% Mizar problem: t17_incsp_1,incsp_1,984,5 
fof(t17_incsp_1, conjecture,  (! [A] :  ( (v15_incsp_1(A) & l2_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)) =>  (v3_incsp_1(k8_domain_1(u1_incsp_1(A), B, C, D), A) => v4_incsp_1(k9_domain_1(u1_incsp_1(A), B, C, D, E), A)) ) ) ) ) ) ) ) ) ) ) ).
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_incsp_1, axiom,  (! [A] :  (l2_incsp_1(A) =>  (v15_incsp_1(A) =>  (v5_incsp_1(A) &  (v6_incsp_1(A) &  (v7_incsp_1(A) &  (v8_incsp_1(A) &  (v9_incsp_1(A) &  (v10_incsp_1(A) &  (v11_incsp_1(A) &  (v12_incsp_1(A) &  (v13_incsp_1(A) & v14_incsp_1(A)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(cc1_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_xboole_0(B)) ) ) ) ).
fof(cc2_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ( ~ (v1_subset_1(B, A))  =>  ~ (v1_xboole_0(B)) ) ) ) ) ) ).
fof(cc3_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  (v1_xboole_0(B) => v1_subset_1(B, A)) ) ) ) ) ).
fof(cc4_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ~ (v1_subset_1(B, A)) ) ) ) ) ).
fof(commutativity_k2_tarski, axiom,  (! [A, B] : k2_tarski(A, B)=k2_tarski(B, A)) ).
fof(commutativity_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, B)=k2_xboole_0(B, A)) ).
fof(commutativity_k4_subset_1, axiom,  (! [A, B, C] :  ( (m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))  => k4_subset_1(A, B, C)=k4_subset_1(A, C, B)) ) ).
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(d12_incsp_1, axiom,  (! [A] :  (l2_incsp_1(A) =>  (v9_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, u4_incsp_1(A)) & r5_incsp_1(A, k8_domain_1(u1_incsp_1(A), B, C, D), E)) ) ) ) ) ) ) ) ) ) ) ).
fof(d14_incsp_1, axiom,  (! [A] :  (l2_incsp_1(A) =>  (v11_incsp_1(A) <=>  (! [B] :  (m1_subset_1(B, u2_incsp_1(A)) =>  (! [C] :  (m1_subset_1(C, u4_incsp_1(A)) =>  ( (? [D] :  (m1_subset_1(D, u1_incsp_1(A)) &  (? [E] :  (m1_subset_1(E, u1_incsp_1(A)) &  ( ~ (D=E)  &  (r4_incsp_1(A, k7_domain_1(u1_incsp_1(A), D, E), B) & r5_incsp_1(A, k7_domain_1(u1_incsp_1(A), D, E), C)) ) ) ) ) )  => r3_incsp_1(A, B, C)) ) ) ) ) ) ) ) ).
fof(d1_incsp_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)) =>  (r1_incsp_1(A, B, C) <=> r2_tarski(k1_domain_1(u1_incsp_1(A), u2_incsp_1(A), B, C), u3_incsp_1(A))) ) ) ) ) ) ) ).
fof(d2_incsp_1, axiom,  (! [A] :  (l2_incsp_1(A) =>  (! [B] :  (m1_subset_1(B, u1_incsp_1(A)) =>  (! [C] :  (m1_subset_1(C, u4_incsp_1(A)) =>  (r2_incsp_1(A, B, C) <=> r2_tarski(k1_domain_1(u1_incsp_1(A), u4_incsp_1(A), B, C), u5_incsp_1(A))) ) ) ) ) ) ) ).
fof(d3_incsp_1, axiom,  (! [A] :  (l2_incsp_1(A) =>  (! [B] :  (m1_subset_1(B, u2_incsp_1(A)) =>  (! [C] :  (m1_subset_1(C, u4_incsp_1(A)) =>  (r3_incsp_1(A, B, C) <=> r2_tarski(k1_domain_1(u2_incsp_1(A), u4_incsp_1(A), B, C), u6_incsp_1(A))) ) ) ) ) ) ) ).
fof(d4_incsp_1, axiom,  (! [A] :  (l1_incsp_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_incsp_1(A))) =>  (! [C] :  (m1_subset_1(C, u2_incsp_1(A)) =>  (r4_incsp_1(A, B, C) <=>  (! [D] :  (m1_subset_1(D, u1_incsp_1(A)) =>  (r2_tarski(D, B) => r1_incsp_1(A, D, C)) ) ) ) ) ) ) ) ) ) ).
fof(d5_incsp_1, axiom,  (! [A] :  (l2_incsp_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_incsp_1(A))) =>  (! [C] :  (m1_subset_1(C, u4_incsp_1(A)) =>  (r5_incsp_1(A, B, C) <=>  (! [D] :  (m1_subset_1(D, u1_incsp_1(A)) =>  (r2_tarski(D, B) => r2_incsp_1(A, D, C)) ) ) ) ) ) ) ) ) ) ).
fof(d6_incsp_1, axiom,  (! [A] :  (l1_incsp_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_incsp_1(A))) =>  (v3_incsp_1(B, A) <=>  (? [C] :  (m1_subset_1(C, u2_incsp_1(A)) & r4_incsp_1(A, B, C)) ) ) ) ) ) ) ).
fof(dt_k1_domain_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  (m1_subset_1(C, A) & m1_subset_1(D, B)) ) )  => m1_subset_1(k1_domain_1(A, B, C, D), k2_zfmisc_1(A, B))) ) ).
fof(dt_k1_enumset1, axiom, $true).
fof(dt_k1_tarski, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_enumset1, axiom, $true).
fof(dt_k2_tarski, axiom, $true).
fof(dt_k2_xboole_0, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k4_subset_1, axiom,  (! [A, B, C] :  ( (m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))  => m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A))) ) ).
fof(dt_k4_tarski, axiom, $true).
fof(dt_k6_domain_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(B, A))  => m1_subset_1(k6_domain_1(A, B), k1_zfmisc_1(A))) ) ).
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_k9_domain_1, axiom,  (! [A, B, C, D, E] :  ( ( ~ (v1_xboole_0(A))  &  (m1_subset_1(B, A) &  (m1_subset_1(C, A) &  (m1_subset_1(D, A) & m1_subset_1(E, A)) ) ) )  => m1_subset_1(k9_domain_1(A, B, C, D, E), k1_zfmisc_1(A))) ) ).
fof(dt_l1_incsp_1, axiom, $true).
fof(dt_l2_incsp_1, axiom,  (! [A] :  (l2_incsp_1(A) => l1_incsp_1(A)) ) ).
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(dt_u3_incsp_1, axiom,  (! [A] :  (l1_incsp_1(A) => m1_subset_1(u3_incsp_1(A), k1_zfmisc_1(k2_zfmisc_1(u1_incsp_1(A), u2_incsp_1(A))))) ) ).
fof(dt_u4_incsp_1, axiom,  (! [A] :  (l2_incsp_1(A) =>  ~ (v1_xboole_0(u4_incsp_1(A))) ) ) ).
fof(dt_u5_incsp_1, axiom,  (! [A] :  (l2_incsp_1(A) => m1_subset_1(u5_incsp_1(A), k1_zfmisc_1(k2_zfmisc_1(u1_incsp_1(A), u4_incsp_1(A))))) ) ).
fof(dt_u6_incsp_1, axiom,  (! [A] :  (l2_incsp_1(A) => m1_subset_1(u6_incsp_1(A), k1_zfmisc_1(k2_zfmisc_1(u2_incsp_1(A), u4_incsp_1(A))))) ) ).
fof(existence_l1_incsp_1, axiom,  (? [A] : l1_incsp_1(A)) ).
fof(existence_l2_incsp_1, axiom,  (? [A] : l2_incsp_1(A)) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc10_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_xboole_0(k2_zfmisc_1(A, B))) ) ) ).
fof(fc1_subset_1, axiom,  (! [A] :  ~ (v1_xboole_0(k1_zfmisc_1(A))) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc2_subset_1, axiom,  (! [A, B, C] :  ~ (v1_xboole_0(k1_enumset1(A, B, C))) ) ).
fof(fc2_xboole_0, axiom,  (! [A] :  ~ (v1_xboole_0(k1_tarski(A))) ) ).
fof(fc3_subset_1, axiom,  (! [A, B, C, D] :  ~ (v1_xboole_0(k2_enumset1(A, B, C, D))) ) ).
fof(fc3_xboole_0, axiom,  (! [A, B] :  ~ (v1_xboole_0(k2_tarski(A, B))) ) ).
fof(fc4_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(A, B))) ) ) ).
fof(fc5_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(B, A))) ) ) ).
fof(idempotence_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, A)=A) ).
fof(idempotence_k4_subset_1, axiom,  (! [A, B, C] :  ( (m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))  => k4_subset_1(A, B, B)=B) ) ).
fof(rc1_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc2_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_xboole_0(B)) ) ) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc3_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_subset_1(B, A)) ) ) ) ).
fof(rc4_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_subset_1(B, A)) ) ) ) ).
fof(redefinition_k1_domain_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  (m1_subset_1(C, A) & m1_subset_1(D, B)) ) )  => k1_domain_1(A, B, C, D)=k4_tarski(C, D)) ) ).
fof(redefinition_k4_subset_1, axiom,  (! [A, B, C] :  ( (m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))  => k4_subset_1(A, B, C)=k2_xboole_0(B, C)) ) ).
fof(redefinition_k6_domain_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(B, A))  => k6_domain_1(A, B)=k1_tarski(B)) ) ).
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(redefinition_k9_domain_1, axiom,  (! [A, B, C, D, E] :  ( ( ~ (v1_xboole_0(A))  &  (m1_subset_1(B, A) &  (m1_subset_1(C, A) &  (m1_subset_1(D, A) & m1_subset_1(E, A)) ) ) )  => k9_domain_1(A, B, C, D, E)=k2_enumset1(B, C, D, E)) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(t11_incsp_1, axiom,  (! [A] :  (l2_incsp_1(A) =>  (! [B] :  (m1_subset_1(B, u4_incsp_1(A)) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(u1_incsp_1(A))) =>  (! [D] :  (m1_subset_1(D, k1_zfmisc_1(u1_incsp_1(A))) =>  (r5_incsp_1(A, k4_subset_1(u1_incsp_1(A), C, D), B) <=>  (r5_incsp_1(A, C, B) & r5_incsp_1(A, D, B)) ) ) ) ) ) ) ) ) ) ).
fof(t14_incsp_1, axiom,  (! [A] :  ( (v15_incsp_1(A) & l2_incsp_1(A))  =>  (! [B] :  (m1_subset_1(B, u2_incsp_1(A)) =>  (! [C] :  (m1_subset_1(C, u4_incsp_1(A)) =>  (! [D] :  (m1_subset_1(D, k1_zfmisc_1(u1_incsp_1(A))) =>  ( (r4_incsp_1(A, D, B) & r3_incsp_1(A, B, C))  => r5_incsp_1(A, D, C)) ) ) ) ) ) ) ) ) ).
fof(t16_incsp_1, axiom,  (! [A] :  ( (v15_incsp_1(A) & l2_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)) => v4_incsp_1(k9_domain_1(u1_incsp_1(A), B, B, C, D), A)) ) ) ) ) ) ) ) ).
fof(t1_boole, axiom,  (! [A] : k2_xboole_0(A, k1_xboole_0)=A) ).
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(t3_enumset1, axiom,  (! [A] :  (! [B] :  (! [C] : k1_enumset1(A, B, C)=k2_xboole_0(k2_tarski(A, B), k1_tarski(C))) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t4_incsp_1, axiom,  (! [A] :  (l2_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, u4_incsp_1(A)) =>  (r5_incsp_1(A, k8_domain_1(u1_incsp_1(A), B, C, D), E) <=>  (r2_incsp_1(A, B, E) &  (r2_incsp_1(A, C, E) & r2_incsp_1(A, D, E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t4_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r2_tarski(A, B) & m1_subset_1(B, k1_zfmisc_1(C)))  => m1_subset_1(A, C)) ) ) ) ).
fof(t5_incsp_1, axiom,  (! [A] :  (l2_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, u4_incsp_1(A)) =>  (r5_incsp_1(A, k9_domain_1(u1_incsp_1(A), B, C, D, E), F) <=>  (r2_incsp_1(A, B, F) &  (r2_incsp_1(A, C, F) &  (r2_incsp_1(A, D, F) & r2_incsp_1(A, E, F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
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(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
fof(t8_incsp_1, axiom,  (! [A] :  (l2_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, k1_zfmisc_1(u1_incsp_1(A))) =>  ( (r4_incsp_1(A, D, C) & r1_incsp_1(A, B, C))  <=> r4_incsp_1(A, k4_subset_1(u1_incsp_1(A), D, k6_domain_1(u1_incsp_1(A), B)), C)) ) ) ) ) ) ) ) ) ).
