% Mizar problem: t6_algstr_2,algstr_2,252,5 
fof(t6_algstr_2, conjecture,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l6_algstr_0(A))  =>  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v1_algstr_1(A) &  (v4_algstr_1(A) &  (v7_algstr_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v2_vectsp_1(A) &  (v4_vectsp_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) )  <=>  ( (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => k1_algstr_0(A, B, k4_struct_0(A))=B) )  &  ( (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (? [C] :  (m1_subset_1(C, u1_struct_0(A)) & k1_algstr_0(A, B, C)=k4_struct_0(A)) ) ) )  &  ( (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) => k1_algstr_0(A, k1_algstr_0(A, B, C), D)=k1_algstr_0(A, B, k1_algstr_0(A, C, D))) ) ) ) ) )  &  ( (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k1_algstr_0(A, B, C)=k1_algstr_0(A, C, B)) ) ) )  &  ( ~ (k4_struct_0(A)=k5_struct_0(A))  &  ( (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => k6_algstr_0(A, B, k5_struct_0(A))=B) )  &  ( (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => k6_algstr_0(A, k5_struct_0(A), B)=B) )  &  ( (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  ~ ( ( ~ (B=k4_struct_0(A))  &  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  ~ (k6_algstr_0(A, B, D)=C) ) ) ) ) ) ) ) )  &  ( (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  ~ ( ( ~ (B=k4_struct_0(A))  &  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  ~ (k6_algstr_0(A, D, B)=C) ) ) ) ) ) ) ) )  &  ( (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (k6_algstr_0(A, B, C)=k6_algstr_0(A, B, D) =>  (B=k4_struct_0(A) | C=D) ) ) ) ) ) ) )  &  ( (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (k6_algstr_0(A, C, B)=k6_algstr_0(A, D, B) =>  (B=k4_struct_0(A) | C=D) ) ) ) ) ) ) )  &  ( (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => k6_algstr_0(A, B, k4_struct_0(A))=k4_struct_0(A)) )  &  ( (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => k6_algstr_0(A, k4_struct_0(A), B)=k4_struct_0(A)) )  &  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) => k6_algstr_0(A, k1_algstr_0(A, C, D), B)=k1_algstr_0(A, k6_algstr_0(A, C, B), k6_algstr_0(A, D, B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(cc1_algstr_0, axiom,  (! [A] :  (l1_algstr_0(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  ( (v2_algstr_0(B, A) & v3_algstr_0(B, A))  => v4_algstr_0(B, 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(cc25_algstr_0, axiom,  (! [A] :  (l5_algstr_0(A) =>  ( (v30_algstr_0(A) & v31_algstr_0(A))  => v32_algstr_0(A)) ) ) ).
fof(cc26_algstr_0, axiom,  (! [A] :  (l5_algstr_0(A) =>  (v32_algstr_0(A) =>  (v30_algstr_0(A) & v31_algstr_0(A)) ) ) ) ).
fof(cc2_algstr_0, axiom,  (! [A] :  (l1_algstr_0(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (v4_algstr_0(B, A) =>  (v2_algstr_0(B, A) & v3_algstr_0(B, 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(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(cc3_vectsp_1, axiom,  (! [A] :  (l4_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  & v4_vectsp_1(A))  =>  ( ~ (v2_struct_0(A))  &  (v3_vectsp_1(A) & v6_vectsp_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_vectsp_1, axiom,  (! [A] :  (l4_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v3_vectsp_1(A) & v6_vectsp_1(A)) )  =>  ( ~ (v2_struct_0(A))  & v1_group_1(A)) ) ) ) ).
fof(cc5_algstr_0, axiom,  (! [A] :  ( (v5_algstr_0(A) & l1_algstr_0(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => v2_algstr_0(B, A)) ) ) ) ).
fof(cc5_vectsp_1, axiom,  (! [A] :  (l4_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  & v4_vectsp_1(A))  =>  ( ~ (v2_struct_0(A))  & v1_group_1(A)) ) ) ) ).
fof(cc6_algstr_0, axiom,  (! [A] :  ( (v6_algstr_0(A) & l1_algstr_0(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => v3_algstr_0(B, A)) ) ) ) ).
fof(cc6_algstr_1, axiom,  (! [A] :  (l5_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  & v7_algstr_1(A))  =>  ( ~ (v2_struct_0(A))  &  (v32_algstr_0(A) & v6_algstr_1(A)) ) ) ) ) ).
fof(d2_algstr_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l2_algstr_0(A))  =>  (v1_algstr_1(A) <=>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => k1_algstr_0(A, k4_struct_0(A), B)=B) ) ) ) ) ).
fof(d2_rlvect_1, axiom,  (! [A] :  (l1_algstr_0(A) =>  (v2_rlvect_1(A) <=>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k1_algstr_0(A, B, C)=k1_algstr_0(A, C, B)) ) ) ) ) ) ) ).
fof(d3_rlvect_1, axiom,  (! [A] :  (l1_algstr_0(A) =>  (v3_rlvect_1(A) <=>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) => k1_algstr_0(A, k1_algstr_0(A, B, C), D)=k1_algstr_0(A, B, k1_algstr_0(A, C, D))) ) ) ) ) ) ) ) ) ).
fof(d3_vectsp_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l6_algstr_0(A))  =>  (v2_vectsp_1(A) <=>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) => k6_algstr_0(A, k1_algstr_0(A, C, D), B)=k1_algstr_0(A, k6_algstr_0(A, C, B), k6_algstr_0(A, D, B))) ) ) ) ) ) ) ) ) ).
fof(d4_rlvect_1, axiom,  (! [A] :  (l2_algstr_0(A) =>  (v4_rlvect_1(A) <=>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => k1_algstr_0(A, B, k4_struct_0(A))=B) ) ) ) ) ).
fof(d6_vectsp_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l4_algstr_0(A))  =>  (v4_vectsp_1(A) <=>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (k6_algstr_0(A, B, k5_struct_0(A))=B & k6_algstr_0(A, k5_struct_0(A), B)=B) ) ) ) ) ) ).
fof(d8_struct_0, axiom,  (! [A] :  (l4_struct_0(A) =>  (v6_struct_0(A) <=> k4_struct_0(A)=k5_struct_0(A)) ) ) ).
fof(dt_k1_algstr_0, axiom,  (! [A, B, C] :  ( (l1_algstr_0(A) &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k1_algstr_0(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k4_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => m1_subset_1(k4_struct_0(A), u1_struct_0(A))) ) ).
fof(dt_k5_struct_0, axiom,  (! [A] :  (l3_struct_0(A) => m1_subset_1(k5_struct_0(A), u1_struct_0(A))) ) ).
fof(dt_k6_algstr_0, axiom,  (! [A, B, C] :  ( (l3_algstr_0(A) &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k6_algstr_0(A, B, C), u1_struct_0(A))) ) ).
fof(dt_l1_algstr_0, axiom,  (! [A] :  (l1_algstr_0(A) => l1_struct_0(A)) ) ).
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_l3_algstr_0, axiom,  (! [A] :  (l3_algstr_0(A) => l1_struct_0(A)) ) ).
fof(dt_l3_struct_0, axiom,  (! [A] :  (l3_struct_0(A) => l1_struct_0(A)) ) ).
fof(dt_l4_algstr_0, axiom,  (! [A] :  (l4_algstr_0(A) =>  (l3_struct_0(A) & l3_algstr_0(A)) ) ) ).
fof(dt_l4_struct_0, axiom,  (! [A] :  (l4_struct_0(A) =>  (l2_struct_0(A) & l3_struct_0(A)) ) ) ).
fof(dt_l5_algstr_0, axiom,  (! [A] :  (l5_algstr_0(A) =>  (l4_algstr_0(A) & l4_struct_0(A)) ) ) ).
fof(dt_l6_algstr_0, axiom,  (! [A] :  (l6_algstr_0(A) =>  (l2_algstr_0(A) & l5_algstr_0(A)) ) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_u1_struct_0, axiom, $true).
fof(existence_l1_algstr_0, axiom,  (? [A] : l1_algstr_0(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_l3_algstr_0, axiom,  (? [A] : l3_algstr_0(A)) ).
fof(existence_l3_struct_0, axiom,  (? [A] : l3_struct_0(A)) ).
fof(existence_l4_algstr_0, axiom,  (? [A] : l4_algstr_0(A)) ).
fof(existence_l4_struct_0, axiom,  (? [A] : l4_struct_0(A)) ).
fof(existence_l5_algstr_0, axiom,  (? [A] : l5_algstr_0(A)) ).
fof(existence_l6_algstr_0, axiom,  (? [A] : l6_algstr_0(A)) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(rc11_vectsp_1, axiom,  (? [A] :  (l4_algstr_0(A) &  ( ~ (v2_struct_0(A))  & v4_vectsp_1(A)) ) ) ).
fof(rc2_vectsp_1, axiom,  (? [A] :  (l5_algstr_0(A) &  ( ~ (v2_struct_0(A))  & v4_vectsp_1(A)) ) ) ).
fof(rd1_vectsp_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v4_vectsp_1(A) & l5_algstr_0(A)) )  & m1_subset_1(B, u1_struct_0(A)))  => k6_algstr_0(A, B, k5_struct_0(A))=B) ) ).
fof(rd2_vectsp_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v4_vectsp_1(A) & l5_algstr_0(A)) )  & m1_subset_1(B, u1_struct_0(A)))  => k6_algstr_0(A, k5_struct_0(A), B)=B) ) ).
fof(rd7_vectsp_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v3_vectsp_1(A) & l4_algstr_0(A)) )  & m1_subset_1(B, u1_struct_0(A)))  => k6_algstr_0(A, B, k5_struct_0(A))=B) ) ).
fof(rd8_vectsp_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v6_vectsp_1(A) & l4_algstr_0(A)) )  & m1_subset_1(B, u1_struct_0(A)))  => k6_algstr_0(A, k5_struct_0(A), B)=B) ) ).
fof(t16_algstr_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l5_algstr_0(A))  =>  (v7_algstr_1(A) <=>  ( (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  ~ ( ( ~ (B=k4_struct_0(A))  &  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  ~ (k6_algstr_0(A, B, D)=C) ) ) ) ) ) ) ) )  &  ( (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  ~ ( ( ~ (B=k4_struct_0(A))  &  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  ~ (k6_algstr_0(A, D, B)=C) ) ) ) ) ) ) ) )  &  ( (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (k6_algstr_0(A, B, C)=k6_algstr_0(A, B, D) =>  (B=k4_struct_0(A) | C=D) ) ) ) ) ) ) )  &  ( (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (k6_algstr_0(A, C, B)=k6_algstr_0(A, D, B) =>  (B=k4_struct_0(A) | C=D) ) ) ) ) ) ) )  &  ( (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => k6_algstr_0(A, B, k4_struct_0(A))=k4_struct_0(A)) )  &  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => k6_algstr_0(A, k4_struct_0(A), B)=k4_struct_0(A)) ) ) ) ) ) ) ) ) ) ).
fof(t3_algstr_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l2_algstr_0(A))  =>  ( ( (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => k1_algstr_0(A, B, k4_struct_0(A))=B) )  &  ( (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (? [C] :  (m1_subset_1(C, u1_struct_0(A)) & k1_algstr_0(A, B, C)=k4_struct_0(A)) ) ) )  &  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) => k1_algstr_0(A, k1_algstr_0(A, B, C), D)=k1_algstr_0(A, B, k1_algstr_0(A, C, D))) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (? [C] :  (m1_subset_1(C, u1_struct_0(A)) & k1_algstr_0(A, C, B)=k4_struct_0(A)) ) ) ) ) ) ) ).
fof(t6_algstr_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l2_algstr_0(A))  =>  (v4_algstr_1(A) <=>  ( (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (? [D] :  (m1_subset_1(D, u1_struct_0(A)) & k1_algstr_0(A, B, D)=C) ) ) ) ) )  &  ( (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (? [D] :  (m1_subset_1(D, u1_struct_0(A)) & k1_algstr_0(A, D, B)=C) ) ) ) ) )  &  ( (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (k1_algstr_0(A, B, C)=k1_algstr_0(A, B, D) => C=D) ) ) ) ) ) )  &  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (k1_algstr_0(A, C, B)=k1_algstr_0(A, D, B) => C=D) ) ) ) ) ) ) ) ) ) ) ) ) ).
