% Mizar problem: t15_measure7,measure7,1178,35 fof(t15_measure7,conjecture,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) & m2_relset_1(A,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) ) => ( ( v2_funct_1(A) & k9_funcop_1(k5_numbers,k5_numbers,k5_numbers,A) = k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ? [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) & ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k5_numbers,k1_zfmisc_1(k6_supinf_1)) & m2_relset_1(D,k5_numbers,k1_zfmisc_1(k6_supinf_1)) ) => ! [E] : ( m2_measure7(E,D) => r1_supinf_1(k8_funct_2(k5_numbers,k3_supinf_1,k18_supinf_2(k4_measure7(k5_setfam_1(k6_supinf_1,k1_measure4(k6_supinf_1,D)),k14_measure7(D,E,A))),B),k8_funct_2(k5_numbers,k3_supinf_1,k18_supinf_2(k8_measure7(D,E)),C)) ) ) ) ) ) ) ), 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_fraenkel,cc1_funct_2,cc1_membered,cc1_relset_1,cc1_supinf_1,cc20_membered,cc2_arytm_3,cc2_membered,cc2_supinf_1,cc3_arytm_3,cc3_membered,cc4_membered,cc5_funct_2,cc6_funct_2,cc6_membered,cc9_membered,commutativity_k1_nat_1,commutativity_k2_supinf_2,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k2_xcmplx_0,connectedness_r1_supinf_1,d12_measure7,d13_measure7,d1_supinf_1,d2_funct_2,d2_measure7,d3_measure7,d3_supinf_1,d3_tarski,d4_measure7,d5_tarski,d6_measure7,d6_supinf_1,d7_measure7,de_c2__measure7,dt_c2__measure7,dt_k12_mcart_1,dt_k12_measure7,dt_k13_measure7,dt_k13_supinf_2,dt_k14_measure7,dt_k15_mcart_1,dt_k16_mcart_1,dt_k18_supinf_2,dt_k19_supinf_2,dt_k1_funct_1,dt_k1_funct_2,dt_k1_measure4,dt_k1_measure7,dt_k1_nat_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_supinf_1,dt_k1_supinf_2,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_funcop_1,dt_k2_relat_1,dt_k2_supinf_1,dt_k2_supinf_2,dt_k2_tarski,dt_k2_xboole_0,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_measure7,dt_k3_supinf_1,dt_k3_tarski,dt_k4_measure7,dt_k4_tarski,dt_k5_measure5,dt_k5_measure7,dt_k5_numbers,dt_k5_ordinal2,dt_k5_relat_1,dt_k5_setfam_1,dt_k6_measure5,dt_k6_supinf_1,dt_k7_funct_2,dt_k7_measure7,dt_k8_funct_2,dt_k8_measure7,dt_k9_funcop_1,dt_m1_measure7,dt_m1_relset_1,dt_m1_subset_1,dt_m2_measure7,dt_m2_relset_1,dt_m2_subset_1,existence_m1_measure7,existence_m1_relset_1,existence_m1_subset_1,existence_m2_measure7,existence_m2_relset_1,existence_m2_subset_1,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc1_fraenkel,fc1_funct_2,fc1_ordinal2,fc1_subset_1,fc1_supinf_1,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_funct_2,fc2_membered,fc2_subset_1,fc3_subset_1,fc4_ordinal2,fc4_subset_1,fc5_membered,fc6_membered,fc7_membered,fc8_membered,fc9_membered,fraenkel_a_2_0_measure7,idempotence_k2_xboole_0,l35_measure7,rc1_arytm_3,rc1_fraenkel,rc1_funct_2,rc1_membered,rc1_subset_1,rc2_subset_1,rc3_supinf_1,redefinition_k12_mcart_1,redefinition_k12_measure7,redefinition_k13_measure7,redefinition_k13_supinf_2,redefinition_k1_measure4,redefinition_k1_measure7,redefinition_k1_nat_1,redefinition_k3_measure7,redefinition_k5_measure7,redefinition_k5_numbers,redefinition_k5_setfam_1,redefinition_k6_measure5,redefinition_k6_supinf_1,redefinition_k7_funct_2,redefinition_k8_funct_2,redefinition_k9_funcop_1,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_supinf_1,reflexivity_r1_tarski,s1_nat_1__e6_32__measure7,s3_funct_2__e22_32_2__measure7,s3_funct_2__e4_32_2__measure7,s3_funct_2__e7_32_2__measure7,spc0_boole,spc1_boole,spc1_numerals,t11_funct_2,t12_measure7,t13_measure7,t14_measure7,t18_supinf_2,t1_arithm,t1_boole,t1_measure7,t1_numerals,t1_subset,t21_funct_2,t22_supinf_1,t25_funct_2,t29_supinf_1,t2_measure7,t2_subset,t2_tarski,t2_xboole_1,t3_measure6,t3_measure7,t3_subset,t4_funct_2,t4_measure1,t4_subset,t58_supinf_2,t59_supinf_2,t5_subset,t60_measure5,t60_supinf_2,t62_supinf_2,t63_supinf_2,t6_boole,t7_boole,t7_measure7,t8_boole]), [file(measure7,t15_measure7)]). 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_fraenkel,axiom,( ! [A] : ( v1_fraenkel(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ) ), file(fraenkel,cc1_fraenkel), []). 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_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_supinf_1,axiom,( ! [A] : ( m1_subset_1(A,k3_supinf_1) => v3_supinf_1(A) ) ), file(supinf_1,cc1_supinf_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_membered,axiom,( ! [A] : ( v4_membered(A) => v3_membered(A) ) ), file(membered,cc2_membered), []). fof(cc2_supinf_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & v3_supinf_1(A) ) ) ), file(supinf_1,cc2_supinf_1), []). 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(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_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_supinf_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k3_supinf_1) & m1_subset_1(B,k3_supinf_1) ) => k2_supinf_2(A,B) = k2_supinf_2(B,A) ) ), file(supinf_2,k2_supinf_2), []). 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(connectedness_r1_supinf_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k3_supinf_1) & m1_subset_1(B,k3_supinf_1) ) => ( r1_supinf_1(A,B) | r1_supinf_1(B,A) ) ) ), file(supinf_1,r1_supinf_1), []). fof(d12_measure7,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) & m2_relset_1(A,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,k5_numbers) & m2_relset_1(B,k5_numbers,k5_numbers) ) => ( B = k13_measure7(A) <=> ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => k8_funct_2(k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers),A,C) = k4_tarski(k8_funct_2(k5_numbers,k5_numbers,k12_measure7(A),C),k8_funct_2(k5_numbers,k5_numbers,B,C)) ) ) ) ) ), file(measure7,d12_measure7), []). fof(d13_measure7,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_zfmisc_1(k6_supinf_1)) & m2_relset_1(A,k5_numbers,k1_zfmisc_1(k6_supinf_1)) ) => ! [B] : ( m2_measure7(B,A) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) & m2_relset_1(C,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) ) => ( k9_funcop_1(k5_numbers,k5_numbers,k5_numbers,C) = k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers) => ! [D] : ( m1_measure7(D,k5_setfam_1(k6_supinf_1,k1_measure4(k6_supinf_1,A))) => ( D = k14_measure7(A,B,C) <=> ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => k3_measure7(k5_setfam_1(k6_supinf_1,k1_measure4(k6_supinf_1,A)),D,E) = k3_measure7(k8_funct_2(k5_numbers,k1_zfmisc_1(k6_supinf_1),A,k8_funct_2(k5_numbers,k5_numbers,k12_measure7(C),E)),k5_measure7(A,B,k8_funct_2(k5_numbers,k5_numbers,k12_measure7(C),E)),k8_funct_2(k5_numbers,k5_numbers,k13_measure7(C),E)) ) ) ) ) ) ) ) ), file(measure7,d13_measure7), []). fof(d1_supinf_1,axiom,( k1_supinf_1 = k1_numbers ), file(supinf_1,d1_supinf_1), []). fof(d2_funct_2,axiom,( ! [A,B,C] : ( C = k1_funct_2(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( v1_relat_1(E) & v1_funct_1(E) & D = E & k1_relat_1(E) = A & r1_tarski(k2_relat_1(E),B) ) ) ) ), file(funct_2,d2_funct_2), []). fof(d2_measure7,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1)) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_zfmisc_1(k6_supinf_1)) & m2_relset_1(B,k5_numbers,k1_zfmisc_1(k6_supinf_1)) ) => ( m1_measure7(B,A) <=> ( r1_tarski(A,k5_setfam_1(k6_supinf_1,k1_measure4(k6_supinf_1,B))) & ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( v5_measure5(k8_funct_2(k5_numbers,k1_zfmisc_1(k6_supinf_1),B,C)) & m1_subset_1(k8_funct_2(k5_numbers,k1_zfmisc_1(k6_supinf_1),B,C),k1_zfmisc_1(k6_supinf_1)) ) ) ) ) ) ) ), file(measure7,d2_measure7), []). fof(d3_measure7,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_zfmisc_1(k6_supinf_1)) & m2_relset_1(A,k5_numbers,k1_zfmisc_1(k6_supinf_1)) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_funct_2(k5_numbers,k1_zfmisc_1(k6_supinf_1))) & m2_relset_1(B,k5_numbers,k1_funct_2(k5_numbers,k1_zfmisc_1(k6_supinf_1))) ) => ( m2_measure7(B,A) <=> ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => m1_measure7(k8_funct_2(k5_numbers,k1_funct_2(k5_numbers,k1_zfmisc_1(k6_supinf_1)),B,C),k8_funct_2(k5_numbers,k1_zfmisc_1(k6_supinf_1),A,C)) ) ) ) ) ), file(measure7,d3_measure7), []). fof(d3_supinf_1,axiom,( k2_supinf_1 = k1_tarski(k1_numbers) ), file(supinf_1,d3_supinf_1), []). 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_measure7,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1)) => ! [B] : ( m1_measure7(B,A) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k5_numbers,k3_supinf_1) & m2_relset_1(C,k5_numbers,k3_supinf_1) ) => ( C = k4_measure7(A,B) <=> ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => k8_funct_2(k5_numbers,k3_supinf_1,C,D) = k5_measure5(k3_measure7(A,B,D)) ) ) ) ) ) ), file(measure7,d4_measure7), []). 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_measure7,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1)) => ! [B] : ( m1_measure7(B,A) => k7_measure7(A,B) = k19_supinf_2(k4_measure7(A,B)) ) ) ), file(measure7,d6_measure7), []). fof(d6_supinf_1,axiom,( k3_supinf_1 = k2_xboole_0(k1_numbers,k2_tarski(k2_supinf_1,k1_supinf_1)) ), file(supinf_1,d6_supinf_1), []). fof(d7_measure7,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_zfmisc_1(k6_supinf_1)) & m2_relset_1(A,k5_numbers,k1_zfmisc_1(k6_supinf_1)) ) => ! [B] : ( m2_measure7(B,A) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k5_numbers,k3_supinf_1) & m2_relset_1(C,k5_numbers,k3_supinf_1) ) => ( C = k8_measure7(A,B) <=> ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => k8_funct_2(k5_numbers,k3_supinf_1,C,D) = k7_measure7(k8_funct_2(k5_numbers,k1_zfmisc_1(k6_supinf_1),A,D),k5_measure7(A,B,D)) ) ) ) ) ) ), file(measure7,d7_measure7), []). fof(de_c2__measure7,axiom,( c2__measure7 = k2_funcop_1(k5_numbers,k6_measure5) ), file(measure7,c2__measure7), []). fof(dt_c2__measure7,axiom, ( v1_funct_1(c2__measure7) & v1_funct_2(c2__measure7,k5_numbers,k1_zfmisc_1(k6_supinf_1)) & m2_relset_1(c2__measure7,k5_numbers,k1_zfmisc_1(k6_supinf_1)) ), file(measure7,c2__measure7), []). fof(dt_k12_mcart_1,axiom,( ! [A,B,C,D] : ( ( m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(D,k1_zfmisc_1(B)) ) => m1_subset_1(k12_mcart_1(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ), file(mcart_1,k12_mcart_1), []). fof(dt_k12_measure7,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) & m1_relset_1(A,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) ) => ( v1_funct_1(k12_measure7(A)) & v1_funct_2(k12_measure7(A),k5_numbers,k5_numbers) & m2_relset_1(k12_measure7(A),k5_numbers,k5_numbers) ) ) ), file(measure7,k12_measure7), []). fof(dt_k13_measure7,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) & m1_relset_1(A,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) ) => ( v1_funct_1(k13_measure7(A)) & v1_funct_2(k13_measure7(A),k5_numbers,k5_numbers) & m2_relset_1(k13_measure7(A),k5_numbers,k5_numbers) ) ) ), file(measure7,k13_measure7), []). fof(dt_k13_supinf_2,axiom,( ! [A,B] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k3_supinf_1) & m1_relset_1(A,k5_numbers,k3_supinf_1) & m1_subset_1(B,k5_numbers) ) => m1_subset_1(k13_supinf_2(A,B),k3_supinf_1) ) ), file(supinf_2,k13_supinf_2), []). fof(dt_k14_measure7,axiom,( ! [A,B,C] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_zfmisc_1(k6_supinf_1)) & m1_relset_1(A,k5_numbers,k1_zfmisc_1(k6_supinf_1)) & m2_measure7(B,A) & v1_funct_1(C) & v1_funct_2(C,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) & m1_relset_1(C,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) ) => m1_measure7(k14_measure7(A,B,C),k5_setfam_1(k6_supinf_1,k1_measure4(k6_supinf_1,A))) ) ), file(measure7,k14_measure7), []). fof(dt_k15_mcart_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k15_mcart_1(A)) & v1_funct_1(k15_mcart_1(A)) ) ) ), file(mcart_1,k15_mcart_1), []). fof(dt_k16_mcart_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k16_mcart_1(A)) & v1_funct_1(k16_mcart_1(A)) ) ) ), file(mcart_1,k16_mcart_1), []). fof(dt_k18_supinf_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k3_supinf_1) & m1_relset_1(A,k5_numbers,k3_supinf_1) ) => ( v1_funct_1(k18_supinf_2(A)) & v1_funct_2(k18_supinf_2(A),k5_numbers,k3_supinf_1) & m2_relset_1(k18_supinf_2(A),k5_numbers,k3_supinf_1) ) ) ), file(supinf_2,k18_supinf_2), []). fof(dt_k19_supinf_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k3_supinf_1) & m1_relset_1(A,k5_numbers,k3_supinf_1) ) => m1_subset_1(k19_supinf_2(A),k3_supinf_1) ) ), file(supinf_2,k19_supinf_2), []). 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_measure4,axiom,( ! [A,B] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A)) & m1_relset_1(B,k5_numbers,k1_zfmisc_1(A)) ) => m1_subset_1(k1_measure4(A,B),k1_zfmisc_1(k1_zfmisc_1(A))) ) ), file(measure4,k1_measure4), []). fof(dt_k1_measure7,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k5_numbers)) & v1_funct_1(B) & v1_funct_2(B,A,k5_numbers) & m1_relset_1(B,A,k5_numbers) & m1_subset_1(C,A) ) => m2_subset_1(k1_measure7(A,B,C),k1_numbers,k5_numbers) ) ), file(measure7,k1_measure7), []). 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_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), []). fof(dt_k1_supinf_1,axiom,( $true ), file(supinf_1,k1_supinf_1), []). fof(dt_k1_supinf_2,axiom,( m1_subset_1(k1_supinf_2,k3_supinf_1) ), file(supinf_2,k1_supinf_2), []). 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_k2_funcop_1,axiom,( $true ), file(funcop_1,k2_funcop_1), []). fof(dt_k2_relat_1,axiom,( $true ), file(relat_1,k2_relat_1), []). fof(dt_k2_supinf_1,axiom,( $true ), file(supinf_1,k2_supinf_1), []). fof(dt_k2_supinf_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k3_supinf_1) & m1_subset_1(B,k3_supinf_1) ) => m1_subset_1(k2_supinf_2(A,B),k3_supinf_1) ) ), file(supinf_2,k2_supinf_2), []). 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_measure7,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1)) & m1_measure7(B,A) & m1_subset_1(C,k5_numbers) ) => ( v5_measure5(k3_measure7(A,B,C)) & m1_subset_1(k3_measure7(A,B,C),k1_zfmisc_1(k6_supinf_1)) ) ) ), file(measure7,k3_measure7), []). fof(dt_k3_supinf_1,axiom,( $true ), file(supinf_1,k3_supinf_1), []). fof(dt_k3_tarski,axiom,( $true ), file(tarski,k3_tarski), []). fof(dt_k4_measure7,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1)) & m1_measure7(B,A) ) => ( v1_funct_1(k4_measure7(A,B)) & v1_funct_2(k4_measure7(A,B),k5_numbers,k3_supinf_1) & m2_relset_1(k4_measure7(A,B),k5_numbers,k3_supinf_1) ) ) ), file(measure7,k4_measure7), []). fof(dt_k4_tarski,axiom,( $true ), file(tarski,k4_tarski), []). fof(dt_k5_measure5,axiom,( ! [A] : ( ( v5_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k6_supinf_1)) ) => m1_subset_1(k5_measure5(A),k3_supinf_1) ) ), file(measure5,k5_measure5), []). fof(dt_k5_measure7,axiom,( ! [A,B,C] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_zfmisc_1(k6_supinf_1)) & m1_relset_1(A,k5_numbers,k1_zfmisc_1(k6_supinf_1)) & m2_measure7(B,A) & m1_subset_1(C,k5_numbers) ) => m1_measure7(k5_measure7(A,B,C),k8_funct_2(k5_numbers,k1_zfmisc_1(k6_supinf_1),A,C)) ) ), file(measure7,k5_measure7), []). 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_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_setfam_1,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => m1_subset_1(k5_setfam_1(A,B),k1_zfmisc_1(A)) ) ), file(setfam_1,k5_setfam_1), []). fof(dt_k6_measure5,axiom, ( v1_xboole_0(k6_measure5) & v5_measure5(k6_measure5) & m1_subset_1(k6_measure5,k1_zfmisc_1(k6_supinf_1)) ), file(measure5,k6_measure5), []). fof(dt_k6_supinf_1,axiom, ( ~ v1_xboole_0(k6_supinf_1) & m1_subset_1(k6_supinf_1,k1_zfmisc_1(k3_supinf_1)) ), file(supinf_1,k6_supinf_1), []). fof(dt_k7_funct_2,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(D,A,B) & m1_relset_1(D,A,B) & v1_funct_1(E) & v1_funct_2(E,B,C) & m1_relset_1(E,B,C) ) => ( v1_funct_1(k7_funct_2(A,B,C,D,E)) & v1_funct_2(k7_funct_2(A,B,C,D,E),A,C) & m2_relset_1(k7_funct_2(A,B,C,D,E),A,C) ) ) ), file(funct_2,k7_funct_2), []). fof(dt_k7_measure7,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1)) & m1_measure7(B,A) ) => m1_subset_1(k7_measure7(A,B),k3_supinf_1) ) ), file(measure7,k7_measure7), []). 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_measure7,axiom,( ! [A,B] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_zfmisc_1(k6_supinf_1)) & m1_relset_1(A,k5_numbers,k1_zfmisc_1(k6_supinf_1)) & m2_measure7(B,A) ) => ( v1_funct_1(k8_measure7(A,B)) & v1_funct_2(k8_measure7(A,B),k5_numbers,k3_supinf_1) & m2_relset_1(k8_measure7(A,B),k5_numbers,k3_supinf_1) ) ) ), file(measure7,k8_measure7), []). fof(dt_k9_funcop_1,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & v1_funct_1(D) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) ) => m2_relset_1(k9_funcop_1(A,B,C,D),B,C) ) ), file(funcop_1,k9_funcop_1), []). fof(dt_m1_measure7,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1)) => ! [B] : ( m1_measure7(B,A) => ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_zfmisc_1(k6_supinf_1)) & m2_relset_1(B,k5_numbers,k1_zfmisc_1(k6_supinf_1)) ) ) ) ), file(measure7,m1_measure7), []). 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_measure7,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_zfmisc_1(k6_supinf_1)) & m1_relset_1(A,k5_numbers,k1_zfmisc_1(k6_supinf_1)) ) => ! [B] : ( m2_measure7(B,A) => ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_funct_2(k5_numbers,k1_zfmisc_1(k6_supinf_1))) & m2_relset_1(B,k5_numbers,k1_funct_2(k5_numbers,k1_zfmisc_1(k6_supinf_1))) ) ) ) ), file(measure7,m2_measure7), []). 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_measure7,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1)) => ? [B] : m1_measure7(B,A) ) ), file(measure7,m1_measure7), []). 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_measure7,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_zfmisc_1(k6_supinf_1)) & m1_relset_1(A,k5_numbers,k1_zfmisc_1(k6_supinf_1)) ) => ? [B] : m2_measure7(B,A) ) ), file(measure7,m2_measure7), []). 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(fc1_fraenkel,axiom,( ! [A,B] : v1_fraenkel(k1_funct_2(A,B)) ), file(fraenkel,fc1_fraenkel), []). 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_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ), file(subset_1,fc1_subset_1), []). fof(fc1_supinf_1,axiom,( ~ v1_xboole_0(k3_supinf_1) ), file(supinf_1,fc1_supinf_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_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_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) ), file(subset_1,fc2_subset_1), []). fof(fc3_subset_1,axiom,( ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ), file(subset_1,fc3_subset_1), []). 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(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(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_measure7,axiom,( ! [A,B,C] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) & m2_relset_1(B,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) & m2_subset_1(C,k1_numbers,k5_numbers) ) => ( r2_hidden(A,a_2_0_measure7(B,C)) <=> ? [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) & A = D & k8_funct_2(k5_numbers,k5_numbers,k12_measure7(B),k1_nat_1(C,1)) = k8_funct_2(k5_numbers,k5_numbers,k12_measure7(B),D) ) ) ) ), file(measure7,a_2_0_measure7), []). fof(idempotence_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,A) = A ), file(xboole_0,k2_xboole_0), []). fof(l35_measure7,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => k8_funct_2(k5_numbers,k1_zfmisc_1(k6_supinf_1),c2__measure7,A) = k6_measure5 ) ), file(measure7,l35_measure7), []). 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_fraenkel,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_fraenkel(A) ) ), file(fraenkel,rc1_fraenkel), []). 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_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_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_supinf_1,axiom,( ? [A] : v3_supinf_1(A) ), file(supinf_1,rc3_supinf_1), []). fof(redefinition_k12_mcart_1,axiom,( ! [A,B,C,D] : ( ( m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(D,k1_zfmisc_1(B)) ) => k12_mcart_1(A,B,C,D) = k2_zfmisc_1(C,D) ) ), file(mcart_1,k12_mcart_1), []). fof(redefinition_k12_measure7,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) & m1_relset_1(A,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) ) => k12_measure7(A) = k15_mcart_1(A) ) ), file(measure7,k12_measure7), []). fof(redefinition_k13_measure7,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) & m1_relset_1(A,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) ) => k13_measure7(A) = k16_mcart_1(A) ) ), file(measure7,k13_measure7), []). fof(redefinition_k13_supinf_2,axiom,( ! [A,B] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k3_supinf_1) & m1_relset_1(A,k5_numbers,k3_supinf_1) & m1_subset_1(B,k5_numbers) ) => k13_supinf_2(A,B) = k1_funct_1(A,B) ) ), file(supinf_2,k13_supinf_2), []). fof(redefinition_k1_measure4,axiom,( ! [A,B] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A)) & m1_relset_1(B,k5_numbers,k1_zfmisc_1(A)) ) => k1_measure4(A,B) = k2_relat_1(B) ) ), file(measure4,k1_measure4), []). fof(redefinition_k1_measure7,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k5_numbers)) & v1_funct_1(B) & v1_funct_2(B,A,k5_numbers) & m1_relset_1(B,A,k5_numbers) & m1_subset_1(C,A) ) => k1_measure7(A,B,C) = k1_funct_1(B,C) ) ), file(measure7,k1_measure7), []). 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_k3_measure7,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1)) & m1_measure7(B,A) & m1_subset_1(C,k5_numbers) ) => k3_measure7(A,B,C) = k1_funct_1(B,C) ) ), file(measure7,k3_measure7), []). fof(redefinition_k5_measure7,axiom,( ! [A,B,C] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_zfmisc_1(k6_supinf_1)) & m1_relset_1(A,k5_numbers,k1_zfmisc_1(k6_supinf_1)) & m2_measure7(B,A) & m1_subset_1(C,k5_numbers) ) => k5_measure7(A,B,C) = k1_funct_1(B,C) ) ), file(measure7,k5_measure7), []). fof(redefinition_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_k5_setfam_1,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => k5_setfam_1(A,B) = k3_tarski(B) ) ), file(setfam_1,k5_setfam_1), []). fof(redefinition_k6_measure5,axiom,( k6_measure5 = k1_xboole_0 ), file(measure5,k6_measure5), []). fof(redefinition_k6_supinf_1,axiom,( k6_supinf_1 = k1_numbers ), file(supinf_1,k6_supinf_1), []). fof(redefinition_k7_funct_2,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(D,A,B) & m1_relset_1(D,A,B) & v1_funct_1(E) & v1_funct_2(E,B,C) & m1_relset_1(E,B,C) ) => k7_funct_2(A,B,C,D,E) = k5_relat_1(D,E) ) ), file(funct_2,k7_funct_2), []). 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_funcop_1,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & v1_funct_1(D) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) ) => k9_funcop_1(A,B,C,D) = k2_relat_1(D) ) ), file(funcop_1,k9_funcop_1), []). 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_supinf_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k3_supinf_1) & m1_subset_1(B,k3_supinf_1) ) => r1_supinf_1(A,A) ) ), file(supinf_1,r1_supinf_1), []). fof(reflexivity_r1_tarski,axiom,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), []). fof(s1_nat_1__e6_32__measure7,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) & m2_relset_1(A,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) ) => ( ( ? [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) & ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k5_numbers,k1_zfmisc_1(k6_supinf_1)) & m2_relset_1(C,k5_numbers,k1_zfmisc_1(k6_supinf_1)) ) => ! [D] : ( m2_measure7(D,C) => r1_supinf_1(k8_funct_2(k5_numbers,k3_supinf_1,k18_supinf_2(k4_measure7(k5_setfam_1(k6_supinf_1,k1_measure4(k6_supinf_1,C)),k14_measure7(C,D,A))),0),k8_funct_2(k5_numbers,k3_supinf_1,k18_supinf_2(k8_measure7(C,D)),B)) ) ) ) & ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ( ? [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) & ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,k5_numbers,k1_zfmisc_1(k6_supinf_1)) & m2_relset_1(G,k5_numbers,k1_zfmisc_1(k6_supinf_1)) ) => ! [H] : ( m2_measure7(H,G) => r1_supinf_1(k8_funct_2(k5_numbers,k3_supinf_1,k18_supinf_2(k4_measure7(k5_setfam_1(k6_supinf_1,k1_measure4(k6_supinf_1,G)),k14_measure7(G,H,A))),E),k8_funct_2(k5_numbers,k3_supinf_1,k18_supinf_2(k8_measure7(G,H)),F)) ) ) ) => ? [I] : ( m2_subset_1(I,k1_numbers,k5_numbers) & ! [J] : ( ( v1_funct_1(J) & v1_funct_2(J,k5_numbers,k1_zfmisc_1(k6_supinf_1)) & m2_relset_1(J,k5_numbers,k1_zfmisc_1(k6_supinf_1)) ) => ! [K] : ( m2_measure7(K,J) => r1_supinf_1(k8_funct_2(k5_numbers,k3_supinf_1,k18_supinf_2(k4_measure7(k5_setfam_1(k6_supinf_1,k1_measure4(k6_supinf_1,J)),k14_measure7(J,K,A))),k1_nat_1(E,1)),k8_funct_2(k5_numbers,k3_supinf_1,k18_supinf_2(k8_measure7(J,K)),I)) ) ) ) ) ) ) => ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ? [L] : ( m2_subset_1(L,k1_numbers,k5_numbers) & ! [M] : ( ( v1_funct_1(M) & v1_funct_2(M,k5_numbers,k1_zfmisc_1(k6_supinf_1)) & m2_relset_1(M,k5_numbers,k1_zfmisc_1(k6_supinf_1)) ) => ! [N] : ( m2_measure7(N,M) => r1_supinf_1(k8_funct_2(k5_numbers,k3_supinf_1,k18_supinf_2(k4_measure7(k5_setfam_1(k6_supinf_1,k1_measure4(k6_supinf_1,M)),k14_measure7(M,N,A))),E),k8_funct_2(k5_numbers,k3_supinf_1,k18_supinf_2(k8_measure7(M,N)),L)) ) ) ) ) ) ) ), file(measure7,s1_nat_1__e6_32__measure7), []). fof(s3_funct_2__e22_32_2__measure7,axiom,( ! [A,B] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) & m2_relset_1(A,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k5_numbers)) ) => ( ! [C] : ( m1_subset_1(C,B) => ? [D] : ( m1_subset_1(D,k5_numbers) & D = k8_funct_2(k5_numbers,k5_numbers,k13_measure7(A),C) ) ) => ? [C] : ( v1_funct_1(C) & v1_funct_2(C,B,k5_numbers) & m2_relset_1(C,B,k5_numbers) & ! [D] : ( m1_subset_1(D,B) => k8_funct_2(B,k5_numbers,C,D) = k8_funct_2(k5_numbers,k5_numbers,k13_measure7(A),D) ) ) ) ) ), file(measure7,s3_funct_2__e22_32_2__measure7), []). fof(s3_funct_2__e4_32_2__measure7,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) & m2_relset_1(A,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) & m2_subset_1(B,k1_numbers,k5_numbers) & v1_funct_1(C) & v1_funct_2(C,k5_numbers,k1_zfmisc_1(k6_supinf_1)) & m2_relset_1(C,k5_numbers,k1_zfmisc_1(k6_supinf_1)) & m2_measure7(D,C) ) => ( ! [E] : ( m1_subset_1(E,k5_numbers) => ? [F] : ( m1_subset_1(F,k1_funct_2(k5_numbers,k1_zfmisc_1(k6_supinf_1))) & ( E = k8_funct_2(k5_numbers,k5_numbers,k12_measure7(A),k1_nat_1(B,1)) => ! [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) => k1_funct_1(F,G) = k3_measure7(k8_funct_2(k5_numbers,k1_zfmisc_1(k6_supinf_1),C,E),k5_measure7(C,D,E),G) ) ) & ( E != k8_funct_2(k5_numbers,k5_numbers,k12_measure7(A),k1_nat_1(B,1)) => ! [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) => k1_funct_1(F,G) = k6_measure5 ) ) ) ) => ? [E] : ( v1_funct_1(E) & v1_funct_2(E,k5_numbers,k1_funct_2(k5_numbers,k1_zfmisc_1(k6_supinf_1))) & m2_relset_1(E,k5_numbers,k1_funct_2(k5_numbers,k1_zfmisc_1(k6_supinf_1))) & ! [F] : ( m1_subset_1(F,k5_numbers) => ( ( F = k8_funct_2(k5_numbers,k5_numbers,k12_measure7(A),k1_nat_1(B,1)) => ! [H] : ( m2_subset_1(H,k1_numbers,k5_numbers) => k1_funct_1(k8_funct_2(k5_numbers,k1_funct_2(k5_numbers,k1_zfmisc_1(k6_supinf_1)),E,F),H) = k3_measure7(k8_funct_2(k5_numbers,k1_zfmisc_1(k6_supinf_1),C,F),k5_measure7(C,D,F),H) ) ) & ( F != k8_funct_2(k5_numbers,k5_numbers,k12_measure7(A),k1_nat_1(B,1)) => ! [H] : ( m2_subset_1(H,k1_numbers,k5_numbers) => k1_funct_1(k8_funct_2(k5_numbers,k1_funct_2(k5_numbers,k1_zfmisc_1(k6_supinf_1)),E,F),H) = k6_measure5 ) ) ) ) ) ) ) ), file(measure7,s3_funct_2__e4_32_2__measure7), []). fof(s3_funct_2__e7_32_2__measure7,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) & m2_relset_1(A,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) & m2_subset_1(B,k1_numbers,k5_numbers) & v1_funct_1(C) & v1_funct_2(C,k5_numbers,k1_zfmisc_1(k6_supinf_1)) & m2_relset_1(C,k5_numbers,k1_zfmisc_1(k6_supinf_1)) & m2_measure7(D,C) ) => ( ! [E] : ( m1_subset_1(E,k5_numbers) => ? [F] : ( m1_subset_1(F,k1_funct_2(k5_numbers,k1_zfmisc_1(k6_supinf_1))) & ( E != k8_funct_2(k5_numbers,k5_numbers,k12_measure7(A),k1_nat_1(B,1)) => ! [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) => k1_funct_1(F,G) = k3_measure7(k8_funct_2(k5_numbers,k1_zfmisc_1(k6_supinf_1),C,E),k5_measure7(C,D,E),G) ) ) & ( E = k8_funct_2(k5_numbers,k5_numbers,k12_measure7(A),k1_nat_1(B,1)) => ! [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) => k1_funct_1(F,G) = k6_measure5 ) ) ) ) => ? [E] : ( v1_funct_1(E) & v1_funct_2(E,k5_numbers,k1_funct_2(k5_numbers,k1_zfmisc_1(k6_supinf_1))) & m2_relset_1(E,k5_numbers,k1_funct_2(k5_numbers,k1_zfmisc_1(k6_supinf_1))) & ! [F] : ( m1_subset_1(F,k5_numbers) => ( ( F != k8_funct_2(k5_numbers,k5_numbers,k12_measure7(A),k1_nat_1(B,1)) => ! [H] : ( m2_subset_1(H,k1_numbers,k5_numbers) => k1_funct_1(k8_funct_2(k5_numbers,k1_funct_2(k5_numbers,k1_zfmisc_1(k6_supinf_1)),E,F),H) = k3_measure7(k8_funct_2(k5_numbers,k1_zfmisc_1(k6_supinf_1),C,F),k5_measure7(C,D,F),H) ) ) & ( F = k8_funct_2(k5_numbers,k5_numbers,k12_measure7(A),k1_nat_1(B,1)) => ! [H] : ( m2_subset_1(H,k1_numbers,k5_numbers) => k1_funct_1(k8_funct_2(k5_numbers,k1_funct_2(k5_numbers,k1_zfmisc_1(k6_supinf_1)),E,F),H) = k6_measure5 ) ) ) ) ) ) ) ), file(measure7,s3_funct_2__e7_32_2__measure7), []). 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_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(t12_measure7,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k3_supinf_1) & m2_relset_1(A,k5_numbers,k3_supinf_1) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,k3_supinf_1) & m2_relset_1(B,k5_numbers,k3_supinf_1) ) => ( ( v6_supinf_2(A,k5_numbers) & v6_supinf_2(B,k5_numbers) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k5_numbers)) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,C,k5_numbers) & m2_relset_1(D,C,k5_numbers) ) => ( ( v2_funct_1(D) & ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ( ( r2_hidden(E,C) => k8_funct_2(k5_numbers,k3_supinf_1,A,E) = k1_funct_1(k7_funct_2(C,k5_numbers,k3_supinf_1,D,B),E) ) & ( ~ r2_hidden(E,C) => k8_funct_2(k5_numbers,k3_supinf_1,A,E) = k1_supinf_2 ) ) ) ) => r1_supinf_1(k19_supinf_2(A),k19_supinf_2(B)) ) ) ) ) ) ) ), file(measure7,t12_measure7), []). fof(t13_measure7,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1)) => ! [B] : ( m1_measure7(B,A) => v6_supinf_2(k4_measure7(A,B),k5_numbers) ) ) ), file(measure7,t13_measure7), []). fof(t14_measure7,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_zfmisc_1(k6_supinf_1)) & m2_relset_1(A,k5_numbers,k1_zfmisc_1(k6_supinf_1)) ) => ! [B] : ( m2_measure7(B,A) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => r1_supinf_1(k1_supinf_2,k8_funct_2(k5_numbers,k3_supinf_1,k8_measure7(A,B),C)) ) ) ) ), file(measure7,t14_measure7), []). fof(t18_supinf_2,axiom,( ! [A] : ( m1_subset_1(A,k3_supinf_1) => ( k2_supinf_2(A,k1_supinf_2) = A & k2_supinf_2(k1_supinf_2,A) = A ) ) ), file(supinf_2,t18_supinf_2), []). fof(t1_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(A,0) = A ) ), file(arithm,t1_arithm), []). fof(t1_boole,axiom,( ! [A] : k2_xboole_0(A,k1_xboole_0) = A ), file(boole,t1_boole), []). fof(t1_measure7,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k3_supinf_1) & m2_relset_1(A,k5_numbers,k3_supinf_1) ) => ( ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => k8_funct_2(k5_numbers,k3_supinf_1,A,B) = k1_supinf_2 ) => k19_supinf_2(A) = k1_supinf_2 ) ) ), file(measure7,t1_measure7), []). 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(t21_funct_2,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ( r2_hidden(C,A) => ( B = k1_xboole_0 | k1_funct_1(k5_relat_1(D,E),C) = k1_funct_1(E,k1_funct_1(D,C)) ) ) ) ) ), file(funct_2,t21_funct_2), []). fof(t22_supinf_1,axiom,( ! [A] : ( m1_subset_1(A,k3_supinf_1) => ! [B] : ( m1_subset_1(B,k3_supinf_1) => ( ( r1_supinf_1(A,B) & r1_supinf_1(B,A) ) => A = B ) ) ) ), file(supinf_1,t22_supinf_1), []). fof(t25_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 ) => ( v2_funct_1(C) <=> ! [D,E] : ( ( r2_hidden(D,A) & r2_hidden(E,A) & k1_funct_1(C,D) = k1_funct_1(C,E) ) => D = E ) ) ) ) ), file(funct_2,t25_funct_2), []). fof(t29_supinf_1,axiom,( ! [A] : ( m1_subset_1(A,k3_supinf_1) => ! [B] : ( m1_subset_1(B,k3_supinf_1) => ! [C] : ( m1_subset_1(C,k3_supinf_1) => ( ( r1_supinf_1(A,B) & r1_supinf_1(B,C) ) => r1_supinf_1(A,C) ) ) ) ) ), file(supinf_1,t29_supinf_1), []). fof(t2_measure7,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k3_supinf_1) & m2_relset_1(A,k5_numbers,k3_supinf_1) ) => ( v6_supinf_2(A,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => r1_supinf_1(k8_funct_2(k5_numbers,k3_supinf_1,A,B),k8_funct_2(k5_numbers,k3_supinf_1,k18_supinf_2(A),B)) ) ) ) ), file(measure7,t2_measure7), []). 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(t2_xboole_1,axiom,( ! [A] : r1_tarski(k1_xboole_0,A) ), file(xboole_1,t2_xboole_1), []). fof(t3_measure6,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k3_supinf_1) & m2_relset_1(A,k5_numbers,k3_supinf_1) ) => ! [B] : ( m1_subset_1(B,k3_supinf_1) => ( v6_supinf_2(A,k5_numbers) => ( ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ~ r1_supinf_1(B,k13_supinf_2(A,C)) ) | r1_supinf_1(B,k19_supinf_2(A)) ) ) ) ) ), file(measure6,t3_measure6), []). fof(t3_measure7,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k3_supinf_1) & m2_relset_1(A,k5_numbers,k3_supinf_1) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,k3_supinf_1) & m2_relset_1(B,k5_numbers,k3_supinf_1) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k5_numbers,k3_supinf_1) & m2_relset_1(C,k5_numbers,k3_supinf_1) ) => ( ( v6_supinf_2(B,k5_numbers) & v6_supinf_2(C,k5_numbers) & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => k8_funct_2(k5_numbers,k3_supinf_1,A,D) = k2_supinf_2(k8_funct_2(k5_numbers,k3_supinf_1,B,D),k8_funct_2(k5_numbers,k3_supinf_1,C,D)) ) ) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => k8_funct_2(k5_numbers,k3_supinf_1,k18_supinf_2(A),D) = k2_supinf_2(k8_funct_2(k5_numbers,k3_supinf_1,k18_supinf_2(B),D),k8_funct_2(k5_numbers,k3_supinf_1,k18_supinf_2(C),D)) ) ) ) ) ) ), file(measure7,t3_measure7), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t4_funct_2,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_tarski(k2_relat_1(B),A) => ( v1_funct_1(B) & v1_funct_2(B,k1_relat_1(B),A) & m2_relset_1(B,k1_relat_1(B),A) ) ) ) ), file(funct_2,t4_funct_2), []). fof(t4_measure1,axiom,( ! [A] : ( m1_subset_1(A,k3_supinf_1) => ! [B] : ( m1_subset_1(B,k3_supinf_1) => ! [C] : ( m1_subset_1(C,k3_supinf_1) => ! [D] : ( m1_subset_1(D,k3_supinf_1) => ( ( r1_supinf_1(k1_supinf_2,A) & r1_supinf_1(k1_supinf_2,C) & r1_supinf_1(A,B) & r1_supinf_1(C,D) ) => r1_supinf_1(k2_supinf_2(A,C),k2_supinf_2(B,D)) ) ) ) ) ) ), file(measure1,t4_measure1), []). 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(t58_supinf_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k3_supinf_1) & m2_relset_1(B,A,k3_supinf_1) ) => ( v6_supinf_2(B,A) <=> ! [C] : ( m1_subset_1(C,A) => r1_supinf_1(k1_supinf_2,k8_funct_2(A,k3_supinf_1,B,C)) ) ) ) ) ), file(supinf_2,t58_supinf_2), []). fof(t59_supinf_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k3_supinf_1) & m2_relset_1(A,k5_numbers,k3_supinf_1) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( v6_supinf_2(A,k5_numbers) => ( r1_supinf_1(k13_supinf_2(k18_supinf_2(A),B),k13_supinf_2(k18_supinf_2(A),k1_nat_1(B,1))) & r1_supinf_1(k1_supinf_2,k13_supinf_2(k18_supinf_2(A),B)) ) ) ) ) ), file(supinf_2,t59_supinf_2), []). 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(t60_measure5,axiom,( k5_measure5(k6_measure5) = k1_supinf_2 ), file(measure5,t60_measure5), []). fof(t60_supinf_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k3_supinf_1) & m2_relset_1(A,k5_numbers,k3_supinf_1) ) => ( v6_supinf_2(A,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => r1_supinf_1(k13_supinf_2(k18_supinf_2(A),B),k13_supinf_2(k18_supinf_2(A),k1_nat_1(B,C))) ) ) ) ) ), file(supinf_2,t60_supinf_2), []). fof(t62_supinf_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k3_supinf_1) & m2_relset_1(A,k5_numbers,k3_supinf_1) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,k3_supinf_1) & m2_relset_1(B,k5_numbers,k3_supinf_1) ) => ( ( v6_supinf_2(A,k5_numbers) & ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => r1_supinf_1(k13_supinf_2(A,C),k13_supinf_2(B,C)) ) ) => r1_supinf_1(k19_supinf_2(A),k19_supinf_2(B)) ) ) ) ), file(supinf_2,t62_supinf_2), []). fof(t63_supinf_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k3_supinf_1) & m2_relset_1(A,k5_numbers,k3_supinf_1) ) => ( k13_supinf_2(k18_supinf_2(A),0) = k13_supinf_2(A,0) & ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m1_subset_1(C,k3_supinf_1) => ( C = k13_supinf_2(k18_supinf_2(A),B) => k13_supinf_2(k18_supinf_2(A),k1_nat_1(B,1)) = k2_supinf_2(C,k13_supinf_2(A,k1_nat_1(B,1))) ) ) ) ) ) ), file(supinf_2,t63_supinf_2), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t7_measure7,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k3_supinf_1) & m2_relset_1(A,k5_numbers,k3_supinf_1) ) => ( v6_supinf_2(A,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => r1_supinf_1(k8_funct_2(k5_numbers,k3_supinf_1,k18_supinf_2(A),B),k19_supinf_2(A)) ) ) ) ), file(measure7,t7_measure7), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []).