% Mizar problem: t16_grcat_1,grcat_1,454,5 
fof(t16_grcat_1, conjecture,  (! [A] :  ( (v2_grcat_1(A) & l1_grcat_1(A))  =>  (! [B] :  ( (v2_grcat_1(B) & l1_grcat_1(B))  =>  ~ ( (k7_grcat_1(A)=k8_grcat_1(B) &  (! [C] :  ( ( ~ (v2_struct_0(C))  &  (v13_algstr_0(C) &  (v3_rlvect_1(C) &  (v4_rlvect_1(C) & l2_algstr_0(C)) ) ) )  =>  (! [D] :  ( ( ~ (v2_struct_0(D))  &  (v13_algstr_0(D) &  (v3_rlvect_1(D) &  (v4_rlvect_1(D) & l2_algstr_0(D)) ) ) )  =>  (! [E] :  ( ( ~ (v2_struct_0(E))  &  (v13_algstr_0(E) &  (v3_rlvect_1(E) &  (v4_rlvect_1(E) & l2_algstr_0(E)) ) ) )  =>  ~ ( (m1_grcat_1(A, D, E) & m1_grcat_1(B, C, 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(cc10_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ( ~ (v2_struct_0(A))  & v7_struct_0(A))  => v13_struct_0(A, 1)) ) ) ).
fof(cc11_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, 1) =>  ( ~ (v2_struct_0(A))  & v7_struct_0(A)) ) ) ) ).
fof(cc17_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc1_algstr_1, axiom,  (! [A] :  (l2_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  & v4_algstr_1(A))  =>  ( ~ (v2_struct_0(A))  &  (v5_algstr_0(A) &  (v6_algstr_0(A) &  (v2_algstr_1(A) & v3_algstr_1(A)) ) ) ) ) ) ) ).
fof(cc1_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v7_struct_0(A)) ) ) ).
fof(cc2_algstr_1, axiom,  (! [A] :  (l2_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v5_algstr_0(A) &  (v6_algstr_0(A) &  (v2_algstr_1(A) & v3_algstr_1(A)) ) ) )  =>  ( ~ (v2_struct_0(A))  & v4_algstr_1(A)) ) ) ) ).
fof(cc2_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc3_algstr_0, axiom,  (! [A] :  (l1_algstr_0(A) =>  ( (v5_algstr_0(A) & v6_algstr_0(A))  => v7_algstr_0(A)) ) ) ).
fof(cc3_algstr_1, axiom,  (! [A] :  (l2_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  & v4_algstr_1(A))  =>  ( ~ (v2_struct_0(A))  & v2_algstr_1(A)) ) ) ) ).
fof(cc4_algstr_0, axiom,  (! [A] :  (l1_algstr_0(A) =>  (v7_algstr_0(A) =>  (v5_algstr_0(A) & v6_algstr_0(A)) ) ) ) ).
fof(cc4_algstr_1, axiom,  (! [A] :  (l2_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) & v4_rlvect_1(A)) ) )  =>  ( ~ (v2_struct_0(A))  &  (v1_algstr_1(A) & v4_algstr_1(A)) ) ) ) ) ).
fof(cc4_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) =>  (v2_struct_0(A) & v8_struct_0(A)) ) ) ) ).
fof(cc5_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ( ~ (v2_struct_0(A))  &  ~ (v8_struct_0(A)) ) ) ) ) ).
fof(cc6_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v7_struct_0(A) => v8_struct_0(A)) ) ) ).
fof(cc7_algstr_1, axiom,  (! [A] :  (l2_algstr_0(A) =>  (v13_struct_0(A, 1) =>  (v13_struct_0(A, 1) &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) & v4_rlvect_1(A)) ) ) ) ) ) ) ).
fof(cc7_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ~ (v7_struct_0(A)) ) ) ) ).
fof(cc8_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v13_struct_0(A, k5_ordinal1)) ) ) ).
fof(cc9_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, k5_ordinal1) => v2_struct_0(A)) ) ) ).
fof(d10_grcat_1, axiom,  (! [A] :  (l1_grcat_1(A) => k8_grcat_1(A)=u2_grcat_1(A)) ) ).
fof(d13_ordinal1, axiom, k5_ordinal1=k1_xboole_0).
fof(d14_grcat_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l2_algstr_0(A)) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l2_algstr_0(B)) ) ) )  =>  (! [C] :  ( (v2_grcat_1(C) & l1_grcat_1(C))  =>  (m1_grcat_1(C, A, B) <=>  (k7_grcat_1(C)=A & k8_grcat_1(C)=B) ) ) ) ) ) ) ) ).
fof(d9_grcat_1, axiom,  (! [A] :  (l1_grcat_1(A) => k7_grcat_1(A)=u1_grcat_1(A)) ) ).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k7_grcat_1, axiom,  (! [A] :  (l1_grcat_1(A) =>  ( ~ (v2_struct_0(k7_grcat_1(A)))  &  (v13_algstr_0(k7_grcat_1(A)) &  (v3_rlvect_1(k7_grcat_1(A)) &  (v4_rlvect_1(k7_grcat_1(A)) & l2_algstr_0(k7_grcat_1(A))) ) ) ) ) ) ).
fof(dt_k8_grcat_1, axiom,  (! [A] :  (l1_grcat_1(A) =>  ( ~ (v2_struct_0(k8_grcat_1(A)))  &  (v13_algstr_0(k8_grcat_1(A)) &  (v3_rlvect_1(k8_grcat_1(A)) &  (v4_rlvect_1(k8_grcat_1(A)) & l2_algstr_0(k8_grcat_1(A))) ) ) ) ) ) ).
fof(dt_l1_algstr_0, axiom,  (! [A] :  (l1_algstr_0(A) => l1_struct_0(A)) ) ).
fof(dt_l1_grcat_1, axiom, $true).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_l2_algstr_0, axiom,  (! [A] :  (l2_algstr_0(A) =>  (l2_struct_0(A) & l1_algstr_0(A)) ) ) ).
fof(dt_l2_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => l1_struct_0(A)) ) ).
fof(dt_m1_grcat_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l2_algstr_0(A)) ) ) )  &  ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l2_algstr_0(B)) ) ) ) )  =>  (! [C] :  (m1_grcat_1(C, A, B) =>  (v2_grcat_1(C) & l1_grcat_1(C)) ) ) ) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_u1_grcat_1, axiom,  (! [A] :  (l1_grcat_1(A) =>  ( ~ (v2_struct_0(u1_grcat_1(A)))  &  (v13_algstr_0(u1_grcat_1(A)) &  (v3_rlvect_1(u1_grcat_1(A)) &  (v4_rlvect_1(u1_grcat_1(A)) & l2_algstr_0(u1_grcat_1(A))) ) ) ) ) ) ).
fof(dt_u2_grcat_1, axiom,  (! [A] :  (l1_grcat_1(A) =>  ( ~ (v2_struct_0(u2_grcat_1(A)))  &  (v13_algstr_0(u2_grcat_1(A)) &  (v3_rlvect_1(u2_grcat_1(A)) &  (v4_rlvect_1(u2_grcat_1(A)) & l2_algstr_0(u2_grcat_1(A))) ) ) ) ) ) ).
fof(existence_l1_algstr_0, axiom,  (? [A] : l1_algstr_0(A)) ).
fof(existence_l1_grcat_1, axiom,  (? [A] : l1_grcat_1(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_l2_algstr_0, axiom,  (? [A] : l2_algstr_0(A)) ).
fof(existence_l2_struct_0, axiom,  (? [A] : l2_struct_0(A)) ).
fof(existence_m1_grcat_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l2_algstr_0(A)) ) ) )  &  ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l2_algstr_0(B)) ) ) ) )  =>  (? [C] : m1_grcat_1(C, A, B)) ) ) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc20_struct_0, axiom,  (? [A] :  (l2_struct_0(A) &  ( ~ (v2_struct_0(A))  & v7_struct_0(A)) ) ) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(t14_grcat_1, axiom,  (! [A] :  ( (v2_grcat_1(A) & l1_grcat_1(A))  =>  (? [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l2_algstr_0(B)) ) ) )  &  (? [C] :  ( ( ~ (v2_struct_0(C))  &  (v13_algstr_0(C) &  (v3_rlvect_1(C) &  (v4_rlvect_1(C) & l2_algstr_0(C)) ) ) )  & m1_grcat_1(A, B, C)) ) ) ) ) ) ).
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(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)) ) ) ) ) ).
