% Mizar problem: t21_bvfunc14,bvfunc14,1702,5 
fof(t21_bvfunc14, conjecture,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k1_bvfunc_2(A))) =>  (! [C] :  (m1_eqrel_1(C, A) =>  (! [D] :  (m1_eqrel_1(D, A) =>  (! [E] :  (m1_eqrel_1(E, A) =>  (! [F] :  (m1_eqrel_1(F, A) =>  (! [G] :  (m1_eqrel_1(G, A) =>  (B=k3_enumset1(C, D, E, F, G) =>  (C=D |  (C=E |  (C=F |  (C=G | k5_bvfunc_2(A, C, B)=k2_partit1(A, k2_partit1(A, k2_partit1(A, D, E), F), G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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_funcop_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funcop_1(A)) ) ) ) ).
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_funcop_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_xboole_0(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_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_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(cc5_subset_1, axiom,  (! [A] :  (v1_zfmisc_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_zfmisc_1(B)) ) ) ) ).
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_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_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_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(d10_xboole_0, axiom,  (! [A] :  (! [B] :  (A=B <=>  (r1_tarski(A, B) & r1_tarski(B, A)) ) ) ) ).
fof(d1_bvfunc_2, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k1_bvfunc_2(A))) =>  (! [C] :  (m1_eqrel_1(C, A) =>  (C=k2_bvfunc_2(A, B) <=>  (! [D] :  (r2_tarski(D, C) <=>  (? [E] :  ( (v1_relat_1(E) & v1_funct_1(E))  &  (? [F] :  (m1_subset_1(F, k1_zfmisc_1(k1_zfmisc_1(A))) &  (k9_xtuple_0(E)=B &  (k10_xtuple_0(E)=F &  ( (! [G] :  (r2_tarski(G, B) => r2_tarski(k1_funct_1(E, G), G)) )  &  (D=k8_setfam_1(A, F) &  ~ (D=k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d1_funct_4, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (! [C] :  ( (v1_relat_1(C) & v1_funct_1(C))  =>  (C=k1_funct_4(A, B) <=>  (k9_xtuple_0(C)=k2_xboole_0(k9_xtuple_0(A), k9_xtuple_0(B)) &  (! [D] :  (r2_hidden(D, k2_xboole_0(k9_xtuple_0(A), k9_xtuple_0(B))) =>  ( (r2_hidden(D, k9_xtuple_0(B)) => k1_funct_1(C, D)=k1_funct_1(B, D))  &  ( ~ (r2_hidden(D, k9_xtuple_0(B)))  => k1_funct_1(C, D)=k1_funct_1(A, D)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d1_setfam_1, axiom,  (! [A] :  (! [B] :  ( ( ~ (A=k1_xboole_0)  =>  (B=k1_setfam_1(A) <=>  (! [C] :  (r2_hidden(C, B) <=>  (! [D] :  (r2_tarski(D, A) => r2_hidden(C, D)) ) ) ) ) )  &  (A=k1_xboole_0 =>  (B=k1_setfam_1(A) <=> B=k1_xboole_0) ) ) ) ) ).
fof(d1_tarski, axiom,  (! [A] :  (! [B] :  (B=k1_tarski(A) <=>  (! [C] :  (r2_hidden(C, B) <=> C=A) ) ) ) ) ).
fof(d2_enumset1, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  (! [E] :  (E=k2_enumset1(A, B, C, D) <=>  (! [F] :  (r2_hidden(F, E) <=>  ~ ( ( ~ (F=A)  &  ( ~ (F=B)  &  ( ~ (F=C)  &  ~ (F=D) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d2_funcop_1, axiom,  (! [A] :  (! [B] : k2_funcop_1(A, B)=k2_zfmisc_1(A, k1_tarski(B))) ) ).
fof(d3_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (B=k10_xtuple_0(A) <=>  (! [C] :  (r2_hidden(C, B) <=>  (? [D] :  (r2_hidden(D, k9_xtuple_0(A)) & C=k1_funct_1(A, D)) ) ) ) ) ) ) ) ).
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(d7_bvfunc_2, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_eqrel_1(B, A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k1_bvfunc_2(A))) => k5_bvfunc_2(A, B, C)=k2_bvfunc_2(A, k7_subset_1(k1_bvfunc_2(A), C, k4_bvfunc_2(A, B)))) ) ) ) ) ) ).
fof(d9_funcop_1, axiom,  (! [A] :  (! [B] : k17_funcop_1(A, B)=k7_funcop_1(k1_tarski(A), B)) ) ).
fof(d9_setfam_1, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) =>  ( ( ~ (B=k1_xboole_0)  => k8_setfam_1(A, B)=k6_setfam_1(A, B))  &  (B=k1_xboole_0 => k8_setfam_1(A, B)=A) ) ) ) ) ).
fof(dt_k10_xtuple_0, axiom, $true).
fof(dt_k17_funcop_1, axiom, $true).
fof(dt_k1_bvfunc_2, axiom,  (! [A] :  (v1_eqrel_1(k1_bvfunc_2(A), A) & m1_subset_1(k1_bvfunc_2(A), k1_zfmisc_1(k1_zfmisc_1(k9_setfam_1(A))))) ) ).
fof(dt_k1_enumset1, axiom, $true).
fof(dt_k1_funct_1, axiom, $true).
fof(dt_k1_funct_4, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) & v1_funct_1(B)) )  =>  (v1_relat_1(k1_funct_4(A, B)) & v1_funct_1(k1_funct_4(A, B))) ) ) ).
fof(dt_k1_partit1, axiom, $true).
fof(dt_k1_setfam_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_bvfunc_2, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(B, k1_zfmisc_1(k1_bvfunc_2(A))))  => m1_eqrel_1(k2_bvfunc_2(A, B), A)) ) ).
fof(dt_k2_enumset1, axiom, $true).
fof(dt_k2_funcop_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_k2_tarski, axiom, $true).
fof(dt_k2_xboole_0, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_enumset1, axiom, $true).
fof(dt_k3_setfam_1, axiom, $true).
fof(dt_k3_tarski, axiom, $true).
fof(dt_k3_xboole_0, axiom, $true).
fof(dt_k4_bvfunc_2, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_eqrel_1(B, A))  => m1_subset_1(k4_bvfunc_2(A, B), k1_zfmisc_1(k1_bvfunc_2(A)))) ) ).
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_xboole_0, axiom, $true).
fof(dt_k5_bvfunc_2, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  (m1_eqrel_1(B, A) & m1_subset_1(C, k1_zfmisc_1(k1_bvfunc_2(A)))) )  => m1_eqrel_1(k5_bvfunc_2(A, B, C), A)) ) ).
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_setfam_1, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) => m1_subset_1(k6_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_k7_funcop_1, axiom,  (! [A, B] :  (v1_funct_1(k7_funcop_1(A, B)) &  (v1_funct_2(k7_funcop_1(A, B), A, k1_tarski(B)) & m1_subset_1(k7_funcop_1(A, B), k1_zfmisc_1(k2_zfmisc_1(A, k1_tarski(B))))) ) ) ).
fof(dt_k7_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(B, k1_zfmisc_1(A)) => m1_subset_1(k7_subset_1(A, B, C), k1_zfmisc_1(A))) ) ).
fof(dt_k8_setfam_1, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) => m1_subset_1(k8_setfam_1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_k9_setfam_1, axiom,  (! [A] : m1_subset_1(k9_setfam_1(A), k1_zfmisc_1(k1_zfmisc_1(A)))) ).
fof(dt_k9_xtuple_0, axiom, $true).
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_eqrel_1, axiom,  (! [A] :  (? [B] : m1_eqrel_1(B, A)) ) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc10_funct_4, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  &  (v1_relat_1(C) &  (v4_relat_1(C, A) & v1_funct_1(C)) ) )  =>  (v1_relat_1(k1_funct_4(C, B)) &  (v4_relat_1(k1_funct_4(C, B), A) &  (v1_funct_1(k1_funct_4(C, B)) & v1_partfun1(k1_funct_4(C, 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(fc11_funcop_1, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  => v2_relat_1(k2_funcop_1(A, B))) ) ).
fof(fc11_funct_4, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v5_relat_1(B, A) & v1_funct_1(B)) )  &  (v1_relat_1(C) &  (v5_relat_1(C, A) & v1_funct_1(C)) ) )  =>  (v1_relat_1(k1_funct_4(B, C)) &  (v5_relat_1(k1_funct_4(B, C), A) & v1_funct_1(k1_funct_4(B, C))) ) ) ) ).
fof(fc12_funcop_1, axiom,  (! [A, B] :  (v1_relat_1(k17_funcop_1(A, B)) & v1_funct_1(k17_funcop_1(A, B))) ) ).
fof(fc13_funcop_1, axiom,  (! [A, B] : v2_funct_1(k17_funcop_1(A, B))) ).
fof(fc14_funct_4, axiom,  (! [A, B] : v1_zfmisc_1(k17_funcop_1(A, B))) ).
fof(fc15_funcop_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v1_funct_1(B))  => v1_funcop_1(k2_funcop_1(A, B))) ) ).
fof(fc16_funcop_1, axiom,  (! [A, B] : v3_funct_1(k2_funcop_1(A, B))) ).
fof(fc18_funcop_1, axiom,  (! [A, B] : v4_relat_1(k2_funcop_1(A, B), A)) ).
fof(fc19_funcop_1, axiom,  (! [A, B] : v4_relat_1(k17_funcop_1(A, B), k1_tarski(A))) ).
fof(fc1_funcop_1, axiom,  (! [A, B] :  (v1_relat_1(k2_funcop_1(A, B)) & v1_funct_1(k2_funcop_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(fc20_funcop_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v1_funct_1(B))  => v1_funcop_1(k17_funcop_1(A, B))) ) ).
fof(fc21_funcop_1, axiom,  (! [A, B] :  (v1_relat_1(k2_funcop_1(A, B)) &  (v4_relat_1(k2_funcop_1(A, B), A) &  (v1_funct_1(k2_funcop_1(A, B)) & v1_partfun1(k2_funcop_1(A, B), A)) ) ) ) ).
fof(fc22_funcop_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(C, A))  => v5_relat_1(k17_funcop_1(B, C), A)) ) ).
fof(fc23_funcop_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(B))  & m1_subset_1(C, B))  => v5_relat_1(k2_funcop_1(A, C), B)) ) ).
fof(fc24_funcop_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(B, A))  => v4_relat_1(k17_funcop_1(B, C), A)) ) ).
fof(fc2_funcop_1, axiom,  (! [A] : v1_xboole_0(k2_funcop_1(k1_xboole_0, A))) ).
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_funcop_1, axiom,  (! [A, B] :  (v1_xboole_0(B) => v1_xboole_0(k2_funcop_1(B, 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_funcop_1, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  ~ (v1_xboole_0(k2_funcop_1(B, A))) ) ) ).
fof(fc4_funct_4, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) &  (v1_funct_1(B) &  ~ (v1_xboole_0(B)) ) ) )  =>  (v1_relat_1(k1_funct_4(A, B)) &  (v1_funct_1(k1_funct_4(A, B)) &  ~ (v1_xboole_0(k1_funct_4(A, B))) ) ) ) ) ).
fof(fc4_subset_1, axiom,  (! [A, B, C, D, E] :  ~ (v1_xboole_0(k3_enumset1(A, B, C, D, E))) ) ).
fof(fc4_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(A, B))) ) ) ).
fof(fc5_funcop_1, axiom,  (! [A] : v3_relat_1(k2_funcop_1(A, k1_xboole_0))) ).
fof(fc5_funct_4, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) &  (v1_funct_1(B) &  ~ (v1_xboole_0(B)) ) ) )  =>  (v1_relat_1(k1_funct_4(B, A)) &  (v1_funct_1(k1_funct_4(B, A)) &  ~ (v1_xboole_0(k1_funct_4(B, A))) ) ) ) ) ).
fof(fc5_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(B, A))) ) ) ).
fof(fc6_funct_4, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) )  &  (v1_relat_1(B) &  (v2_relat_1(B) & v1_funct_1(B)) ) )  =>  (v1_relat_1(k1_funct_4(A, B)) &  (v2_relat_1(k1_funct_4(A, B)) & v1_funct_1(k1_funct_4(A, B))) ) ) ) ).
fof(fc7_funct_4, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_funcop_1(B)) ) )  =>  (v1_relat_1(k1_funct_4(A, B)) &  (v1_funct_1(k1_funct_4(A, B)) & v1_funcop_1(k1_funct_4(A, B))) ) ) ) ).
fof(fc8_funct_4, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) & v1_funct_1(B)) )  &  (v1_relat_1(C) &  (v4_relat_1(C, A) & v1_funct_1(C)) ) )  =>  (v1_relat_1(k1_funct_4(B, C)) &  (v4_relat_1(k1_funct_4(B, C), A) & v1_funct_1(k1_funct_4(B, C))) ) ) ) ).
fof(fc9_funcop_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(k1_funct_1(A, B)) & v1_funct_1(k1_funct_1(A, B))) ) ) ).
fof(fc9_funct_4, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  &  (v1_relat_1(C) &  (v4_relat_1(C, A) & v1_funct_1(C)) ) )  =>  (v1_relat_1(k1_funct_4(B, C)) &  (v4_relat_1(k1_funct_4(B, C), A) &  (v1_funct_1(k1_funct_4(B, C)) & v1_partfun1(k1_funct_4(B, C), A)) ) ) ) ) ).
fof(idempotence_k1_funct_4, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) & v1_funct_1(B)) )  => k1_funct_4(A, A)=A) ) ).
fof(idempotence_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, A)=A) ).
fof(idempotence_k3_xboole_0, axiom,  (! [A, B] : k3_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_funcop_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_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_eqrel_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(k9_setfam_1(A)))) & v1_eqrel_1(B, A)) ) ) ).
fof(rc2_funcop_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  (v3_funct_1(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_funcop_1, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) &  (v3_funct_1(C) &  (v1_partfun1(C, A) & v1_funct_2(C, A, B)) ) ) ) ) ) ) ) ) ) ).
fof(rc3_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_subset_1(B, A)) ) ) ) ).
fof(rc4_eqrel_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(k9_setfam_1(A)))) &  ( ~ (v1_xboole_0(B))  & v1_eqrel_1(B, A)) ) ) ) ).
fof(rc4_funcop_1, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_partfun1(C, 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(rc5_funcop_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) ) ) ) ).
fof(rc5_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc6_subset_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(rd1_funcop_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(C, A))  => k1_funct_1(k2_funcop_1(A, B), C)=B) ) ).
fof(rd1_funct_4, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_xboole_0(B)) ) )  => k1_funct_4(B, A)=A) ) ).
fof(rd2_funcop_1, axiom,  (! [A, B] : k9_xtuple_0(k2_funcop_1(A, B))=A) ).
fof(rd2_funct_4, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_xboole_0(B)) ) )  => k1_funct_4(A, B)=A) ) ).
fof(rd4_funct_4, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) & v1_funct_1(B)) )  => k1_funct_4(k1_funct_4(A, B), B)=k1_funct_4(A, B)) ) ).
fof(redefinition_k1_bvfunc_2, axiom,  (! [A] : k1_bvfunc_2(A)=k1_partit1(A)) ).
fof(redefinition_k4_bvfunc_2, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_eqrel_1(B, A))  => k4_bvfunc_2(A, B)=k1_tarski(B)) ) ).
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_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_setfam_1, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) => k6_setfam_1(A, B)=k1_setfam_1(B)) ) ).
fof(redefinition_k6_subset_1, axiom,  (! [A, B] : k6_subset_1(A, B)=k4_xboole_0(A, B)) ).
fof(redefinition_k7_funcop_1, axiom,  (! [A, B] : k7_funcop_1(A, B)=k2_funcop_1(A, B)) ).
fof(redefinition_k7_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(B, k1_zfmisc_1(A)) => k7_subset_1(A, B, C)=k4_xboole_0(B, C)) ) ).
fof(redefinition_k9_setfam_1, axiom,  (! [A] : k9_setfam_1(A)=k1_zfmisc_1(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(symmetry_r1_xboole_0, axiom,  (! [A, B] :  (r1_xboole_0(A, B) => r1_xboole_0(B, A)) ) ).
fof(t10_enumset1, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  (! [E] : k3_enumset1(A, B, C, D, E)=k2_xboole_0(k2_enumset1(A, B, C, D), k1_tarski(E))) ) ) ) ) ).
fof(t11_funct_4, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (! [C] :  ( ~ (r2_hidden(C, k9_xtuple_0(B)))  => k1_funct_1(k1_funct_4(A, B), C)=k1_funct_1(A, C)) ) ) ) ) ) ).
fof(t13_funct_4, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (! [C] :  (r2_hidden(C, k9_xtuple_0(B)) => k1_funct_1(k1_funct_4(A, B), C)=k1_funct_1(B, C)) ) ) ) ) ) ).
fof(t13_partit1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_eqrel_1(B, A) => k2_partit1(A, B, B)=B) ) ) ) ).
fof(t14_partit1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_eqrel_1(B, A) =>  (! [C] :  (m1_eqrel_1(C, A) =>  (! [D] :  (m1_eqrel_1(D, A) => k2_partit1(A, k2_partit1(A, B, C), D)=k2_partit1(A, B, k2_partit1(A, C, D))) ) ) ) ) ) ) ) ).
fof(t16_xboole_1, axiom,  (! [A] :  (! [B] :  (! [C] : k3_xboole_0(k3_xboole_0(A, B), C)=k3_xboole_0(A, k3_xboole_0(B, C))) ) ) ).
fof(t1_boole, axiom,  (! [A] : k2_xboole_0(A, k1_xboole_0)=A) ).
fof(t1_enumset1, axiom,  (! [A] :  (! [B] : k2_tarski(A, B)=k2_xboole_0(k1_tarski(A), k1_tarski(B))) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t1_tarski, axiom, $true).
fof(t2_boole, axiom,  (! [A] : k3_xboole_0(A, k1_xboole_0)=k1_xboole_0) ).
fof(t2_enumset1, axiom,  (! [A] :  (! [B] :  (! [C] : k1_enumset1(A, B, C)=k2_xboole_0(k1_tarski(A), k2_tarski(B, C))) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t31_enumset1, axiom,  (! [A] :  (! [B] :  (! [C] : k2_enumset1(A, A, B, C)=k1_enumset1(A, B, C)) ) ) ).
fof(t32_enumset1, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] : k3_enumset1(A, A, B, C, D)=k2_enumset1(A, B, C, D)) ) ) ) ).
fof(t3_boole, axiom,  (! [A] : k4_xboole_0(A, k1_xboole_0)=A) ).
fof(t3_enumset1, axiom,  (! [A] :  (! [B] :  (! [C] : k1_enumset1(A, B, C)=k2_xboole_0(k2_tarski(A, B), k1_tarski(C))) ) ) ).
fof(t3_funct_1, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (r2_hidden(A, k9_xtuple_0(B)) => r2_tarski(k1_funct_1(B, A), k10_xtuple_0(B))) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t42_xboole_1, axiom,  (! [A] :  (! [B] :  (! [C] : k4_xboole_0(k2_xboole_0(A, B), C)=k2_xboole_0(k4_xboole_0(A, C), k4_xboole_0(B, C))) ) ) ).
fof(t4_boole, axiom,  (! [A] : k4_xboole_0(k1_xboole_0, A)=k1_xboole_0) ).
fof(t4_enumset1, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] : k2_enumset1(A, B, C, D)=k2_xboole_0(k1_tarski(A), k1_enumset1(B, C, D))) ) ) ) ).
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(t59_zfmisc_1, axiom,  (! [A] :  (! [B] :  (k4_xboole_0(k1_tarski(A), B)=k1_tarski(A) <=>  ~ (r2_hidden(A, B)) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t60_zfmisc_1, axiom,  (! [A] :  (! [B] :  (k4_xboole_0(k1_tarski(A), B)=k1_xboole_0 <=> r2_hidden(A, B)) ) ) ).
fof(t62_enumset1, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] : k2_enumset1(A, B, C, D)=k2_enumset1(A, C, B, D)) ) ) ) ).
fof(t63_enumset1, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] : k2_enumset1(A, B, C, D)=k2_enumset1(A, C, D, B)) ) ) ) ).
fof(t63_zfmisc_1, axiom,  (! [A] :  (! [B] :  (! [C] :  (k4_xboole_0(k2_tarski(A, B), C)=k2_tarski(A, B) <=>  ( ~ (r2_hidden(A, C))  &  ~ (r2_hidden(B, C)) ) ) ) ) ) ).
fof(t65_enumset1, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] : k2_enumset1(A, B, C, D)=k2_enumset1(B, A, C, D)) ) ) ) ).
fof(t67_enumset1, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] : k2_enumset1(A, B, C, D)=k2_enumset1(B, C, A, D)) ) ) ) ).
fof(t69_enumset1, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] : k2_enumset1(A, B, C, D)=k2_enumset1(B, D, A, C)) ) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t6_enumset1, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] : k2_enumset1(A, B, C, D)=k2_xboole_0(k1_enumset1(A, B, C), k1_tarski(D))) ) ) ) ).
fof(t72_enumset1, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] : k2_enumset1(A, B, C, D)=k2_enumset1(C, B, D, A)) ) ) ) ).
fof(t72_funcop_1, axiom,  (! [A] :  (! [B] : k1_funct_1(k17_funcop_1(A, B), A)=B) ) ).
fof(t73_enumset1, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] : k2_enumset1(A, B, C, D)=k2_enumset1(C, D, A, B)) ) ) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t7_bvfunc14, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k1_bvfunc_2(A))) =>  (! [C] :  (m1_eqrel_1(C, A) =>  (! [D] :  (m1_eqrel_1(D, A) =>  (! [E] :  (m1_eqrel_1(E, A) =>  (! [F] :  (m1_eqrel_1(F, A) =>  (B=k2_enumset1(C, D, E, F) =>  (C=D |  (C=E |  (C=F | k5_bvfunc_2(A, C, B)=k2_partit1(A, k2_partit1(A, D, E), F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t7_enumset1, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  (! [E] : k3_enumset1(A, B, C, D, E)=k2_xboole_0(k1_tarski(A), k2_enumset1(B, C, D, E))) ) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
