% Mizar problem: t39_valuat_1,valuat_1,1000,71 fof(t39_valuat_1,conjecture,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) => ! [C] : ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang) => ! [D] : ( m1_valuat_1(D,A) => ( ~ r2_hidden(B,k24_qc_lang1(C)) => ! [E] : ( m2_fraenkel(E,k2_qc_lang1,A,k2_valuat_1(A)) => ! [F] : ( m2_fraenkel(F,k2_qc_lang1,A,k2_valuat_1(A)) => ( ! [G] : ( m2_subset_1(G,k1_qc_lang1,k2_qc_lang1) => ( B != G => k8_funct_2(k2_qc_lang1,A,F,G) = k8_funct_2(k2_qc_lang1,A,E,G) ) ) => k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,D,C),E) = k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,D,C),F) ) ) ) ) ) ) ) ) ), 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_funct_1,cc1_margrel1,cc1_membered,cc1_relset_1,cc1_valuat_1,cc20_membered,cc2_arytm_3,cc2_funct_1,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc6_membered,cc9_membered,commutativity_k10_margrel1,commutativity_k12_margrel1,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k4_subset_1,commutativity_k4_valuat_1,commutativity_k6_valuat_1,connectedness_r1_xreal_0,d12_margrel1,d13_margrel1,d14_margrel1,d1_tarski,d1_valuat_1,d2_qc_lang3,d2_xboole_0,d4_xboole_0,d5_cqc_lang,d5_funct_1,d8_qc_lang1,d8_valuat_1,d9_valuat_1,dt_k10_cqc_lang,dt_k10_margrel1,dt_k11_cqc_lang,dt_k11_margrel1,dt_k11_qc_lang1,dt_k11_valuat_1,dt_k12_margrel1,dt_k12_qc_lang1,dt_k12_valuat_1,dt_k13_qc_lang1,dt_k14_qc_lang1,dt_k15_cqc_lang,dt_k1_card_1,dt_k1_fraenkel,dt_k1_funct_1,dt_k1_funct_2,dt_k1_margrel1,dt_k1_numbers,dt_k1_qc_lang1,dt_k1_qc_lang3,dt_k1_relat_1,dt_k1_tarski,dt_k1_valuat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k22_qc_lang1,dt_k23_qc_lang1,dt_k24_qc_lang1,dt_k2_funcop_1,dt_k2_qc_lang1,dt_k2_relat_1,dt_k2_tarski,dt_k2_valuat_1,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_finseq_1,dt_k3_margrel1,dt_k3_valuat_1,dt_k4_finseq_1,dt_k4_subset_1,dt_k4_valuat_1,dt_k4_xboole_0,dt_k5_numbers,dt_k5_ordinal2,dt_k5_qc_lang1,dt_k5_relat_1,dt_k5_valuat_1,dt_k6_margrel1,dt_k6_subset_1,dt_k6_valuat_1,dt_k7_cqc_lang,dt_k7_margrel1,dt_k7_qc_lang1,dt_k7_valuat_1,dt_k8_cqc_lang,dt_k8_funct_2,dt_k8_margrel1,dt_k8_qc_lang1,dt_k8_valuat_1,dt_k9_cqc_lang,dt_k9_margrel1,dt_k9_qc_lang1,dt_k9_valuat_1,dt_m1_finseq_1,dt_m1_fraenkel,dt_m1_qc_lang1,dt_m1_relset_1,dt_m1_subset_1,dt_m1_valuat_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_m1_valuat_1,existence_m2_finseq_1,existence_m2_fraenkel,existence_m2_relset_1,existence_m2_subset_1,fc10_membered,fc11_finseq_1,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc17_finseq_1,fc1_funct_1,fc1_margrel1,fc1_qc_lang1,fc1_valuat_1,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_cqc_lang,fc2_finseq_1,fc2_margrel1,fc2_membered,fc2_qc_lang1,fc2_valuat_1,fc37_membered,fc38_membered,fc39_membered,fc3_margrel1,fc3_valuat_1,fc40_membered,fc41_membered,fc4_margrel1,fc4_valuat_1,fc5_margrel1,fc5_membered,fc5_qc_lang1,fc6_membered,fc6_qc_lang1,fc7_membered,fc8_membered,fc9_membered,fraenkel_a_2_0_qc_lang3,fraenkel_a_2_0_valuat_1,idempotence_k2_xboole_0,idempotence_k4_subset_1,involutiveness_k11_margrel1,involutiveness_k9_margrel1,l20_valuat_1,rc1_arytm_3,rc1_cqc_lang,rc1_finseq_1,rc1_funct_1,rc1_margrel1,rc1_membered,rc1_valuat_1,rc2_finseq_1,rc2_funct_1,rc2_margrel1,rc3_finseq_1,rc3_funct_1,rc4_finseq_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,redefinition_k10_cqc_lang,redefinition_k11_cqc_lang,redefinition_k11_margrel1,redefinition_k11_valuat_1,redefinition_k12_margrel1,redefinition_k15_cqc_lang,redefinition_k1_fraenkel,redefinition_k1_margrel1,redefinition_k23_qc_lang1,redefinition_k2_valuat_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k4_subset_1,redefinition_k5_numbers,redefinition_k5_valuat_1,redefinition_k6_subset_1,redefinition_k6_valuat_1,redefinition_k8_cqc_lang,redefinition_k8_funct_2,redefinition_k8_valuat_1,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,s1_cqc_lang__e2_44__valuat_1,s1_valuat_1__e2_44_1_5_1_1_1_1__valuat_1,s1_valuat_1__e2_44_1_5_1_2_1_1__valuat_1,spc0_boole,spc1_boole,spc1_numerals,t11_qc_lang3,t14_qc_lang3,t14_valuat_1,t16_qc_lang3,t18_finseq_1,t1_boole,t1_numerals,t1_subset,t20_valuat_1,t22_valuat_1,t27_finseq_3,t2_subset,t2_tarski,t39_margrel1,t3_boole,t3_subset,t41_margrel1,t45_margrel1,t4_boole,t4_subset,t5_subset,t6_boole,t6_qc_lang3,t7_boole,t7_valuat_1,t8_boole,t8_valuat_1,t9_qc_lang3]), [file(valuat_1,t39_valuat_1)]). 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_funct_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_funct_1(A) ) ), file(funct_1,cc1_funct_1), []). fof(cc1_margrel1,axiom,( ! [A] : ( m1_subset_1(A,k6_margrel1) => v2_margrel1(A) ) ), file(margrel1,cc1_margrel1), []). fof(cc1_membered,axiom,( ! [A] : ( v5_membered(A) => v4_membered(A) ) ), file(membered,cc1_membered), []). 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(cc1_valuat_1,axiom,( ! [A,B] : ( m1_subset_1(B,k1_fraenkel(A,k6_margrel1)) => v1_valuat_1(B) ) ), file(valuat_1,cc1_valuat_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_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ) ), file(funct_1,cc2_funct_1), []). 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_membered,axiom,( ! [A] : ( v3_membered(A) => v2_membered(A) ) ), file(membered,cc3_membered), []). fof(cc4_membered,axiom,( ! [A] : ( v2_membered(A) => v1_membered(A) ) ), file(membered,cc4_membered), []). 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_k10_margrel1,axiom,( ! [A,B] : ( ( v2_margrel1(A) & v2_margrel1(B) ) => k10_margrel1(A,B) = k10_margrel1(B,A) ) ), file(margrel1,k10_margrel1), []). fof(commutativity_k12_margrel1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k6_margrel1) & m1_subset_1(B,k6_margrel1) ) => k12_margrel1(A,B) = k12_margrel1(B,A) ) ), file(margrel1,k12_margrel1), []). 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_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_k4_valuat_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valuat_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_valuat_1(B) ) => k4_valuat_1(A,B) = k4_valuat_1(B,A) ) ), file(valuat_1,k4_valuat_1), []). fof(commutativity_k6_valuat_1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k1_fraenkel(A,k6_margrel1)) & m1_subset_1(C,k1_fraenkel(A,k6_margrel1)) ) => k6_valuat_1(A,B,C) = k6_valuat_1(A,C,B) ) ), file(valuat_1,k6_valuat_1), []). 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(d12_margrel1,axiom,( k6_margrel1 = k2_tarski(0,1) ), file(margrel1,d12_margrel1), []). fof(d13_margrel1,axiom,( k7_margrel1 = 0 ), file(margrel1,d13_margrel1), []). fof(d14_margrel1,axiom,( k8_margrel1 = 1 ), file(margrel1,d14_margrel1), []). fof(d1_tarski,axiom,( ! [A,B] : ( B = k1_tarski(A) <=> ! [C] : ( r2_hidden(C,B) <=> C = A ) ) ), file(tarski,d1_tarski), []). fof(d1_valuat_1,axiom,( ! [A] : k1_valuat_1(A) = k1_funct_2(k2_qc_lang1,A) ), file(valuat_1,d1_valuat_1), []). 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(d2_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) ) ) ) ), file(xboole_0,d2_xboole_0), []). fof(d4_xboole_0,axiom,( ! [A,B,C] : ( C = k4_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) & ~ r2_hidden(D,B) ) ) ) ), file(xboole_0,d4_xboole_0), []). fof(d5_cqc_lang,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m1_qc_lang1(B,A) => ( v1_cqc_lang(B,A) <=> r1_tarski(k2_relat_1(B),k2_qc_lang1) ) ) ) ), file(cqc_lang,d5_cqc_lang), []). fof(d5_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( B = k2_relat_1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( r2_hidden(D,k1_relat_1(A)) & C = k1_funct_1(A,D) ) ) ) ) ), file(funct_1,d5_funct_1), []). 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(d8_valuat_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( ( v1_cqc_lang(C,B) & m1_qc_lang1(C,B) ) => ! [D] : ( m2_fraenkel(D,k2_qc_lang1,A,k2_valuat_1(A)) => ! [E] : ( m2_finseq_1(E,A) => ( E = k8_valuat_1(A,B,C,D) <=> ( k3_finseq_1(E) = B & ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ( ( r1_xreal_0(1,F) & r1_xreal_0(F,B) ) => k1_funct_1(E,F) = k1_funct_1(D,k1_funct_1(C,F)) ) ) ) ) ) ) ) ) ) ), file(valuat_1,d8_valuat_1), []). fof(d9_valuat_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( ( v1_cqc_lang(C,B) & m1_qc_lang1(C,B) ) => ! [D] : ( m1_subset_1(D,k3_margrel1(A)) => ! [E] : ( m2_fraenkel(E,k2_valuat_1(A),k6_margrel1,k1_fraenkel(k2_valuat_1(A),k6_margrel1)) => ( E = k9_valuat_1(A,B,C,D) <=> ! [F] : ( m2_fraenkel(F,k2_qc_lang1,A,k2_valuat_1(A)) => ( ( r2_hidden(k8_valuat_1(A,B,C,F),D) => k8_funct_2(k2_valuat_1(A),k6_margrel1,E,F) = k8_margrel1 ) & ( ~ r2_hidden(k8_valuat_1(A,B,C,F),D) => k8_funct_2(k2_valuat_1(A),k6_margrel1,E,F) = k7_margrel1 ) ) ) ) ) ) ) ) ) ), file(valuat_1,d9_valuat_1), []). 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_margrel1,axiom,( $true ), file(margrel1,k10_margrel1), []). 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_margrel1,axiom,( ! [A] : ( m1_subset_1(A,k6_margrel1) => m1_subset_1(k11_margrel1(A),k6_margrel1) ) ), file(margrel1,k11_margrel1), []). fof(dt_k11_qc_lang1,axiom,( m1_subset_1(k11_qc_lang1,k8_qc_lang1) ), file(qc_lang1,k11_qc_lang1), []). fof(dt_k11_valuat_1,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k5_numbers) & m1_valuat_1(C,A) & m1_subset_1(D,k7_qc_lang1(B)) ) => m1_subset_1(k11_valuat_1(A,B,C,D),k3_margrel1(A)) ) ), file(valuat_1,k11_valuat_1), []). fof(dt_k12_margrel1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k6_margrel1) & m1_subset_1(B,k6_margrel1) ) => m1_subset_1(k12_margrel1(A,B),k6_margrel1) ) ), file(margrel1,k12_margrel1), []). 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_k12_valuat_1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_valuat_1(B,A) & m1_subset_1(C,k7_cqc_lang) ) => m2_fraenkel(k12_valuat_1(A,B,C),k2_valuat_1(A),k6_margrel1,k1_fraenkel(k2_valuat_1(A),k6_margrel1)) ) ), file(valuat_1,k12_valuat_1), []). 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_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_k1_card_1,axiom,( ! [A] : v1_card_1(k1_card_1(A)) ), file(card_1,k1_card_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_margrel1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(C,A) ) => m2_fraenkel(k1_margrel1(A,B,C),B,A,k1_fraenkel(B,A)) ) ), file(margrel1,k1_margrel1), []). 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_tarski,axiom,( $true ), file(tarski,k1_tarski), []). fof(dt_k1_valuat_1,axiom,( $true ), file(valuat_1,k1_valuat_1), []). 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_funcop_1,axiom,( $true ), file(funcop_1,k2_funcop_1), []). 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_relat_1,axiom,( $true ), file(relat_1,k2_relat_1), []). fof(dt_k2_tarski,axiom,( $true ), file(tarski,k2_tarski), []). fof(dt_k2_valuat_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_fraenkel(k2_valuat_1(A),k2_qc_lang1,A) ) ), file(valuat_1,k2_valuat_1), []). fof(dt_k2_xboole_0,axiom,( $true ), file(xboole_0,k2_xboole_0), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). 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_k3_margrel1,axiom,( $true ), file(margrel1,k3_margrel1), []). fof(dt_k3_valuat_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valuat_1(A) ) => ( v1_relat_1(k3_valuat_1(A)) & v1_funct_1(k3_valuat_1(A)) ) ) ), file(valuat_1,k3_valuat_1), []). 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_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_valuat_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valuat_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_valuat_1(B) ) => ( v1_relat_1(k4_valuat_1(A,B)) & v1_funct_1(k4_valuat_1(A,B)) ) ) ), file(valuat_1,k4_valuat_1), []). fof(dt_k4_xboole_0,axiom,( $true ), file(xboole_0,k4_xboole_0), []). 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_valuat_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k1_fraenkel(A,k6_margrel1)) ) => m2_fraenkel(k5_valuat_1(A,B),A,k6_margrel1,k1_fraenkel(A,k6_margrel1)) ) ), file(valuat_1,k5_valuat_1), []). fof(dt_k6_margrel1,axiom,( $true ), file(margrel1,k6_margrel1), []). 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_k6_valuat_1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k1_fraenkel(A,k6_margrel1)) & m1_subset_1(C,k1_fraenkel(A,k6_margrel1)) ) => m2_fraenkel(k6_valuat_1(A,B,C),A,k6_margrel1,k1_fraenkel(A,k6_margrel1)) ) ), file(valuat_1,k6_valuat_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_margrel1,axiom,( m1_subset_1(k7_margrel1,k6_margrel1) ), file(margrel1,k7_margrel1), []). 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_k7_valuat_1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k2_qc_lang1) & m1_subset_1(C,k1_fraenkel(k2_valuat_1(A),k6_margrel1)) ) => m2_fraenkel(k7_valuat_1(A,B,C),k2_valuat_1(A),k6_margrel1,k1_fraenkel(k2_valuat_1(A),k6_margrel1)) ) ), file(valuat_1,k7_valuat_1), []). 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_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_margrel1,axiom,( m1_subset_1(k8_margrel1,k6_margrel1) ), file(margrel1,k8_margrel1), []). fof(dt_k8_qc_lang1,axiom,( ~ v1_xboole_0(k8_qc_lang1) ), file(qc_lang1,k8_qc_lang1), []). fof(dt_k8_valuat_1,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k5_numbers) & v1_cqc_lang(C,B) & m1_qc_lang1(C,B) & m1_subset_1(D,k2_valuat_1(A)) ) => m2_finseq_1(k8_valuat_1(A,B,C,D),A) ) ), file(valuat_1,k8_valuat_1), []). 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_margrel1,axiom,( ! [A] : ( v2_margrel1(A) => v2_margrel1(k9_margrel1(A)) ) ), file(margrel1,k9_margrel1), []). 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_valuat_1,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k5_numbers) & v1_cqc_lang(C,B) & m1_qc_lang1(C,B) & m1_subset_1(D,k3_margrel1(A)) ) => m2_fraenkel(k9_valuat_1(A,B,C,D),k2_valuat_1(A),k6_margrel1,k1_fraenkel(k2_valuat_1(A),k6_margrel1)) ) ), file(valuat_1,k9_valuat_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_m1_valuat_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_valuat_1(B,A) => ( v1_funct_1(B) & v1_funct_2(B,k5_qc_lang1,k3_margrel1(A)) & m2_relset_1(B,k5_qc_lang1,k3_margrel1(A)) ) ) ) ), file(valuat_1,m1_valuat_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_m1_valuat_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : m1_valuat_1(B,A) ) ), file(valuat_1,m1_valuat_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_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_finset_1(A) ) => v1_finset_1(k2_relat_1(A)) ) ), file(finseq_1,fc11_finseq_1), []). 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_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => ( v1_relat_1(k5_relat_1(A,B)) & v1_funct_1(k5_relat_1(A,B)) ) ) ), file(funct_1,fc1_funct_1), []). fof(fc1_margrel1,axiom, ( v1_xboole_0(k1_xboole_0) & v1_margrel1(k1_xboole_0) ), file(margrel1,fc1_margrel1), []). fof(fc1_qc_lang1,axiom,( ~ v1_xboole_0(k1_qc_lang1) ), file(qc_lang1,fc1_qc_lang1), []). fof(fc1_valuat_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ v1_xboole_0(k1_valuat_1(A)) & v1_fraenkel(k1_valuat_1(A)) ) ) ), file(valuat_1,fc1_valuat_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_margrel1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k3_margrel1(A)) ) ), file(margrel1,fc2_margrel1), []). fof(fc2_membered,axiom, ( ~ v1_xboole_0(k1_numbers) & v1_membered(k1_numbers) & v2_membered(k1_numbers) ), file(membered,fc2_membered), []). fof(fc2_qc_lang1,axiom,( ~ v1_xboole_0(k2_qc_lang1) ), file(qc_lang1,fc2_qc_lang1), []). fof(fc2_valuat_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valuat_1(A) ) => v2_margrel1(k1_funct_1(A,B)) ) ), file(valuat_1,fc2_valuat_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_margrel1,axiom,( ~ v1_xboole_0(k6_margrel1) ), file(margrel1,fc3_margrel1), []). fof(fc3_valuat_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valuat_1(A) ) => ( v1_relat_1(k3_valuat_1(A)) & v1_funct_1(k3_valuat_1(A)) & v1_valuat_1(k3_valuat_1(A)) ) ) ), file(valuat_1,fc3_valuat_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_margrel1,axiom,( ! [A] : ( v2_margrel1(A) => v2_margrel1(k9_margrel1(A)) ) ), file(margrel1,fc4_margrel1), []). fof(fc4_valuat_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valuat_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_valuat_1(B) ) => ( v1_relat_1(k4_valuat_1(A,B)) & v1_funct_1(k4_valuat_1(A,B)) & v1_valuat_1(k4_valuat_1(A,B)) ) ) ), file(valuat_1,fc4_valuat_1), []). fof(fc5_margrel1,axiom,( ! [A,B] : ( ( v2_margrel1(A) & v2_margrel1(B) ) => v2_margrel1(k10_margrel1(A,B)) ) ), file(margrel1,fc5_margrel1), []). 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(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_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_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_0_valuat_1,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_0_valuat_1(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(valuat_1,a_2_0_valuat_1), []). 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(involutiveness_k11_margrel1,axiom,( ! [A] : ( m1_subset_1(A,k6_margrel1) => k11_margrel1(k11_margrel1(A)) = A ) ), file(margrel1,k11_margrel1), []). fof(involutiveness_k9_margrel1,axiom,( ! [A] : ( v2_margrel1(A) => k9_margrel1(k9_margrel1(A)) = A ) ), file(margrel1,k9_margrel1), []). fof(l20_valuat_1,axiom,( ! [A] : ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_valuat_1(C,B) => ( k12_valuat_1(B,C,k9_cqc_lang) = k1_margrel1(k6_margrel1,k2_valuat_1(B),k8_margrel1) & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ! [E] : ( ( v1_cqc_lang(E,D) & m1_qc_lang1(E,D) ) => ! [F] : ( m2_subset_1(F,k5_qc_lang1,k7_qc_lang1(D)) => k12_valuat_1(B,C,k8_cqc_lang(D,F,E)) = k9_valuat_1(B,D,E,k11_valuat_1(B,D,C,F)) ) ) ) & ! [D] : ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang) => k12_valuat_1(B,C,k10_cqc_lang(D)) = k5_valuat_1(k2_valuat_1(B),k12_valuat_1(B,C,D)) ) & ! [D] : ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang) => k12_valuat_1(B,C,k11_cqc_lang(A,D)) = k6_valuat_1(k2_valuat_1(B),k12_valuat_1(B,C,A),k12_valuat_1(B,C,D)) ) & ! [D] : ( m2_subset_1(D,k1_qc_lang1,k2_qc_lang1) => k12_valuat_1(B,C,k15_cqc_lang(D,A)) = k7_valuat_1(B,D,k12_valuat_1(B,C,A)) ) ) ) ) ) ), file(valuat_1,l20_valuat_1), []). 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_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc1_funct_1), []). fof(rc1_margrel1,axiom,( ? [A] : v1_margrel1(A) ), file(margrel1,rc1_margrel1), []). 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_valuat_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_valuat_1(A) ) ), file(valuat_1,rc1_valuat_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_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) ), file(funct_1,rc2_funct_1), []). fof(rc2_margrel1,axiom,( ? [A] : v2_margrel1(A) ), file(margrel1,rc2_margrel1), []). 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_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ), file(funct_1,rc3_funct_1), []). 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(rc4_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc4_funct_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_k11_margrel1,axiom,( ! [A] : ( m1_subset_1(A,k6_margrel1) => k11_margrel1(A) = k9_margrel1(A) ) ), file(margrel1,k11_margrel1), []). fof(redefinition_k11_valuat_1,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k5_numbers) & m1_valuat_1(C,A) & m1_subset_1(D,k7_qc_lang1(B)) ) => k11_valuat_1(A,B,C,D) = k1_funct_1(C,D) ) ), file(valuat_1,k11_valuat_1), []). fof(redefinition_k12_margrel1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k6_margrel1) & m1_subset_1(B,k6_margrel1) ) => k12_margrel1(A,B) = k10_margrel1(A,B) ) ), file(margrel1,k12_margrel1), []). 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_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_margrel1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(C,A) ) => k1_margrel1(A,B,C) = k2_funcop_1(B,C) ) ), file(margrel1,k1_margrel1), []). 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_valuat_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k2_valuat_1(A) = k1_valuat_1(A) ) ), file(valuat_1,k2_valuat_1), []). 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_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_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_valuat_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k1_fraenkel(A,k6_margrel1)) ) => k5_valuat_1(A,B) = k3_valuat_1(B) ) ), file(valuat_1,k5_valuat_1), []). 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_k6_valuat_1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k1_fraenkel(A,k6_margrel1)) & m1_subset_1(C,k1_fraenkel(A,k6_margrel1)) ) => k6_valuat_1(A,B,C) = k4_valuat_1(B,C) ) ), file(valuat_1,k6_valuat_1), []). 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_k8_valuat_1,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k5_numbers) & v1_cqc_lang(C,B) & m1_qc_lang1(C,B) & m1_subset_1(D,k2_valuat_1(A)) ) => k8_valuat_1(A,B,C,D) = k5_relat_1(C,D) ) ), file(valuat_1,k8_valuat_1), []). 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(s1_cqc_lang__e2_44__valuat_1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) & m1_valuat_1(C,A) ) => ( ! [D] : ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang) => ! [E] : ( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang) => ! [F] : ( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) => ! [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) => ! [H] : ( ( v1_cqc_lang(H,G) & m1_qc_lang1(H,G) ) => ! [I] : ( m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G)) => ( ( ~ r2_hidden(B,k24_qc_lang1(k9_cqc_lang)) => ! [J] : ( m2_fraenkel(J,k2_qc_lang1,A,k2_valuat_1(A)) => ! [K] : ( m2_fraenkel(K,k2_qc_lang1,A,k2_valuat_1(A)) => ( ! [L] : ( m2_subset_1(L,k1_qc_lang1,k2_qc_lang1) => ( B != L => k8_funct_2(k2_qc_lang1,A,K,L) = k8_funct_2(k2_qc_lang1,A,J,L) ) ) => k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,C,k9_cqc_lang),J) = k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,C,k9_cqc_lang),K) ) ) ) ) & ( ~ r2_hidden(B,k24_qc_lang1(k8_cqc_lang(G,I,H))) => ! [M] : ( m2_fraenkel(M,k2_qc_lang1,A,k2_valuat_1(A)) => ! [N] : ( m2_fraenkel(N,k2_qc_lang1,A,k2_valuat_1(A)) => ( ! [O] : ( m2_subset_1(O,k1_qc_lang1,k2_qc_lang1) => ( B != O => k8_funct_2(k2_qc_lang1,A,N,O) = k8_funct_2(k2_qc_lang1,A,M,O) ) ) => k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,C,k8_cqc_lang(G,I,H)),M) = k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,C,k8_cqc_lang(G,I,H)),N) ) ) ) ) & ( ( ~ r2_hidden(B,k24_qc_lang1(D)) => ! [P] : ( m2_fraenkel(P,k2_qc_lang1,A,k2_valuat_1(A)) => ! [Q] : ( m2_fraenkel(Q,k2_qc_lang1,A,k2_valuat_1(A)) => ( ! [R] : ( m2_subset_1(R,k1_qc_lang1,k2_qc_lang1) => ( B != R => k8_funct_2(k2_qc_lang1,A,Q,R) = k8_funct_2(k2_qc_lang1,A,P,R) ) ) => k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,C,D),P) = k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,C,D),Q) ) ) ) ) => ( ~ r2_hidden(B,k24_qc_lang1(k10_cqc_lang(D))) => ! [S] : ( m2_fraenkel(S,k2_qc_lang1,A,k2_valuat_1(A)) => ! [T] : ( m2_fraenkel(T,k2_qc_lang1,A,k2_valuat_1(A)) => ( ! [U] : ( m2_subset_1(U,k1_qc_lang1,k2_qc_lang1) => ( B != U => k8_funct_2(k2_qc_lang1,A,T,U) = k8_funct_2(k2_qc_lang1,A,S,U) ) ) => k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,C,k10_cqc_lang(D)),S) = k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,C,k10_cqc_lang(D)),T) ) ) ) ) ) & ( ( ( ~ r2_hidden(B,k24_qc_lang1(D)) => ! [V] : ( m2_fraenkel(V,k2_qc_lang1,A,k2_valuat_1(A)) => ! [W] : ( m2_fraenkel(W,k2_qc_lang1,A,k2_valuat_1(A)) => ( ! [X] : ( m2_subset_1(X,k1_qc_lang1,k2_qc_lang1) => ( B != X => k8_funct_2(k2_qc_lang1,A,W,X) = k8_funct_2(k2_qc_lang1,A,V,X) ) ) => k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,C,D),V) = k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,C,D),W) ) ) ) ) & ( ~ r2_hidden(B,k24_qc_lang1(E)) => ! [Y] : ( m2_fraenkel(Y,k2_qc_lang1,A,k2_valuat_1(A)) => ! [Z] : ( m2_fraenkel(Z,k2_qc_lang1,A,k2_valuat_1(A)) => ( ! [A1] : ( m2_subset_1(A1,k1_qc_lang1,k2_qc_lang1) => ( B != A1 => k8_funct_2(k2_qc_lang1,A,Z,A1) = k8_funct_2(k2_qc_lang1,A,Y,A1) ) ) => k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,C,E),Y) = k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,C,E),Z) ) ) ) ) ) => ( ~ r2_hidden(B,k24_qc_lang1(k11_cqc_lang(D,E))) => ! [B1] : ( m2_fraenkel(B1,k2_qc_lang1,A,k2_valuat_1(A)) => ! [C1] : ( m2_fraenkel(C1,k2_qc_lang1,A,k2_valuat_1(A)) => ( ! [D1] : ( m2_subset_1(D1,k1_qc_lang1,k2_qc_lang1) => ( B != D1 => k8_funct_2(k2_qc_lang1,A,C1,D1) = k8_funct_2(k2_qc_lang1,A,B1,D1) ) ) => k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,C,k11_cqc_lang(D,E)),B1) = k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,C,k11_cqc_lang(D,E)),C1) ) ) ) ) ) & ( ( ~ r2_hidden(B,k24_qc_lang1(D)) => ! [E1] : ( m2_fraenkel(E1,k2_qc_lang1,A,k2_valuat_1(A)) => ! [F1] : ( m2_fraenkel(F1,k2_qc_lang1,A,k2_valuat_1(A)) => ( ! [G1] : ( m2_subset_1(G1,k1_qc_lang1,k2_qc_lang1) => ( B != G1 => k8_funct_2(k2_qc_lang1,A,F1,G1) = k8_funct_2(k2_qc_lang1,A,E1,G1) ) ) => k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,C,D),E1) = k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,C,D),F1) ) ) ) ) => ( ~ r2_hidden(B,k24_qc_lang1(k15_cqc_lang(F,D))) => ! [H1] : ( m2_fraenkel(H1,k2_qc_lang1,A,k2_valuat_1(A)) => ! [I1] : ( m2_fraenkel(I1,k2_qc_lang1,A,k2_valuat_1(A)) => ( ! [J1] : ( m2_subset_1(J1,k1_qc_lang1,k2_qc_lang1) => ( B != J1 => k8_funct_2(k2_qc_lang1,A,I1,J1) = k8_funct_2(k2_qc_lang1,A,H1,J1) ) ) => k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,C,k15_cqc_lang(F,D)),H1) = k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,C,k15_cqc_lang(F,D)),I1) ) ) ) ) ) ) ) ) ) ) ) ) => ! [D] : ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang) => ( ~ r2_hidden(B,k24_qc_lang1(D)) => ! [K1] : ( m2_fraenkel(K1,k2_qc_lang1,A,k2_valuat_1(A)) => ! [L1] : ( m2_fraenkel(L1,k2_qc_lang1,A,k2_valuat_1(A)) => ( ! [M1] : ( m2_subset_1(M1,k1_qc_lang1,k2_qc_lang1) => ( B != M1 => k8_funct_2(k2_qc_lang1,A,L1,M1) = k8_funct_2(k2_qc_lang1,A,K1,M1) ) ) => k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,C,D),K1) = k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,C,D),L1) ) ) ) ) ) ) ) ), file(valuat_1,s1_cqc_lang__e2_44__valuat_1), []). fof(s1_valuat_1__e2_44_1_5_1_1_1_1__valuat_1,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) & m2_fraenkel(C,k2_qc_lang1,A,k2_valuat_1(A)) & m2_fraenkel(D,k2_qc_lang1,A,k2_valuat_1(A)) ) => ? [E] : ( m2_fraenkel(E,k2_qc_lang1,A,k2_valuat_1(A)) & ! [F] : ( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) => ( F != B => k8_funct_2(k2_qc_lang1,A,E,F) = k8_funct_2(k2_qc_lang1,A,C,F) ) ) & k8_funct_2(k2_qc_lang1,A,E,B) = k8_funct_2(k2_qc_lang1,A,D,B) ) ) ), file(valuat_1,s1_valuat_1__e2_44_1_5_1_1_1_1__valuat_1), []). fof(s1_valuat_1__e2_44_1_5_1_2_1_1__valuat_1,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) & m2_fraenkel(C,k2_qc_lang1,A,k2_valuat_1(A)) & m2_fraenkel(D,k2_qc_lang1,A,k2_valuat_1(A)) ) => ? [E] : ( m2_fraenkel(E,k2_qc_lang1,A,k2_valuat_1(A)) & ! [F] : ( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) => ( F != B => k8_funct_2(k2_qc_lang1,A,E,F) = k8_funct_2(k2_qc_lang1,A,C,F) ) ) & k8_funct_2(k2_qc_lang1,A,E,B) = k8_funct_2(k2_qc_lang1,A,D,B) ) ) ), file(valuat_1,s1_valuat_1__e2_44_1_5_1_2_1_1__valuat_1), []). fof(spc0_boole,axiom,( v1_xboole_0(0) ), file(boole,spc0_boole), []). 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_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(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(t14_valuat_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_fraenkel(B,k2_qc_lang1,A,k2_valuat_1(A)) => ! [C] : ( m1_valuat_1(C,A) => k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,C,k9_cqc_lang),B) = k8_margrel1 ) ) ) ), file(valuat_1,t14_valuat_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(t18_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( ( r1_xreal_0(1,C) & r1_xreal_0(C,k3_finseq_1(A)) ) => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) ) => A = B ) ) ) ), file(finseq_1,t18_finseq_1), []). fof(t1_boole,axiom,( ! [A] : k2_xboole_0(A,k1_xboole_0) = A ), file(boole,t1_boole), []). fof(t1_numerals,axiom,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t20_valuat_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_fraenkel(B,k2_qc_lang1,A,k2_valuat_1(A)) => ! [C] : ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang) => ! [D] : ( m1_valuat_1(D,A) => k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,D,k10_cqc_lang(C)),B) = k11_margrel1(k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,D,C),B)) ) ) ) ) ), file(valuat_1,t20_valuat_1), []). fof(t22_valuat_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_fraenkel(B,k2_qc_lang1,A,k2_valuat_1(A)) => ! [C] : ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang) => ! [D] : ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang) => ! [E] : ( m1_valuat_1(E,A) => k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,E,k11_cqc_lang(C,D)),B) = k12_margrel1(k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,E,C),B),k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,E,D),B)) ) ) ) ) ) ), file(valuat_1,t22_valuat_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(t39_margrel1,axiom,( ! [A] : ( v2_margrel1(A) => ( A = k7_margrel1 | A = k8_margrel1 ) ) ), file(margrel1,t39_margrel1), []). fof(t3_boole,axiom,( ! [A] : k4_xboole_0(A,k1_xboole_0) = A ), file(boole,t3_boole), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t41_margrel1,axiom,( ! [A] : ( v2_margrel1(A) => ( ( A = k7_margrel1 => k9_margrel1(A) = k8_margrel1 ) & ( k9_margrel1(A) = k8_margrel1 => A = k7_margrel1 ) & ( A = k8_margrel1 => k9_margrel1(A) = k7_margrel1 ) & ( k9_margrel1(A) = k7_margrel1 => A = k8_margrel1 ) ) ) ), file(margrel1,t41_margrel1), []). fof(t45_margrel1,axiom,( ! [A] : ( v2_margrel1(A) => ! [B] : ( v2_margrel1(B) => ( ( k10_margrel1(A,B) = k8_margrel1 => ( A = k8_margrel1 & B = k8_margrel1 ) ) & ( ( A = k8_margrel1 & B = k8_margrel1 ) => k10_margrel1(A,B) = k8_margrel1 ) & ~ ( k10_margrel1(A,B) = k7_margrel1 & A != k7_margrel1 & B != k7_margrel1 ) & ( ( A = k7_margrel1 | B = k7_margrel1 ) => k10_margrel1(A,B) = k7_margrel1 ) ) ) ) ), file(margrel1,t45_margrel1), []). fof(t4_boole,axiom,( ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ), file(boole,t4_boole), []). 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_valuat_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) => ! [C] : ( m2_fraenkel(C,k2_qc_lang1,A,k2_valuat_1(A)) => ! [D] : ( m2_fraenkel(D,k2_valuat_1(A),k6_margrel1,k1_fraenkel(k2_valuat_1(A),k6_margrel1)) => ( k8_funct_2(k2_valuat_1(A),k6_margrel1,k7_valuat_1(A,B,D),C) = k7_margrel1 <=> ? [E] : ( m2_fraenkel(E,k2_qc_lang1,A,k2_valuat_1(A)) & k8_funct_2(k2_valuat_1(A),k6_margrel1,D,E) = k7_margrel1 & ! [F] : ( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) => ( B != F => k8_funct_2(k2_qc_lang1,A,E,F) = k8_funct_2(k2_qc_lang1,A,C,F) ) ) ) ) ) ) ) ) ), file(valuat_1,t7_valuat_1), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t8_valuat_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) => ! [C] : ( m2_fraenkel(C,k2_qc_lang1,A,k2_valuat_1(A)) => ! [D] : ( m2_fraenkel(D,k2_valuat_1(A),k6_margrel1,k1_fraenkel(k2_valuat_1(A),k6_margrel1)) => ( k8_funct_2(k2_valuat_1(A),k6_margrel1,k7_valuat_1(A,B,D),C) = k8_margrel1 <=> ! [E] : ( m2_fraenkel(E,k2_qc_lang1,A,k2_valuat_1(A)) => ( ! [F] : ( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) => ( B != F => k8_funct_2(k2_qc_lang1,A,E,F) = k8_funct_2(k2_qc_lang1,A,C,F) ) ) => k8_funct_2(k2_valuat_1(A),k6_margrel1,D,E) = k8_margrel1 ) ) ) ) ) ) ) ), file(valuat_1,t8_valuat_1), []). 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), []).