% Mizar problem: t60_partpr_1,partpr_1,1991,7 
fof(t60_partpr_1, conjecture,  (! [A] :  ( ~ (v1_xboole_0(A))  => k6_lattices(k14_partpr_1(A))=k8_partpr_1(A)) ) ).
fof(abstractness_v4_robbins1, axiom,  (! [A] :  (l4_robbins1(A) =>  (v4_robbins1(A) => A=g4_robbins1(u1_struct_0(A), u2_lattices(A), u1_lattices(A), u1_robbins1(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(cc10_lattices, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v5_lattices(A) &  (v6_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) & l3_lattices(A)) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (v19_lattices(B, A) => v21_lattices(B, A)) ) ) ) ) ).
fof(cc1_funcop_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  ( (v1_relat_1(B) &  (v5_relat_1(B, A) & v1_funct_1(B)) )  =>  (v1_relat_1(B) &  (v1_funct_1(B) & v1_funcop_1(B)) ) ) ) ) ) ).
fof(cc1_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_funct_1(A)) ) ).
fof(cc1_lattices, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  & v10_lattices(A))  =>  ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v5_lattices(A) &  (v6_lattices(A) &  (v7_lattices(A) &  (v8_lattices(A) & v9_lattices(A)) ) ) ) ) ) ) ) ) ).
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_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_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_relat_1(A)) ) ).
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_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_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_lattices, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v5_lattices(A) &  (v6_lattices(A) &  (v7_lattices(A) &  (v8_lattices(A) & v9_lattices(A)) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  & v10_lattices(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_relat_1, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_relat_1(B)) ) ) ) ).
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(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_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(cc3_lattices, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v13_lattices(A) & v14_lattices(A)) )  =>  ( ~ (v2_struct_0(A))  & v15_lattices(A)) ) ) ) ).
fof(cc3_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v3_relat_1(A)) ) ) ).
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_lattices, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  & v15_lattices(A))  =>  ( ~ (v2_struct_0(A))  &  (v13_lattices(A) & v14_lattices(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_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_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(cc5_nat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v8_ordinal1(A)) ) ).
fof(cc5_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(B)) => v4_relat_1(C, A)) ) ) ) ).
fof(cc5_robbins1, axiom,  (! [A] :  (l4_robbins1(A) =>  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v5_lattices(A) & v10_robbins1(A)) ) )  =>  ( ~ (v2_struct_0(A))  & v6_lattices(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_nat_1, axiom,  (! [A] :  ( ~ (v8_ordinal1(A))  =>  ~ (v1_xboole_0(A)) ) ) ).
fof(cc6_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(B)) => v5_relat_1(C, A)) ) ) ) ).
fof(cc7_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_funct_1(A)) ) ).
fof(cc7_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  =>  (v1_xboole_0(B) &  (v1_relat_1(B) & v4_relat_1(B, A)) ) ) ) ) ) ).
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(cc8_lattices, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l3_lattices(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (v1_xboole_0(B) =>  (v18_lattices(B, A) & v19_lattices(B, A)) ) ) ) ) ) ).
fof(cc8_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_xboole_0(B) &  (v1_relat_1(B) & v5_relat_1(B, A)) ) ) ) ) ) ).
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_lattices, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v6_lattices(A) &  (v8_lattices(A) & l3_lattices(A)) ) )  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (v18_lattices(B, A) => v20_lattices(B, A)) ) ) ) ) ).
fof(commutativity_k2_tarski, axiom,  (! [A, B] : k2_tarski(A, B)=k2_tarski(B, A)) ).
fof(commutativity_k3_lattices, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) & l2_lattices(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k3_lattices(A, B, C)=k3_lattices(A, C, B)) ) ).
fof(commutativity_k5_partpr_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1))))  &  (v1_funct_1(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1)))) ) )  => k5_partpr_1(A, B, C)=k5_partpr_1(A, C, B)) ) ).
fof(d11_margrel1, axiom, k5_margrel1=k2_tarski(k5_numbers, 1)).
fof(d12_partpr_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(k1_partpr_1(A), k1_partpr_1(A)), k1_partpr_1(A)) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k1_partpr_1(A), k1_partpr_1(A)), k1_partpr_1(A))))) )  =>  (B=k12_partpr_1(A) <=>  (! [C] :  ( (v1_funct_1(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1))))  =>  (! [D] :  ( (v1_funct_1(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1))))  => k1_binop_1(B, C, D)=k5_partpr_1(A, C, D)) ) ) ) ) ) ) ) ) ).
fof(d14_partpr_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  => k14_partpr_1(A)=g4_robbins1(k1_partpr_1(A), k12_partpr_1(A), k11_partpr_1(A), k13_partpr_1(A))) ) ).
fof(d17_lattices, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l2_lattices(A))  =>  (v14_lattices(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (B=k6_lattices(A) <=>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (k1_lattices(A, B, C)=B & k1_lattices(A, C, B)=B) ) ) ) ) ) ) ) ) ).
fof(d1_lattices, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l2_lattices(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k1_lattices(A, B, C)=k4_binop_1(u1_struct_0(A), u2_lattices(A), B, C)) ) ) ) ) ) ).
fof(d1_partpr_1, axiom,  (! [A] : k1_partpr_1(A)=k4_partfun1(A, k5_margrel1)) ).
fof(d2_xboolean, axiom, k2_xboolean=1).
fof(d5_partpr_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_funct_1(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1))))  =>  (! [C] :  ( (v1_funct_1(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1))))  => k5_partpr_1(A, B, C)=k1_binop_1(k4_partpr_1(A), B, C)) ) ) ) ) ) ).
fof(d8_partpr_1, axiom,  (! [A] : k8_partpr_1(A)=k7_funcop_1(A, k7_margrel1)) ).
fof(dt_g4_robbins1, axiom,  (! [A, B, C, D] :  ( ( (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)))) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, A, A) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, A)))) ) ) )  =>  (v4_robbins1(g4_robbins1(A, B, C, D)) & l4_robbins1(g4_robbins1(A, B, C, D))) ) ) ).
fof(dt_k11_partpr_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (v1_funct_1(k11_partpr_1(A)) &  (v1_funct_2(k11_partpr_1(A), k2_zfmisc_1(k1_partpr_1(A), k1_partpr_1(A)), k1_partpr_1(A)) & m1_subset_1(k11_partpr_1(A), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k1_partpr_1(A), k1_partpr_1(A)), k1_partpr_1(A))))) ) ) ) ).
fof(dt_k12_partpr_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (v1_funct_1(k12_partpr_1(A)) &  (v1_funct_2(k12_partpr_1(A), k2_zfmisc_1(k1_partpr_1(A), k1_partpr_1(A)), k1_partpr_1(A)) & m1_subset_1(k12_partpr_1(A), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k1_partpr_1(A), k1_partpr_1(A)), k1_partpr_1(A))))) ) ) ) ).
fof(dt_k13_partpr_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (v1_funct_1(k13_partpr_1(A)) &  (v1_funct_2(k13_partpr_1(A), k1_partpr_1(A), k1_partpr_1(A)) & m1_subset_1(k13_partpr_1(A), k1_zfmisc_1(k2_zfmisc_1(k1_partpr_1(A), k1_partpr_1(A))))) ) ) ) ).
fof(dt_k14_partpr_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (v4_robbins1(k14_partpr_1(A)) & l4_robbins1(k14_partpr_1(A))) ) ) ).
fof(dt_k1_binop_1, axiom, $true).
fof(dt_k1_lattices, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  & l2_lattices(A))  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k1_lattices(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k1_partpr_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_funcop_1, axiom, $true).
fof(dt_k2_tarski, axiom, $true).
fof(dt_k2_xboolean, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_lattices, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) & l2_lattices(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k4_binop_1, axiom,  (! [A, B, C, D] :  ( ( (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)))) )  &  (m1_subset_1(C, A) & m1_subset_1(D, A)) )  => m1_subset_1(k4_binop_1(A, B, C, D), A)) ) ).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k4_partfun1, axiom, $true).
fof(dt_k4_partpr_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (v1_funct_1(k4_partpr_1(A)) &  (v1_funct_2(k4_partpr_1(A), k2_zfmisc_1(k1_partpr_1(A), k1_partpr_1(A)), k1_partpr_1(A)) & m1_subset_1(k4_partpr_1(A), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k1_partpr_1(A), k1_partpr_1(A)), k1_partpr_1(A))))) ) ) ) ).
fof(dt_k5_margrel1, axiom, $true).
fof(dt_k5_numbers, axiom, m1_subset_1(k5_numbers, k4_ordinal1)).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k5_partpr_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1))))  &  (v1_funct_1(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1)))) ) )  =>  (v1_funct_1(k5_partpr_1(A, B, C)) & m1_subset_1(k5_partpr_1(A, B, C), k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1)))) ) ) ).
fof(dt_k6_lattices, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l2_lattices(A))  => m1_subset_1(k6_lattices(A), u1_struct_0(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_margrel1, axiom, m1_subset_1(k7_margrel1, k5_margrel1)).
fof(dt_k8_partpr_1, axiom,  (! [A] :  (v1_funct_1(k8_partpr_1(A)) & m1_subset_1(k8_partpr_1(A), k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1)))) ) ).
fof(dt_l1_lattices, axiom,  (! [A] :  (l1_lattices(A) => l1_struct_0(A)) ) ).
fof(dt_l1_robbins1, axiom,  (! [A] :  (l1_robbins1(A) => l1_struct_0(A)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_l2_lattices, axiom,  (! [A] :  (l2_lattices(A) => l1_struct_0(A)) ) ).
fof(dt_l2_robbins1, axiom,  (! [A] :  (l2_robbins1(A) =>  (l2_lattices(A) & l1_robbins1(A)) ) ) ).
fof(dt_l3_lattices, axiom,  (! [A] :  (l3_lattices(A) =>  (l1_lattices(A) & l2_lattices(A)) ) ) ).
fof(dt_l4_robbins1, axiom,  (! [A] :  (l4_robbins1(A) =>  (l2_robbins1(A) & l3_lattices(A)) ) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_u1_lattices, axiom,  (! [A] :  (l1_lattices(A) =>  (v1_funct_1(u1_lattices(A)) &  (v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m1_subset_1(u1_lattices(A), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))) ) ) ) ).
fof(dt_u1_robbins1, axiom,  (! [A] :  (l1_robbins1(A) =>  (v1_funct_1(u1_robbins1(A)) &  (v1_funct_2(u1_robbins1(A), u1_struct_0(A), u1_struct_0(A)) & m1_subset_1(u1_robbins1(A), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A))))) ) ) ) ).
fof(dt_u1_struct_0, axiom, $true).
fof(dt_u2_lattices, axiom,  (! [A] :  (l2_lattices(A) =>  (v1_funct_1(u2_lattices(A)) &  (v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m1_subset_1(u2_lattices(A), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))) ) ) ) ).
fof(existence_l1_lattices, axiom,  (? [A] : l1_lattices(A)) ).
fof(existence_l1_robbins1, axiom,  (? [A] : l1_robbins1(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_l2_lattices, axiom,  (? [A] : l2_lattices(A)) ).
fof(existence_l2_robbins1, axiom,  (? [A] : l2_robbins1(A)) ).
fof(existence_l3_lattices, axiom,  (? [A] : l3_lattices(A)) ).
fof(existence_l4_robbins1, axiom,  (? [A] : l4_robbins1(A)) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc11_funcop_1, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  => v2_relat_1(k2_funcop_1(A, B))) ) ).
fof(fc11_nat_1, axiom,  (! [A] :  ( ~ (v8_ordinal1(A))  => v1_setfam_1(k1_tarski(A))) ) ).
fof(fc12_nat_1, axiom,  (! [A, B] :  ( ( ~ (v8_ordinal1(A))  &  ~ (v8_ordinal1(B)) )  => v1_setfam_1(k2_tarski(A, B))) ) ).
fof(fc14_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  => v4_funct_1(k1_tarski(A))) ) ).
fof(fc15_funcop_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v1_funct_1(B))  => v1_funcop_1(k2_funcop_1(A, B))) ) ).
fof(fc15_funct_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) & v1_funct_1(B)) )  => v4_funct_1(k2_tarski(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(fc1_funcop_1, axiom,  (! [A, B] :  (v1_relat_1(k2_funcop_1(A, B)) & v1_funct_1(k2_funcop_1(A, B))) ) ).
fof(fc1_partfun1, axiom,  (! [A, B] :  ~ (v1_xboole_0(k4_partfun1(A, B))) ) ).
fof(fc1_partpr_1, axiom,  (! [A] :  (v4_funct_1(k1_partpr_1(A)) &  ~ (v1_xboole_0(k1_partpr_1(A))) ) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
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(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(fc25_funcop_1, axiom,  (! [A, B, C] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(k1_binop_1(A, B, C)) & v1_funct_1(k1_binop_1(A, B, C))) ) ) ).
fof(fc2_funcop_1, axiom,  (! [A] : v1_xboole_0(k2_funcop_1(k1_xboole_0, A))) ).
fof(fc2_partpr_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( (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)))) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, A, A) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, A)))) ) ) ) )  =>  ( ~ (v2_struct_0(g4_robbins1(A, B, C, D)))  & v4_robbins1(g4_robbins1(A, B, C, D))) ) ) ).
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_partpr_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  ( ~ (v2_struct_0(k14_partpr_1(A)))  &  (v1_monoid_0(k14_partpr_1(A)) & v4_robbins1(k14_partpr_1(A))) ) ) ) ).
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_partfun1, axiom,  (! [A, B] : v4_funct_1(k4_partfun1(A, B))) ).
fof(fc4_partpr_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (v10_lattices(k14_partpr_1(A)) & v4_robbins1(k14_partpr_1(A))) ) ) ).
fof(fc5_funcop_1, axiom,  (! [A] : v3_relat_1(k2_funcop_1(A, k1_xboole_0))) ).
fof(fc5_partpr_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (v15_lattices(k14_partpr_1(A)) & v4_robbins1(k14_partpr_1(A))) ) ) ).
fof(fc6_partpr_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (v4_robbins1(k14_partpr_1(A)) &  (v7_robbins1(k14_partpr_1(A)) &  (v9_robbins1(k14_partpr_1(A)) & v10_robbins1(k14_partpr_1(A))) ) ) ) ) ).
fof(fc6_relat_1, axiom,  (! [A, B] : v1_relat_1(k2_zfmisc_1(A, B))) ).
fof(free_g4_robbins1, axiom,  (! [A, B, C, D] :  ( ( (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)))) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, A, A) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, A)))) ) ) )  =>  (! [E, F, G, H] :  (g4_robbins1(A, B, C, D)=g4_robbins1(E, F, G, H) =>  (A=E &  (B=F &  (C=G & D=H) ) ) ) ) ) ) ).
fof(idempotence_k5_partpr_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1))))  &  (v1_funct_1(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1)))) ) )  => k5_partpr_1(A, B, B)=B) ) ).
fof(rc14_lattices, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l3_lattices(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  &  (v18_lattices(B, A) & v19_lattices(B, A)) ) ) ) ) ) ).
fof(rc15_lattices, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) & l3_lattices(A)) )  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  &  (v18_lattices(B, A) & v19_lattices(B, A)) ) ) ) ) ) ).
fof(rc1_funcop_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) ) ) ).
fof(rc1_funct_1, axiom,  (? [A] :  (v1_relat_1(A) & v1_funct_1(A)) ) ).
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(rc1_partpr_1, axiom,  (? [A] :  (l3_lattices(A) &  ( ~ (v2_struct_0(A))  & v1_monoid_0(A)) ) ) ).
fof(rc1_relat_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_relat_1(A)) ) ).
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_funcop_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  (v3_funct_1(A) &  ~ (v1_xboole_0(A)) ) ) ) ) ).
fof(rc2_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ).
fof(rc2_partpr_1, axiom,  (? [A] :  (l4_robbins1(A) &  ( ~ (v2_struct_0(A))  &  (v1_monoid_0(A) & v4_robbins1(A)) ) ) ) ).
fof(rc2_relat_1, axiom,  (? [A] :  (v1_relat_1(A) & v2_relat_1(A)) ) ).
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_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_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(rc3_relat_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ).
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_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) ) ) ) ).
fof(rc4_robbins1, axiom,  (? [A] :  (l4_robbins1(A) & v4_robbins1(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_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_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(rc7_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v4_funct_1(A)) ) ).
fof(rc9_funct_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) & v1_funct_1(B)) ) ) ) ) ).
fof(rd1_lattices, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v6_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) & l3_lattices(A)) ) ) )  & m1_subset_1(B, u1_struct_0(A)))  => k1_lattices(A, B, B)=B) ) ).
fof(rd6_lattices, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v14_lattices(A) & l3_lattices(A)) ) )  & m1_subset_1(B, u1_struct_0(A)))  => k3_lattices(A, k6_lattices(A), B)=k6_lattices(A)) ) ).
fof(redefinition_k3_lattices, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) & l2_lattices(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k3_lattices(A, B, C)=k1_lattices(A, B, C)) ) ).
fof(redefinition_k4_binop_1, axiom,  (! [A, B, C, D] :  ( ( (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)))) )  &  (m1_subset_1(C, A) & m1_subset_1(D, A)) )  => k4_binop_1(A, B, C, D)=k1_binop_1(B, C, D)) ) ).
fof(redefinition_k5_numbers, axiom, k5_numbers=k5_ordinal1).
fof(redefinition_k7_funcop_1, axiom,  (! [A, B] : k7_funcop_1(A, B)=k2_funcop_1(A, B)) ).
fof(redefinition_k7_margrel1, axiom, k7_margrel1=k2_xboolean).
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(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(spc1_numerals, axiom,  (v2_xxreal_0(1) & m1_subset_1(1, k4_ordinal1)) ).
fof(t1_numerals, axiom, m1_subset_1(k1_xboole_0, k4_ordinal1)).
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_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t45_partfun1, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (v1_funct_1(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))  => r2_tarski(C, k4_partfun1(A, B))) ) ) ) ).
fof(t45_partpr_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_funct_1(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1))))  => k5_partpr_1(A, B, k8_partpr_1(A))=k8_partpr_1(A)) ) ) ) ).
fof(t46_partfun1, axiom,  (! [A] :  (! [B] :  (! [C] :  (r2_tarski(C, k4_partfun1(A, B)) =>  (v1_funct_1(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_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(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)) ) ) ) ) ).
