% Mizar problem: t1_bvfunc14,bvfunc14,39,5 
fof(t1_bvfunc14, conjecture,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, A) =>  (! [C] :  (m1_eqrel_1(C, A) =>  (! [D] :  (m1_eqrel_1(D, A) => k15_bvfunc_1(A, B, k2_partit1(A, C, D))=k9_subset_1(A, k15_bvfunc_1(A, B, C), k15_bvfunc_1(A, B, D))) ) ) ) ) ) ) ) ).
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_eqrel_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_eqrel_1(B, A) => v1_xboole_0(B)) ) ) ) ).
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_eqrel_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_eqrel_1(B, 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_eqrel_1, axiom,  (! [A] :  (! [B] :  (m1_eqrel_1(B, A) => v1_setfam_1(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_eqrel_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_eqrel_1(B, A) => v1_xboole_0(B)) ) ) ) ).
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_partit1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  (m1_eqrel_1(B, A) & m1_eqrel_1(C, A)) )  => k2_partit1(A, B, C)=k2_partit1(A, C, B)) ) ).
fof(commutativity_k3_setfam_1, axiom,  (! [A, B] : k3_setfam_1(A, B)=k3_setfam_1(B, A)) ).
fof(commutativity_k3_xboole_0, axiom,  (! [A, B] : k3_xboole_0(A, B)=k3_xboole_0(B, A)) ).
fof(commutativity_k9_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(C, k1_zfmisc_1(A)) => k9_subset_1(A, B, C)=k9_subset_1(A, C, B)) ) ).
fof(d10_xboole_0, axiom,  (! [A] :  (! [B] :  (A=B <=>  (r1_tarski(A, B) & r1_tarski(B, A)) ) ) ) ).
fof(d3_tarski, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) <=>  (! [C] :  (r2_hidden(C, A) => r2_hidden(C, B)) ) ) ) ) ).
fof(d4_eqrel_1, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) =>  (m1_eqrel_1(B, A) <=>  (k5_setfam_1(A, B)=A &  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(A)) =>  (r2_tarski(C, B) =>  ( ~ (C=k1_xboole_0)  &  (! [D] :  (m1_subset_1(D, k1_zfmisc_1(A)) =>  ~ ( (r2_tarski(D, B) &  ( ~ (C=D)  &  ~ (r1_xboole_0(C, D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d4_partit1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_eqrel_1(B, A) =>  (! [C] :  (m1_eqrel_1(C, A) => k2_partit1(A, B, C)=k6_subset_1(k3_setfam_1(B, C), k1_tarski(k1_xboole_0))) ) ) ) ) ) ).
fof(d4_xboole_0, axiom,  (! [A] :  (! [B] :  (! [C] :  (C=k3_xboole_0(A, B) <=>  (! [D] :  (r2_hidden(D, C) <=>  (r2_hidden(D, A) & r2_hidden(D, B)) ) ) ) ) ) ) ).
fof(d5_setfam_1, axiom,  (! [A] :  (! [B] :  (! [C] :  (C=k3_setfam_1(A, B) <=>  (! [D] :  (r2_tarski(D, C) <=>  (? [E] :  (? [F] :  (r2_tarski(E, A) &  (r2_tarski(F, B) & D=k3_xboole_0(E, F)) ) ) ) ) ) ) ) ) ) ).
fof(d5_xboole_0, axiom,  (! [A] :  (! [B] :  (! [C] :  (C=k4_xboole_0(A, B) <=>  (! [D] :  (r2_hidden(D, C) <=>  (r2_hidden(D, A) &  ~ (r2_hidden(D, B)) ) ) ) ) ) ) ) ).
fof(d6_eqrel_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, A) =>  (! [C] :  (m1_eqrel_1(C, A) =>  (! [D] :  (m1_subset_1(D, k1_zfmisc_1(A)) =>  (D=k12_eqrel_1(A, B, C) <=>  (r2_tarski(B, D) & r2_tarski(D, C)) ) ) ) ) ) ) ) ) ) ).
fof(dt_k12_eqrel_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  (m1_subset_1(B, A) & m1_eqrel_1(C, A)) )  => m1_subset_1(k12_eqrel_1(A, B, C), k1_zfmisc_1(A))) ) ).
fof(dt_k15_bvfunc_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  (m1_subset_1(B, A) & m1_eqrel_1(C, A)) )  => m1_bvfunc_1(k15_bvfunc_1(A, B, C), A, C)) ) ).
fof(dt_k1_tarski, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_partit1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  (m1_eqrel_1(B, A) & m1_eqrel_1(C, A)) )  => m1_eqrel_1(k2_partit1(A, B, C), A)) ) ).
fof(dt_k3_setfam_1, axiom, $true).
fof(dt_k3_tarski, axiom, $true).
fof(dt_k3_xboole_0, axiom, $true).
fof(dt_k4_xboole_0, axiom, $true).
fof(dt_k5_setfam_1, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) => m1_subset_1(k5_setfam_1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_k6_subset_1, axiom,  (! [A, B] : m1_subset_1(k6_subset_1(A, B), k1_zfmisc_1(A))) ).
fof(dt_k9_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(C, k1_zfmisc_1(A)) => m1_subset_1(k9_subset_1(A, B, C), k1_zfmisc_1(A))) ) ).
fof(dt_m1_bvfunc_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_eqrel_1(B, A))  =>  (! [C] :  (m1_bvfunc_1(C, A, B) => m1_subset_1(C, k1_zfmisc_1(A))) ) ) ) ).
fof(dt_m1_eqrel_1, axiom,  (! [A] :  (! [B] :  (m1_eqrel_1(B, A) => m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(existence_m1_bvfunc_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_eqrel_1(B, A))  =>  (? [C] : m1_bvfunc_1(C, A, B)) ) ) ).
fof(existence_m1_eqrel_1, axiom,  (! [A] :  (? [B] : m1_eqrel_1(B, A)) ) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, 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(idempotence_k3_xboole_0, axiom,  (! [A, B] : k3_xboole_0(A, A)=A) ).
fof(idempotence_k9_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(C, k1_zfmisc_1(A)) => k9_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_k15_bvfunc_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  (m1_subset_1(B, A) & m1_eqrel_1(C, A)) )  => k15_bvfunc_1(A, B, C)=k12_eqrel_1(A, B, C)) ) ).
fof(redefinition_k5_setfam_1, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) => k5_setfam_1(A, B)=k3_tarski(B)) ) ).
fof(redefinition_k6_subset_1, axiom,  (! [A, B] : k6_subset_1(A, B)=k4_xboole_0(A, B)) ).
fof(redefinition_k9_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(C, k1_zfmisc_1(A)) => k9_subset_1(A, B, C)=k3_xboole_0(B, C)) ) ).
fof(redefinition_m1_bvfunc_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_eqrel_1(B, A))  =>  (! [C] :  (m1_bvfunc_1(C, A, B) <=> m1_subset_1(C, B)) ) ) ) ).
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(symmetry_r1_xboole_0, axiom,  (! [A, B] :  (r1_xboole_0(A, B) => r1_xboole_0(B, A)) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t2_boole, axiom,  (! [A] : k3_xboole_0(A, k1_xboole_0)=k1_xboole_0) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t3_boole, axiom,  (! [A] : k4_xboole_0(A, k1_xboole_0)=A) ).
fof(t3_bvfunc11, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, A) =>  (! [C] :  (m1_eqrel_1(C, A) =>  (! [D] :  (m1_eqrel_1(D, A) => r1_tarski(k15_bvfunc_1(A, B, k2_partit1(A, C, D)), k15_bvfunc_1(A, B, C))) ) ) ) ) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t3_xboole_0, axiom,  (! [A] :  (! [B] :  ( ~ ( ( ~ (r1_xboole_0(A, B))  &  (! [C] :  ~ ( (r2_hidden(C, A) & r2_hidden(C, B)) ) ) ) )  &  ~ ( ( (? [C] :  (r2_hidden(C, A) & r2_hidden(C, B)) )  & r1_xboole_0(A, B)) ) ) ) ) ).
fof(t41_eqrel_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_eqrel_1(B, A) =>  (! [C] :  (m1_subset_1(C, A) =>  (! [D] :  (m1_subset_1(D, A) =>  ( ~ (r1_xboole_0(k12_eqrel_1(A, C, B), k12_eqrel_1(A, D, B)))  => k12_eqrel_1(A, C, B)=k12_eqrel_1(A, D, B)) ) ) ) ) ) ) ) ) ).
fof(t4_boole, axiom,  (! [A] : k4_xboole_0(k1_xboole_0, A)=k1_xboole_0) ).
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)) ) ) ) ) ).
