc_1, axiom,  (! [A] :  (! [B] :  (! [C] :  (r1_zfmisc_1(A, B, C) <=>  ( ~ (A=B)  &  ( ~ (A=C)  &  ~ (B=C) ) ) ) ) ) ) ).
fof(d9_incproj, axiom,  (! [A] :  ( (v6_incsp_1(A) &  (v1_incproj(A) &  (v2_incproj(A) &  (v3_incproj(A) &  (v4_incproj(A) & l1_incsp_1(A)) ) ) ) )  =>  (v5_incproj(A) <=>  (! [B] :  (m1_subset_1(B, u2_incsp_1(A)) =>  (! [C] :  (m1_subset_1(C, u2_incsp_1(A)) =>  (? [D] :  (m1_subset_1(D, u1_incsp_1(A)) &  (r1_incsp_1(A, D, B) & r1_incsp_1(A, D, C)) ) ) ) ) ) ) ) ) ) ).
fof(dt_k10_xtuple_0, axiom, $true).
fof(dt_k1_enumset1, axiom, $true).
fof(dt_k1_funct_1, axiom, $true).
fof(dt_k1_projred1, axiom,  (! [A, B, C, D] :  ( ( (v6_incsp_1(A) &  (v1_incproj(A) &  (v2_incproj(A) &  (v3_incproj(A) &  (v4_incproj(A) &  (v5_incproj(A) &  (v9_incproj(A) & l1_incsp_1(A)) ) ) ) ) ) )  &  (m1_subset_1(B, u2_incsp_1(A)) &  (m1_subset_1(C, u2_incsp_1(A)) & m1_subset_1(D, u1_incsp_1(A))) ) )  =>  (v1_funct_1(k1_projred1(A, B, C, D)) & m1_subset_1(k1_projred1(A, B, C, D), k1_zfmisc_1(k2_zfmisc_1(u1_incsp_1(A), u1_incsp_1(A))))) ) ) ).
fof(dt_k1_projred2, axiom,  (! [A, B] :  ( ( (v6_incsp_1(A) &  (v1_incproj(A) &  (v2_incproj(A) &  (v3_incproj(A) &  (v4_incproj(A) & l1_incsp_1(A)) ) ) ) )  & m1_subset_1(B, u2_incsp_1(A)))  => m1_subset_1(k1_projred2(A, B), k1_zfmisc_1(u1_incsp_1(A)))) ) ).
fof(dt_k1_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  => m1_subset_1(k1_relset_1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_tarski, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_relat_1, axiom,  (! [A, B] : v1_relat_1(k3_relat_1(A, B))) ).
fof(dt_k7_domain_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  (m1_subset_1(B, A) & m1_subset_1(C, A)) )  => m1_subset_1(k7_domain_1(A, B, C), k1_zfmisc_1(A))) ) ).
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))) ) ).
fof(dt_k9_xtuple_0, axiom, $true).
fof(dt_l1_incsp_1, axiom, $true).
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_u2_incsp_1, axiom,  (! [A] :  (l1_incsp_1(A) =>  ~ (v1_xboole_0(u2_incsp_1(A))) ) ) ).
fof(existence_l1_incsp_1, axiom,  (? [A] : l1_incsp_1(A)) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc12_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) )  => v1_zfmisc_1(k10_xtuple_0(A))) ) ).
fof(fc13_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) )  =>  ~ (v1_zfmisc_1(k10_xtuple_0(A))) ) ) ).
fof(fc15_funct_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) & v1_funct_1(B)) )  => v4_funct_1(k2_tarski(A, B))) ) ).
fof(fc17_funct_1, axiom,  (! [A, B, C] :  ( (v4_funct_1(A) &  (v1_relat_1(C) &  (v5_relat_1(C, A) & v1_funct_1(C)) ) )  =>  (v1_relat_1(k1_funct_1(C, B)) & v1_funct_1(k1_funct_1(C, B))) ) ) ).
fof(fc18_funct_1, axiom,  (! [A] :  ( ( ~ (v1_zfmisc_1(A))  &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  ~ (v1_zfmisc_1(k9_xtuple_0(A))) ) ) ).
fof(fc2_funct_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) & v1_funct_1(B)) )  =>  (v1_relat_1(k3_relat_1(A, B)) & v1_funct_1(k3_relat_1(A, B))) ) ) ).
fof(fc7_funct_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v2_funct_1(B)) ) )  =>  (v1_relat_1(k3_relat_1(A, B)) & v2_funct_1(k3_relat_1(A, B))) ) ) ).
fof(fc8_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, B), C))) => v1_relat_1(k9_xtuple_0(D))) ) ).
fof(fc9_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, k2_zfmisc_1(B, C)))) => v1_relat_1(k10_xtuple_0(D))) ) ).
fof(fraenkel_a_2_0_projred2, axiom,  (! [A, B, C] :  ( ( (v6_incsp_1(B) &  (v1_incproj(B) &  (v2_incproj(B) &  (v3_incproj(B) &  (v4_incproj(B) & l1_incsp_1(B)) ) ) ) )  & m1_subset_1(C, u2_incsp_1(B)))  =>  (r2_hidden(A, a_2_0_projred2(B, C)) <=>  (? [D] :  (m1_subset_1(D, u1_incsp_1(B)) &  (A=D & r1_incsp_1(B, D, C)) ) ) ) ) ) ).
fof(rc1_funct_1, axiom,  (? [A] :  (v1_relat_1(A) & v1_funct_1(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(rc2_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ).
fof(rc5_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) ) ) ).
fof(rc6_funct_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) & v1_funct_1(C)) ) ) ) ) ).
fof(rc7_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v4_funct_1(A)) ) ).
fof(redefinition_k1_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  => k1_relset_1(A, B)=k9_xtuple_0(B)) ) ).
fof(redefinition_k7_domain_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  (m1_subset_1(B, A) & m1_subset_1(C, A)) )  => k7_domain_1(A, B, C)=k2_tarski(B, C)) ) ).
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)) ) ).
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(t12_projred1, axiom,  (! [A] :  ( (v6_incsp_1(A) &  (v1_incproj(A) &  (v2_incproj(A) &  (v3_incproj(A) &  (v4_incproj(A) &  (v9_incproj(A) & l1_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)) =>  (! [E] :  (m1_subset_1(E, u1_incsp_1(A)) =>  (! [F] :  (m1_subset_1(F, u1_incsp_1(A)) =>  (! [G] :  (m1_subset_1(G, u1_incsp_1(A)) =>  (! [H] :  (m1_subset_1(H, u1_incsp_1(A)) =>  (! [I] :  (m1_subset_1(I, u1_incsp_1(A)) =>  (! [J] :  (m1_subset_1(J, u1_incsp_1(A)) =>  (! [K] :  (m1_subset_1(K, u1_incsp_1(A)) =>  (! [L] :  (m1_subset_1(L, u2_incsp_1(A)) =>  (! [M] :  (m1_subset_1(M, u2_incsp_1(A)) =>  (! [N] :  (m1_subset_1(N, u2_incsp_1(A)) =>  (! [O] :  (m1_subset_1(O, u2_incsp_1(A)) =>  (! [P] :  (m1_subset_1(P, u2_incsp_1(A)) =>  (! [Q] :  (m1_subset_1(Q, u2_incsp_1(A)) =>  (! [R] :  (m1_subset_1(R, u2_incsp_1(A)) =>  (! [S] :  (m1_subset_1(S, u2_incsp_1(A)) =>  (! [T] :  (m1_subset_1(T, u2_incsp_1(A)) =>  ~ ( (r4_incsp_1(A, k8_domain_1(u1_incsp_1(A), B, C, D), L) &  (r4_incsp_1(A, k8_domain_1(u1_incsp_1(A), B, F, E), M) &  (r4_incsp_1(A, k8_domain_1(u1_incsp_1(A), B, H, G), N) &  (r4_incsp_1(A, k8_domain_1(u1_incsp_1(A), H, F, K), O) &  (r4_incsp_1(A, k8_domain_1(u1_incsp_1(A), H, I, D), P) &  (r4_incsp_1(A, k8_domain_1(u1_incsp_1(A), F, J, D), Q) &  (r4_incsp_1(A, k8_domain_1(u1_incsp_1(A), K, E, G), R) &  (r4_incsp_1(A, k8_domain_1(u1_incsp_1(A), C, I, G), S) &  (r4_incsp_1(A, k8_domain_1(u1_incsp_1(A), C, J, E), T) &  (r1_zfmisc_1(L, M, N) &  ( ~ (B=H)  &  ( ~ (B=C)  &  ( ~ (B=E)  &  ( ~ (F=E)  &  (! [U] :  (m1_subset_1(U, u2_incsp_1(A)) =>  ~ (r4_incsp_1(A, k8_domain_1(u1_incsp_1(A), I, J, K), U)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t13_funct_1, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (! [C] :  ( (v1_relat_1(C) & v1_funct_1(C))  =>  (r2_hidden(A, k9_xtuple_0(B)) => k1_funct_1(k3_relat_1(B, C), A)=k1_funct_1(C, k1_funct_1(B, A))) ) ) ) ) ) ).
fof(t1_incsp_1, axiom,  (! [A] :  (l1_incsp_1(A) =>  (! [B] :  (m1_subset_1(B, u2_incsp_1(A)) =>  (! [C] :  (m1_subset_1(C, u1_incsp_1(A)) =>  (! [D] :  (m1_subset_1(D, u1_incsp_1(A)) =>  (r4_incsp_1(A, k7_domain_1(u1_incsp_1(A), C, D), B) <=>  (r1_incsp_1(A, C, B) & r1_incsp_1(A, D, B)) ) ) ) ) ) ) ) ) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t22_projred1, axiom,  (! [A] :  ( (v6_incsp_1(A) &  (v1_incproj(A) &  (v2_incproj(A) &  (v3_incproj(A) &  (v4_incproj(A) &  (v5_incproj(A) &  (v9_incproj(A) & l1_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, u2_incsp_1(A)) =>  (! [E] :  (m1_subset_1(E, u2_incsp_1(A)) =>  (! [F] :  (m1_subset_1(F, u2_incsp_1(A)) =>  ~ ( ( ~ (r1_incsp_1(A, B, D))  &  ( ~ (r1_incsp_1(A, B, E))  &  ( ~ (r1_incsp_1(A, C, E))  &  ( ~ (r1_incsp_1(A, C, F))  &  ~ ( (k9_xtuple_0(k3_relat_1(k1_projred1(A, D, E, B), k1_projred1(A, E, F, C)))=k1_relset_1(u1_incsp_1(A), k1_projred1(A, D, E, B)) & k10_xtuple_0(k3_relat_1(k1_projred1(A, D, E, B), k1_projred1(A, E, F, C)))=k10_xtuple_0(k1_projred1(A, E, F, C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t2_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  ( (k9_xtuple_0(A)=k9_xtuple_0(B) &  (! [C] :  (r2_hidden(C, k9_xtuple_0(A)) => k1_funct_1(A, C)=k1_funct_1(B, C)) ) )  => A=B) ) ) ) ) ).
fof(t2_incsp_1, axiom,  (! [A] :  (l1_incsp_1(A) =>  (! [B] :  (m1_subset_1(B, u2_incsp_1(A)) =>  (! [C] :  (m1_subset_1(C, u1_incsp_1(A)) =>  (! [D] :  (m1_subset_1(D, u1_incsp_1(A)) =>  (! [E] :  (m1_subset_1(E, u1_incsp_1(A)) =>  (r4_incsp_1(A, k8_domain_1(u1_incsp_1(A), C, D, E), B) <=>  (r1_incsp_1(A, C, B) &  (r1_incsp_1(A, D, B) & r1_incsp_1(A, E, 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(t4_projred2, axiom,  (! [A] :  ( (v6_incsp_1(A) &  (v1_incproj(A) &  (v2_incproj(A) &  (v3_incproj(A) &  (v4_incproj(A) &  (v5_incproj(A) &  (v9_incproj(A) & l1_incsp_1(A)) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_incsp_1(A)) =>  (! [C] :  (m1_subset_1(C, u2_incsp_1(A)) =>  (! [D] :  (m1_subset_1(D, u2_incsp_1(A)) =>  ~ ( ( ~ (r1_incsp_1(A, B, C))  &  ( ~ (r1_incsp_1(A, B, D))  &  ~ (k1_relset_1(u1_incsp_1(A), k1_projred1(A, C, D, B))=k1_projred2(A, 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)) ) ) ) ) ).
