% Mizar problem: t26_net_1,net_1,785,5 
fof(t26_net_1, conjecture,  (! [A] :  ( (v1_net_1(A) & l1_petri(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_net_1(A))) =>  (! [C] :  (m1_subset_1(C, k2_net_1(A)) =>  ( ~ (k2_net_1(A)=k1_xboole_0)  =>  (r2_tarski(C, k13_net_1(A, B)) <=>  ~ ( ( ~ ( (r2_tarski(C, B) & r2_tarski(C, u1_struct_0(A))) )  &  (! [D] :  (m1_subset_1(D, k2_net_1(A)) =>  ~ ( (r2_tarski(D, B) &  (r2_tarski(D, u4_struct_0(A)) & r2_net_1(A, D, C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_relat_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_relat_1, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_relat_1(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_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v3_relat_1(A)) ) ) ).
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_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v2_relat_1(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_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, B)=k2_xboole_0(B, A)) ).
fof(d14_net_1, axiom,  (! [A] :  ( (v1_net_1(A) & l1_petri(A))  =>  (! [B] :  (! [C] :  (C=k11_net_1(A, B) <=>  (! [D] :  (r2_tarski(D, C) <=>  (r1_tarski(D, k2_net_1(A)) &  (? [E] :  (m1_subset_1(E, k2_net_1(A)) &  (r2_tarski(E, B) & D=k6_net_1(A, E)) ) ) ) ) ) ) ) ) ) ) ).
fof(d16_net_1, axiom,  (! [A] :  ( (v1_net_1(A) & l1_petri(A))  =>  (! [B] : k13_net_1(A, B)=k3_tarski(k11_net_1(A, B))) ) ) ).
fof(d1_net_1, axiom,  (! [A] :  (l1_petri(A) => k1_net_1(A)=k2_xboole_0(u1_petri(A), u2_petri(A))) ) ).
fof(d1_tarski, axiom,  (! [A] :  (! [B] :  (B=k1_tarski(A) <=>  (! [C] :  (r2_hidden(C, B) <=> C=A) ) ) ) ) ).
fof(d3_net_1, axiom,  (! [A] :  (l1_petri(A) => k2_net_1(A)=k2_xboole_0(u1_struct_0(A), u4_struct_0(A))) ) ).
fof(d3_xboole_0, axiom,  (! [A] :  (! [B] :  (! [C] :  (C=k2_xboole_0(A, B) <=>  (! [D] :  (r2_hidden(D, C) <=>  (r2_hidden(D, A) | r2_hidden(D, B)) ) ) ) ) ) ) ).
fof(d4_tarski, axiom,  (! [A] :  (! [B] :  (B=k3_tarski(A) <=>  (! [C] :  (r2_hidden(C, B) <=>  (? [D] :  (r2_hidden(C, D) & r2_hidden(D, A)) ) ) ) ) ) ) ).
fof(d5_net_1, axiom,  (! [A] :  ( (v1_net_1(A) & l1_petri(A))  =>  (! [B] :  (! [C] :  (r2_net_1(A, B, C) <=>  (r2_hidden(k4_tarski(B, C), k1_net_1(A)) & r2_tarski(B, u4_struct_0(A))) ) ) ) ) ) ).
fof(d7_net_1, axiom,  (! [A] :  (l1_petri(A) =>  (! [B] :  (m1_subset_1(B, k2_net_1(A)) =>  (! [C] :  (C=k4_net_1(A, B) <=>  (! [D] :  (r2_hidden(D, C) <=>  (r2_hidden(D, k2_net_1(A)) & r2_hidden(k4_tarski(B, D), k1_net_1(A))) ) ) ) ) ) ) ) ) ).
fof(d9_net_1, axiom,  (! [A] :  ( (v1_net_1(A) & l1_petri(A))  =>  (! [B] :  (m1_subset_1(B, k2_net_1(A)) =>  ( ~ (k2_net_1(A)=k1_xboole_0)  =>  (! [C] :  (C=k6_net_1(A, B) <=>  ( (r2_tarski(B, u1_struct_0(A)) => C=k1_tarski(B))  &  (r2_tarski(B, u4_struct_0(A)) => C=k4_net_1(A, B)) ) ) ) ) ) ) ) ) ).
fof(dt_k11_net_1, axiom, $true).
fof(dt_k13_net_1, axiom, $true).
fof(dt_k1_net_1, 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_net_1, axiom, $true).
fof(dt_k2_xboole_0, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_tarski, axiom, $true).
fof(dt_k4_net_1, axiom, $true).
fof(dt_k4_tarski, axiom, $true).
fof(dt_k6_net_1, axiom, $true).
fof(dt_l1_petri, axiom,  (! [A] :  (l1_petri(A) => l5_struct_0(A)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_l5_struct_0, axiom,  (! [A] :  (l5_struct_0(A) => l1_struct_0(A)) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_u1_petri, axiom,  (! [A] :  (l1_petri(A) => m1_subset_1(u1_petri(A), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u4_struct_0(A))))) ) ).
fof(dt_u1_struct_0, axiom, $true).
fof(dt_u2_petri, axiom,  (! [A] :  (l1_petri(A) => m1_subset_1(u2_petri(A), k1_zfmisc_1(k2_zfmisc_1(u4_struct_0(A), u1_struct_0(A))))) ) ).
fof(dt_u4_struct_0, axiom, $true).
fof(existence_l1_petri, axiom,  (? [A] : l1_petri(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_l5_struct_0, axiom,  (? [A] : l5_struct_0(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_net_1, axiom,  (! [A] :  (l1_petri(A) => v1_relat_1(k1_net_1(A))) ) ).
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_xboole_0, axiom,  (! [A] :  ~ (v1_xboole_0(k1_tarski(A))) ) ).
fof(fc3_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_relat_1(B))  => v1_relat_1(k2_xboole_0(A, B))) ) ).
fof(fc4_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(A, B))) ) ) ).
fof(fc5_relat_1, axiom,  (! [A, B] : v1_relat_1(k1_tarski(k4_tarski(A, B)))) ).
fof(fc5_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(B, A))) ) ) ).
fof(fc6_relat_1, axiom,  (! [A, B] : v1_relat_1(k2_zfmisc_1(A, B))) ).
fof(idempotence_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, A)=A) ).
fof(rc1_relat_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_relat_1(A)) ) ).
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_relat_1, axiom,  (? [A] :  (v1_relat_1(A) & v2_relat_1(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_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(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(t22_net_1, axiom,  (! [A] :  ( (v1_net_1(A) & l1_petri(A))  =>  (! [B] :  (m1_subset_1(B, k2_net_1(A)) =>  (! [C] :  (r2_tarski(B, C) =>  (k2_net_1(A)=k1_xboole_0 | r2_tarski(k6_net_1(A, B), k11_net_1(A, C))) ) ) ) ) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t31_zfmisc_1, axiom,  (! [A] :  (! [B] :  (r1_tarski(k1_tarski(A), B) <=> r2_hidden(A, B)) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
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_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)) ) ) ) ) ).
