% Mizar problem: t45_cqc_sim1,cqc_sim1,2167,62 fof(t45_cqc_sim1,conjecture,( ! [A] : ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) => k24_qc_lang1(A) = k24_qc_lang1(k14_cqc_sim1(A)) ) ), inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_arytm_3,cc1_finseq_1,cc1_finsub_1,cc1_funct_2,cc1_membered,cc1_partfun1,cc1_relset_1,cc20_membered,cc2_arytm_3,cc2_finsub_1,cc2_funct_2,cc2_membered,cc3_arytm_3,cc3_finsub_1,cc3_funct_2,cc3_membered,cc4_funct_2,cc4_membered,cc5_funct_2,cc6_funct_2,cc6_membered,cc9_membered,commutativity_k1_finsub_1,commutativity_k1_nat_1,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k2_xcmplx_0,commutativity_k4_subset_1,commutativity_k5_setwiseo,connectedness_r1_xreal_0,d10_cqc_sim1,d10_xboole_0,d11_cqc_sim1,d12_funct_1,d1_cqc_sim1,d1_funct_2,d2_cqc_sim1,d2_qc_lang3,d3_cqc_sim1,d3_tarski,d4_cqc_sim1,d5_tarski,d6_cqc_sim1,d7_cqc_sim1,d8_qc_lang1,d9_cqc_sim1,dt_k10_cqc_lang,dt_k10_cqc_sim1,dt_k11_cqc_lang,dt_k11_cqc_sim1,dt_k11_qc_lang1,dt_k12_cqc_sim1,dt_k12_qc_lang1,dt_k13_cqc_sim1,dt_k13_qc_lang1,dt_k14_cqc_sim1,dt_k14_qc_lang1,dt_k15_cqc_lang,dt_k15_cqc_sim1,dt_k16_cqc_sim1,dt_k1_card_1,dt_k1_cqc_sim1,dt_k1_domain_1,dt_k1_finsub_1,dt_k1_fraenkel,dt_k1_funct_1,dt_k1_funct_2,dt_k1_funct_4,dt_k1_nat_1,dt_k1_numbers,dt_k1_qc_lang1,dt_k1_qc_lang3,dt_k1_relat_1,dt_k1_setwiseo,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k22_qc_lang1,dt_k23_qc_lang1,dt_k24_qc_lang1,dt_k2_cqc_sim1,dt_k2_funcop_1,dt_k2_funct_2,dt_k2_qc_lang1,dt_k2_qc_lang3,dt_k2_tarski,dt_k2_xboole_0,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_cqc_sim1,dt_k3_finseq_1,dt_k4_cqc_sim1,dt_k4_finseq_1,dt_k4_mcart_1,dt_k4_relset_1,dt_k4_subset_1,dt_k4_tarski,dt_k4_xboole_0,dt_k4_zfmisc_1,dt_k5_cqc_sim1,dt_k5_finsub_1,dt_k5_numbers,dt_k5_ordinal2,dt_k5_qc_lang1,dt_k5_relat_1,dt_k5_setwiseo,dt_k6_cqc_sim1,dt_k6_relat_1,dt_k6_subset_1,dt_k7_cqc_lang,dt_k7_cqc_sim1,dt_k7_qc_lang1,dt_k8_cqc_lang,dt_k8_cqc_sim1,dt_k8_funct_2,dt_k8_qc_lang1,dt_k9_cqc_lang,dt_k9_cqc_sim1,dt_k9_qc_lang1,dt_k9_relat_1,dt_m1_finseq_1,dt_m1_fraenkel,dt_m1_qc_lang1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_fraenkel,dt_m2_relset_1,dt_m2_subset_1,existence_m1_finseq_1,existence_m1_fraenkel,existence_m1_qc_lang1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_fraenkel,existence_m2_relset_1,existence_m2_subset_1,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc17_finseq_1,fc1_cqc_sim1,fc1_finsub_1,fc1_funcop_1,fc1_funct_2,fc1_ordinal2,fc1_qc_lang1,fc1_subset_1,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_cqc_lang,fc2_finseq_1,fc2_finsub_1,fc2_funcop_1,fc2_funct_2,fc2_membered,fc2_partfun1,fc2_qc_lang1,fc2_subset_1,fc37_membered,fc38_membered,fc39_membered,fc3_funcop_1,fc3_subset_1,fc40_membered,fc41_membered,fc4_ordinal2,fc4_subset_1,fc5_membered,fc5_qc_lang1,fc6_membered,fc6_qc_lang1,fc6_subset_1,fc7_membered,fc8_membered,fc9_funcop_1,fc9_membered,fraenkel_a_1_4_cqc_sim1,fraenkel_a_2_0_qc_lang3,fraenkel_a_2_2_cqc_sim1,fraenkel_a_3_0_cqc_sim1,idempotence_k1_finsub_1,idempotence_k1_funct_4,idempotence_k2_xboole_0,idempotence_k4_subset_1,idempotence_k5_setwiseo,l16_cqc_sim1,rc1_arytm_3,rc1_cqc_lang,rc1_finseq_1,rc1_funct_2,rc1_membered,rc1_partfun1,rc1_subset_1,rc2_finseq_1,rc2_funct_2,rc2_partfun1,rc2_subset_1,rc3_finseq_1,rc3_partfun1,rc4_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,redefinition_k10_cqc_lang,redefinition_k11_cqc_lang,redefinition_k13_cqc_sim1,redefinition_k15_cqc_lang,redefinition_k15_cqc_sim1,redefinition_k1_domain_1,redefinition_k1_finsub_1,redefinition_k1_fraenkel,redefinition_k1_nat_1,redefinition_k23_qc_lang1,redefinition_k2_funct_2,redefinition_k3_finseq_1,redefinition_k4_cqc_sim1,redefinition_k4_finseq_1,redefinition_k4_relset_1,redefinition_k4_subset_1,redefinition_k5_numbers,redefinition_k5_setwiseo,redefinition_k6_subset_1,redefinition_k7_cqc_sim1,redefinition_k8_cqc_lang,redefinition_k8_funct_2,redefinition_k9_cqc_lang,redefinition_m2_finseq_1,redefinition_m2_fraenkel,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,s5_cqc_sim1__e7_69__cqc_sim1,spc1_boole,spc1_numerals,t11_funct_2,t11_qc_lang3,t13_cqc_sim1,t13_funcop_1,t149_relat_1,t14_qc_lang3,t153_relat_1,t162_funct_1,t16_qc_lang3,t1_boole,t1_real,t1_subset,t23_funct_1,t27_finseq_3,t2_subset,t2_tarski,t31_cqc_sim1,t32_cqc_sim1,t33_cqc_sim1,t34_cqc_sim1,t3_boole,t3_cqc_sim1,t3_subset,t43_cqc_sim1,t4_boole,t4_cqc_sim1,t4_real,t4_subset,t5_subset,t6_boole,t6_qc_lang3,t7_boole,t7_qc_lang3,t8_boole,t9_qc_lang3]), [file(cqc_sim1,t45_cqc_sim1)]). fof(antisymmetry_r2_hidden,axiom,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), []). fof(cc10_membered,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,A) => v1_xcmplx_0(B) ) ) ), file(membered,cc10_membered), []). fof(cc11_membered,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) ) ) ) ), file(membered,cc11_membered), []). fof(cc12_membered,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_rat_1(B) ) ) ) ), file(membered,cc12_membered), []). fof(cc13_membered,axiom,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc13_membered), []). fof(cc14_membered,axiom,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v4_ordinal2(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc14_membered), []). fof(cc15_membered,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc15_membered), []). fof(cc16_membered,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_membered(B) ) ) ), file(membered,cc16_membered), []). fof(cc17_membered,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) ) ) ) ), file(membered,cc17_membered), []). fof(cc18_membered,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) ) ) ) ), file(membered,cc18_membered), []). fof(cc19_membered,axiom,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) ) ) ) ), file(membered,cc19_membered), []). fof(cc1_arytm_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_ordinal1(B) & v2_ordinal1(B) & v3_ordinal1(B) ) ) ) ), file(arytm_3,cc1_arytm_3), []). fof(cc1_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ) ), file(finseq_1,cc1_finseq_1), []). fof(cc1_finsub_1,axiom,( ! [A] : ( v4_finsub_1(A) => ( v1_finsub_1(A) & v3_finsub_1(A) ) ) ), file(finsub_1,cc1_finsub_1), []). fof(cc1_funct_2,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_partfun1(C,A,B) ) => ( v1_funct_1(C) & v1_funct_2(C,A,B) ) ) ) ), file(funct_2,cc1_funct_2), []). fof(cc1_membered,axiom,( ! [A] : ( v5_membered(A) => v4_membered(A) ) ), file(membered,cc1_membered), []). fof(cc1_partfun1,axiom,( ! [A] : ( ( v1_relat_1(A) & v3_relat_2(A) & v8_relat_2(A) ) => ( v1_relat_1(A) & v1_relat_2(A) ) ) ), file(partfun1,cc1_partfun1), []). fof(cc1_relset_1,axiom,( ! [A,B,C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => v1_relat_1(C) ) ), file(relset_1,cc1_relset_1), []). fof(cc20_membered,axiom,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) ) ) ) ), file(membered,cc20_membered), []). fof(cc2_arytm_3,axiom,( ! [A] : ( ( v1_xboole_0(A) & v3_ordinal1(A) ) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ) ), file(arytm_3,cc2_arytm_3), []). fof(cc2_finsub_1,axiom,( ! [A] : ( ( v1_finsub_1(A) & v3_finsub_1(A) ) => v4_finsub_1(A) ) ), file(finsub_1,cc2_finsub_1), []). fof(cc2_funct_2,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & v3_funct_2(C,A,B) ) => ( v1_funct_1(C) & v2_funct_1(C) & v1_funct_2(C,A,B) & v2_funct_2(C,A,B) ) ) ) ), file(funct_2,cc2_funct_2), []). fof(cc2_membered,axiom,( ! [A] : ( v4_membered(A) => v3_membered(A) ) ), file(membered,cc2_membered), []). fof(cc3_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_ordinal2) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ) ), file(arytm_3,cc3_arytm_3), []). fof(cc3_finsub_1,axiom,( ! [A,B] : ( m1_subset_1(B,k5_finsub_1(A)) => v1_finset_1(B) ) ), file(finsub_1,cc3_finsub_1), []). fof(cc3_funct_2,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v2_funct_1(C) & v1_funct_2(C,A,B) & v2_funct_2(C,A,B) ) => ( v1_funct_1(C) & v1_funct_2(C,A,B) & v3_funct_2(C,A,B) ) ) ) ), file(funct_2,cc3_funct_2), []). fof(cc3_membered,axiom,( ! [A] : ( v3_membered(A) => v2_membered(A) ) ), file(membered,cc3_membered), []). fof(cc4_funct_2,axiom,( ! [A,B] : ( m1_relset_1(B,A,A) => ( ( v1_funct_1(B) & v1_partfun1(B,A,A) & v1_relat_2(B) & v1_funct_2(B,A,A) ) => ( v1_funct_1(B) & v2_funct_1(B) & v1_funct_2(B,A,A) & v2_funct_2(B,A,A) & v3_funct_2(B,A,A) ) ) ) ), file(funct_2,cc4_funct_2), []). fof(cc4_membered,axiom,( ! [A] : ( v2_membered(A) => v1_membered(A) ) ), file(membered,cc4_membered), []). fof(cc5_funct_2,axiom,( ! [A,B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_funct_2(C,A,B) ) => ( v1_funct_1(C) & v1_partfun1(C,A,B) & v1_funct_2(C,A,B) ) ) ) ) ), file(funct_2,cc5_funct_2), []). fof(cc6_funct_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ! [C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_funct_2(C,A,B) ) => ( v1_funct_1(C) & ~ v1_xboole_0(C) & v1_partfun1(C,A,B) & v1_funct_2(C,A,B) ) ) ) ) ), file(funct_2,cc6_funct_2), []). fof(cc6_membered,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v1_membered(A) & v2_membered(A) ) ) ), file(membered,cc6_membered), []). fof(cc9_membered,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k5_numbers)) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc9_membered), []). fof(commutativity_k1_finsub_1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v4_finsub_1(A) & m1_subset_1(B,A) & m1_subset_1(C,A) ) => k1_finsub_1(A,B,C) = k1_finsub_1(A,C,B) ) ), file(finsub_1,k1_finsub_1), []). fof(commutativity_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k1_nat_1(A,B) = k1_nat_1(B,A) ) ), file(nat_1,k1_nat_1), []). fof(commutativity_k2_tarski,axiom,( ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ), file(tarski,k2_tarski), []). fof(commutativity_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ), file(xboole_0,k2_xboole_0), []). fof(commutativity_k2_xcmplx_0,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ), file(xcmplx_0,k2_xcmplx_0), []). 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) ) ), file(subset_1,k4_subset_1), []). fof(commutativity_k5_setwiseo,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k5_finsub_1(A)) & m1_subset_1(C,k5_finsub_1(A)) ) => k5_setwiseo(A,B,C) = k5_setwiseo(A,C,B) ) ), file(setwiseo,k5_setwiseo), []). fof(connectedness_r1_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( r1_xreal_0(A,B) | r1_xreal_0(B,A) ) ) ), file(xreal_0,r1_xreal_0), []). fof(d10_cqc_sim1,axiom,( ! [A] : ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) => k12_cqc_sim1(A) = k10_cqc_sim1(k11_cqc_sim1(A)) ) ), file(cqc_sim1,d10_cqc_sim1), []). fof(d10_xboole_0,axiom,( ! [A,B] : ( A = B <=> ( r1_tarski(A,B) & r1_tarski(B,A) ) ) ), file(xboole_0,d10_xboole_0), []). fof(d11_cqc_sim1,axiom,( ! [A] : ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) => k14_cqc_sim1(A) = k9_cqc_sim1(A,k12_cqc_sim1(A),k13_cqc_sim1(k2_qc_lang1)) ) ), file(cqc_sim1,d11_cqc_sim1), []). fof(d12_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B,C] : ( C = k9_relat_1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( r2_hidden(E,k1_relat_1(A)) & r2_hidden(E,B) & D = k1_funct_1(A,E) ) ) ) ) ), file(funct_1,d12_funct_1), []). fof(d1_cqc_sim1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k7_cqc_lang) & m2_relset_1(B,A,k7_cqc_lang) ) => ! [C] : ( m2_fraenkel(C,A,k7_cqc_lang,k1_fraenkel(A,k7_cqc_lang)) => ( C = k1_cqc_sim1(A,B) <=> ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang) => ( E = k8_funct_2(A,k7_cqc_lang,B,D) => k8_funct_2(A,k7_cqc_lang,C,D) = k10_cqc_lang(E) ) ) ) ) ) ) ) ), file(cqc_sim1,d1_cqc_sim1), []). fof(d1_funct_2,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => ( ( ( B = k1_xboole_0 => A = k1_xboole_0 ) => ( v1_funct_2(C,A,B) <=> A = k4_relset_1(A,B,C) ) ) & ( B = k1_xboole_0 => ( A = k1_xboole_0 | ( v1_funct_2(C,A,B) <=> C = k1_xboole_0 ) ) ) ) ) ), file(funct_2,d1_funct_2), []). fof(d2_cqc_sim1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang) & m2_relset_1(A,k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang) & m2_relset_1(B,k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang) ) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( m2_fraenkel(D,k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang,k1_fraenkel(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang)) => ( D = k2_cqc_sim1(A,B,C) <=> ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ! [F] : ( m2_fraenkel(F,k2_qc_lang1,k2_qc_lang1,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)) => ! [G] : ( m2_subset_1(G,k8_qc_lang1,k7_cqc_lang) => ! [H] : ( m2_subset_1(H,k8_qc_lang1,k7_cqc_lang) => ( ( G = k8_funct_2(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang,A,k1_domain_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1),E,F)) & H = k8_funct_2(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang,B,k1_domain_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1),k1_nat_1(E,C),F)) ) => k8_funct_2(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang,D,k1_domain_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1),E,F)) = k11_cqc_lang(G,H) ) ) ) ) ) ) ) ) ) ) ), file(cqc_sim1,d2_cqc_sim1), []). fof(d2_qc_lang3,axiom,( ! [A] : ( m2_finseq_1(A,k1_qc_lang1) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_qc_lang1)) ) => k1_qc_lang3(A,B) = a_2_0_qc_lang3(A,B) ) ) ), file(qc_lang3,d2_qc_lang3), []). fof(d3_cqc_sim1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang) & m2_relset_1(A,k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang) ) => ! [B] : ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) => ! [C] : ( m2_fraenkel(C,k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang,k1_fraenkel(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang)) => ( C = k3_cqc_sim1(A,B) <=> ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ! [E] : ( m2_fraenkel(E,k2_qc_lang1,k2_qc_lang1,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)) => ! [F] : ( m2_subset_1(F,k8_qc_lang1,k7_cqc_lang) => ( F = k1_funct_1(A,k4_tarski(k1_nat_1(D,1),k1_funct_4(E,k2_funcop_1(k23_qc_lang1(B),k2_qc_lang3(D))))) => k8_funct_2(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang,C,k1_domain_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1),D,E)) = k15_cqc_lang(k2_qc_lang3(D),F) ) ) ) ) ) ) ) ) ), file(cqc_sim1,d3_cqc_sim1), []). fof(d3_tarski,axiom,( ! [A,B] : ( r1_tarski(A,B) <=> ! [C] : ( r2_hidden(C,A) => r2_hidden(C,B) ) ) ), file(tarski,d3_tarski), []). fof(d4_cqc_sim1,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A)) => ! [C] : ( ( v1_cqc_lang(C,A) & m1_qc_lang1(C,A) ) => ! [D] : ( m2_fraenkel(D,k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang,k1_fraenkel(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang)) => ( D = k5_cqc_sim1(A,B,C) <=> ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ! [F] : ( m2_fraenkel(F,k2_qc_lang1,k2_qc_lang1,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)) => k8_funct_2(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang,D,k1_domain_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1),E,F)) = k8_cqc_lang(A,B,k4_cqc_sim1(A,C,F)) ) ) ) ) ) ) ) ), file(cqc_sim1,d4_cqc_sim1), []). fof(d5_tarski,axiom,( ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ), file(tarski,d5_tarski), []). fof(d6_cqc_sim1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k7_cqc_lang,k1_fraenkel(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang)) & m2_relset_1(A,k7_cqc_lang,k1_fraenkel(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang)) ) => ( A = k8_cqc_sim1 <=> ( k7_cqc_sim1(A,k9_cqc_lang) = k2_funcop_1(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k9_cqc_lang) & ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( ( v1_cqc_lang(C,B) & m1_qc_lang1(C,B) ) => ! [D] : ( m2_subset_1(D,k5_qc_lang1,k7_qc_lang1(B)) => k7_cqc_sim1(A,k8_cqc_lang(B,D,C)) = k5_cqc_sim1(B,D,C) ) ) ) & ! [B] : ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) => ! [C] : ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang) => ! [D] : ( m2_subset_1(D,k1_qc_lang1,k2_qc_lang1) => ( k7_cqc_sim1(A,k10_cqc_lang(B)) = k1_cqc_sim1(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_sim1(A,B)) & k7_cqc_sim1(A,k11_cqc_lang(B,C)) = k2_cqc_sim1(k7_cqc_sim1(A,B),k7_cqc_sim1(A,C),k6_cqc_sim1(B)) & k7_cqc_sim1(A,k15_cqc_lang(D,B)) = k3_cqc_sim1(k7_cqc_sim1(A,B),D) ) ) ) ) ) ) ) ), file(cqc_sim1,d6_cqc_sim1), []). fof(d7_cqc_sim1,axiom,( ! [A] : ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_fraenkel(C,k2_qc_lang1,k2_qc_lang1,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)) => k9_cqc_sim1(A,B,C) = k8_funct_2(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang,k7_cqc_sim1(k8_cqc_sim1,A),k1_domain_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1),B,C)) ) ) ) ), file(cqc_sim1,d7_cqc_sim1), []). fof(d8_qc_lang1,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_finseq_1(B,k1_qc_lang1) => ( m1_qc_lang1(B,A) <=> k3_finseq_1(B) = A ) ) ) ), file(qc_lang1,d8_qc_lang1), []). fof(d9_cqc_sim1,axiom,( ! [A] : ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) => k11_cqc_sim1(A) = a_1_4_cqc_sim1(A) ) ), file(cqc_sim1,d9_cqc_sim1), []). fof(dt_k10_cqc_lang,axiom,( ! [A] : ( m1_subset_1(A,k7_cqc_lang) => m2_subset_1(k10_cqc_lang(A),k8_qc_lang1,k7_cqc_lang) ) ), file(cqc_lang,k10_cqc_lang), []). fof(dt_k10_cqc_sim1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k5_numbers)) ) => m2_subset_1(k10_cqc_sim1(A),k1_numbers,k5_numbers) ) ), file(cqc_sim1,k10_cqc_sim1), []). fof(dt_k11_cqc_lang,axiom,( ! [A,B] : ( ( m1_subset_1(A,k7_cqc_lang) & m1_subset_1(B,k7_cqc_lang) ) => m2_subset_1(k11_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang) ) ), file(cqc_lang,k11_cqc_lang), []). fof(dt_k11_cqc_sim1,axiom,( ! [A] : ( m1_subset_1(A,k7_cqc_lang) => m1_subset_1(k11_cqc_sim1(A),k1_zfmisc_1(k5_numbers)) ) ), file(cqc_sim1,k11_cqc_sim1), []). fof(dt_k11_qc_lang1,axiom,( m1_subset_1(k11_qc_lang1,k8_qc_lang1) ), file(qc_lang1,k11_qc_lang1), []). fof(dt_k12_cqc_sim1,axiom,( ! [A] : ( m1_subset_1(A,k7_cqc_lang) => m2_subset_1(k12_cqc_sim1(A),k1_numbers,k5_numbers) ) ), file(cqc_sim1,k12_cqc_sim1), []). fof(dt_k12_qc_lang1,axiom,( ! [A] : ( m1_subset_1(A,k8_qc_lang1) => m1_subset_1(k12_qc_lang1(A),k8_qc_lang1) ) ), file(qc_lang1,k12_qc_lang1), []). fof(dt_k13_cqc_sim1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m2_fraenkel(k13_cqc_sim1(A),A,A,k1_fraenkel(A,A)) ) ), file(cqc_sim1,k13_cqc_sim1), []). fof(dt_k13_qc_lang1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k8_qc_lang1) & m1_subset_1(B,k8_qc_lang1) ) => m1_subset_1(k13_qc_lang1(A,B),k8_qc_lang1) ) ), file(qc_lang1,k13_qc_lang1), []). fof(dt_k14_cqc_sim1,axiom,( ! [A] : ( m1_subset_1(A,k7_cqc_lang) => m2_subset_1(k14_cqc_sim1(A),k8_qc_lang1,k7_cqc_lang) ) ), file(cqc_sim1,k14_cqc_sim1), []). fof(dt_k14_qc_lang1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k2_qc_lang1) & m1_subset_1(B,k8_qc_lang1) ) => m1_subset_1(k14_qc_lang1(A,B),k8_qc_lang1) ) ), file(qc_lang1,k14_qc_lang1), []). fof(dt_k15_cqc_lang,axiom,( ! [A,B] : ( ( m1_subset_1(A,k2_qc_lang1) & m1_subset_1(B,k7_cqc_lang) ) => m2_subset_1(k15_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang) ) ), file(cqc_lang,k15_cqc_lang), []). fof(dt_k15_cqc_sim1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m1_subset_1(k15_cqc_sim1(A,B),k5_finsub_1(A)) ) ), file(cqc_sim1,k15_cqc_sim1), []). fof(dt_k16_cqc_sim1,axiom,( ! [A] : ( m1_subset_1(A,k7_cqc_lang) => m1_subset_1(k16_cqc_sim1(A),k1_zfmisc_1(k4_zfmisc_1(k7_cqc_lang,k5_numbers,k5_finsub_1(k2_qc_lang1),k1_fraenkel(k2_qc_lang1,k2_qc_lang1)))) ) ), file(cqc_sim1,k16_cqc_sim1), []). fof(dt_k1_card_1,axiom,( ! [A] : v1_card_1(k1_card_1(A)) ), file(card_1,k1_card_1), []). fof(dt_k1_cqc_sim1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,A,k7_cqc_lang) & m1_relset_1(B,A,k7_cqc_lang) ) => m2_fraenkel(k1_cqc_sim1(A,B),A,k7_cqc_lang,k1_fraenkel(A,k7_cqc_lang)) ) ), file(cqc_sim1,k1_cqc_sim1), []). fof(dt_k1_domain_1,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(C,A) & m1_subset_1(D,B) ) => m1_subset_1(k1_domain_1(A,B,C,D),k2_zfmisc_1(A,B)) ) ), file(domain_1,k1_domain_1), []). fof(dt_k1_finsub_1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v4_finsub_1(A) & m1_subset_1(B,A) & m1_subset_1(C,A) ) => m1_subset_1(k1_finsub_1(A,B,C),A) ) ), file(finsub_1,k1_finsub_1), []). fof(dt_k1_fraenkel,axiom,( ! [A,B] : ( ~ v1_xboole_0(B) => m1_fraenkel(k1_fraenkel(A,B),A,B) ) ), file(fraenkel,k1_fraenkel), []). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). fof(dt_k1_funct_2,axiom,( $true ), file(funct_2,k1_funct_2), []). fof(dt_k1_funct_4,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => ( v1_relat_1(k1_funct_4(A,B)) & v1_funct_1(k1_funct_4(A,B)) ) ) ), file(funct_4,k1_funct_4), []). fof(dt_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => m2_subset_1(k1_nat_1(A,B),k1_numbers,k5_numbers) ) ), file(nat_1,k1_nat_1), []). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), []). fof(dt_k1_qc_lang1,axiom,( $true ), file(qc_lang1,k1_qc_lang1), []). fof(dt_k1_qc_lang3,axiom,( ! [A,B] : ( ( m1_finseq_1(A,k1_qc_lang1) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_qc_lang1)) ) => m1_subset_1(k1_qc_lang3(A,B),k1_zfmisc_1(B)) ) ), file(qc_lang3,k1_qc_lang3), []). fof(dt_k1_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), []). fof(dt_k1_setwiseo,axiom,( ! [A] : ( v1_xboole_0(k1_setwiseo(A)) & m1_subset_1(k1_setwiseo(A),k5_finsub_1(A)) ) ), file(setwiseo,k1_setwiseo), []). fof(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), []). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), []). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), []). fof(dt_k22_qc_lang1,axiom,( ! [A] : ( m1_finseq_1(A,k1_qc_lang1) => m1_subset_1(k22_qc_lang1(A),k1_zfmisc_1(k2_qc_lang1)) ) ), file(qc_lang1,k22_qc_lang1), []). fof(dt_k23_qc_lang1,axiom,( ! [A] : ( m1_subset_1(A,k2_qc_lang1) => m1_subset_1(k23_qc_lang1(A),k1_zfmisc_1(k2_qc_lang1)) ) ), file(qc_lang1,k23_qc_lang1), []). fof(dt_k24_qc_lang1,axiom,( ! [A] : ( m1_subset_1(A,k8_qc_lang1) => m1_subset_1(k24_qc_lang1(A),k1_zfmisc_1(k2_qc_lang1)) ) ), file(qc_lang1,k24_qc_lang1), []). fof(dt_k2_cqc_sim1,axiom,( ! [A,B,C] : ( ( v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang) & m1_relset_1(A,k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang) & v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang) & m1_relset_1(B,k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang) & m1_subset_1(C,k5_numbers) ) => m2_fraenkel(k2_cqc_sim1(A,B,C),k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang,k1_fraenkel(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang)) ) ), file(cqc_sim1,k2_cqc_sim1), []). fof(dt_k2_funcop_1,axiom,( $true ), file(funcop_1,k2_funcop_1), []). fof(dt_k2_funct_2,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) ) => m1_subset_1(k2_funct_2(A,B,C,D),k1_zfmisc_1(B)) ) ), file(funct_2,k2_funct_2), []). fof(dt_k2_qc_lang1,axiom,( m1_subset_1(k2_qc_lang1,k1_zfmisc_1(k1_qc_lang1)) ), file(qc_lang1,k2_qc_lang1), []). fof(dt_k2_qc_lang3,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => m2_subset_1(k2_qc_lang3(A),k1_qc_lang1,k2_qc_lang1) ) ), file(qc_lang3,k2_qc_lang3), []). fof(dt_k2_tarski,axiom,( $true ), file(tarski,k2_tarski), []). fof(dt_k2_xboole_0,axiom,( $true ), file(xboole_0,k2_xboole_0), []). fof(dt_k2_xcmplx_0,axiom,( $true ), file(xcmplx_0,k2_xcmplx_0), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). fof(dt_k3_cqc_sim1,axiom,( ! [A,B] : ( ( v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang) & m1_relset_1(A,k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang) & m1_subset_1(B,k2_qc_lang1) ) => m2_fraenkel(k3_cqc_sim1(A,B),k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang,k1_fraenkel(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang)) ) ), file(cqc_sim1,k3_cqc_sim1), []). fof(dt_k3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers) ) ), file(finseq_1,k3_finseq_1), []). fof(dt_k4_cqc_sim1,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & v1_cqc_lang(B,A) & m1_qc_lang1(B,A) & m1_subset_1(C,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)) ) => ( v1_cqc_lang(k4_cqc_sim1(A,B,C),A) & m1_qc_lang1(k4_cqc_sim1(A,B,C),A) ) ) ), file(cqc_sim1,k4_cqc_sim1), []). fof(dt_k4_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m1_subset_1(k4_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ), file(finseq_1,k4_finseq_1), []). fof(dt_k4_mcart_1,axiom,( $true ), file(mcart_1,k4_mcart_1), []). fof(dt_k4_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(relset_1,k4_relset_1), []). 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)) ) ), file(subset_1,k4_subset_1), []). fof(dt_k4_tarski,axiom,( $true ), file(tarski,k4_tarski), []). fof(dt_k4_xboole_0,axiom,( $true ), file(xboole_0,k4_xboole_0), []). fof(dt_k4_zfmisc_1,axiom,( $true ), file(zfmisc_1,k4_zfmisc_1), []). fof(dt_k5_cqc_sim1,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k7_qc_lang1(A)) & v1_cqc_lang(C,A) & m1_qc_lang1(C,A) ) => m2_fraenkel(k5_cqc_sim1(A,B,C),k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang,k1_fraenkel(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang)) ) ), file(cqc_sim1,k5_cqc_sim1), []). fof(dt_k5_finsub_1,axiom,( ! [A] : v4_finsub_1(k5_finsub_1(A)) ), file(finsub_1,k5_finsub_1), []). fof(dt_k5_numbers,axiom,( m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ), file(numbers,k5_numbers), []). fof(dt_k5_ordinal2,axiom,( $true ), file(ordinal2,k5_ordinal2), []). fof(dt_k5_qc_lang1,axiom,( $true ), file(qc_lang1,k5_qc_lang1), []). fof(dt_k5_relat_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => v1_relat_1(k5_relat_1(A,B)) ) ), file(relat_1,k5_relat_1), []). fof(dt_k5_setwiseo,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k5_finsub_1(A)) & m1_subset_1(C,k5_finsub_1(A)) ) => m1_subset_1(k5_setwiseo(A,B,C),k5_finsub_1(A)) ) ), file(setwiseo,k5_setwiseo), []). fof(dt_k6_cqc_sim1,axiom,( ! [A] : ( m1_subset_1(A,k7_cqc_lang) => m2_subset_1(k6_cqc_sim1(A),k1_numbers,k5_numbers) ) ), file(cqc_sim1,k6_cqc_sim1), []). fof(dt_k6_relat_1,axiom,( ! [A] : v1_relat_1(k6_relat_1(A)) ), file(relat_1,k6_relat_1), []). fof(dt_k6_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(k6_subset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(subset_1,k6_subset_1), []). fof(dt_k7_cqc_lang,axiom,( m1_subset_1(k7_cqc_lang,k1_zfmisc_1(k8_qc_lang1)) ), file(cqc_lang,k7_cqc_lang), []). fof(dt_k7_cqc_sim1,axiom,( ! [A,B] : ( ( v1_funct_1(A) & v1_funct_2(A,k7_cqc_lang,k1_fraenkel(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang)) & m1_relset_1(A,k7_cqc_lang,k1_fraenkel(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang)) & m1_subset_1(B,k7_cqc_lang) ) => m2_fraenkel(k7_cqc_sim1(A,B),k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang,k1_fraenkel(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang)) ) ), file(cqc_sim1,k7_cqc_sim1), []). fof(dt_k7_qc_lang1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => m1_subset_1(k7_qc_lang1(A),k1_zfmisc_1(k5_qc_lang1)) ) ), file(qc_lang1,k7_qc_lang1), []). fof(dt_k8_cqc_lang,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k7_qc_lang1(A)) & v1_cqc_lang(C,A) & m1_qc_lang1(C,A) ) => m2_subset_1(k8_cqc_lang(A,B,C),k8_qc_lang1,k7_cqc_lang) ) ), file(cqc_lang,k8_cqc_lang), []). fof(dt_k8_cqc_sim1,axiom, ( v1_funct_1(k8_cqc_sim1) & v1_funct_2(k8_cqc_sim1,k7_cqc_lang,k1_fraenkel(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang)) & m2_relset_1(k8_cqc_sim1,k7_cqc_lang,k1_fraenkel(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang)) ), file(cqc_sim1,k8_cqc_sim1), []). fof(dt_k8_funct_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,A) ) => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ), file(funct_2,k8_funct_2), []). fof(dt_k8_qc_lang1,axiom,( ~ v1_xboole_0(k8_qc_lang1) ), file(qc_lang1,k8_qc_lang1), []). fof(dt_k9_cqc_lang,axiom,( m2_subset_1(k9_cqc_lang,k8_qc_lang1,k7_cqc_lang) ), file(cqc_lang,k9_cqc_lang), []). fof(dt_k9_cqc_sim1,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k7_cqc_lang) & m1_subset_1(B,k5_numbers) & m1_subset_1(C,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)) ) => m2_subset_1(k9_cqc_sim1(A,B,C),k8_qc_lang1,k7_cqc_lang) ) ), file(cqc_sim1,k9_cqc_sim1), []). fof(dt_k9_qc_lang1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_qc_lang1) & m1_finseq_1(B,k1_qc_lang1) ) => m1_subset_1(k9_qc_lang1(A,B),k8_qc_lang1) ) ), file(qc_lang1,k9_qc_lang1), []). fof(dt_k9_relat_1,axiom,( $true ), file(relat_1,k9_relat_1), []). 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) ) ) ), file(finseq_1,m1_finseq_1), []). fof(dt_m1_fraenkel,axiom,( ! [A,B,C] : ( m1_fraenkel(C,A,B) => ( ~ v1_xboole_0(C) & v1_fraenkel(C) ) ) ), file(fraenkel,m1_fraenkel), []). fof(dt_m1_qc_lang1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ! [B] : ( m1_qc_lang1(B,A) => m2_finseq_1(B,k1_qc_lang1) ) ) ), file(qc_lang1,m1_qc_lang1), []). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), []). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), []). fof(dt_m2_finseq_1,axiom,( ! [A,B] : ( m2_finseq_1(B,A) => ( v1_funct_1(B) & v1_finseq_1(B) & m2_relset_1(B,k5_numbers,A) ) ) ), file(finseq_1,m2_finseq_1), []). fof(dt_m2_fraenkel,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(B) & m1_fraenkel(C,A,B) ) => ! [D] : ( m2_fraenkel(D,A,B,C) => ( v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) ) ) ) ), file(fraenkel,m2_fraenkel), []). fof(dt_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ), file(relset_1,m2_relset_1), []). 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) ) ) ), file(subset_1,m2_subset_1), []). fof(existence_m1_finseq_1,axiom,( ! [A] : ? [B] : m1_finseq_1(B,A) ), file(finseq_1,m1_finseq_1), []). fof(existence_m1_fraenkel,axiom,( ! [A,B] : ? [C] : m1_fraenkel(C,A,B) ), file(fraenkel,m1_fraenkel), []). fof(existence_m1_qc_lang1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ? [B] : m1_qc_lang1(B,A) ) ), file(qc_lang1,m1_qc_lang1), []). fof(existence_m1_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), []). fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), []). fof(existence_m2_finseq_1,axiom,( ! [A] : ? [B] : m2_finseq_1(B,A) ), file(finseq_1,m2_finseq_1), []). fof(existence_m2_fraenkel,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(B) & m1_fraenkel(C,A,B) ) => ? [D] : m2_fraenkel(D,A,B,C) ) ), file(fraenkel,m2_fraenkel), []). fof(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), []). 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) ) ), file(subset_1,m2_subset_1), []). fof(fc10_membered,axiom,( ! [A] : ( v1_int_1(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) ) ) ), file(membered,fc10_membered), []). fof(fc11_membered,axiom,( ! [A] : ( v4_ordinal2(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) & v5_membered(k1_tarski(A)) ) ) ), file(membered,fc11_membered), []). fof(fc12_membered,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => v1_membered(k2_tarski(A,B)) ) ), file(membered,fc12_membered), []). fof(fc13_membered,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) ) ) ), file(membered,fc13_membered), []). fof(fc14_membered,axiom,( ! [A,B] : ( ( v1_rat_1(A) & v1_rat_1(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) ) ) ), file(membered,fc14_membered), []). fof(fc15_membered,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) ) ) ), file(membered,fc15_membered), []). fof(fc16_membered,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) & v5_membered(k2_tarski(A,B)) ) ) ), file(membered,fc16_membered), []). fof(fc17_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) => v1_finset_1(k1_relat_1(A)) ) ), file(finseq_1,fc17_finseq_1), []). fof(fc1_cqc_sim1,axiom,( ! [A] : ( m1_subset_1(A,k7_cqc_lang) => ( ~ v1_xboole_0(k11_cqc_sim1(A)) & v1_membered(k11_cqc_sim1(A)) & v2_membered(k11_cqc_sim1(A)) & v3_membered(k11_cqc_sim1(A)) & v4_membered(k11_cqc_sim1(A)) & v5_membered(k11_cqc_sim1(A)) ) ) ), file(cqc_sim1,fc1_cqc_sim1), []). fof(fc1_finsub_1,axiom,( ! [A] : ( ~ v1_xboole_0(k1_zfmisc_1(A)) & v1_finsub_1(k1_zfmisc_1(A)) & v3_finsub_1(k1_zfmisc_1(A)) & v4_finsub_1(k1_zfmisc_1(A)) ) ), file(finsub_1,fc1_finsub_1), []). fof(fc1_funcop_1,axiom,( ! [A,B] : ( v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) ) ), file(funcop_1,fc1_funcop_1), []). fof(fc1_funct_2,axiom,( ! [A,B] : ( ~ v1_xboole_0(B) => ~ v1_xboole_0(k1_funct_2(A,B)) ) ), file(funct_2,fc1_funct_2), []). fof(fc1_ordinal2,axiom, ( v1_ordinal1(k5_ordinal2) & v2_ordinal1(k5_ordinal2) & v3_ordinal1(k5_ordinal2) & ~ v1_xboole_0(k5_ordinal2) ), file(ordinal2,fc1_ordinal2), []). fof(fc1_qc_lang1,axiom,( ~ v1_xboole_0(k1_qc_lang1) ), file(qc_lang1,fc1_qc_lang1), []). fof(fc1_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ), file(subset_1,fc1_subset_1), []). fof(fc22_membered,axiom,( ! [A,B] : ( ( v1_membered(A) & v1_membered(B) ) => v1_membered(k2_xboole_0(A,B)) ) ), file(membered,fc22_membered), []). fof(fc23_membered,axiom,( ! [A,B] : ( ( v2_membered(A) & v2_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc23_membered), []). fof(fc24_membered,axiom,( ! [A,B] : ( ( v3_membered(A) & v3_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc24_membered), []). fof(fc25_membered,axiom,( ! [A,B] : ( ( v4_membered(A) & v4_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc25_membered), []). fof(fc26_membered,axiom,( ! [A,B] : ( ( v5_membered(A) & v5_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) & v5_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc26_membered), []). fof(fc2_cqc_lang,axiom,( ~ v1_xboole_0(k7_cqc_lang) ), file(cqc_lang,fc2_cqc_lang), []). fof(fc2_finseq_1,axiom, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) & v1_funct_1(k1_xboole_0) & v2_funct_1(k1_xboole_0) & v1_finset_1(k1_xboole_0) & v1_finseq_1(k1_xboole_0) ), file(finseq_1,fc2_finseq_1), []). fof(fc2_finsub_1,axiom,( ! [A] : ( ~ v1_xboole_0(k5_finsub_1(A)) & v1_finsub_1(k5_finsub_1(A)) & v3_finsub_1(k5_finsub_1(A)) & v4_finsub_1(k5_finsub_1(A)) ) ), file(finsub_1,fc2_finsub_1), []). fof(fc2_funcop_1,axiom,( ! [A] : ( v1_xboole_0(k2_funcop_1(k1_xboole_0,A)) & v1_relat_1(k2_funcop_1(k1_xboole_0,A)) & v1_funct_1(k2_funcop_1(k1_xboole_0,A)) & v2_funct_1(k2_funcop_1(k1_xboole_0,A)) ) ), file(funcop_1,fc2_funcop_1), []). fof(fc2_funct_2,axiom,( ! [A] : ~ v1_xboole_0(k1_funct_2(A,A)) ), file(funct_2,fc2_funct_2), []). fof(fc2_membered,axiom, ( ~ v1_xboole_0(k1_numbers) & v1_membered(k1_numbers) & v2_membered(k1_numbers) ), file(membered,fc2_membered), []). fof(fc2_partfun1,axiom,( ! [A] : ( v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)) & v8_relat_2(k6_relat_1(A)) ) ), file(partfun1,fc2_partfun1), []). fof(fc2_qc_lang1,axiom,( ~ v1_xboole_0(k2_qc_lang1) ), file(qc_lang1,fc2_qc_lang1), []). fof(fc2_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) ), file(subset_1,fc2_subset_1), []). fof(fc37_membered,axiom,( ! [A,B] : ( v1_membered(A) => v1_membered(k4_xboole_0(A,B)) ) ), file(membered,fc37_membered), []). fof(fc38_membered,axiom,( ! [A,B] : ( v2_membered(A) => ( v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) ) ) ), file(membered,fc38_membered), []). fof(fc39_membered,axiom,( ! [A,B] : ( v3_membered(A) => ( v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) ) ) ), file(membered,fc39_membered), []). fof(fc3_funcop_1,axiom,( ! [A,B] : ( v1_xboole_0(B) => ( v1_xboole_0(k2_funcop_1(B,A)) & v1_relat_1(k2_funcop_1(B,A)) & v1_funct_1(k2_funcop_1(B,A)) & v2_funct_1(k2_funcop_1(B,A)) ) ) ), file(funcop_1,fc3_funcop_1), []). fof(fc3_subset_1,axiom,( ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ), file(subset_1,fc3_subset_1), []). fof(fc40_membered,axiom,( ! [A,B] : ( v4_membered(A) => ( v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) & v4_membered(k4_xboole_0(A,B)) ) ) ), file(membered,fc40_membered), []). fof(fc41_membered,axiom,( ! [A,B] : ( v5_membered(A) => ( v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) & v4_membered(k4_xboole_0(A,B)) & v5_membered(k4_xboole_0(A,B)) ) ) ), file(membered,fc41_membered), []). fof(fc4_ordinal2,axiom,( ! [A,B] : ( v3_ordinal1(B) => ( v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v1_ordinal2(k2_funcop_1(A,B)) ) ) ), file(ordinal2,fc4_ordinal2), []). fof(fc4_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ), file(subset_1,fc4_subset_1), []). fof(fc5_membered,axiom, ( v1_membered(k5_ordinal2) & v2_membered(k5_ordinal2) & v3_membered(k5_ordinal2) & v4_membered(k5_ordinal2) & v5_membered(k5_ordinal2) ), file(membered,fc5_membered), []). fof(fc5_qc_lang1,axiom,( ~ v1_xboole_0(k5_qc_lang1) ), file(qc_lang1,fc5_qc_lang1), []). fof(fc6_membered,axiom, ( v1_xboole_0(k1_xboole_0) & v1_membered(k1_xboole_0) & v2_membered(k1_xboole_0) & v3_membered(k1_xboole_0) & v4_membered(k1_xboole_0) & v5_membered(k1_xboole_0) ), file(membered,fc6_membered), []). fof(fc6_qc_lang1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ~ v1_xboole_0(k7_qc_lang1(A)) ) ), file(qc_lang1,fc6_qc_lang1), []). fof(fc6_subset_1,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & ~ v1_xboole_0(D) ) => ~ v1_xboole_0(k4_zfmisc_1(A,B,C,D)) ) ), file(subset_1,fc6_subset_1), []). fof(fc7_membered,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_membered(k1_tarski(A)) ) ), file(membered,fc7_membered), []). fof(fc8_membered,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) ) ) ), file(membered,fc8_membered), []). fof(fc9_funcop_1,axiom,( ! [A,B] : ( ~ v1_xboole_0(B) => ( v1_relat_1(k2_funcop_1(A,B)) & v2_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) ) ) ), file(funcop_1,fc9_funcop_1), []). fof(fc9_membered,axiom,( ! [A] : ( v1_rat_1(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) ) ) ), file(membered,fc9_membered), []). fof(fraenkel_a_1_4_cqc_sim1,axiom,( ! [A,B] : ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) => ( r2_hidden(A,a_1_4_cqc_sim1(B)) <=> ? [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) & A = C & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ~ ( r1_xreal_0(C,D) & r2_hidden(k2_qc_lang3(D),k24_qc_lang1(B)) ) ) ) ) ) ), file(cqc_sim1,a_1_4_cqc_sim1), []). fof(fraenkel_a_2_0_qc_lang3,axiom,( ! [A,B,C] : ( ( m2_finseq_1(B,k1_qc_lang1) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_qc_lang1)) ) => ( r2_hidden(A,a_2_0_qc_lang3(B,C)) <=> ? [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) & A = k1_funct_1(B,D) & r1_xreal_0(1,D) & r1_xreal_0(D,k3_finseq_1(B)) & r2_hidden(k1_funct_1(B,D),C) ) ) ) ), file(qc_lang3,a_2_0_qc_lang3), []). fof(fraenkel_a_2_2_cqc_sim1,axiom,( ! [A,B,C] : ( ( m2_subset_1(B,k1_numbers,k5_numbers) & v1_cqc_lang(C,B) & m1_qc_lang1(C,B) ) => ( r2_hidden(A,a_2_2_cqc_sim1(B,C)) <=> ? [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) & A = k1_funct_1(C,D) & r1_xreal_0(1,D) & r1_xreal_0(D,k3_finseq_1(C)) & r2_hidden(k1_funct_1(C,D),k2_qc_lang1) ) ) ) ), file(cqc_sim1,a_2_2_cqc_sim1), []). fof(fraenkel_a_3_0_cqc_sim1,axiom,( ! [A,B,C,D] : ( ( m2_subset_1(B,k1_numbers,k5_numbers) & v1_cqc_lang(C,B) & m1_qc_lang1(C,B) & m2_fraenkel(D,k2_qc_lang1,k2_qc_lang1,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)) ) => ( r2_hidden(A,a_3_0_cqc_sim1(B,C,D)) <=> ? [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) & A = k1_funct_1(k4_cqc_sim1(B,C,D),E) & r1_xreal_0(1,E) & r1_xreal_0(E,k3_finseq_1(k4_cqc_sim1(B,C,D))) & r2_hidden(k1_funct_1(k4_cqc_sim1(B,C,D),E),k2_qc_lang1) ) ) ) ), file(cqc_sim1,a_3_0_cqc_sim1), []). fof(idempotence_k1_finsub_1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v4_finsub_1(A) & m1_subset_1(B,A) & m1_subset_1(C,A) ) => k1_finsub_1(A,B,B) = B ) ), file(finsub_1,k1_finsub_1), []). fof(idempotence_k1_funct_4,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => k1_funct_4(A,A) = A ) ), file(funct_4,k1_funct_4), []). fof(idempotence_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,A) = A ), file(xboole_0,k2_xboole_0), []). 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 ) ), file(subset_1,k4_subset_1), []). fof(idempotence_k5_setwiseo,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k5_finsub_1(A)) & m1_subset_1(C,k5_finsub_1(A)) ) => k5_setwiseo(A,B,B) = B ) ), file(setwiseo,k5_setwiseo), []). fof(l16_cqc_sim1,axiom,( ! [A] : ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_fraenkel(C,k2_qc_lang1,k2_qc_lang1,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)) => ( v1_funct_1(k1_funct_4(C,k2_funcop_1(k23_qc_lang1(A),k2_qc_lang3(B)))) & v1_funct_2(k1_funct_4(C,k2_funcop_1(k23_qc_lang1(A),k2_qc_lang3(B))),k2_qc_lang1,k2_qc_lang1) & m2_relset_1(k1_funct_4(C,k2_funcop_1(k23_qc_lang1(A),k2_qc_lang3(B))),k2_qc_lang1,k2_qc_lang1) ) ) ) ) ), file(cqc_sim1,l16_cqc_sim1), []). fof(rc1_arytm_3,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ), file(arytm_3,rc1_arytm_3), []). fof(rc1_cqc_lang,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ? [B] : ( m1_qc_lang1(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_cqc_lang(B,A) ) ) ), file(cqc_lang,rc1_cqc_lang), []). fof(rc1_finseq_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc1_finseq_1), []). fof(rc1_funct_2,axiom,( ! [A,B] : ? [C] : ( m1_relset_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C) & v1_funct_2(C,A,B) ) ), file(funct_2,rc1_funct_2), []). fof(rc1_membered,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ), file(membered,rc1_membered), []). fof(rc1_partfun1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_xboole_0(A) ) ), file(partfun1,rc1_partfun1), []). fof(rc1_subset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) ) ) ), file(subset_1,rc1_subset_1), []). fof(rc2_finseq_1,axiom,( ! [A] : ? [B] : ( m1_relset_1(B,k5_numbers,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc2_finseq_1), []). fof(rc2_funct_2,axiom,( ! [A] : ? [B] : ( m1_relset_1(B,A,A) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_funct_2(B,A,A) & v2_funct_2(B,A,A) & v3_funct_2(B,A,A) ) ), file(funct_2,rc2_funct_2), []). fof(rc2_partfun1,axiom,( ! [A,B] : ? [C] : ( m1_relset_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C) ) ), file(partfun1,rc2_partfun1), []). fof(rc2_subset_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) ) ), file(subset_1,rc2_subset_1), []). fof(rc3_finseq_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc3_finseq_1), []). fof(rc3_partfun1,axiom,( ! [A] : ? [B] : ( m1_relset_1(B,A,A) & v1_relat_1(B) & v1_relat_2(B) & v3_relat_2(B) & v4_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) ) ), file(partfun1,rc3_partfun1), []). fof(rc4_finseq_1,axiom,( ! [A] : ? [B] : ( m1_finseq_1(B,A) & v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc4_finseq_1), []). fof(rc6_finseq_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc6_finseq_1), []). fof(rc7_finseq_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc7_finseq_1), []). fof(rc8_finseq_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc8_finseq_1), []). fof(redefinition_k10_cqc_lang,axiom,( ! [A] : ( m1_subset_1(A,k7_cqc_lang) => k10_cqc_lang(A) = k12_qc_lang1(A) ) ), file(cqc_lang,k10_cqc_lang), []). fof(redefinition_k11_cqc_lang,axiom,( ! [A,B] : ( ( m1_subset_1(A,k7_cqc_lang) & m1_subset_1(B,k7_cqc_lang) ) => k11_cqc_lang(A,B) = k13_qc_lang1(A,B) ) ), file(cqc_lang,k11_cqc_lang), []). fof(redefinition_k13_cqc_sim1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k13_cqc_sim1(A) = k6_relat_1(A) ) ), file(cqc_sim1,k13_cqc_sim1), []). fof(redefinition_k15_cqc_lang,axiom,( ! [A,B] : ( ( m1_subset_1(A,k2_qc_lang1) & m1_subset_1(B,k7_cqc_lang) ) => k15_cqc_lang(A,B) = k14_qc_lang1(A,B) ) ), file(cqc_lang,k15_cqc_lang), []). fof(redefinition_k15_cqc_sim1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => k15_cqc_sim1(A,B) = k1_tarski(B) ) ), file(cqc_sim1,k15_cqc_sim1), []). fof(redefinition_k1_domain_1,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(C,A) & m1_subset_1(D,B) ) => k1_domain_1(A,B,C,D) = k4_tarski(C,D) ) ), file(domain_1,k1_domain_1), []). fof(redefinition_k1_finsub_1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v4_finsub_1(A) & m1_subset_1(B,A) & m1_subset_1(C,A) ) => k1_finsub_1(A,B,C) = k2_xboole_0(B,C) ) ), file(finsub_1,k1_finsub_1), []). fof(redefinition_k1_fraenkel,axiom,( ! [A,B] : ( ~ v1_xboole_0(B) => k1_fraenkel(A,B) = k1_funct_2(A,B) ) ), file(fraenkel,k1_fraenkel), []). fof(redefinition_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k1_nat_1(A,B) = k2_xcmplx_0(A,B) ) ), file(nat_1,k1_nat_1), []). fof(redefinition_k23_qc_lang1,axiom,( ! [A] : ( m1_subset_1(A,k2_qc_lang1) => k23_qc_lang1(A) = k1_tarski(A) ) ), file(qc_lang1,k23_qc_lang1), []). fof(redefinition_k2_funct_2,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) ) => k2_funct_2(A,B,C,D) = k9_relat_1(C,D) ) ), file(funct_2,k2_funct_2), []). 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) ) ), file(finseq_1,k3_finseq_1), []). fof(redefinition_k4_cqc_sim1,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & v1_cqc_lang(B,A) & m1_qc_lang1(B,A) & m1_subset_1(C,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)) ) => k4_cqc_sim1(A,B,C) = k5_relat_1(B,C) ) ), file(cqc_sim1,k4_cqc_sim1), []). fof(redefinition_k4_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k4_finseq_1(A) = k1_relat_1(A) ) ), file(finseq_1,k4_finseq_1), []). fof(redefinition_k4_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => k4_relset_1(A,B,C) = k1_relat_1(C) ) ), file(relset_1,k4_relset_1), []). 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) ) ), file(subset_1,k4_subset_1), []). fof(redefinition_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_k5_setwiseo,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k5_finsub_1(A)) & m1_subset_1(C,k5_finsub_1(A)) ) => k5_setwiseo(A,B,C) = k2_xboole_0(B,C) ) ), file(setwiseo,k5_setwiseo), []). fof(redefinition_k6_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k6_subset_1(A,B,C) = k4_xboole_0(B,C) ) ), file(subset_1,k6_subset_1), []). fof(redefinition_k7_cqc_sim1,axiom,( ! [A,B] : ( ( v1_funct_1(A) & v1_funct_2(A,k7_cqc_lang,k1_fraenkel(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang)) & m1_relset_1(A,k7_cqc_lang,k1_fraenkel(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang)) & m1_subset_1(B,k7_cqc_lang) ) => k7_cqc_sim1(A,B) = k1_funct_1(A,B) ) ), file(cqc_sim1,k7_cqc_sim1), []). fof(redefinition_k8_cqc_lang,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k7_qc_lang1(A)) & v1_cqc_lang(C,A) & m1_qc_lang1(C,A) ) => k8_cqc_lang(A,B,C) = k9_qc_lang1(B,C) ) ), file(cqc_lang,k8_cqc_lang), []). fof(redefinition_k8_funct_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,A) ) => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ), file(funct_2,k8_funct_2), []). fof(redefinition_k9_cqc_lang,axiom,( k9_cqc_lang = k11_qc_lang1 ), file(cqc_lang,k9_cqc_lang), []). fof(redefinition_m2_finseq_1,axiom,( ! [A,B] : ( m2_finseq_1(B,A) <=> m1_finseq_1(B,A) ) ), file(finseq_1,m2_finseq_1), []). fof(redefinition_m2_fraenkel,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(B) & m1_fraenkel(C,A,B) ) => ! [D] : ( m2_fraenkel(D,A,B,C) <=> m1_subset_1(D,C) ) ) ), file(fraenkel,m2_fraenkel), []). fof(redefinition_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) <=> m1_relset_1(C,A,B) ) ), file(relset_1,m2_relset_1), []). 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) ) ) ), file(subset_1,m2_subset_1), []). fof(reflexivity_r1_tarski,axiom,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), []). fof(reflexivity_r1_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => r1_xreal_0(A,A) ) ), file(xreal_0,r1_xreal_0), []). fof(s5_cqc_sim1__e7_69__cqc_sim1,axiom,( ! [A] : ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) => ( ( ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m1_subset_1(C,k5_finsub_1(k2_qc_lang1)) => ! [D] : ( m2_fraenkel(D,k2_qc_lang1,k2_qc_lang1,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)) => ( r2_hidden(k4_mcart_1(k9_cqc_lang,B,C,D),k16_cqc_sim1(A)) => k2_funct_2(k2_qc_lang1,k2_qc_lang1,D,k24_qc_lang1(k9_cqc_lang)) = k24_qc_lang1(k8_funct_2(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang,k7_cqc_sim1(k8_cqc_sim1,k9_cqc_lang),k1_domain_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1),B,D))) ) ) ) ) & ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ! [F] : ( ( v1_cqc_lang(F,E) & m1_qc_lang1(F,E) ) => ! [G] : ( m2_subset_1(G,k5_qc_lang1,k7_qc_lang1(E)) => ! [H] : ( m2_subset_1(H,k1_numbers,k5_numbers) => ! [I] : ( m1_subset_1(I,k5_finsub_1(k2_qc_lang1)) => ! [J] : ( m2_fraenkel(J,k2_qc_lang1,k2_qc_lang1,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)) => ( r2_hidden(k4_mcart_1(k8_cqc_lang(E,G,F),H,I,J),k16_cqc_sim1(A)) => k2_funct_2(k2_qc_lang1,k2_qc_lang1,J,k24_qc_lang1(k8_cqc_lang(E,G,F))) = k24_qc_lang1(k8_funct_2(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang,k7_cqc_sim1(k8_cqc_sim1,k8_cqc_lang(E,G,F)),k1_domain_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1),H,J))) ) ) ) ) ) ) ) & ! [E] : ( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang) => ( ! [K] : ( m2_subset_1(K,k1_numbers,k5_numbers) => ! [L] : ( m1_subset_1(L,k5_finsub_1(k2_qc_lang1)) => ! [M] : ( m2_fraenkel(M,k2_qc_lang1,k2_qc_lang1,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)) => ( r2_hidden(k4_mcart_1(E,K,L,M),k16_cqc_sim1(A)) => k2_funct_2(k2_qc_lang1,k2_qc_lang1,M,k24_qc_lang1(E)) = k24_qc_lang1(k8_funct_2(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang,k7_cqc_sim1(k8_cqc_sim1,E),k1_domain_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1),K,M))) ) ) ) ) => ! [N] : ( m2_subset_1(N,k1_numbers,k5_numbers) => ! [O] : ( m1_subset_1(O,k5_finsub_1(k2_qc_lang1)) => ! [P] : ( m2_fraenkel(P,k2_qc_lang1,k2_qc_lang1,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)) => ( r2_hidden(k4_mcart_1(k10_cqc_lang(E),N,O,P),k16_cqc_sim1(A)) => k2_funct_2(k2_qc_lang1,k2_qc_lang1,P,k24_qc_lang1(k10_cqc_lang(E))) = k24_qc_lang1(k8_funct_2(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang,k7_cqc_sim1(k8_cqc_sim1,k10_cqc_lang(E)),k1_domain_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1),N,P))) ) ) ) ) ) ) & ! [E] : ( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang) => ! [F] : ( m2_subset_1(F,k8_qc_lang1,k7_cqc_lang) => ( ( ! [Q] : ( m2_subset_1(Q,k1_numbers,k5_numbers) => ! [R] : ( m1_subset_1(R,k5_finsub_1(k2_qc_lang1)) => ! [S] : ( m2_fraenkel(S,k2_qc_lang1,k2_qc_lang1,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)) => ( r2_hidden(k4_mcart_1(E,Q,R,S),k16_cqc_sim1(A)) => k2_funct_2(k2_qc_lang1,k2_qc_lang1,S,k24_qc_lang1(E)) = k24_qc_lang1(k8_funct_2(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang,k7_cqc_sim1(k8_cqc_sim1,E),k1_domain_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1),Q,S))) ) ) ) ) & ! [T] : ( m2_subset_1(T,k1_numbers,k5_numbers) => ! [U] : ( m1_subset_1(U,k5_finsub_1(k2_qc_lang1)) => ! [V] : ( m2_fraenkel(V,k2_qc_lang1,k2_qc_lang1,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)) => ( r2_hidden(k4_mcart_1(F,T,U,V),k16_cqc_sim1(A)) => k2_funct_2(k2_qc_lang1,k2_qc_lang1,V,k24_qc_lang1(F)) = k24_qc_lang1(k8_funct_2(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang,k7_cqc_sim1(k8_cqc_sim1,F),k1_domain_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1),T,V))) ) ) ) ) ) => ! [W] : ( m2_subset_1(W,k1_numbers,k5_numbers) => ! [X] : ( m1_subset_1(X,k5_finsub_1(k2_qc_lang1)) => ! [Y] : ( m2_fraenkel(Y,k2_qc_lang1,k2_qc_lang1,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)) => ( r2_hidden(k4_mcart_1(k11_cqc_lang(E,F),W,X,Y),k16_cqc_sim1(A)) => k2_funct_2(k2_qc_lang1,k2_qc_lang1,Y,k24_qc_lang1(k11_cqc_lang(E,F))) = k24_qc_lang1(k8_funct_2(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang,k7_cqc_sim1(k8_cqc_sim1,k11_cqc_lang(E,F)),k1_domain_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1),W,Y))) ) ) ) ) ) ) ) & ! [E] : ( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang) => ! [F] : ( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) => ( ! [Z] : ( m2_subset_1(Z,k1_numbers,k5_numbers) => ! [A1] : ( m1_subset_1(A1,k5_finsub_1(k2_qc_lang1)) => ! [B1] : ( m2_fraenkel(B1,k2_qc_lang1,k2_qc_lang1,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)) => ( r2_hidden(k4_mcart_1(E,Z,A1,B1),k16_cqc_sim1(A)) => k2_funct_2(k2_qc_lang1,k2_qc_lang1,B1,k24_qc_lang1(E)) = k24_qc_lang1(k8_funct_2(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang,k7_cqc_sim1(k8_cqc_sim1,E),k1_domain_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1),Z,B1))) ) ) ) ) => ! [C1] : ( m2_subset_1(C1,k1_numbers,k5_numbers) => ! [D1] : ( m1_subset_1(D1,k5_finsub_1(k2_qc_lang1)) => ! [E1] : ( m2_fraenkel(E1,k2_qc_lang1,k2_qc_lang1,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)) => ( r2_hidden(k4_mcart_1(k15_cqc_lang(F,E),C1,D1,E1),k16_cqc_sim1(A)) => k2_funct_2(k2_qc_lang1,k2_qc_lang1,E1,k24_qc_lang1(k15_cqc_lang(F,E))) = k24_qc_lang1(k8_funct_2(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang,k7_cqc_sim1(k8_cqc_sim1,k15_cqc_lang(F,E)),k1_domain_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1),C1,E1))) ) ) ) ) ) ) ) ) => ! [E] : ( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang) => ! [F1] : ( m2_subset_1(F1,k1_numbers,k5_numbers) => ! [G1] : ( m1_subset_1(G1,k5_finsub_1(k2_qc_lang1)) => ! [H1] : ( m2_fraenkel(H1,k2_qc_lang1,k2_qc_lang1,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)) => ( r2_hidden(k4_mcart_1(E,F1,G1,H1),k16_cqc_sim1(A)) => k2_funct_2(k2_qc_lang1,k2_qc_lang1,H1,k24_qc_lang1(E)) = k24_qc_lang1(k8_funct_2(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang,k7_cqc_sim1(k8_cqc_sim1,E),k1_domain_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1),F1,H1))) ) ) ) ) ) ) ) ), file(cqc_sim1,s5_cqc_sim1__e7_69__cqc_sim1), []). fof(spc1_boole,axiom,( ~ v1_xboole_0(1) ), file(boole,spc1_boole), []). fof(spc1_numerals,axiom, ( v2_xreal_0(1) & m1_subset_1(1,k5_numbers) ), file(numerals,spc1_numerals), []). fof(t11_funct_2,axiom,( ! [A,B,C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) ) => ( ( B = k1_xboole_0 => A = k1_xboole_0 ) => r2_hidden(C,k1_funct_2(A,B)) ) ) ), file(funct_2,t11_funct_2), []). fof(t11_qc_lang3,axiom,( ! [A] : ( m1_subset_1(A,k8_qc_lang1) => k24_qc_lang1(k12_qc_lang1(A)) = k24_qc_lang1(A) ) ), file(qc_lang3,t11_qc_lang3), []). fof(t13_cqc_sim1,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( ( v1_cqc_lang(B,A) & m1_qc_lang1(B,A) ) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( ( r1_xreal_0(1,C) & r1_xreal_0(C,k3_finseq_1(B)) ) => r2_hidden(k1_funct_1(B,C),k2_qc_lang1) ) ) ) ) ), file(cqc_sim1,t13_cqc_sim1), []). fof(t13_funcop_1,axiom,( ! [A,B,C] : ( r2_hidden(B,A) => k1_funct_1(k2_funcop_1(A,C),B) = C ) ), file(funcop_1,t13_funcop_1), []). fof(t149_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => k9_relat_1(A,k1_xboole_0) = k1_xboole_0 ) ), file(relat_1,t149_relat_1), []). fof(t14_qc_lang3,axiom,( ! [A] : ( m1_subset_1(A,k8_qc_lang1) => ! [B] : ( m1_subset_1(B,k8_qc_lang1) => k24_qc_lang1(k13_qc_lang1(A,B)) = k4_subset_1(k2_qc_lang1,k24_qc_lang1(A),k24_qc_lang1(B)) ) ) ), file(qc_lang3,t14_qc_lang3), []). fof(t153_relat_1,axiom,( ! [A,B,C] : ( v1_relat_1(C) => k9_relat_1(C,k2_xboole_0(A,B)) = k2_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)) ) ), file(relat_1,t153_relat_1), []). fof(t162_funct_1,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => k9_relat_1(k6_relat_1(A),B) = B ) ), file(funct_1,t162_funct_1), []). fof(t16_qc_lang3,axiom,( ! [A] : ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) => ! [B] : ( m1_subset_1(B,k8_qc_lang1) => k24_qc_lang1(k14_qc_lang1(A,B)) = k6_subset_1(k2_qc_lang1,k24_qc_lang1(B),k23_qc_lang1(A)) ) ) ), file(qc_lang3,t16_qc_lang3), []). fof(t1_boole,axiom,( ! [A] : k2_xboole_0(A,k1_xboole_0) = A ), file(boole,t1_boole), []). fof(t1_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & v2_xreal_0(A) ) => v2_xreal_0(B) ) ) ) ), file(real,t1_real), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t23_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(A,k1_relat_1(B)) => k1_funct_1(k5_relat_1(B,C),A) = k1_funct_1(C,k1_funct_1(B,A)) ) ) ) ), file(funct_1,t23_funct_1), []). fof(t27_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v4_ordinal2(B) => ( r2_hidden(B,k4_finseq_1(A)) <=> ( r1_xreal_0(1,B) & r1_xreal_0(B,k3_finseq_1(A)) ) ) ) ) ), file(finseq_3,t27_finseq_3), []). fof(t2_subset,axiom,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), []). fof(t2_tarski,axiom,( ! [A,B] : ( ! [C] : ( r2_hidden(C,A) <=> r2_hidden(C,B) ) => A = B ) ), file(tarski,t2_tarski), []). fof(t31_cqc_sim1,axiom,( ! [A] : ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) => r2_hidden(k4_mcart_1(A,k12_cqc_sim1(A),k1_setwiseo(k2_qc_lang1),k13_cqc_sim1(k2_qc_lang1)),k16_cqc_sim1(A)) ) ), file(cqc_sim1,t31_cqc_sim1), []). fof(t32_cqc_sim1,axiom,( ! [A] : ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) => ! [B] : ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( m1_subset_1(D,k5_finsub_1(k2_qc_lang1)) => ! [E] : ( m2_fraenkel(E,k2_qc_lang1,k2_qc_lang1,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)) => ( r2_hidden(k4_mcart_1(k10_cqc_lang(B),C,D,E),k16_cqc_sim1(A)) => r2_hidden(k4_mcart_1(B,C,D,E),k16_cqc_sim1(A)) ) ) ) ) ) ) ), file(cqc_sim1,t32_cqc_sim1), []). fof(t33_cqc_sim1,axiom,( ! [A] : ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) => ! [B] : ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) => ! [C] : ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ! [E] : ( m1_subset_1(E,k5_finsub_1(k2_qc_lang1)) => ! [F] : ( m2_fraenkel(F,k2_qc_lang1,k2_qc_lang1,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)) => ( r2_hidden(k4_mcart_1(k11_cqc_lang(B,C),D,E,F),k16_cqc_sim1(A)) => ( r2_hidden(k4_mcart_1(B,D,E,F),k16_cqc_sim1(A)) & r2_hidden(k4_mcart_1(C,k1_nat_1(D,k6_cqc_sim1(B)),E,F),k16_cqc_sim1(A)) ) ) ) ) ) ) ) ) ), file(cqc_sim1,t33_cqc_sim1), []). fof(t34_cqc_sim1,axiom,( ! [A] : ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) => ! [B] : ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) => ! [C] : ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ! [E] : ( m1_subset_1(E,k5_finsub_1(k2_qc_lang1)) => ! [F] : ( m2_fraenkel(F,k2_qc_lang1,k2_qc_lang1,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)) => ( r2_hidden(k4_mcart_1(k15_cqc_lang(C,B),D,E,F),k16_cqc_sim1(A)) => r2_hidden(k4_mcart_1(B,k1_nat_1(D,1),k5_setwiseo(k2_qc_lang1,E,k15_cqc_sim1(k2_qc_lang1,C)),k1_funct_4(F,k2_funcop_1(k15_cqc_sim1(k2_qc_lang1,C),k2_qc_lang3(D)))),k16_cqc_sim1(A)) ) ) ) ) ) ) ) ), file(cqc_sim1,t34_cqc_sim1), []). fof(t3_boole,axiom,( ! [A] : k4_xboole_0(A,k1_xboole_0) = A ), file(boole,t3_boole), []). fof(t3_cqc_sim1,axiom,( ! [A,B,C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : k9_relat_1(k1_funct_4(C,k2_funcop_1(k1_tarski(A),B)),k4_xboole_0(D,k1_tarski(A))) = k9_relat_1(C,k4_xboole_0(D,k1_tarski(A))) ) ), file(cqc_sim1,t3_cqc_sim1), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t43_cqc_sim1,axiom,( ! [A] : ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) => ! [B] : ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ! [E] : ( m2_fraenkel(E,k2_qc_lang1,k2_qc_lang1,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)) => ! [F] : ( m1_subset_1(F,k5_finsub_1(k2_qc_lang1)) => ~ ( r2_hidden(k4_mcart_1(A,C,F,E),k16_cqc_sim1(B)) & r2_hidden(k2_qc_lang3(D),k2_funct_2(k2_qc_lang1,k2_qc_lang1,E,k24_qc_lang1(A))) & r1_xreal_0(C,D) ) ) ) ) ) ) ) ), file(cqc_sim1,t43_cqc_sim1), []). fof(t4_boole,axiom,( ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ), file(boole,t4_boole), []). fof(t4_cqc_sim1,axiom,( ! [A,B,C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ~ r2_hidden(B,k9_relat_1(C,k4_xboole_0(D,k1_tarski(A)))) => k9_relat_1(k1_funct_4(C,k2_funcop_1(k1_tarski(A),B)),k4_xboole_0(D,k1_tarski(A))) = k4_xboole_0(k9_relat_1(k1_funct_4(C,k2_funcop_1(k1_tarski(A),B)),D),k1_tarski(B)) ) ) ), file(cqc_sim1,t4_cqc_sim1), []). fof(t4_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xreal_0(A,B) & ~ v2_xreal_0(B) & v2_xreal_0(A) ) ) ) ), file(real,t4_real), []). fof(t4_subset,axiom,( ! [A,B,C] : ( ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) ) => m1_subset_1(A,C) ) ), file(subset,t4_subset), []). fof(t5_subset,axiom,( ! [A,B,C] : ~ ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C) ) ), file(subset,t5_subset), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t6_qc_lang3,axiom,( ! [A] : ( m2_finseq_1(A,k1_qc_lang1) => k22_qc_lang1(A) = k1_qc_lang3(A,k2_qc_lang1) ) ), file(qc_lang3,t6_qc_lang3), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t7_qc_lang3,axiom,( k24_qc_lang1(k11_qc_lang1) = k1_xboole_0 ), file(qc_lang3,t7_qc_lang3), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t9_qc_lang3,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A)) => ! [C] : ( m1_qc_lang1(C,A) => k24_qc_lang1(k9_qc_lang1(B,C)) = k22_qc_lang1(C) ) ) ) ), file(qc_lang3,t9_qc_lang3), []).