% Mizar problem: t24_projpl_1,projpl_1,738,5 
fof(t24_projpl_1, conjecture,  (! [A] :  ( (v6_incsp_1(A) &  (v1_incproj(A) &  (v2_incproj(A) &  (v3_incproj(A) &  (v4_incproj(A) &  (v5_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)) =>  ( ~ (C=D)  =>  (r1_incsp_1(A, k2_projpl_1(A, C, D), C) &  (r1_incsp_1(A, k2_projpl_1(A, C, D), D) &  (k2_projpl_1(A, C, D)=k2_projpl_1(A, D, C) &  ( (r1_incsp_1(A, B, C) & r1_incsp_1(A, B, D))  => B=k2_projpl_1(A, C, D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d2_projpl_1, axiom,  (! [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)) =>  (r2_projpl_1(A, B, C, D) <=>  (r1_incsp_1(A, B, C) & r1_incsp_1(A, B, D)) ) ) ) ) ) ) ) ) ) ).
fof(d9_projpl_1, axiom,  (! [A] :  ( (v6_incsp_1(A) &  (v1_incproj(A) &  (v2_incproj(A) &  (v3_incproj(A) &  (v4_incproj(A) &  (v5_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)  =>  (! [D] :  (m1_subset_1(D, u1_incsp_1(A)) =>  (D=k2_projpl_1(A, B, C) <=> r2_projpl_1(A, D, B, C)) ) ) ) ) ) ) ) ) ) ).
fof(dt_k2_projpl_1, axiom,  (! [A, B, C] :  ( ( (v6_incsp_1(A) &  (v1_incproj(A) &  (v2_incproj(A) &  (v3_incproj(A) &  (v4_incproj(A) &  (v5_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(k2_projpl_1(A, B, C), u1_incsp_1(A))) ) ).
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)) ) ).
