% Mizar problem: t92_cqc_the2,cqc_the2,1303,5 
fof(t92_cqc_the2, conjecture,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k3_cqc_lang(A))) =>  (! [C] :  (m2_subset_1(C, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [D] :  (m2_subset_1(D, k9_qc_lang1(A), k3_cqc_lang(A)) =>  ( (v6_qc_lang1(C, A) & r3_cqc_the1(A, k4_subset_1(k3_cqc_lang(A), B, k6_domain_1(k3_cqc_lang(A), C)), D))  => r3_cqc_the1(A, B, k8_cqc_lang(A, 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_ordinal1, axiom,  (! [A] :  (v6_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_ordinal1(B)) ) ) ) ).
fof(cc11_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v7_ordinal1(A)) ) ).
fof(cc12_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v1_zfmisc_1(A)) ) ).
fof(cc13_ordinal1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  ~ (v8_ordinal1(A)) ) ) ).
fof(cc14_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc15_ordinal1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v9_ordinal1(A)) ) ) ).
fof(cc16_ordinal1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) )  =>  (! [B] :  (m1_subset_1(B, A) =>  ~ (v8_ordinal1(B)) ) ) ) ) ).
fof(cc17_ordinal1, axiom,  (! [A] :  ( ~ (v10_ordinal1(A))  => v1_setfam_1(A)) ) ).
fof(cc18_ordinal1, axiom,  (! [A] :  (v10_ordinal1(A) =>  ~ (v1_setfam_1(A)) ) ) ).
fof(cc19_ordinal1, axiom,  (! [A] :  (v1_setfam_1(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc1_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (v1_ordinal1(A) & v2_ordinal1(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(cc20_ordinal1, axiom,  (! [A] :  ( ~ (v1_setfam_1(A))  => v10_ordinal1(A)) ) ).
fof(cc2_ordinal1, axiom,  (! [A] :  ( (v1_ordinal1(A) & v2_ordinal1(A))  => v3_ordinal1(A)) ) ).
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(cc2_xreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xreal_0(A)) ) ).
fof(cc3_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_ordinal1(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(cc3_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xcmplx_0(A)) ) ).
fof(cc4_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v5_ordinal1(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(cc4_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xxreal_0(A)) ) ).
fof(cc5_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, A) => v3_ordinal1(B)) ) ) ) ).
fof(cc6_ordinal1, axiom,  (! [A] :  (v7_ordinal1(A) => v3_ordinal1(A)) ) ).
fof(cc7_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v7_ordinal1(A)) ) ).
fof(cc8_ordinal1, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) => v7_ordinal1(A)) ) ).
fof(cc9_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v6_ordinal1(A)) ) ).
fof(commutativity_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, B)=k2_xboole_0(B, A)) ).
fof(commutativity_k4_subset_1, axiom,  (! [A, B, C] :  ( (m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))  => k4_subset_1(A, B, C)=k4_subset_1(A, C, B)) ) ).
fof(connectedness_r1_xxreal_0, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  =>  (r1_xxreal_0(A, B) | r1_xxreal_0(B, A)) ) ) ).
fof(d1_tarski, axiom,  (! [A] :  (! [B] :  (B=k1_tarski(A) <=>  (! [C] :  (r2_hidden(C, B) <=> C=A) ) ) ) ) ).
fof(d31_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m1_subset_1(B, k9_qc_lang1(A)) =>  (v6_qc_lang1(B, A) <=> k24_qc_lang1(A, B)=k1_xboole_0) ) ) ) ) ).
fof(d3_xboole_0, axiom,  (! [A] :  (! [B] :  (! [C] :  (C=k2_xboole_0(A, B) <=>  (! [D] :  (r2_hidden(D, C) <=>  (r2_hidden(D, A) | r2_hidden(D, B)) ) ) ) ) ) ) ).
fof(d4_cqc_the1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m2_finseq_1(B, k2_zfmisc_1(k3_cqc_lang(A), k2_cqc_the1)) =>  (! [C] :  (v7_ordinal1(C) =>  (! [D] :  (m1_subset_1(D, k1_zfmisc_1(k3_cqc_lang(A))) =>  ( (k2_xtuple_0(k1_funct_1(B, C))=k5_numbers =>  (r1_cqc_the1(A, B, C, D) <=> r2_hidden(k1_xtuple_0(k1_funct_1(B, C)), D)) )  &  ( (k2_xtuple_0(k1_funct_1(B, C))=1 =>  (r1_cqc_the1(A, B, C, D) <=> k1_xtuple_0(k1_funct_1(B, C))=k5_cqc_lang(A)) )  &  ( (k2_xtuple_0(k1_funct_1(B, C))=2 =>  (r1_cqc_the1(A, B, C, D) <=>  (? [E] :  (m2_subset_1(E, k9_qc_lang1(A), k3_cqc_lang(A)) & k1_xtuple_0(k1_funct_1(B, C))=k8_cqc_lang(A, k8_cqc_lang(A, k6_cqc_lang(A, E), E), E)) ) ) )  &  ( (k2_xtuple_0(k1_funct_1(B, C))=3 =>  (r1_cqc_the1(A, B, C, D) <=>  (? [E] :  (m2_subset_1(E, k9_qc_lang1(A), k3_cqc_lang(A)) &  (? [F] :  (m2_subset_1(F, k9_qc_lang1(A), k3_cqc_lang(A)) & k1_xtuple_0(k1_funct_1(B, C))=k8_cqc_lang(A, E, k8_cqc_lang(A, k6_cqc_lang(A, E), F))) ) ) ) ) )  &  ( (k2_xtuple_0(k1_funct_1(B, C))=4 =>  (r1_cqc_the1(A, B, C, D) <=>  (? [E] :  (m2_subset_1(E, k9_qc_lang1(A), k3_cqc_lang(A)) &  (? [F] :  (m2_subset_1(F, k9_qc_lang1(A), k3_cqc_lang(A)) &  (? [G] :  (m2_subset_1(G, k9_qc_lang1(A), k3_cqc_lang(A)) & k1_xtuple_0(k1_funct_1(B, C))=k8_cqc_lang(A, k8_cqc_lang(A, E, F), k8_cqc_lang(A, k6_cqc_lang(A, k7_cqc_lang(A, F, G)), k6_cqc_lang(A, k7_cqc_lang(A, E, G))))) ) ) ) ) ) ) )  &  ( (k2_xtuple_0(k1_funct_1(B, C))=5 =>  (r1_cqc_the1(A, B, C, D) <=>  (? [E] :  (m2_subset_1(E, k9_qc_lang1(A), k3_cqc_lang(A)) &  (? [F] :  (m2_subset_1(F, k9_qc_lang1(A), k3_cqc_lang(A)) & k1_xtuple_0(k1_funct_1(B, C))=k8_cqc_lang(A, k7_cqc_lang(A, E, F), k7_cqc_lang(A, F, E))) ) ) ) ) )  &  ( (k2_xtuple_0(k1_funct_1(B, C))=6 =>  (r1_cqc_the1(A, B, C, D) <=>  (? [E] :  (m2_subset_1(E, k9_qc_lang1(A), k3_cqc_lang(A)) &  (? [F] :  (m2_subset_1(F, k2_qc_lang1(A), k3_qc_lang1(A)) & k1_xtuple_0(k1_funct_1(B, C))=k8_cqc_lang(A, k11_cqc_lang(A, F, E), E)) ) ) ) ) )  &  ( (k2_xtuple_0(k1_funct_1(B, C))=7 =>  (r1_cqc_the1(A, B, C, D) <=>  (? [E] :  (v7_ordinal1(E) &  (? [F] :  (v7_ordinal1(F) &  (? [G] :  (m2_subset_1(G, k9_qc_lang1(A), k3_cqc_lang(A)) &  (? [H] :  (m2_subset_1(H, k9_qc_lang1(A), k3_cqc_lang(A)) &  (r1_xxreal_0(1, E) &  ( ~ (r1_xxreal_0(C, E))  &  (r1_xxreal_0(1, F) &  ( ~ (r1_xxreal_0(E, F))  &  (G=k1_xtuple_0(k1_funct_1(B, F)) &  (H=k1_xtuple_0(k1_funct_1(B, C)) & k1_xtuple_0(k1_funct_1(B, E))=k8_cqc_lang(A, G, H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (k2_xtuple_0(k1_funct_1(B, C))=8 =>  (r1_cqc_the1(A, B, C, D) <=>  (? [E] :  (v7_ordinal1(E) &  (? [F] :  (m2_subset_1(F, k9_qc_lang1(A), k3_cqc_lang(A)) &  (? [G] :  (m2_subset_1(G, k9_qc_lang1(A), k3_cqc_lang(A)) &  (? [H] :  (m2_subset_1(H, k2_qc_lang1(A), k3_qc_lang1(A)) &  (r1_xxreal_0(1, E) &  ( ~ (r1_xxreal_0(C, E))  &  (k1_xtuple_0(k1_funct_1(B, E))=k8_cqc_lang(A, F, G) &  ( ~ (r2_tarski(H, k24_qc_lang1(A, F)))  & k1_xtuple_0(k1_funct_1(B, C))=k8_cqc_lang(A, F, k11_cqc_lang(A, H, G))) ) ) ) ) ) ) ) ) ) ) ) ) )  &  (k2_xtuple_0(k1_funct_1(B, C))=9 =>  (r1_cqc_the1(A, B, C, D) <=>  (? [E] :  (v7_ordinal1(E) &  (? [F] :  (m2_subset_1(F, k2_qc_lang1(A), k3_qc_lang1(A)) &  (? [G] :  (m2_subset_1(G, k2_qc_lang1(A), k3_qc_lang1(A)) &  (? [H] :  (m1_subset_1(H, k9_qc_lang1(A)) &  (r1_xxreal_0(1, E) &  ( ~ (r1_xxreal_0(C, E))  &  (r2_tarski(k13_cqc_lang(A, H, F), k3_cqc_lang(A)) &  (r2_tarski(k13_cqc_lang(A, H, G), k3_cqc_lang(A)) &  ( ~ (r2_tarski(F, k24_qc_lang1(A, H)))  &  (k13_cqc_lang(A, H, F)=k1_xtuple_0(k1_funct_1(B, E)) & k13_cqc_lang(A, H, G)=k1_xtuple_0(k1_funct_1(B, C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d5_cqc_the1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k3_cqc_lang(A))) =>  (! [C] :  (m2_finseq_1(C, k2_zfmisc_1(k3_cqc_lang(A), k2_cqc_the1)) =>  (r2_cqc_the1(A, B, C) <=>  ( ~ (C=k1_xboole_0)  &  (! [D] :  (v7_ordinal1(D) =>  ( (r1_xxreal_0(1, D) & r1_xxreal_0(D, k3_finseq_1(C)))  => r1_cqc_the1(A, C, D, B)) ) ) ) ) ) ) ) ) ) ) ).
fof(d6_cqc_the1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m2_finseq_1(B, k2_zfmisc_1(k3_cqc_lang(A), k2_cqc_the1)) =>  ( ~ (B=k1_xboole_0)  => k3_cqc_the1(A, B)=k1_xtuple_0(k1_funct_1(B, k3_finseq_1(B)))) ) ) ) ) ).
fof(d8_cqc_the1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k3_cqc_lang(A))) =>  (! [C] :  (m1_subset_1(C, k9_qc_lang1(A)) =>  (r3_cqc_the1(A, B, C) <=> r2_tarski(C, k1_cqc_the1(A, B))) ) ) ) ) ) ) ).
fof(dt_k11_cqc_lang, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k3_qc_lang1(A)) & m1_subset_1(C, k3_cqc_lang(A))) )  => m2_subset_1(k11_cqc_lang(A, B, C), k9_qc_lang1(A), k3_cqc_lang(A))) ) ).
fof(dt_k12_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) => m1_subset_1(k12_qc_lang1(A), k9_qc_lang1(A))) ) ).
fof(dt_k13_cqc_lang, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k9_qc_lang1(A)) & m1_subset_1(C, k3_qc_lang1(A))) )  => m1_subset_1(k13_cqc_lang(A, B, C), k9_qc_lang1(A))) ) ).
fof(dt_k13_qc_lang1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k9_qc_lang1(A)))  => m1_subset_1(k13_qc_lang1(A, B), k9_qc_lang1(A))) ) ).
fof(dt_k14_qc_lang1, 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(k14_qc_lang1(A, B, C), k9_qc_lang1(A))) ) ).
fof(dt_k15_qc_lang1, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k3_qc_lang1(A)) & m1_subset_1(C, k9_qc_lang1(A))) )  => m1_subset_1(k15_qc_lang1(A, B, C), k9_qc_lang1(A))) ) ).
fof(dt_k1_card_1, axiom,  (! [A] : v1_card_1(k1_card_1(A))) ).
fof(dt_k1_cqc_the1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k1_zfmisc_1(k3_cqc_lang(A))))  => m1_subset_1(k1_cqc_the1(A, B), k1_zfmisc_1(k3_cqc_lang(A)))) ) ).
fof(dt_k1_funct_1, axiom, $true).
fof(dt_k1_tarski, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_xtuple_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k24_qc_lang1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k9_qc_lang1(A)))  => m1_subset_1(k24_qc_lang1(A, B), k1_zfmisc_1(k3_qc_lang1(A)))) ) ).
fof(dt_k2_cqc_the1, axiom, $true).
fof(dt_k2_qc_lang1, 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_k2_xboole_0, axiom, $true).
fof(dt_k2_xtuple_0, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
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_k3_cqc_the1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_finseq_1(B, k2_zfmisc_1(k3_cqc_lang(A), k2_cqc_the1)))  => m2_subset_1(k3_cqc_the1(A, B), k9_qc_lang1(A), k3_cqc_lang(A))) ) ).
fof(dt_k3_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => m1_subset_1(k3_finseq_1(A), k4_ordinal1)) ) ).
fof(dt_k3_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) => m1_subset_1(k3_qc_lang1(A), k1_zfmisc_1(k2_qc_lang1(A)))) ) ).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k4_subset_1, axiom,  (! [A, B, C] :  ( (m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))  => m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A))) ) ).
fof(dt_k5_cqc_lang, axiom,  (! [A] :  (m1_qc_lang1(A) => m2_subset_1(k5_cqc_lang(A), k9_qc_lang1(A), k3_cqc_lang(A))) ) ).
fof(dt_k5_numbers, axiom, m1_subset_1(k5_numbers, k4_ordinal1)).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k6_cqc_lang, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k3_cqc_lang(A)))  => m2_subset_1(k6_cqc_lang(A, B), k9_qc_lang1(A), k3_cqc_lang(A))) ) ).
fof(dt_k6_domain_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(B, A))  => m1_subset_1(k6_domain_1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_k7_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(k7_cqc_lang(A, B, C), k9_qc_lang1(A), k3_cqc_lang(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_finseq_1, axiom,  (! [A] :  (! [B] :  (m1_finseq_1(B, A) =>  (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) ) ) ) ) ).
fof(dt_m1_qc_lang1, axiom, $true).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_m2_finseq_1, axiom,  (! [A] :  (! [B] :  (m2_finseq_1(B, A) =>  (v1_funct_1(B) &  (v1_finseq_1(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, A)))) ) ) ) ) ).
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_finseq_1, axiom,  (! [A] :  (? [B] : m1_finseq_1(B, 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_finseq_1, axiom,  (! [A] :  (? [B] : m2_finseq_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(fc10_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, C), k8_cqc_lang(A, k6_cqc_lang(A, C), k6_cqc_lang(A, B))), A)) ) ).
fof(fc11_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, k6_cqc_lang(A, B), k6_cqc_lang(A, C)), k8_cqc_lang(A, C, B)), A)) ) ).
fof(fc12_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, k6_cqc_lang(A, k6_cqc_lang(A, B))), A)) ) ).
fof(fc13_lukasi_1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k3_cqc_lang(A)))  => v2_cqc_the1(k2_qc_lang2(A, k6_cqc_lang(A, k6_cqc_lang(A, B)), B), A)) ) ).
fof(fc14_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, k6_cqc_lang(A, k6_cqc_lang(A, B)), C), k8_cqc_lang(A, B, C)), A)) ) ).
fof(fc15_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, k6_cqc_lang(A, k6_cqc_lang(A, C))), k8_cqc_lang(A, B, C)), A)) ) ).
fof(fc16_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, k6_cqc_lang(A, C)), k8_cqc_lang(A, C, k6_cqc_lang(A, B))), A)) ) ).
fof(fc17_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, k6_cqc_lang(A, B), C), k8_cqc_lang(A, k6_cqc_lang(A, C), B)), A)) ) ).
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(fc1_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v4_relat_1(B, A))  &  (v1_relat_1(C) & v4_relat_1(C, A)) )  => v4_relat_1(k2_xboole_0(B, C), A)) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
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(fc2_xboole_0, axiom,  (! [A] :  ~ (v1_xboole_0(k1_tarski(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(fc4_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v5_relat_1(B, A))  &  (v1_relat_1(C) & v5_relat_1(C, A)) )  => v5_relat_1(k2_xboole_0(B, C), A)) ) ).
fof(fc4_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(A, B))) ) ) ).
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(fc5_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(B, 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(fc6_ordinal1, axiom,  ( ~ (v1_xboole_0(k4_ordinal1))  & v3_ordinal1(k4_ordinal1)) ).
fof(fc7_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, k8_cqc_lang(A, C, D)), k8_cqc_lang(A, k8_cqc_lang(A, B, C), k8_cqc_lang(A, B, D))), A)) ) ).
fof(fc8_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, k8_cqc_lang(A, B, C), D), k8_cqc_lang(A, C, D)), A)) ) ).
fof(fc8_ordinal1, axiom, v7_ordinal1(k5_ordinal1)).
fof(fc9_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, D, B), k8_cqc_lang(A, D, C))), A)) ) ).
fof(fc9_ordinal1, axiom, v8_ordinal1(k5_ordinal1)).
fof(idempotence_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, A)=A) ).
fof(idempotence_k4_subset_1, axiom,  (! [A, B, C] :  ( (m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))  => k4_subset_1(A, B, B)=B) ) ).
fof(projectivity_k1_card_1, axiom,  (! [A] : k1_card_1(k1_card_1(A))=k1_card_1(A)) ).
fof(projectivity_k3_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => k3_finseq_1(k3_finseq_1(A))=k3_finseq_1(A)) ) ).
fof(rc10_ordinal1, axiom,  (? [A] :  ~ (v8_ordinal1(A)) ) ).
fof(rc11_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) ) ) ).
fof(rc12_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) & v9_ordinal1(A)) ) ).
fof(rc13_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) &  ~ (v9_ordinal1(A)) ) ) ).
fof(rc1_ordinal1, axiom,  (? [A] :  (v1_ordinal1(A) & v2_ordinal1(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(rc1_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc2_ordinal1, axiom,  (? [A] : v3_ordinal1(A)) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc2_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc3_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_ordinal1(A) &  (v2_ordinal1(A) & v3_ordinal1(A)) ) ) ) ).
fof(rc3_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v2_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc4_ordinal1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) & v5_ordinal1(B)) ) ) ) ) ).
fof(rc5_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc5_xreal_0, axiom,  (? [A] :  (v8_ordinal1(A) &  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc6_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc7_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v7_ordinal1(A)) ) ).
fof(rc8_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rc9_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(redefinition_k11_cqc_lang, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k3_qc_lang1(A)) & m1_subset_1(C, k3_cqc_lang(A))) )  => k11_cqc_lang(A, B, C)=k15_qc_lang1(A, B, C)) ) ).
fof(redefinition_k3_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => k3_finseq_1(A)=k1_card_1(A)) ) ).
fof(redefinition_k4_subset_1, axiom,  (! [A, B, C] :  ( (m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))  => k4_subset_1(A, B, C)=k2_xboole_0(B, C)) ) ).
fof(redefinition_k5_cqc_lang, axiom,  (! [A] :  (m1_qc_lang1(A) => k5_cqc_lang(A)=k12_qc_lang1(A)) ) ).
fof(redefinition_k5_numbers, axiom, k5_numbers=k5_ordinal1).
fof(redefinition_k6_cqc_lang, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k3_cqc_lang(A)))  => k6_cqc_lang(A, B)=k13_qc_lang1(A, B)) ) ).
fof(redefinition_k6_domain_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(B, A))  => k6_domain_1(A, B)=k1_tarski(B)) ) ).
fof(redefinition_k7_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))) )  => k7_cqc_lang(A, B, C)=k14_qc_lang1(A, B, C)) ) ).
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_finseq_1, axiom,  (! [A] :  (! [B] :  (m2_finseq_1(B, A) <=> m1_finseq_1(B, A)) ) ) ).
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(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(reflexivity_r1_xxreal_0, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => r1_xxreal_0(A, A)) ) ).
fof(rqLessOrEqual__r1_xxreal_0__r0_r0, axiom, r1_xxreal_0(0, 0)).
fof(rqLessOrEqual__r1_xxreal_0__r0_r1, axiom, r1_xxreal_0(0, 1)).
fof(rqLessOrEqual__r1_xxreal_0__r0_r2, axiom, r1_xxreal_0(0, 2)).
fof(rqLessOrEqual__r1_xxreal_0__r0_r3, axiom, r1_xxreal_0(0, 3)).
fof(rqLessOrEqual__r1_xxreal_0__r0_r4, axiom, r1_xxreal_0(0, 4)).
fof(rqLessOrEqual__r1_xxreal_0__r0_r5, axiom, r1_xxreal_0(0, 5)).
fof(rqLessOrEqual__r1_xxreal_0__r0_r6, axiom, r1_xxreal_0(0, 6)).
fof(rqLessOrEqual__r1_xxreal_0__r0_r7, axiom, r1_xxreal_0(0, 7)).
fof(rqLessOrEqual__r1_xxreal_0__r0_r8, axiom, r1_xxreal_0(0, 8)).
fof(rqLessOrEqual__r1_xxreal_0__r0_r9, axiom, r1_xxreal_0(0, 9)).
fof(rqLessOrEqual__r1_xxreal_0__r1_r1, axiom, r1_xxreal_0(1, 1)).
fof(rqLessOrEqual__r1_xxreal_0__r1_r2, axiom, r1_xxreal_0(1, 2)).
fof(rqLessOrEqual__r1_xxreal_0__r1_r3, axiom, r1_xxreal_0(1, 3)).
fof(rqLessOrEqual__r1_xxreal_0__r1_r4, axiom, r1_xxreal_0(1, 4)).
fof(rqLessOrEqual__r1_xxreal_0__r1_r5, axiom, r1_xxreal_0(1, 5)).
fof(rqLessOrEqual__r1_xxreal_0__r1_r6, axiom, r1_xxreal_0(1, 6)).
fof(rqLessOrEqual__r1_xxreal_0__r1_r7, axiom, r1_xxreal_0(1, 7)).
fof(rqLessOrEqual__r1_xxreal_0__r1_r8, axiom, r1_xxreal_0(1, 8)).
fof(rqLessOrEqual__r1_xxreal_0__r1_r9, axiom, r1_xxreal_0(1, 9)).
fof(rqLessOrEqual__r1_xxreal_0__r2_r2, axiom, r1_xxreal_0(2, 2)).
fof(rqLessOrEqual__r1_xxreal_0__r2_r3, axiom, r1_xxreal_0(2, 3)).
fof(rqLessOrEqual__r1_xxreal_0__r2_r4, axiom, r1_xxreal_0(2, 4)).
fof(rqLessOrEqual__r1_xxreal_0__r2_r5, axiom, r1_xxreal_0(2, 5)).
fof(rqLessOrEqual__r1_xxreal_0__r2_r6, axiom, r1_xxreal_0(2, 6)).
fof(rqLessOrEqual__r1_xxreal_0__r2_r7, axiom, r1_xxreal_0(2, 7)).
fof(rqLessOrEqual__r1_xxreal_0__r2_r8, axiom, r1_xxreal_0(2, 8)).
fof(rqLessOrEqual__r1_xxreal_0__r2_r9, axiom, r1_xxreal_0(2, 9)).
fof(rqLessOrEqual__r1_xxreal_0__r3_r3, axiom, r1_xxreal_0(3, 3)).
fof(rqLessOrEqual__r1_xxreal_0__r3_r4, axiom, r1_xxreal_0(3, 4)).
fof(rqLessOrEqual__r1_xxreal_0__r3_r5, axiom, r1_xxreal_0(3, 5)).
fof(rqLessOrEqual__r1_xxreal_0__r3_r6, axiom, r1_xxreal_0(3, 6)).
fof(rqLessOrEqual__r1_xxreal_0__r3_r7, axiom, r1_xxreal_0(3, 7)).
fof(rqLessOrEqual__r1_xxreal_0__r3_r8, axiom, r1_xxreal_0(3, 8)).
fof(rqLessOrEqual__r1_xxreal_0__r3_r9, axiom, r1_xxreal_0(3, 9)).
fof(rqLessOrEqual__r1_xxreal_0__r4_r4, axiom, r1_xxreal_0(4, 4)).
fof(rqLessOrEqual__r1_xxreal_0__r4_r5, axiom, r1_xxreal_0(4, 5)).
fof(rqLessOrEqual__r1_xxreal_0__r4_r6, axiom, r1_xxreal_0(4, 6)).
fof(rqLessOrEqual__r1_xxreal_0__r4_r7, axiom, r1_xxreal_0(4, 7)).
fof(rqLessOrEqual__r1_xxreal_0__r4_r8, axiom, r1_xxreal_0(4, 8)).
fof(rqLessOrEqual__r1_xxreal_0__r4_r9, axiom, r1_xxreal_0(4, 9)).
fof(rqLessOrEqual__r1_xxreal_0__r5_r5, axiom, r1_xxreal_0(5, 5)).
fof(rqLessOrEqual__r1_xxreal_0__r5_r6, axiom, r1_xxreal_0(5, 6)).
fof(rqLessOrEqual__r1_xxreal_0__r5_r7, axiom, r1_xxreal_0(5, 7)).
fof(rqLessOrEqual__r1_xxreal_0__r5_r8, axiom, r1_xxreal_0(5, 8)).
fof(rqLessOrEqual__r1_xxreal_0__r5_r9, axiom, r1_xxreal_0(5, 9)).
fof(rqLessOrEqual__r1_xxreal_0__r6_r6, axiom, r1_xxreal_0(6, 6)).
fof(rqLessOrEqual__r1_xxreal_0__r6_r7, axiom, r1_xxreal_0(6, 7)).
fof(rqLessOrEqual__r1_xxreal_0__r6_r8, axiom, r1_xxreal_0(6, 8)).
fof(rqLessOrEqual__r1_xxreal_0__r6_r9, axiom, r1_xxreal_0(6, 9)).
fof(rqLessOrEqual__r1_xxreal_0__r7_r7, axiom, r1_xxreal_0(7, 7)).
fof(rqLessOrEqual__r1_xxreal_0__r7_r8, axiom, r1_xxreal_0(7, 8)).
fof(rqLessOrEqual__r1_xxreal_0__r7_r9, axiom, r1_xxreal_0(7, 9)).
fof(rqLessOrEqual__r1_xxreal_0__r8_r8, axiom, r1_xxreal_0(8, 8)).
fof(rqLessOrEqual__r1_xxreal_0__r8_r9, axiom, r1_xxreal_0(8, 9)).
fof(rqLessOrEqual__r1_xxreal_0__r9_r9, axiom, r1_xxreal_0(9, 9)).
fof(s4_nat_1__e10_97__cqc_the2, axiom,  (! [A, B, C, D] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k1_zfmisc_1(k3_cqc_lang(A))) &  (m2_subset_1(C, k9_qc_lang1(A), k3_cqc_lang(A)) & m2_finseq_1(D, k2_zfmisc_1(k3_cqc_lang(A), k2_cqc_the1))) ) )  =>  ( (! [E] :  (v7_ordinal1(E) =>  ( (! [F] :  (v7_ordinal1(F) =>  ( ~ (r1_xxreal_0(E, F))  =>  ( (r1_xxreal_0(1, F) & r1_xxreal_0(F, k3_finseq_1(D)))  =>  (! [G] :  (m2_subset_1(G, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (G=k1_xtuple_0(k1_funct_1(D, F)) => r3_cqc_the1(A, B, k8_cqc_lang(A, C, G))) ) ) ) ) ) )  =>  ( (r1_xxreal_0(1, E) & r1_xxreal_0(E, k3_finseq_1(D)))  =>  (! [H] :  (m2_subset_1(H, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (H=k1_xtuple_0(k1_funct_1(D, E)) => r3_cqc_the1(A, B, k8_cqc_lang(A, C, H))) ) ) ) ) ) )  =>  (! [E] :  (v7_ordinal1(E) =>  ( (r1_xxreal_0(1, E) & r1_xxreal_0(E, k3_finseq_1(D)))  =>  (! [I] :  (m2_subset_1(I, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (I=k1_xtuple_0(k1_funct_1(D, E)) => r3_cqc_the1(A, B, k8_cqc_lang(A, C, I))) ) ) ) ) ) ) ) ) ).
fof(spc0_boole, axiom, v1_xboole_0(0)).
fof(spc0_numerals, axiom, m1_subset_1(0, k4_ordinal1)).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(spc1_numerals, axiom,  (v2_xxreal_0(1) & m1_subset_1(1, k4_ordinal1)) ).
fof(spc2_boole, axiom,  ~ (v1_xboole_0(2)) ).
fof(spc2_numerals, axiom,  (v2_xxreal_0(2) & m1_subset_1(2, k4_ordinal1)) ).
fof(spc3_boole, axiom,  ~ (v1_xboole_0(3)) ).
fof(spc3_numerals, axiom,  (v2_xxreal_0(3) & m1_subset_1(3, k4_ordinal1)) ).
fof(spc4_boole, axiom,  ~ (v1_xboole_0(4)) ).
fof(spc4_numerals, axiom,  (v2_xxreal_0(4) & m1_subset_1(4, k4_ordinal1)) ).
fof(spc5_boole, axiom,  ~ (v1_xboole_0(5)) ).
fof(spc5_numerals, axiom,  (v2_xxreal_0(5) & m1_subset_1(5, k4_ordinal1)) ).
fof(spc6_boole, axiom,  ~ (v1_xboole_0(6)) ).
fof(spc6_numerals, axiom,  (v2_xxreal_0(6) & m1_subset_1(6, k4_ordinal1)) ).
fof(spc7_boole, axiom,  ~ (v1_xboole_0(7)) ).
fof(spc7_numerals, axiom,  (v2_xxreal_0(7) & m1_subset_1(7, k4_ordinal1)) ).
fof(spc8_boole, axiom,  ~ (v1_xboole_0(8)) ).
fof(spc8_numerals, axiom,  (v2_xxreal_0(8) & m1_subset_1(8, k4_ordinal1)) ).
fof(spc9_boole, axiom,  ~ (v1_xboole_0(9)) ).
fof(spc9_numerals, axiom,  (v2_xxreal_0(9) & m1_subset_1(9, k4_ordinal1)) ).
fof(t17_cqc_the1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k3_cqc_lang(A))) => r1_tarski(B, k1_cqc_the1(A, B))) ) ) ) ).
fof(t1_boole, axiom,  (! [A] : k2_xboole_0(A, k1_xboole_0)=A) ).
fof(t1_numerals, axiom, m1_subset_1(k1_xboole_0, k4_ordinal1)).
fof(t1_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ( (r1_xxreal_0(A, B) & v2_xxreal_0(A))  => v2_xxreal_0(B)) ) ) ) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t23_cqc_the1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m2_finseq_1(B, k2_zfmisc_1(k3_cqc_lang(A), k2_cqc_the1)) =>  (! [C] :  (v7_ordinal1(C) =>  ~ ( (r1_xxreal_0(1, C) &  (r1_xxreal_0(C, k3_finseq_1(B)) &  (! [D] :  (v7_ordinal1(D) =>  ~ ( (r1_xxreal_0(k5_numbers, D) &  (r1_xxreal_0(D, 9) & k2_xtuple_0(k1_funct_1(B, C))=D) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t25_cqc_the1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k3_cqc_lang(A))) =>  (! [C] :  (m2_finseq_1(C, k2_zfmisc_1(k3_cqc_lang(A), k2_cqc_the1)) =>  (r2_cqc_the1(A, B, C) => r1_xxreal_0(1, k3_finseq_1(C))) ) ) ) ) ) ) ).
fof(t25_cqc_the2, 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)) =>  (! [D] :  (m1_subset_1(D, k9_qc_lang1(A)) =>  (! [E] :  (m2_subset_1(E, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (! [F] :  (m2_subset_1(F, k2_qc_lang1(A), k3_qc_lang1(A)) =>  ( (B=k13_cqc_lang(A, D, E) & C=k13_cqc_lang(A, D, F))  =>  (r2_tarski(E, k24_qc_lang1(A, D)) | v2_cqc_the1(k8_cqc_lang(A, k11_cqc_lang(A, E, B), C), A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t2_xxreal_0, axiom,  (! [A] :  (v1_xxreal_0(A) =>  (! [B] :  (v1_xxreal_0(B) =>  (! [C] :  (v1_xxreal_0(C) =>  ( (r1_xxreal_0(A, B) & r1_xxreal_0(B, C))  => r1_xxreal_0(A, C)) ) ) ) ) ) ) ).
fof(t36_cqc_the1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k3_cqc_lang(A))) =>  (! [C] :  (m2_subset_1(C, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (r2_tarski(C, k1_cqc_the1(A, B)) <=>  (? [D] :  (m2_finseq_1(D, k2_zfmisc_1(k3_cqc_lang(A), k2_cqc_the1)) &  (r2_cqc_the1(A, B, D) & k3_cqc_the1(A, D)=C) ) ) ) ) ) ) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t46_lukasi_1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m2_subset_1(B, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (v2_cqc_the1(k8_cqc_lang(A, B, k5_cqc_lang(A)), A) & v2_cqc_the1(k8_cqc_lang(A, k6_cqc_lang(A, k5_cqc_lang(A)), B), A)) ) ) ) ) ).
fof(t4_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( (r1_xxreal_0(A, B) &  ( ~ (v2_xxreal_0(B))  & v2_xxreal_0(A)) ) ) ) ) ) ) ).
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(t55_cqc_the1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k3_cqc_lang(A))) =>  (! [C] :  (m2_subset_1(C, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [D] :  (m2_subset_1(D, k9_qc_lang1(A), k3_cqc_lang(A)) =>  ( (r3_cqc_the1(A, B, C) & r3_cqc_the1(A, B, k8_cqc_lang(A, C, D)))  => r3_cqc_the1(A, B, D)) ) ) ) ) ) ) ) ) ).
fof(t59_cqc_the1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k3_cqc_lang(A))) =>  (! [C] :  (m2_subset_1(C, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (v2_cqc_the1(C, A) => r3_cqc_the1(A, B, C)) ) ) ) ) ) ) ).
fof(t59_lukasi_1, 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)) =>  (! [D] :  (m2_subset_1(D, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [E] :  (m1_subset_1(E, k1_zfmisc_1(k3_cqc_lang(A))) =>  ( (r3_cqc_the1(A, E, k8_cqc_lang(A, B, C)) & r3_cqc_the1(A, E, k8_cqc_lang(A, C, D)))  => r3_cqc_the1(A, E, k8_cqc_lang(A, B, D))) ) ) ) ) ) ) ) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t61_cqc_the1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m2_subset_1(B, k9_qc_lang1(A), k3_cqc_lang(A)) => v2_cqc_the1(k8_cqc_lang(A, k8_cqc_lang(A, k6_cqc_lang(A, B), B), B), A)) ) ) ) ).
fof(t61_lukasi_1, 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)) =>  (! [D] :  (m1_subset_1(D, k1_zfmisc_1(k3_cqc_lang(A))) =>  (r3_cqc_the1(A, D, B) => r3_cqc_the1(A, D, k8_cqc_lang(A, C, B))) ) ) ) ) ) ) ) ) ).
fof(t62_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(k8_cqc_lang(A, B, k8_cqc_lang(A, k6_cqc_lang(A, B), C)), A)) ) ) ) ) ) ).
fof(t63_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)) =>  (! [D] :  (m2_subset_1(D, k9_qc_lang1(A), k3_cqc_lang(A)) => v2_cqc_the1(k8_cqc_lang(A, k8_cqc_lang(A, B, C), k8_cqc_lang(A, k6_cqc_lang(A, k7_cqc_lang(A, C, D)), k6_cqc_lang(A, k7_cqc_lang(A, B, D)))), A)) ) ) ) ) ) ) ) ).
fof(t64_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(k8_cqc_lang(A, k7_cqc_lang(A, B, C), k7_cqc_lang(A, C, B)), A)) ) ) ) ) ) ).
fof(t66_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, k2_qc_lang1(A), k3_qc_lang1(A)) => v2_cqc_the1(k8_cqc_lang(A, k11_cqc_lang(A, C, B), B), A)) ) ) ) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t74_cqc_the2, 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)) =>  (! [D] :  (m2_subset_1(D, k2_qc_lang1(A), k3_qc_lang1(A)) =>  ( ~ (r2_tarski(D, k24_qc_lang1(A, B)))  =>  (v2_cqc_the1(k8_cqc_lang(A, k11_cqc_lang(A, D, k8_cqc_lang(A, B, C)), k8_cqc_lang(A, B, k11_cqc_lang(A, D, C))), A) & v2_cqc_the1(k8_cqc_lang(A, k8_cqc_lang(A, B, k11_cqc_lang(A, D, C)), k11_cqc_lang(A, D, k8_cqc_lang(A, B, C))), A)) ) ) ) ) ) ) ) ) ) ).
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(t90_cqc_the2, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k3_cqc_lang(A))) =>  (! [C] :  (m2_subset_1(C, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [D] :  (m2_subset_1(D, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (r3_cqc_the1(A, B, C) => r3_cqc_the1(A, B, k11_cqc_lang(A, D, C))) ) ) ) ) ) ) ) ) ).
