% Mizar problem: t47_lukasi_1,lukasi_1,697,5 
fof(t47_lukasi_1, conjecture,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m2_subset_1(B, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [C] :  (m2_subset_1(C, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (v2_cqc_the1(k8_cqc_lang(A, B, k8_cqc_lang(A, B, C)), A) => v2_cqc_the1(k8_cqc_lang(A, B, C), A)) ) ) ) ) ) ) ).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_qc_lang2, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k9_qc_lang1(A)) & m1_subset_1(C, k9_qc_lang1(A))) )  => m1_subset_1(k2_qc_lang2(A, B, C), k9_qc_lang1(A))) ) ).
fof(dt_k3_cqc_lang, axiom,  (! [A] :  (m1_qc_lang1(A) => m1_subset_1(k3_cqc_lang(A), k1_zfmisc_1(k9_qc_lang1(A)))) ) ).
fof(dt_k8_cqc_lang, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k3_cqc_lang(A)) & m1_subset_1(C, k3_cqc_lang(A))) )  => m2_subset_1(k8_cqc_lang(A, B, C), k9_qc_lang1(A), k3_cqc_lang(A))) ) ).
fof(dt_k9_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k9_qc_lang1(A))) ) ) ).
fof(dt_m1_qc_lang1, axiom, $true).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_m2_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(A))) )  =>  (! [C] :  (m2_subset_1(C, A, B) => m1_subset_1(C, A)) ) ) ) ).
fof(existence_m1_qc_lang1, axiom,  (? [A] : m1_qc_lang1(A)) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(existence_m2_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(A))) )  =>  (? [C] : m2_subset_1(C, A, B)) ) ) ).
fof(fc1_lukasi_1, axiom,  (! [A, B, C, D] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k3_cqc_lang(A)) &  (m1_subset_1(C, k3_cqc_lang(A)) & m1_subset_1(D, k3_cqc_lang(A))) ) )  => v2_cqc_the1(k2_qc_lang2(A, k8_cqc_lang(A, B, C), k8_cqc_lang(A, k8_cqc_lang(A, C, D), k8_cqc_lang(A, B, D))), A)) ) ).
fof(fc2_cqc_lang, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k3_cqc_lang(A))) ) ) ).
fof(fc2_lukasi_1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k3_cqc_lang(A)))  => v2_cqc_the1(k2_qc_lang2(A, B, B), A)) ) ).
fof(fc3_lukasi_1, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k3_cqc_lang(A)) & m1_subset_1(C, k3_cqc_lang(A))) )  => v2_cqc_the1(k2_qc_lang2(A, B, k8_cqc_lang(A, C, B)), A)) ) ).
fof(fc4_lukasi_1, axiom,  (! [A, B, C, D] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k3_cqc_lang(A)) &  (m1_subset_1(C, k3_cqc_lang(A)) & m1_subset_1(D, k3_cqc_lang(A))) ) )  => v2_cqc_the1(k2_qc_lang2(A, k8_cqc_lang(A, D, k8_cqc_lang(A, C, B)), k8_cqc_lang(A, C, k8_cqc_lang(A, D, B))), A)) ) ).
fof(fc5_lukasi_1, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k3_cqc_lang(A)) & m1_subset_1(C, k3_cqc_lang(A))) )  => v2_cqc_the1(k2_qc_lang2(A, B, k8_cqc_lang(A, k8_cqc_lang(A, B, C), C)), A)) ) ).
fof(fc6_lukasi_1, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k3_cqc_lang(A)) & m1_subset_1(C, k3_cqc_lang(A))) )  => v2_cqc_the1(k2_qc_lang2(A, k8_cqc_lang(A, B, k8_cqc_lang(A, B, C)), k8_cqc_lang(A, B, C)), A)) ) ).
fof(redefinition_k8_cqc_lang, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k3_cqc_lang(A)) & m1_subset_1(C, k3_cqc_lang(A))) )  => k8_cqc_lang(A, B, C)=k2_qc_lang2(A, B, C)) ) ).
fof(redefinition_m2_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(A))) )  =>  (! [C] :  (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) ) ) ) ).
fof(t65_cqc_the1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m2_subset_1(B, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [C] :  (m2_subset_1(C, k9_qc_lang1(A), k3_cqc_lang(A)) =>  ( (v2_cqc_the1(B, A) & v2_cqc_the1(k8_cqc_lang(A, B, C), A))  => v2_cqc_the1(C, A)) ) ) ) ) ) ) ).
