% Mizar problem: t11_projpl_1,projpl_1,357,5 
fof(t11_projpl_1, conjecture,  (! [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)) =>  (r4_projpl_1(A, B, C, D) =>  (r4_projpl_1(A, B, D, C) &  (r4_projpl_1(A, C, B, D) &  (r4_projpl_1(A, C, D, B) &  (r4_projpl_1(A, D, B, C) & r4_projpl_1(A, D, C, 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(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(d3_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)) =>  (! [E] :  (m1_subset_1(E, u2_incsp_1(A)) =>  (r3_projpl_1(A, B, C, D, E) <=>  (r1_incsp_1(A, B, C) &  (r1_incsp_1(A, B, D) & r1_incsp_1(A, B, E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d5_projpl_1, axiom,  (! [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)) =>  (r4_projpl_1(A, B, C, D) <=>  (? [E] :  (m1_subset_1(E, u2_incsp_1(A)) & r4_incsp_1(A, k8_domain_1(u1_incsp_1(A), B, C, D), E)) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_k1_enumset1, axiom, $true).
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_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_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(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(t1_projpl_1, axiom,  (! [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, u2_incsp_1(A)) =>  (! [F] :  (m1_subset_1(F, u2_incsp_1(A)) =>  (! [G] :  (m1_subset_1(G, u2_incsp_1(A)) =>  ( (r4_incsp_1(A, k7_domain_1(u1_incsp_1(A), B, C), E) => r4_incsp_1(A, k7_domain_1(u1_incsp_1(A), C, B), E))  &  ( (r4_incsp_1(A, k8_domain_1(u1_incsp_1(A), B, C, D), E) =>  (r4_incsp_1(A, k8_domain_1(u1_incsp_1(A), B, D, C), E) &  (r4_incsp_1(A, k8_domain_1(u1_incsp_1(A), C, B, D), E) &  (r4_incsp_1(A, k8_domain_1(u1_incsp_1(A), C, D, B), E) &  (r4_incsp_1(A, k8_domain_1(u1_incsp_1(A), D, B, C), E) & r4_incsp_1(A, k8_domain_1(u1_incsp_1(A), D, C, B), E)) ) ) ) )  &  ( (r2_projpl_1(A, B, E, F) => r2_projpl_1(A, B, F, E))  &  (r3_projpl_1(A, B, E, F, G) =>  (r3_projpl_1(A, B, E, G, F) &  (r3_projpl_1(A, B, F, E, G) &  (r3_projpl_1(A, B, F, G, E) &  (r3_projpl_1(A, B, G, E, F) & r3_projpl_1(A, B, G, F, E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
