% Mizar problem: t9_projpl_1,projpl_1,313,5 
fof(t9_projpl_1, conjecture,  (! [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)) =>  ~ ( ( (v6_incsp_1(A) &  (v1_incproj(A) &  (v2_incproj(A) &  (v3_incproj(A) &  (v4_incproj(A) & l1_incsp_1(A)) ) ) ) )  &  ( ~ (C=D)  &  (! [E] :  (m1_subset_1(E, u1_incsp_1(A)) =>  ~ ( (r1_incsp_1(A, E, C) &  ( ~ (r1_incsp_1(A, E, D))  &  ~ (B=E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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(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_zfmisc_1, axiom,  (! [A] :  (! [B] :  (! [C] :  (r1_zfmisc_1(A, B, C) <=>  ( ~ (A=B)  &  ( ~ (A=C)  &  ~ (B=C) ) ) ) ) ) ) ).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_tarski, axiom, $true).
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_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(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(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(t8_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)) =>  ~ ( ( (v6_incsp_1(A) &  (v1_incproj(A) &  (v2_incproj(A) &  (v3_incproj(A) &  (v4_incproj(A) & l1_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, k7_domain_1(u1_incsp_1(A), D, E), C) & r1_zfmisc_1(B, D, E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
