% Mizar problem: t13_projred1,projred1,732,5 
fof(t13_projred1, conjecture,  (! [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, 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)) &  (r1_incsp_1(A, C, B) &  (r1_incsp_1(A, D, B) &  (r1_incsp_1(A, E, B) &  (r1_incsp_1(A, F, B) & r2_zfmisc_1(C, D, E, F)) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [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)) &  (? [F] :  (m1_subset_1(F, u1_incsp_1(A)) &  (r1_incsp_1(A, C, B) &  (r1_incsp_1(A, D, B) &  (r1_incsp_1(A, E, B) &  (r1_incsp_1(A, F, B) & r2_zfmisc_1(C, D, E, F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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(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(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(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(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(dt_k1_xboole_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(l13_projred1, 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, 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, u2_incsp_1(A)) =>  (! [G] :  (m1_subset_1(G, u2_incsp_1(A)) =>  ~ ( ( (? [H] :  (m1_subset_1(H, u1_incsp_1(A)) &  (r1_incsp_1(A, H, F) & r1_incsp_1(A, H, G)) ) )  &  (r1_incsp_1(A, B, F) &  (r1_incsp_1(A, C, F) &  (r1_incsp_1(A, D, F) &  (r1_incsp_1(A, E, F) &  (r2_zfmisc_1(B, C, D, E) &  (! [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)) =>  ~ ( (r1_incsp_1(A, H, G) &  (r1_incsp_1(A, I, G) &  (r1_incsp_1(A, J, G) &  (r1_incsp_1(A, K, G) & r2_zfmisc_1(H, I, J, K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc1_funct_1, axiom,  (? [A] :  (v1_relat_1(A) & v1_funct_1(A)) ) ).
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(rc7_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v4_funct_1(A)) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
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(t7_projred1, 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, u1_incsp_1(A)) & r1_incsp_1(A, C, B)) ) ) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
