% Mizar problem: t7_projpl_1,projpl_1,283,5 
fof(t7_projpl_1, conjecture,  (! [A] :  (l1_incsp_1(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)) => B=C) ) ) ) ) ) ) ) ).
fof(dt_l1_incsp_1, axiom, $true).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_o_1_0_projpl_1, axiom,  (! [A] :  (l1_incsp_1(A) => m1_subset_1(o_1_0_projpl_1(A), u1_incsp_1(A))) ) ).
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(t5_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, u2_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, C) &  (r1_incsp_1(A, B, D) &  (r1_incsp_1(A, B, E) &  ( ~ (C=D)  &  ( ~ (D=E)  &  ~ (E=C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
