% Mizar problem: t14_cayley,cayley,574,41 
fof(t14_cayley, conjecture,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  => r2_group_6(A, k10_group_6(A, k2_cayley(u1_struct_0(A)), k4_cayley(A)))) ) ).
fof(antisymmetry_r2_hidden, axiom,  (! [A, B] :  (r2_hidden(A, B) =>  ~ (r2_hidden(B, A)) ) ) ).
fof(cc2_group_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l3_algstr_0(A)) ) ) )  =>  (! [B] :  (m1_group_2(B, A) => v5_group_1(B)) ) ) ) ).
fof(asymmetry_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) =>  ~ (r2_tarski(B, A)) ) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(dt_k1_xboole_0, axiom, $true).
fof(cc11_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, 1) =>  ( ~ (v2_struct_0(A))  & v7_struct_0(A)) ) ) ) ).
fof(cc2_finset_1, axiom,  (! [A] :  (v1_finset_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_finset_1(B)) ) ) ) ).
fof(cc2_zfmisc_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  ~ (v1_xboole_0(A)) ) ) ).
fof(cc3_finset_1, axiom,  (! [A, B] :  (v1_finset_1(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  ( (v1_funct_1(C) & v1_funct_2(C, A, B))  =>  (v1_funct_1(C) &  (v1_funct_2(C, A, B) & v1_finset_1(C)) ) ) ) ) ) ) ).
fof(cc4_finset_1, axiom,  (! [A] :  (v1_zfmisc_1(A) => v1_finset_1(A)) ) ).
fof(cc5_finset_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ~ (v1_zfmisc_1(A)) ) ) ).
fof(cc5_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) )  =>  ( ~ (v1_zfmisc_1(A))  &  (v1_relat_1(A) & v1_funct_1(A)) ) ) ) ).
fof(cc6_funct_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) ) ) ) ).
fof(cc6_topgrp_1, axiom,  (! [A] :  (l3_algstr_0(A) =>  (v13_struct_0(A, 1) =>  (v13_struct_0(A, 1) &  (v2_group_1(A) &  (v3_group_1(A) & v5_group_1(A)) ) ) ) ) ) ).
fof(cc7_finset_1, axiom,  (! [A] :  (v5_finset_1(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_finset_1(B)) ) ) ) ).
fof(cc8_finset_1, axiom,  (! [A] :  (v5_finset_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v5_finset_1(B)) ) ) ) ).
fof(cc8_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, A) =>  (v1_relat_1(B) & v1_funct_1(B)) ) ) ) ) ).
fof(cc9_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_funct_1(B)) ) ) ) ).
fof(cc9_monoid_0, axiom,  (! [A] :  (l3_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v14_monoid_0(A) & v15_monoid_0(A)) )  =>  ( ~ (v2_struct_0(A))  & v16_monoid_0(A)) ) ) ) ).
fof(fc14_finset_1, axiom,  (! [A, B] :  ( (v1_finset_1(A) & v1_finset_1(B))  => v1_finset_1(k2_zfmisc_1(A, B))) ) ).
fof(fc17_finset_1, axiom,  (! [A] :  (v1_finset_1(A) => v1_finset_1(k1_zfmisc_1(A))) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc31_finset_1, axiom,  (! [A] :  (v1_finset_1(A) => v5_finset_1(k1_zfmisc_1(A))) ) ).
fof(fc4_zfmisc_1, axiom,  (! [A, B] :  ( (v1_zfmisc_1(A) & v1_zfmisc_1(B))  => v1_zfmisc_1(k2_zfmisc_1(A, B))) ) ).
fof(fc6_cayley, axiom,  (! [A] :  (v1_finset_1(A) =>  (v8_struct_0(k2_cayley(A)) &  (v15_algstr_0(k2_cayley(A)) & v1_monoid_0(k2_cayley(A))) ) ) ) ).
fof(fc7_cayley, axiom,  (v7_struct_0(k2_cayley(k1_xboole_0)) &  (v15_algstr_0(k2_cayley(k1_xboole_0)) & v1_monoid_0(k2_cayley(k1_xboole_0))) ) ).
fof(rc10_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v1_funct_1(A) & v2_finset_1(A)) ) ) ) ).
fof(rc1_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_finset_1(A)) ) ).
fof(rc1_zfmisc_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_zfmisc_1(A)) ) ).
fof(rc21_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc22_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc2_finset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_finset_1(B)) ) ) ).
fof(rc2_zfmisc_1, axiom,  (? [A] :  ~ (v1_zfmisc_1(A)) ) ).
fof(rc3_finset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_xboole_0(B))  & v1_finset_1(B)) ) ) ) ) ).
fof(rc4_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) ) ) ).
fof(rc5_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) ) ) ).
fof(rc6_finset_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_finset_1(C)) ) ) ) ) ) ).
fof(rc7_finset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  (? [C] :  ( ~ (v1_xboole_0(C))  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_finset_1(C)) ) ) ) ) ) ) ) ).
fof(rc7_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v4_funct_1(A)) ) ).
fof(rc8_finset_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_zfmisc_1(B))  & v1_finset_1(B)) ) ) ) ) ).
fof(rc9_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) & v5_finset_1(A)) ) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(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(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(free_g3_algstr_0, axiom,  (! [A, B] :  ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  =>  (! [C, D] :  (g3_algstr_0(A, B)=g3_algstr_0(C, D) =>  (A=C & B=D) ) ) ) ) ).
fof(dt_g3_algstr_0, axiom,  (! [A, B] :  ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  =>  (v15_algstr_0(g3_algstr_0(A, B)) & l3_algstr_0(g3_algstr_0(A, B))) ) ) ).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_u2_algstr_0, axiom,  (! [A] :  (l3_algstr_0(A) =>  (v1_funct_1(u2_algstr_0(A)) &  (v1_funct_2(u2_algstr_0(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m1_subset_1(u2_algstr_0(A), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))) ) ) ) ).
fof(cc10_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ( ~ (v2_struct_0(A))  & v7_struct_0(A))  => v13_struct_0(A, 1)) ) ) ).
fof(cc17_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc1_finset_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_finset_1(A)) ) ).
fof(cc1_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_funct_1(A)) ) ).
fof(cc1_partfun1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_partfun1(C, A)) ) ) ) ).
fof(cc1_zfmisc_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_zfmisc_1(A)) ) ).
fof(cc2_funct_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ) ).
fof(cc2_funct_2, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_funct_2(C, A, B) => v1_partfun1(C, A)) ) ) ) ) ).
fof(cc2_partfun1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & v1_xboole_0(B))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  ~ (v1_partfun1(C, A)) ) ) ) ) ).
fof(cc2_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc3_funct_2, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_funct_2(C, A, B) => v1_partfun1(C, A)) ) ) ) ) ).
fof(cc3_group_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v8_struct_0(A) &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) ) )  =>  (! [B] :  (m1_group_2(B, A) => v8_struct_0(B)) ) ) ) ).
fof(cc3_relset_1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_xboole_0(C)) ) ) ) ).
fof(cc4_funct_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) ) ) ) ).
fof(cc4_relset_1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A))) => v1_xboole_0(C)) ) ) ) ).
fof(cc5_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ( ~ (v2_struct_0(A))  &  ~ (v8_struct_0(A)) ) ) ) ) ).
fof(cc6_finset_1, axiom,  (! [A] :  (v1_xboole_0(A) => v5_finset_1(A)) ) ).
fof(cc6_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v7_struct_0(A) => v8_struct_0(A)) ) ) ).
fof(cc7_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_funct_1(A)) ) ).
fof(cc7_monoid_0, axiom,  (! [A] :  (l3_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v11_monoid_0(A) & v12_monoid_0(A)) )  =>  ( ~ (v2_struct_0(A))  & v13_monoid_0(A)) ) ) ) ).
fof(cc7_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ~ (v7_struct_0(A)) ) ) ) ).
fof(cc8_monoid_0, axiom,  (! [A] :  (l3_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  & v16_monoid_0(A))  =>  ( ~ (v2_struct_0(A))  &  (v14_monoid_0(A) & v15_monoid_0(A)) ) ) ) ) ).
fof(cc9_finset_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v2_finset_1(A)) ) ) ).
fof(cc9_funct_2, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  ( (v1_funct_1(C) & v1_funct_2(C, A, B))  =>  (v1_funct_1(C) &  ( ~ (v1_xboole_0(C))  & v1_funct_2(C, A, B)) ) ) ) ) ) ) ).
fof(cc9_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, k5_ordinal1) => v2_struct_0(A)) ) ) ).
fof(fc2_zfmisc_1, axiom,  (! [A, B] :  (v1_xboole_0(B) => v1_xboole_0(k2_zfmisc_1(A, B))) ) ).
fof(fc3_zfmisc_1, axiom,  (! [A, B] :  (v1_xboole_0(A) => v1_xboole_0(k2_zfmisc_1(A, B))) ) ).
fof(fc6_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(fc7_struct_0, axiom,  (! [A] :  ( (v7_struct_0(A) & l1_struct_0(A))  => v1_zfmisc_1(u1_struct_0(A))) ) ).
fof(fc8_struct_0, axiom,  (! [A] :  ( (v8_struct_0(A) & l1_struct_0(A))  => v1_finset_1(u1_struct_0(A))) ) ).
fof(fc9_struct_0, axiom,  (! [A] :  ( ( ~ (v8_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_finset_1(u1_struct_0(A))) ) ) ).
fof(rc1_group_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  =>  (? [B] :  (m1_group_2(B, A) &  ( ~ (v2_struct_0(B))  &  (v15_algstr_0(B) &  (v1_group_1(B) &  (v2_group_1(B) & v3_group_1(B)) ) ) ) ) ) ) ) ).
fof(rc1_relset_1, axiom,  (! [A, B] :  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_xboole_0(C) &  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc2_group_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  =>  (? [B] :  (m1_group_2(B, A) &  ( ~ (v2_struct_0(B))  &  (v8_struct_0(B) &  (v15_algstr_0(B) &  (v1_group_1(B) &  (v2_group_1(B) & v3_group_1(B)) ) ) ) ) ) ) ) ) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc3_group_2, axiom,  (? [A] :  (l3_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  (v8_struct_0(A) &  (v15_algstr_0(A) &  (v1_group_1(A) &  (v2_group_1(A) & v3_group_1(A)) ) ) ) ) ) ) ).
fof(rc3_partfun1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (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_xboole_0(C)) ) ) ) ) ) ) ) ) ).
fof(rc4_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
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(d13_ordinal1, axiom, k5_ordinal1=k1_xboole_0).
fof(reflexivity_r1_group_6, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  &  ( ~ (v2_struct_0(B))  &  (v2_group_1(B) &  (v3_group_1(B) & l3_algstr_0(B)) ) ) )  => r1_group_6(A, A)) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(abstractness_v15_algstr_0, axiom,  (! [A] :  (l3_algstr_0(A) =>  (v15_algstr_0(A) => A=g3_algstr_0(u1_struct_0(A), u2_algstr_0(A))) ) ) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_m1_group_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) & l3_algstr_0(A)) )  =>  (? [B] : m1_group_2(B, A)) ) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_m1_group_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) & l3_algstr_0(A)) )  =>  (! [B] :  (m1_group_2(B, A) =>  ( ~ (v2_struct_0(B))  &  (v2_group_1(B) & l3_algstr_0(B)) ) ) ) ) ) ).
fof(cc10_monoid_0, axiom,  (! [A] :  (l3_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v3_group_1(A) & v13_monoid_0(A)) )  =>  ( ~ (v2_struct_0(A))  &  (v1_group_1(A) & v16_monoid_0(A)) ) ) ) ) ).
fof(cc1_funct_2, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_partfun1(C, A) => v1_funct_2(C, A, B)) ) ) ) ).
fof(cc1_group_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  =>  (! [B] :  (m1_group_2(B, A) => v3_group_1(B)) ) ) ) ).
fof(cc1_monoid_0, axiom,  (! [A] :  ( (v1_monoid_0(A) & l1_struct_0(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (v1_relat_1(B) & v1_funct_1(B)) ) ) ) ) ).
fof(cc1_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v7_struct_0(A)) ) ) ).
fof(cc3_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_funct_1(B)) ) ) ) ).
fof(cc4_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) =>  (v2_struct_0(A) & v8_struct_0(A)) ) ) ) ).
fof(cc5_monoid_0, axiom,  (! [A] :  (l3_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v3_group_1(A) & v13_monoid_0(A)) )  =>  ( ~ (v2_struct_0(A))  & v2_group_1(A)) ) ) ) ).
fof(cc6_monoid_0, axiom,  (! [A] :  (l3_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  & v13_monoid_0(A))  =>  ( ~ (v2_struct_0(A))  &  (v11_monoid_0(A) & v12_monoid_0(A)) ) ) ) ) ).
fof(cc8_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v13_struct_0(A, k5_ordinal1)) ) ) ).
fof(fc1_struct_0, axiom,  (! [A] :  ( (v2_struct_0(A) & l1_struct_0(A))  => v1_xboole_0(u1_struct_0(A))) ) ).
fof(fc2_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_xboole_0(u1_struct_0(A))) ) ) ).
fof(rc1_funct_1, axiom,  (? [A] :  (v1_relat_1(A) & v1_funct_1(A)) ) ).
fof(rc1_funct_2, axiom,  (! [A, 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_funct_2(C, A, B)) ) ) ) ) ) ) ).
fof(rc1_monoid_0, axiom,  (? [A] :  (l1_struct_0(A) & v1_monoid_0(A)) ) ).
fof(rc1_partfun1, axiom,  (! [A, 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)) ) ) ) ) ) ).
fof(rc2_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ).
fof(rc6_funct_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) & v1_funct_1(C)) ) ) ) ) ).
fof(symmetry_r2_group_6, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  &  ( ~ (v2_struct_0(B))  &  (v2_group_1(B) &  (v3_group_1(B) & l3_algstr_0(B)) ) ) )  =>  (r2_group_6(A, B) => r2_group_6(B, A)) ) ) ).
fof(reflexivity_r2_group_6, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  &  ( ~ (v2_struct_0(B))  &  (v2_group_1(B) &  (v3_group_1(B) & l3_algstr_0(B)) ) ) )  => r2_group_6(A, A)) ) ).
fof(existence_l3_algstr_0, axiom,  (? [A] : l3_algstr_0(A)) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(redefinition_r2_group_6, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  &  ( ~ (v2_struct_0(B))  &  (v2_group_1(B) &  (v3_group_1(B) & l3_algstr_0(B)) ) ) )  =>  (r2_group_6(A, B) <=> r1_group_6(A, B)) ) ) ).
fof(dt_k10_group_6, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  &  ( ( ~ (v2_struct_0(B))  &  (v2_group_1(B) &  (v3_group_1(B) & l3_algstr_0(B)) ) )  &  (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) &  (v1_group_6(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) ) ) ) )  =>  (v15_algstr_0(k10_group_6(A, B, C)) & m1_group_2(k10_group_6(A, B, C), B)) ) ) ).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_cayley, axiom,  (! [A] :  (v15_algstr_0(k2_cayley(A)) &  (v1_monoid_0(k2_cayley(A)) & l3_algstr_0(k2_cayley(A))) ) ) ).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k4_cayley, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  =>  (v1_funct_1(k4_cayley(A)) &  (v1_funct_2(k4_cayley(A), u1_struct_0(A), u1_struct_0(k2_cayley(u1_struct_0(A)))) & m1_subset_1(k4_cayley(A), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(k2_cayley(u1_struct_0(A))))))) ) ) ) ).
fof(dt_l3_algstr_0, axiom,  (! [A] :  (l3_algstr_0(A) => l1_struct_0(A)) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_u1_struct_0, axiom, $true).
fof(cc1_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C)) ) ) ).
fof(cc2_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ).
fof(cc4_funct_2, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, A))) =>  (v1_funct_2(B, A, A) => v1_partfun1(B, A)) ) ) ) ).
fof(cc4_monoid_0, axiom,  (! [A] :  (l3_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) & v3_group_1(A)) )  =>  ( ~ (v2_struct_0(A))  & v13_monoid_0(A)) ) ) ) ).
fof(cc5_funct_2, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A))) =>  (v1_funct_2(B, k2_zfmisc_1(A, A), A) => v1_partfun1(B, k2_zfmisc_1(A, A))) ) ) ) ).
fof(fc4_cayley, axiom,  (! [A] :  ( ~ (v2_struct_0(k2_cayley(A)))  &  (v15_algstr_0(k2_cayley(A)) &  (v2_group_1(k2_cayley(A)) &  (v3_group_1(k2_cayley(A)) & v1_monoid_0(k2_cayley(A))) ) ) ) ) ).
fof(fc8_cayley, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  =>  (v1_funct_1(k4_cayley(A)) &  (v1_funct_2(k4_cayley(A), u1_struct_0(A), u1_struct_0(k2_cayley(u1_struct_0(A)))) & v1_group_6(k4_cayley(A), A, k2_cayley(u1_struct_0(A)))) ) ) ) ).
fof(fc9_cayley, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  =>  (v1_funct_1(k4_cayley(A)) &  (v2_funct_1(k4_cayley(A)) & v1_funct_2(k4_cayley(A), u1_struct_0(A), u1_struct_0(k2_cayley(u1_struct_0(A))))) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t68_group_6, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v2_group_1(B) &  (v3_group_1(B) & l3_algstr_0(B)) ) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) &  (v1_group_6(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) ) )  =>  (v2_funct_1(C) => r2_group_6(A, k10_group_6(A, B, C))) ) ) ) ) ) ) ).
