% Mizar problem: t11_integra5,integra5,329,24 fof(t11_integra5,conjecture,( ! [A] : ( ( v1_integra1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m2_relset_1(B,k1_numbers,k1_numbers) ) => ( r2_fcont_1(B,A) => r1_integra5(A,B) ) ) ) ), 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_integra1,cc1_membered,cc1_relset_1,cc1_seq_1,cc1_xreal_0,cc20_membered,cc2_arytm_3,cc2_integra1,cc2_membered,cc2_xreal_0,cc3_arytm_3,cc3_membered,cc3_xreal_0,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,commutativity_k11_binop_2,commutativity_k2_xcmplx_0,commutativity_k3_real_1,commutativity_k3_seq_1,commutativity_k3_xboole_0,commutativity_k3_xcmplx_0,commutativity_k5_subset_1,commutativity_k6_seq_1,commutativity_k9_binop_2,commutativity_k9_seq_1,connectedness_r1_xreal_0,d10_integra1,d10_xboole_0,d11_rfunct_1,d12_funct_1,d19_integra1,d1_absvalue,d1_fcont_2,d1_integra5,d1_pre_circ,d1_xreal_0,d2_integra5,d3_finseq_1,d3_integra2,d3_seq_4,d3_tarski,d4_integra2,d4_partfun1,d5_funct_1,d5_integra2,d6_integra1,d6_seq_2,d7_integra1,d7_seq_2,d8_integra1,d9_integra1,dt_k10_binop_2,dt_k10_relset_1,dt_k10_rvsum_1,dt_k10_seq_1,dt_k11_binop_2,dt_k11_integra1,dt_k12_integra1,dt_k14_integra1,dt_k15_integra1,dt_k15_rvsum_1,dt_k15_seq_1,dt_k16_complex1,dt_k16_integra1,dt_k17_integra1,dt_k17_seq_1,dt_k18_complex1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_funct_1,dt_k1_goboard1,dt_k1_integra1,dt_k1_integra5,dt_k1_numbers,dt_k1_pre_circ,dt_k1_real_1,dt_k1_relat_1,dt_k1_seq_2,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_finseq_1,dt_k2_integra1,dt_k2_integra2,dt_k2_partfun1,dt_k2_relat_1,dt_k2_seq_1,dt_k2_seq_2,dt_k2_seq_4,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_finseq_1,dt_k3_integra1,dt_k3_integra2,dt_k3_pscomp_1,dt_k3_real_1,dt_k3_seq_1,dt_k3_seq_4,dt_k3_xboole_0,dt_k3_xcmplx_0,dt_k4_finseq_1,dt_k4_finseq_2,dt_k4_funct_3,dt_k4_integra1,dt_k4_integra2,dt_k4_pscomp_1,dt_k4_relset_1,dt_k4_seq_1,dt_k4_xcmplx_0,dt_k5_integra1,dt_k5_numbers,dt_k5_ordinal2,dt_k5_real_1,dt_k5_relset_1,dt_k5_rfunct_1,dt_k5_subset_1,dt_k6_integra1,dt_k6_seq_1,dt_k6_xcmplx_0,dt_k7_binop_2,dt_k7_integra1,dt_k7_relat_1,dt_k7_rvsum_1,dt_k7_xcmplx_0,dt_k8_funct_2,dt_k8_integra1,dt_k8_relset_1,dt_k8_rvsum_1,dt_k9_binop_2,dt_k9_relat_1,dt_k9_rvsum_1,dt_k9_seq_1,dt_m1_finseq_1,dt_m1_finseq_2,dt_m1_integra1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_integra1,dt_m2_relset_1,dt_m2_subset_1,dt_m3_integra1,existence_m1_finseq_1,existence_m1_finseq_2,existence_m1_integra1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_finseq_2,existence_m2_integra1,existence_m2_relset_1,existence_m2_subset_1,existence_m3_integra1,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc13_xreal_0,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc17_xreal_0,fc18_xreal_0,fc19_xreal_0,fc1_finseq_2,fc1_integra1,fc1_ordinal2,fc1_seq_1,fc1_xreal_0,fc20_xreal_0,fc21_xreal_0,fc22_xreal_0,fc23_xreal_0,fc24_xreal_0,fc27_membered,fc27_xreal_0,fc28_membered,fc28_xreal_0,fc29_membered,fc29_xreal_0,fc2_membered,fc2_seq_1,fc30_membered,fc30_xreal_0,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc3_seq_1,fc3_xreal_0,fc4_seq_1,fc4_xreal_0,fc5_membered,fc5_xreal_0,fc6_membered,fc6_xreal_0,fc7_seq_1,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,idempotence_k3_xboole_0,idempotence_k5_subset_1,involutiveness_k1_real_1,involutiveness_k4_xcmplx_0,involutiveness_k7_binop_2,projectivity_k16_complex1,projectivity_k18_complex1,rc1_arytm_3,rc1_finseq_2,rc1_integra1,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_integra1,rc2_xreal_0,rc3_integra1,rc3_xreal_0,rc4_xreal_0,redefinition_k10_binop_2,redefinition_k10_relset_1,redefinition_k10_rvsum_1,redefinition_k10_seq_1,redefinition_k11_binop_2,redefinition_k14_integra1,redefinition_k15_integra1,redefinition_k16_integra1,redefinition_k17_seq_1,redefinition_k18_complex1,redefinition_k1_goboard1,redefinition_k1_pre_circ,redefinition_k1_real_1,redefinition_k2_finseq_1,redefinition_k2_partfun1,redefinition_k2_seq_1,redefinition_k2_seq_2,redefinition_k3_finseq_1,redefinition_k3_pscomp_1,redefinition_k3_real_1,redefinition_k4_finseq_1,redefinition_k4_pscomp_1,redefinition_k4_relset_1,redefinition_k5_numbers,redefinition_k5_real_1,redefinition_k5_relset_1,redefinition_k5_rfunct_1,redefinition_k5_subset_1,redefinition_k6_seq_1,redefinition_k7_binop_2,redefinition_k8_funct_2,redefinition_k8_integra1,redefinition_k8_relset_1,redefinition_k8_rvsum_1,redefinition_k9_binop_2,redefinition_k9_seq_1,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_relset_1,redefinition_m2_subset_1,redefinition_m3_integra1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,spc0_boole,spc1_boole,spc1_numerals,t105_real_2,t10_integra1,t110_finseq_2,t112_rvsum_1,t117_rvsum_1,t11_fcont_2,t11_integra1,t11_seq_1,t120_rvsum_1,t127_real_2,t12_integra4,t131_funct_2,t14_integra1,t14_seq_1,t15_seq_1,t16_integra1,t177_real_2,t17_xboole_1,t18_integra4,t19_integra4,t1_arithm,t1_integra2,t1_numerals,t1_real,t1_subset,t22_integra1,t24_integra4,t26_integra1,t26_seq_2,t28_rcomp_1,t28_xboole_1,t2_arithm,t2_boole,t2_real,t2_subset,t2_xreal_1,t30_fcont_1,t30_integra1,t3_arithm,t3_real,t3_subset,t43_partfun1,t48_rvsum_1,t4_arithm,t4_real,t4_subset,t50_xreal_1,t5_arithm,t5_real,t5_subset,t66_xreal_1,t67_rvsum_1,t68_funct_1,t6_arithm,t6_boole,t6_real,t7_boole,t7_real,t7_xreal_1,t8_boole,t8_integra4,t8_real,t92_real_1,t9_integra4]), [file(integra5,t11_integra5)]). 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_integra1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v1_integra1(A) => ( ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v1_rcomp_1(A) ) ) ) ), file(integra1,cc1_integra1), []). 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_seq_1,axiom,( ! [A,B] : ( v2_membered(B) => ! [C] : ( m1_relset_1(C,A,B) => ( v1_funct_1(C) => ( v1_funct_1(C) & v1_seq_1(C) ) ) ) ) ), file(seq_1,cc1_seq_1), []). fof(cc1_xreal_0,axiom,( ! [A] : ( v4_ordinal2(A) => v1_xreal_0(A) ) ), file(xreal_0,cc1_xreal_0), []). 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_integra1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v1_integra1(A) => ( v1_membered(A) & v2_membered(A) & v3_seq_4(A) ) ) ) ), file(integra1,cc2_integra1), []). fof(cc2_membered,axiom,( ! [A] : ( v4_membered(A) => v3_membered(A) ) ), file(membered,cc2_membered), []). fof(cc2_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xcmplx_0(A) ) ), file(xreal_0,cc2_xreal_0), []). 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(cc3_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xreal_0(A) ) => ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(xreal_0,cc3_xreal_0), []). fof(cc4_membered,axiom,( ! [A] : ( v2_membered(A) => v1_membered(A) ) ), file(membered,cc4_membered), []). fof(cc4_xreal_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A) ) ) ), file(xreal_0,cc4_xreal_0), []). fof(cc5_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & v3_xreal_0(A) ) => ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) ) ) ), file(xreal_0,cc5_xreal_0), []). 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(cc6_xreal_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & v3_xreal_0(A) ) ) ), file(xreal_0,cc6_xreal_0), []). fof(cc7_xreal_0,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(xreal_0,cc7_xreal_0), []). fof(cc8_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(xreal_0,cc8_xreal_0), []). 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_k11_binop_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k11_binop_2(A,B) = k11_binop_2(B,A) ) ), file(binop_2,k11_binop_2), []). fof(commutativity_k2_xcmplx_0,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ), file(xcmplx_0,k2_xcmplx_0), []). fof(commutativity_k3_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k3_real_1(A,B) = k3_real_1(B,A) ) ), file(real_1,k3_real_1), []). fof(commutativity_k3_seq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_seq_1(B) ) => k3_seq_1(A,B) = k3_seq_1(B,A) ) ), file(seq_1,k3_seq_1), []). fof(commutativity_k3_xboole_0,axiom,( ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ), file(xboole_0,k3_xboole_0), []). fof(commutativity_k3_xcmplx_0,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k3_xcmplx_0(A,B) = k3_xcmplx_0(B,A) ) ), file(xcmplx_0,k3_xcmplx_0), []). fof(commutativity_k5_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k5_subset_1(A,B,C) = k5_subset_1(A,C,B) ) ), file(subset_1,k5_subset_1), []). fof(commutativity_k6_seq_1,axiom,( ! [A,B,C,D] : ( ( v2_membered(B) & v1_funct_1(C) & m1_relset_1(C,A,B) & v1_funct_1(D) & m1_relset_1(D,A,B) ) => k6_seq_1(A,B,C,D) = k6_seq_1(A,B,D,C) ) ), file(seq_1,k6_seq_1), []). fof(commutativity_k9_binop_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k9_binop_2(A,B) = k9_binop_2(B,A) ) ), file(binop_2,k9_binop_2), []). fof(commutativity_k9_seq_1,axiom,( ! [A,B] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & m1_relset_1(A,k5_numbers,k1_numbers) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_numbers) & m1_relset_1(B,k5_numbers,k1_numbers) ) => k9_seq_1(A,B) = k9_seq_1(B,A) ) ), file(seq_1,k9_seq_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(d10_integra1,axiom,( ! [A] : ( ( v1_integra1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m2_relset_1(B,A,k1_numbers) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m2_integra1(C,A) ) => ! [D] : ( m3_integra1(D,A,C) => k7_integra1(A,B,C,D) = k15_rvsum_1(k5_integra1(A,B,C,D)) ) ) ) ) ), file(integra1,d10_integra1), []). fof(d10_xboole_0,axiom,( ! [A,B] : ( A = B <=> ( r1_tarski(A,B) & r1_tarski(B,A) ) ) ), file(xboole_0,d10_xboole_0), []). fof(d11_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) ) => ! [B] : ( r3_rfunct_1(A,B) <=> ( r1_rfunct_1(A,B) & r2_rfunct_1(A,B) ) ) ) ), file(rfunct_1,d11_rfunct_1), []). fof(d12_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B,C] : ( C = k9_relat_1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( r2_hidden(E,k1_relat_1(A)) & r2_hidden(E,B) & D = k1_funct_1(A,E) ) ) ) ) ), file(funct_1,d12_funct_1), []). fof(d19_integra1,axiom,( ! [A] : ( ( v1_integra1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m3_integra1(B,A,k8_integra1(A)) => k17_integra1(A,B) = k2_seq_4(k16_integra1(k14_integra1(A,k5_rfunct_1(A,A),k8_integra1(A),B))) ) ) ), file(integra1,d19_integra1), []). fof(d1_absvalue,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xreal_0(0,A) => k16_complex1(A) = A ) & ( ~ r1_xreal_0(0,A) => k16_complex1(A) = k4_xcmplx_0(A) ) ) ) ), file(absvalue,d1_absvalue), []). fof(d1_fcont_2,axiom,( ! [A] : ( ( v1_funct_1(A) & m2_relset_1(A,k1_numbers,k1_numbers) ) => ! [B] : ( r1_fcont_2(A,B) <=> ( r1_tarski(B,k4_relset_1(k1_numbers,k1_numbers,A)) & ! [C] : ( m1_subset_1(C,k1_numbers) => ~ ( ~ r1_xreal_0(C,0) & ! [D] : ( m1_subset_1(D,k1_numbers) => ~ ( ~ r1_xreal_0(D,0) & ! [E] : ( m1_subset_1(E,k1_numbers) => ! [F] : ( m1_subset_1(F,k1_numbers) => ~ ( r2_hidden(E,B) & r2_hidden(F,B) & ~ r1_xreal_0(D,k18_complex1(k5_real_1(E,F))) & r1_xreal_0(C,k18_complex1(k5_real_1(k2_seq_1(k1_numbers,k1_numbers,A,E),k2_seq_1(k1_numbers,k1_numbers,A,F)))) ) ) ) ) ) ) ) ) ) ) ), file(fcont_2,d1_fcont_2), []). fof(d1_integra5,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m2_relset_1(B,k1_numbers,k1_numbers) ) => k1_integra5(A,B) = k2_partfun1(k1_numbers,k1_numbers,B,A) ) ) ), file(integra5,d1_integra5), []). fof(d1_pre_circ,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v2_membered(A) ) => ! [B] : ( v1_xreal_0(B) => ( B = k1_pre_circ(A) <=> ( r2_hidden(B,A) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => r1_xreal_0(C,B) ) ) ) ) ) ) ), file(pre_circ,d1_pre_circ), []). fof(d1_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) <=> r2_hidden(A,k1_numbers) ) ), file(xreal_0,d1_xreal_0), []). fof(d2_integra5,axiom,( ! [A] : ( ( v1_integra1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m2_relset_1(B,k1_numbers,k1_numbers) ) => ( r1_integra5(A,B) <=> r3_integra1(A,k1_integra5(A,B)) ) ) ) ), file(integra5,d2_integra5), []). fof(d3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( B = k3_finseq_1(A) <=> k2_finseq_1(B) = k1_relat_1(A) ) ) ) ), file(finseq_1,d3_finseq_1), []). fof(d3_integra2,axiom,( ! [A] : ( ( v1_integra1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,k8_integra1(A)) & m2_relset_1(B,k5_numbers,k8_integra1(A)) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k5_numbers,k1_numbers) & m2_relset_1(C,k5_numbers,k1_numbers) ) => ( C = k2_integra2(A,B) <=> ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => k2_seq_1(k5_numbers,k1_numbers,C,D) = k17_integra1(A,k8_funct_2(k5_numbers,k8_integra1(A),B,D)) ) ) ) ) ) ), file(integra2,d3_integra2), []). fof(d3_seq_4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v3_seq_4(A) <=> ( v2_seq_4(A) & v1_seq_4(A) ) ) ) ), file(seq_4,d3_seq_4), []). 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_integra2,axiom,( ! [A] : ( ( v1_integra1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m2_relset_1(B,A,k1_numbers) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k5_numbers,k8_integra1(A)) & m2_relset_1(C,k5_numbers,k8_integra1(A)) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k5_numbers,k1_numbers) & m2_relset_1(D,k5_numbers,k1_numbers) ) => ( D = k3_integra2(A,B,C) <=> ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => k2_seq_1(k5_numbers,k1_numbers,D,E) = k6_integra1(A,B,k8_integra1(A),k8_funct_2(k5_numbers,k8_integra1(A),C,E)) ) ) ) ) ) ) ), file(integra2,d4_integra2), []). fof(d4_partfun1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => ( v1_partfun1(C,A,B) <=> k4_relset_1(A,B,C) = A ) ) ), file(partfun1,d4_partfun1), []). 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(d5_integra2,axiom,( ! [A] : ( ( v1_integra1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m2_relset_1(B,A,k1_numbers) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k5_numbers,k8_integra1(A)) & m2_relset_1(C,k5_numbers,k8_integra1(A)) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k5_numbers,k1_numbers) & m2_relset_1(D,k5_numbers,k1_numbers) ) => ( D = k4_integra2(A,B,C) <=> ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => k2_seq_1(k5_numbers,k1_numbers,D,E) = k7_integra1(A,B,k8_integra1(A),k8_funct_2(k5_numbers,k8_integra1(A),C,E)) ) ) ) ) ) ) ), file(integra2,d5_integra2), []). fof(d6_integra1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => k3_integra1(A) = k10_binop_2(k3_pscomp_1(A),k4_pscomp_1(A)) ) ), file(integra1,d6_integra1), []). fof(d6_seq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) ) => ( v4_seq_2(A) <=> ? [B] : ( v1_xreal_0(B) & ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xreal_0(C,0) & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ? [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) & r1_xreal_0(D,E) & r1_xreal_0(C,k18_complex1(k6_xcmplx_0(k2_seq_1(k5_numbers,k1_numbers,A,E),B))) ) ) ) ) ) ) ) ), file(seq_2,d6_seq_2), []). fof(d7_integra1,axiom,( ! [A] : ( ( v1_integra1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m2_relset_1(B,A,k1_numbers) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m2_integra1(C,A) ) => ! [D] : ( m3_integra1(D,A,C) => ! [E] : ( m2_finseq_1(E,k1_numbers) => ( E = k4_integra1(A,B,C,D) <=> ( k3_finseq_1(E) = k3_finseq_1(D) & ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ( r2_hidden(F,k2_finseq_1(k3_finseq_1(D))) => k1_goboard1(E,F) = k11_binop_2(k3_pscomp_1(k5_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,k2_integra1(A,C,D,F)))),k3_integra1(k2_integra1(A,C,D,F))) ) ) ) ) ) ) ) ) ) ), file(integra1,d7_integra1), []). fof(d7_seq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) ) => ( v4_seq_2(A) => ! [B] : ( v1_xreal_0(B) => ( B = k1_seq_2(A) <=> ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xreal_0(C,0) & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ? [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) & r1_xreal_0(D,E) & r1_xreal_0(C,k18_complex1(k6_xcmplx_0(k2_seq_1(k5_numbers,k1_numbers,A,E),B))) ) ) ) ) ) ) ) ) ), file(seq_2,d7_seq_2), []). fof(d8_integra1,axiom,( ! [A] : ( ( v1_integra1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m2_relset_1(B,A,k1_numbers) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m2_integra1(C,A) ) => ! [D] : ( m3_integra1(D,A,C) => ! [E] : ( m2_finseq_1(E,k1_numbers) => ( E = k5_integra1(A,B,C,D) <=> ( k3_finseq_1(E) = k3_finseq_1(D) & ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ( r2_hidden(F,k2_finseq_1(k3_finseq_1(D))) => k1_goboard1(E,F) = k11_binop_2(k4_pscomp_1(k5_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,k2_integra1(A,C,D,F)))),k3_integra1(k2_integra1(A,C,D,F))) ) ) ) ) ) ) ) ) ) ), file(integra1,d8_integra1), []). fof(d9_integra1,axiom,( ! [A] : ( ( v1_integra1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m2_relset_1(B,A,k1_numbers) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m2_integra1(C,A) ) => ! [D] : ( m3_integra1(D,A,C) => k6_integra1(A,B,C,D) = k15_rvsum_1(k4_integra1(A,B,C,D)) ) ) ) ) ), file(integra1,d9_integra1), []). fof(dt_k10_binop_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k10_binop_2(A,B),k1_numbers) ) ), file(binop_2,k10_binop_2), []). fof(dt_k10_relset_1,axiom,( ! [A,B,C,D] : ( m1_relset_1(C,A,B) => m1_subset_1(k10_relset_1(A,B,C,D),k1_zfmisc_1(B)) ) ), file(relset_1,k10_relset_1), []). fof(dt_k10_rvsum_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & v1_xreal_0(B) & m1_subset_1(C,k4_finseq_2(A,k1_numbers)) ) => m2_finseq_2(k10_rvsum_1(A,B,C),k1_numbers,k4_finseq_2(A,k1_numbers)) ) ), file(rvsum_1,k10_rvsum_1), []). fof(dt_k10_seq_1,axiom,( ! [A,B] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & m1_relset_1(A,k5_numbers,k1_numbers) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_numbers) & m1_relset_1(B,k5_numbers,k1_numbers) ) => ( v1_funct_1(k10_seq_1(A,B)) & v1_funct_2(k10_seq_1(A,B),k5_numbers,k1_numbers) & m2_relset_1(k10_seq_1(A,B),k5_numbers,k1_numbers) ) ) ), file(seq_1,k10_seq_1), []). fof(dt_k11_binop_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k11_binop_2(A,B),k1_numbers) ) ), file(binop_2,k11_binop_2), []). fof(dt_k11_integra1,axiom,( ! [A,B] : ( ( v1_integra1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & v1_funct_1(B) & m1_relset_1(B,A,k1_numbers) ) => m1_subset_1(k11_integra1(A,B),k1_numbers) ) ), file(integra1,k11_integra1), []). fof(dt_k12_integra1,axiom,( ! [A,B] : ( ( v1_integra1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & v1_funct_1(B) & m1_relset_1(B,A,k1_numbers) ) => m1_subset_1(k12_integra1(A,B),k1_numbers) ) ), file(integra1,k12_integra1), []). fof(dt_k14_integra1,axiom,( ! [A,B,C,D] : ( ( v1_integra1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & v1_funct_1(B) & m1_relset_1(B,A,k1_numbers) & ~ v1_xboole_0(C) & m2_integra1(C,A) & m1_subset_1(D,C) ) => ( ~ v1_xboole_0(k14_integra1(A,B,C,D)) & m2_finseq_1(k14_integra1(A,B,C,D),k1_numbers) ) ) ), file(integra1,k14_integra1), []). fof(dt_k15_integra1,axiom,( ! [A,B,C,D] : ( ( v1_integra1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & v1_funct_1(B) & m1_relset_1(B,A,k1_numbers) & ~ v1_xboole_0(C) & m2_integra1(C,A) & m1_subset_1(D,C) ) => ( ~ v1_xboole_0(k15_integra1(A,B,C,D)) & m2_finseq_1(k15_integra1(A,B,C,D),k1_numbers) ) ) ), file(integra1,k15_integra1), []). fof(dt_k15_rvsum_1,axiom,( ! [A] : ( m1_finseq_1(A,k1_numbers) => m1_subset_1(k15_rvsum_1(A),k1_numbers) ) ), file(rvsum_1,k15_rvsum_1), []). fof(dt_k15_seq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) ) => ( v1_relat_1(k15_seq_1(A)) & v1_funct_1(k15_seq_1(A)) ) ) ), file(seq_1,k15_seq_1), []). fof(dt_k16_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_xcmplx_0(k16_complex1(A)) ) ), file(complex1,k16_complex1), []). fof(dt_k16_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(A,k1_numbers) ) => ( ~ v1_xboole_0(k16_integra1(A)) & v1_finset_1(k16_integra1(A)) & m1_subset_1(k16_integra1(A),k1_zfmisc_1(k1_numbers)) ) ) ), file(integra1,k16_integra1), []). fof(dt_k17_integra1,axiom,( ! [A,B] : ( ( v1_integra1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & m1_subset_1(B,k8_integra1(A)) ) => m1_subset_1(k17_integra1(A,B),k1_numbers) ) ), file(integra1,k17_integra1), []). fof(dt_k17_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & m1_relset_1(A,k5_numbers,k1_numbers) ) => ( v1_funct_1(k17_seq_1(A)) & v1_funct_2(k17_seq_1(A),k5_numbers,k1_numbers) & m2_relset_1(k17_seq_1(A),k5_numbers,k1_numbers) ) ) ), file(seq_1,k17_seq_1), []). fof(dt_k18_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => m1_subset_1(k18_complex1(A),k1_numbers) ) ), file(complex1,k18_complex1), []). fof(dt_k1_card_1,axiom,( ! [A] : v1_card_1(k1_card_1(A)) ), file(card_1,k1_card_1), []). fof(dt_k1_finseq_1,axiom,( $true ), file(finseq_1,k1_finseq_1), []). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). fof(dt_k1_goboard1,axiom,( ! [A,B] : ( ( m1_finseq_1(A,k1_numbers) & m1_subset_1(B,k5_numbers) ) => m1_subset_1(k1_goboard1(A,B),k1_numbers) ) ), file(goboard1,k1_goboard1), []). fof(dt_k1_integra1,axiom,( $true ), file(integra1,k1_integra1), []). fof(dt_k1_integra5,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & v1_funct_1(B) & m1_relset_1(B,k1_numbers,k1_numbers) ) => ( v1_funct_1(k1_integra5(A,B)) & m2_relset_1(k1_integra5(A,B),A,k1_numbers) ) ) ), file(integra5,k1_integra5), []). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), []). fof(dt_k1_pre_circ,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v2_membered(A) ) => v1_xreal_0(k1_pre_circ(A)) ) ), file(pre_circ,k1_pre_circ), []). fof(dt_k1_real_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => m1_subset_1(k1_real_1(A),k1_numbers) ) ), file(real_1,k1_real_1), []). fof(dt_k1_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), []). fof(dt_k1_seq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & m1_relset_1(A,k5_numbers,k1_numbers) ) => v1_xreal_0(k1_seq_2(A)) ) ), file(seq_2,k1_seq_2), []). 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_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => m1_subset_1(k2_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ), file(finseq_1,k2_finseq_1), []). fof(dt_k2_integra1,axiom,( ! [A,B,C,D] : ( ( v1_integra1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(B) & m2_integra1(B,A) & m1_subset_1(C,B) & m1_subset_1(D,k5_numbers) ) => ( v1_integra1(k2_integra1(A,B,C,D)) & m1_subset_1(k2_integra1(A,B,C,D),k1_zfmisc_1(k1_numbers)) ) ) ), file(integra1,k2_integra1), []). fof(dt_k2_integra2,axiom,( ! [A,B] : ( ( v1_integra1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,k8_integra1(A)) & m1_relset_1(B,k5_numbers,k8_integra1(A)) ) => ( v1_funct_1(k2_integra2(A,B)) & v1_funct_2(k2_integra2(A,B),k5_numbers,k1_numbers) & m2_relset_1(k2_integra2(A,B),k5_numbers,k1_numbers) ) ) ), file(integra2,k2_integra2), []). fof(dt_k2_partfun1,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & m1_relset_1(C,A,B) ) => ( v1_funct_1(k2_partfun1(A,B,C,D)) & m2_relset_1(k2_partfun1(A,B,C,D),A,B) ) ) ), file(partfun1,k2_partfun1), []). fof(dt_k2_relat_1,axiom,( $true ), file(relat_1,k2_relat_1), []). fof(dt_k2_seq_1,axiom,( ! [A,B,C,D] : ( ( v2_membered(B) & v1_funct_1(C) & m1_relset_1(C,A,B) ) => m1_subset_1(k2_seq_1(A,B,C,D),k1_numbers) ) ), file(seq_1,k2_seq_1), []). fof(dt_k2_seq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & m1_relset_1(A,k5_numbers,k1_numbers) ) => m1_subset_1(k2_seq_2(A),k1_numbers) ) ), file(seq_2,k2_seq_2), []). fof(dt_k2_seq_4,axiom,( ! [A] : ( v2_membered(A) => v1_xreal_0(k2_seq_4(A)) ) ), file(seq_4,k2_seq_4), []). 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_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_integra1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => m1_subset_1(k3_integra1(A),k1_numbers) ) ), file(integra1,k3_integra1), []). fof(dt_k3_integra2,axiom,( ! [A,B,C] : ( ( v1_integra1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & v1_funct_1(B) & m1_relset_1(B,A,k1_numbers) & v1_funct_1(C) & v1_funct_2(C,k5_numbers,k8_integra1(A)) & m1_relset_1(C,k5_numbers,k8_integra1(A)) ) => ( v1_funct_1(k3_integra2(A,B,C)) & v1_funct_2(k3_integra2(A,B,C),k5_numbers,k1_numbers) & m2_relset_1(k3_integra2(A,B,C),k5_numbers,k1_numbers) ) ) ), file(integra2,k3_integra2), []). fof(dt_k3_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => m1_subset_1(k3_pscomp_1(A),k1_numbers) ) ), file(pscomp_1,k3_pscomp_1), []). fof(dt_k3_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k3_real_1(A,B),k1_numbers) ) ), file(real_1,k3_real_1), []). fof(dt_k3_seq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_seq_1(B) ) => ( v1_relat_1(k3_seq_1(A,B)) & v1_funct_1(k3_seq_1(A,B)) ) ) ), file(seq_1,k3_seq_1), []). fof(dt_k3_seq_4,axiom,( ! [A] : ( v2_membered(A) => v1_xreal_0(k3_seq_4(A)) ) ), file(seq_4,k3_seq_4), []). fof(dt_k3_xboole_0,axiom,( $true ), file(xboole_0,k3_xboole_0), []). fof(dt_k3_xcmplx_0,axiom,( $true ), file(xcmplx_0,k3_xcmplx_0), []). 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_finseq_2,axiom,( ! [A,B] : ( v4_ordinal2(A) => m1_finseq_2(k4_finseq_2(A,B),B) ) ), file(finseq_2,k4_finseq_2), []). fof(dt_k4_funct_3,axiom,( ! [A,B] : ( v1_relat_1(k4_funct_3(A,B)) & v1_funct_1(k4_funct_3(A,B)) ) ), file(funct_3,k4_funct_3), []). fof(dt_k4_integra1,axiom,( ! [A,B,C,D] : ( ( v1_integra1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & v1_funct_1(B) & m1_relset_1(B,A,k1_numbers) & ~ v1_xboole_0(C) & m2_integra1(C,A) & m1_subset_1(D,C) ) => m2_finseq_1(k4_integra1(A,B,C,D),k1_numbers) ) ), file(integra1,k4_integra1), []). fof(dt_k4_integra2,axiom,( ! [A,B,C] : ( ( v1_integra1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & v1_funct_1(B) & m1_relset_1(B,A,k1_numbers) & v1_funct_1(C) & v1_funct_2(C,k5_numbers,k8_integra1(A)) & m1_relset_1(C,k5_numbers,k8_integra1(A)) ) => ( v1_funct_1(k4_integra2(A,B,C)) & v1_funct_2(k4_integra2(A,B,C),k5_numbers,k1_numbers) & m2_relset_1(k4_integra2(A,B,C),k5_numbers,k1_numbers) ) ) ), file(integra2,k4_integra2), []). fof(dt_k4_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => m1_subset_1(k4_pscomp_1(A),k1_numbers) ) ), file(pscomp_1,k4_pscomp_1), []). fof(dt_k4_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(relset_1,k4_relset_1), []). fof(dt_k4_seq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_seq_1(B) ) => ( v1_relat_1(k4_seq_1(A,B)) & v1_funct_1(k4_seq_1(A,B)) ) ) ), file(seq_1,k4_seq_1), []). fof(dt_k4_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_xcmplx_0(k4_xcmplx_0(A)) ) ), file(xcmplx_0,k4_xcmplx_0), []). fof(dt_k5_integra1,axiom,( ! [A,B,C,D] : ( ( v1_integra1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & v1_funct_1(B) & m1_relset_1(B,A,k1_numbers) & ~ v1_xboole_0(C) & m2_integra1(C,A) & m1_subset_1(D,C) ) => m2_finseq_1(k5_integra1(A,B,C,D),k1_numbers) ) ), file(integra1,k5_integra1), []). 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_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k5_real_1(A,B),k1_numbers) ) ), file(real_1,k5_real_1), []). fof(dt_k5_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => m1_subset_1(k5_relset_1(A,B,C),k1_zfmisc_1(B)) ) ), file(relset_1,k5_relset_1), []). fof(dt_k5_rfunct_1,axiom,( ! [A,B] : ( v1_funct_1(k5_rfunct_1(A,B)) & m2_relset_1(k5_rfunct_1(A,B),B,k1_numbers) ) ), file(rfunct_1,k5_rfunct_1), []). fof(dt_k5_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(k5_subset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(subset_1,k5_subset_1), []). fof(dt_k6_integra1,axiom,( ! [A,B,C,D] : ( ( v1_integra1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & v1_funct_1(B) & m1_relset_1(B,A,k1_numbers) & ~ v1_xboole_0(C) & m2_integra1(C,A) & m1_subset_1(D,C) ) => m1_subset_1(k6_integra1(A,B,C,D),k1_numbers) ) ), file(integra1,k6_integra1), []). fof(dt_k6_seq_1,axiom,( ! [A,B,C,D] : ( ( v2_membered(B) & v1_funct_1(C) & m1_relset_1(C,A,B) & v1_funct_1(D) & m1_relset_1(D,A,B) ) => ( v1_funct_1(k6_seq_1(A,B,C,D)) & m2_relset_1(k6_seq_1(A,B,C,D),A,k1_numbers) ) ) ), file(seq_1,k6_seq_1), []). fof(dt_k6_xcmplx_0,axiom,( $true ), file(xcmplx_0,k6_xcmplx_0), []). fof(dt_k7_binop_2,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => m1_subset_1(k7_binop_2(A),k1_numbers) ) ), file(binop_2,k7_binop_2), []). fof(dt_k7_integra1,axiom,( ! [A,B,C,D] : ( ( v1_integra1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & v1_funct_1(B) & m1_relset_1(B,A,k1_numbers) & ~ v1_xboole_0(C) & m2_integra1(C,A) & m1_subset_1(D,C) ) => m1_subset_1(k7_integra1(A,B,C,D),k1_numbers) ) ), file(integra1,k7_integra1), []). fof(dt_k7_relat_1,axiom,( ! [A,B] : ( v1_relat_1(A) => v1_relat_1(k7_relat_1(A,B)) ) ), file(relat_1,k7_relat_1), []). fof(dt_k7_rvsum_1,axiom,( ! [A,B] : ( ( m1_finseq_1(A,k1_numbers) & m1_finseq_1(B,k1_numbers) ) => m2_finseq_1(k7_rvsum_1(A,B),k1_numbers) ) ), file(rvsum_1,k7_rvsum_1), []). fof(dt_k7_xcmplx_0,axiom,( $true ), file(xcmplx_0,k7_xcmplx_0), []). 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_integra1,axiom,( ! [A] : ( ( v1_integra1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => m2_integra1(k8_integra1(A),A) ) ), file(integra1,k8_integra1), []). fof(dt_k8_relset_1,axiom,( ! [A,B,C,D] : ( m1_relset_1(C,A,B) => m2_relset_1(k8_relset_1(A,B,C,D),A,B) ) ), file(relset_1,k8_relset_1), []). fof(dt_k8_rvsum_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k4_finseq_2(A,k1_numbers)) & m1_subset_1(C,k4_finseq_2(A,k1_numbers)) ) => m2_finseq_2(k8_rvsum_1(A,B,C),k1_numbers,k4_finseq_2(A,k1_numbers)) ) ), file(rvsum_1,k8_rvsum_1), []). fof(dt_k9_binop_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k9_binop_2(A,B),k1_numbers) ) ), file(binop_2,k9_binop_2), []). fof(dt_k9_relat_1,axiom,( $true ), file(relat_1,k9_relat_1), []). fof(dt_k9_rvsum_1,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & m1_finseq_1(B,k1_numbers) ) => m2_finseq_1(k9_rvsum_1(A,B),k1_numbers) ) ), file(rvsum_1,k9_rvsum_1), []). fof(dt_k9_seq_1,axiom,( ! [A,B] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & m1_relset_1(A,k5_numbers,k1_numbers) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_numbers) & m1_relset_1(B,k5_numbers,k1_numbers) ) => ( v1_funct_1(k9_seq_1(A,B)) & v1_funct_2(k9_seq_1(A,B),k5_numbers,k1_numbers) & m2_relset_1(k9_seq_1(A,B),k5_numbers,k1_numbers) ) ) ), file(seq_1,k9_seq_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_finseq_2,axiom,( $true ), file(finseq_2,m1_finseq_2), []). fof(dt_m1_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_integra1(B,A) => ( ~ v1_xboole_0(B) & v1_goboard1(B) & m2_finseq_1(B,k1_numbers) ) ) ) ), file(integra1,m1_integra1), []). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), []). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), []). fof(dt_m2_finseq_1,axiom,( ! [A,B] : ( m2_finseq_1(B,A) => ( v1_funct_1(B) & v1_finseq_1(B) & m2_relset_1(B,k5_numbers,A) ) ) ), file(finseq_1,m2_finseq_1), []). fof(dt_m2_finseq_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) ) => ! [C] : ( m2_finseq_2(C,A,B) => m2_finseq_1(C,A) ) ) ), file(finseq_2,m2_finseq_2), []). fof(dt_m2_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m2_integra1(B,A) => ~ v1_xboole_0(B) ) ) ), file(integra1,m2_integra1), []). 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(dt_m3_integra1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v1_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(B) & m2_integra1(B,A) ) => ! [C] : ( m3_integra1(C,A,B) => m1_integra1(C,A) ) ) ), file(integra1,m3_integra1), []). fof(existence_m1_finseq_1,axiom,( ! [A] : ? [B] : m1_finseq_1(B,A) ), file(finseq_1,m1_finseq_1), []). fof(existence_m1_finseq_2,axiom,( ! [A] : ? [B] : m1_finseq_2(B,A) ), file(finseq_2,m1_finseq_2), []). fof(existence_m1_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ? [B] : m1_integra1(B,A) ) ), file(integra1,m1_integra1), []). fof(existence_m1_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), []). fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), []). fof(existence_m2_finseq_1,axiom,( ! [A] : ? [B] : m2_finseq_1(B,A) ), file(finseq_1,m2_finseq_1), []). fof(existence_m2_finseq_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) ) => ? [C] : m2_finseq_2(C,A,B) ) ), file(finseq_2,m2_finseq_2), []). fof(existence_m2_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ? [B] : m2_integra1(B,A) ) ), file(integra1,m2_integra1), []). 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(existence_m3_integra1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v1_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(B) & m2_integra1(B,A) ) => ? [C] : m3_integra1(C,A,B) ) ), file(integra1,m3_integra1), []). fof(fc10_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v2_xreal_0(k2_xcmplx_0(B,A)) & ~ v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc10_xreal_0), []). fof(fc11_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v2_xreal_0(k2_xcmplx_0(A,B)) & v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc11_xreal_0), []). fof(fc12_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & ~ v2_xreal_0(k2_xcmplx_0(B,A)) & v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc12_xreal_0), []). fof(fc13_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) ) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & ~ v3_xreal_0(k4_xcmplx_0(A)) ) ) ), file(xreal_0,fc13_xreal_0), []). fof(fc14_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & ~ v2_xreal_0(k4_xcmplx_0(A)) ) ) ), file(xreal_0,fc14_xreal_0), []). fof(fc15_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & ~ v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc15_xreal_0), []). fof(fc16_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & ~ v2_xreal_0(k6_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc16_xreal_0), []). fof(fc17_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v2_xreal_0(k6_xcmplx_0(A,B)) & ~ v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc17_xreal_0), []). fof(fc18_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k6_xcmplx_0(B,A)) & v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & ~ v2_xreal_0(k6_xcmplx_0(B,A)) & v3_xreal_0(k6_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc18_xreal_0), []). fof(fc19_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & ~ v2_xreal_0(k6_xcmplx_0(A,B)) & v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc19_xreal_0), []). fof(fc1_finseq_2,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k4_finseq_2(A,B)) ) ), file(finseq_2,fc1_finseq_2), []). fof(fc1_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ~ v1_xboole_0(k1_integra1(A)) ) ), file(integra1,fc1_integra1), []). 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_seq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) ) => ( v1_xcmplx_0(k1_funct_1(A,B)) & v1_xreal_0(k1_funct_1(A,B)) ) ) ), file(seq_1,fc1_seq_1), []). fof(fc1_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) ) ) ), file(xreal_0,fc1_xreal_0), []). fof(fc20_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k6_xcmplx_0(B,A)) & v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & v2_xreal_0(k6_xcmplx_0(B,A)) & ~ v3_xreal_0(k6_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc20_xreal_0), []). fof(fc21_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & ~ v2_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc21_xreal_0), []). fof(fc22_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(B,A)) & v1_xreal_0(k3_xcmplx_0(B,A)) & ~ v2_xreal_0(k3_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc22_xreal_0), []). fof(fc23_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & ~ v3_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc23_xreal_0), []). fof(fc24_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & ~ v3_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc24_xreal_0), []). fof(fc27_membered,axiom,( ! [A,B] : ( v1_membered(A) => v1_membered(k3_xboole_0(A,B)) ) ), file(membered,fc27_membered), []). fof(fc27_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) & ~ v2_xreal_0(k7_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc27_xreal_0), []). fof(fc28_membered,axiom,( ! [A,B] : ( v1_membered(A) => v1_membered(k3_xboole_0(B,A)) ) ), file(membered,fc28_membered), []). fof(fc28_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k7_xcmplx_0(B,A)) & v1_xreal_0(k7_xcmplx_0(B,A)) & ~ v2_xreal_0(k7_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc28_xreal_0), []). fof(fc29_membered,axiom,( ! [A,B] : ( v2_membered(A) => ( v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) ) ) ), file(membered,fc29_membered), []). fof(fc29_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) & ~ v3_xreal_0(k7_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc29_xreal_0), []). fof(fc2_membered,axiom, ( ~ v1_xboole_0(k1_numbers) & v1_membered(k1_numbers) & v2_membered(k1_numbers) ), file(membered,fc2_membered), []). fof(fc2_seq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_seq_1(A) ) => ( v1_relat_1(k7_relat_1(A,B)) & v1_seq_1(k7_relat_1(A,B)) ) ) ), file(seq_1,fc2_seq_1), []). fof(fc30_membered,axiom,( ! [A,B] : ( v2_membered(A) => ( v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) ) ) ), file(membered,fc30_membered), []). fof(fc30_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) & ~ v3_xreal_0(k7_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc30_xreal_0), []). fof(fc31_membered,axiom,( ! [A,B] : ( v3_membered(A) => ( v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) ) ) ), file(membered,fc31_membered), []). fof(fc32_membered,axiom,( ! [A,B] : ( v3_membered(A) => ( v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) ) ) ), file(membered,fc32_membered), []). fof(fc33_membered,axiom,( ! [A,B] : ( v4_membered(A) => ( v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) ) ) ), file(membered,fc33_membered), []). fof(fc34_membered,axiom,( ! [A,B] : ( v4_membered(A) => ( v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) & v4_membered(k3_xboole_0(B,A)) ) ) ), file(membered,fc34_membered), []). fof(fc35_membered,axiom,( ! [A,B] : ( v5_membered(A) => ( v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) & v5_membered(k3_xboole_0(A,B)) ) ) ), file(membered,fc35_membered), []). fof(fc36_membered,axiom,( ! [A,B] : ( v5_membered(A) => ( v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) & v4_membered(k3_xboole_0(B,A)) & v5_membered(k3_xboole_0(B,A)) ) ) ), file(membered,fc36_membered), []). fof(fc3_seq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_seq_1(B) ) => ( v1_relat_1(k3_seq_1(A,B)) & v1_funct_1(k3_seq_1(A,B)) & v1_seq_1(k3_seq_1(A,B)) ) ) ), file(seq_1,fc3_seq_1), []). fof(fc3_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc3_xreal_0), []). fof(fc4_seq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_seq_1(B) ) => ( v1_relat_1(k4_seq_1(A,B)) & v1_funct_1(k4_seq_1(A,B)) & v1_seq_1(k4_seq_1(A,B)) ) ) ), file(seq_1,fc4_seq_1), []). fof(fc4_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc4_xreal_0), []). 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_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc5_xreal_0), []). 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_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc6_xreal_0), []). fof(fc7_seq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) ) => ( v1_relat_1(k15_seq_1(A)) & v1_funct_1(k15_seq_1(A)) & v1_seq_1(k15_seq_1(A)) ) ) ), file(seq_1,fc7_seq_1), []). fof(fc7_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc7_xreal_0), []). fof(fc8_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v2_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc8_xreal_0), []). fof(fc9_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v2_xreal_0(k2_xcmplx_0(A,B)) & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc9_xreal_0), []). fof(idempotence_k3_xboole_0,axiom,( ! [A,B] : k3_xboole_0(A,A) = A ), file(xboole_0,k3_xboole_0), []). fof(idempotence_k5_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k5_subset_1(A,B,B) = B ) ), file(subset_1,k5_subset_1), []). fof(involutiveness_k1_real_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => k1_real_1(k1_real_1(A)) = A ) ), file(real_1,k1_real_1), []). fof(involutiveness_k4_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => k4_xcmplx_0(k4_xcmplx_0(A)) = A ) ), file(xcmplx_0,k4_xcmplx_0), []). fof(involutiveness_k7_binop_2,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => k7_binop_2(k7_binop_2(A)) = A ) ), file(binop_2,k7_binop_2), []). fof(projectivity_k16_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k16_complex1(k16_complex1(A)) = k16_complex1(A) ) ), file(complex1,k16_complex1), []). fof(projectivity_k18_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k18_complex1(k18_complex1(A)) = k18_complex1(A) ) ), file(complex1,k18_complex1), []). 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_finseq_2,axiom,( ! [A] : ? [B] : ( m1_finseq_2(B,A) & ~ v1_xboole_0(B) ) ), file(finseq_2,rc1_finseq_2), []). fof(rc1_integra1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & v1_membered(A) & v2_membered(A) & v1_integra1(A) ) ), file(integra1,rc1_integra1), []). 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_seq_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) ) ), file(seq_1,rc1_seq_1), []). fof(rc1_xreal_0,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(xreal_0,rc1_xreal_0), []). fof(rc2_integra1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_seq_4(A) & v1_rcomp_1(A) & v1_integra1(A) ) ), file(integra1,rc2_integra1), []). fof(rc2_xreal_0,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc2_xreal_0), []). fof(rc3_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ? [B] : ( m2_integra1(B,A) & ~ v1_xboole_0(B) ) ) ), file(integra1,rc3_integra1), []). fof(rc3_xreal_0,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & v3_xreal_0(A) ) ), file(xreal_0,rc3_xreal_0), []). fof(rc4_xreal_0,axiom,( ? [A] : ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc4_xreal_0), []). fof(redefinition_k10_binop_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k10_binop_2(A,B) = k6_xcmplx_0(A,B) ) ), file(binop_2,k10_binop_2), []). fof(redefinition_k10_relset_1,axiom,( ! [A,B,C,D] : ( m1_relset_1(C,A,B) => k10_relset_1(A,B,C,D) = k9_relat_1(C,D) ) ), file(relset_1,k10_relset_1), []). fof(redefinition_k10_rvsum_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & v1_xreal_0(B) & m1_subset_1(C,k4_finseq_2(A,k1_numbers)) ) => k10_rvsum_1(A,B,C) = k9_rvsum_1(B,C) ) ), file(rvsum_1,k10_rvsum_1), []). fof(redefinition_k10_seq_1,axiom,( ! [A,B] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & m1_relset_1(A,k5_numbers,k1_numbers) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_numbers) & m1_relset_1(B,k5_numbers,k1_numbers) ) => k10_seq_1(A,B) = k4_seq_1(A,B) ) ), file(seq_1,k10_seq_1), []). fof(redefinition_k11_binop_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k11_binop_2(A,B) = k3_xcmplx_0(A,B) ) ), file(binop_2,k11_binop_2), []). fof(redefinition_k14_integra1,axiom,( ! [A,B,C,D] : ( ( v1_integra1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & v1_funct_1(B) & m1_relset_1(B,A,k1_numbers) & ~ v1_xboole_0(C) & m2_integra1(C,A) & m1_subset_1(D,C) ) => k14_integra1(A,B,C,D) = k4_integra1(A,B,C,D) ) ), file(integra1,k14_integra1), []). fof(redefinition_k15_integra1,axiom,( ! [A,B,C,D] : ( ( v1_integra1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & v1_funct_1(B) & m1_relset_1(B,A,k1_numbers) & ~ v1_xboole_0(C) & m2_integra1(C,A) & m1_subset_1(D,C) ) => k15_integra1(A,B,C,D) = k5_integra1(A,B,C,D) ) ), file(integra1,k15_integra1), []). fof(redefinition_k16_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(A,k1_numbers) ) => k16_integra1(A) = k2_relat_1(A) ) ), file(integra1,k16_integra1), []). fof(redefinition_k17_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & m1_relset_1(A,k5_numbers,k1_numbers) ) => k17_seq_1(A) = k15_seq_1(A) ) ), file(seq_1,k17_seq_1), []). fof(redefinition_k18_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k18_complex1(A) = k16_complex1(A) ) ), file(complex1,k18_complex1), []). fof(redefinition_k1_goboard1,axiom,( ! [A,B] : ( ( m1_finseq_1(A,k1_numbers) & m1_subset_1(B,k5_numbers) ) => k1_goboard1(A,B) = k1_funct_1(A,B) ) ), file(goboard1,k1_goboard1), []). fof(redefinition_k1_pre_circ,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v2_membered(A) ) => k1_pre_circ(A) = k2_seq_4(A) ) ), file(pre_circ,k1_pre_circ), []). fof(redefinition_k1_real_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => k1_real_1(A) = k4_xcmplx_0(A) ) ), file(real_1,k1_real_1), []). fof(redefinition_k2_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => k2_finseq_1(A) = k1_finseq_1(A) ) ), file(finseq_1,k2_finseq_1), []). fof(redefinition_k2_partfun1,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & m1_relset_1(C,A,B) ) => k2_partfun1(A,B,C,D) = k7_relat_1(C,D) ) ), file(partfun1,k2_partfun1), []). fof(redefinition_k2_seq_1,axiom,( ! [A,B,C,D] : ( ( v2_membered(B) & v1_funct_1(C) & m1_relset_1(C,A,B) ) => k2_seq_1(A,B,C,D) = k1_funct_1(C,D) ) ), file(seq_1,k2_seq_1), []). fof(redefinition_k2_seq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & m1_relset_1(A,k5_numbers,k1_numbers) ) => k2_seq_2(A) = k1_seq_2(A) ) ), file(seq_2,k2_seq_2), []). fof(redefinition_k3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k3_finseq_1(A) = k1_card_1(A) ) ), file(finseq_1,k3_finseq_1), []). fof(redefinition_k3_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => k3_pscomp_1(A) = k2_seq_4(A) ) ), file(pscomp_1,k3_pscomp_1), []). fof(redefinition_k3_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k3_real_1(A,B) = k2_xcmplx_0(A,B) ) ), file(real_1,k3_real_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_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => k4_pscomp_1(A) = k3_seq_4(A) ) ), file(pscomp_1,k4_pscomp_1), []). fof(redefinition_k4_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => k4_relset_1(A,B,C) = k1_relat_1(C) ) ), file(relset_1,k4_relset_1), []). fof(redefinition_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_k5_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k5_real_1(A,B) = k6_xcmplx_0(A,B) ) ), file(real_1,k5_real_1), []). fof(redefinition_k5_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => k5_relset_1(A,B,C) = k2_relat_1(C) ) ), file(relset_1,k5_relset_1), []). fof(redefinition_k5_rfunct_1,axiom,( ! [A,B] : k5_rfunct_1(A,B) = k4_funct_3(A,B) ), file(rfunct_1,k5_rfunct_1), []). fof(redefinition_k5_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k5_subset_1(A,B,C) = k3_xboole_0(B,C) ) ), file(subset_1,k5_subset_1), []). fof(redefinition_k6_seq_1,axiom,( ! [A,B,C,D] : ( ( v2_membered(B) & v1_funct_1(C) & m1_relset_1(C,A,B) & v1_funct_1(D) & m1_relset_1(D,A,B) ) => k6_seq_1(A,B,C,D) = k3_seq_1(C,D) ) ), file(seq_1,k6_seq_1), []). fof(redefinition_k7_binop_2,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => k7_binop_2(A) = k4_xcmplx_0(A) ) ), file(binop_2,k7_binop_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_k8_integra1,axiom,( ! [A] : ( ( v1_integra1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => k8_integra1(A) = k1_integra1(A) ) ), file(integra1,k8_integra1), []). fof(redefinition_k8_relset_1,axiom,( ! [A,B,C,D] : ( m1_relset_1(C,A,B) => k8_relset_1(A,B,C,D) = k7_relat_1(C,D) ) ), file(relset_1,k8_relset_1), []). fof(redefinition_k8_rvsum_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k4_finseq_2(A,k1_numbers)) & m1_subset_1(C,k4_finseq_2(A,k1_numbers)) ) => k8_rvsum_1(A,B,C) = k7_rvsum_1(B,C) ) ), file(rvsum_1,k8_rvsum_1), []). fof(redefinition_k9_binop_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k9_binop_2(A,B) = k2_xcmplx_0(A,B) ) ), file(binop_2,k9_binop_2), []). fof(redefinition_k9_seq_1,axiom,( ! [A,B] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & m1_relset_1(A,k5_numbers,k1_numbers) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_numbers) & m1_relset_1(B,k5_numbers,k1_numbers) ) => k9_seq_1(A,B) = k3_seq_1(A,B) ) ), file(seq_1,k9_seq_1), []). 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_finseq_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) ) => ! [C] : ( m2_finseq_2(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(finseq_2,m2_finseq_2), []). 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(redefinition_m3_integra1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v1_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(B) & m2_integra1(B,A) ) => ! [C] : ( m3_integra1(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(integra1,m3_integra1), []). 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(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(t105_real_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ~ ( ~ r1_xreal_0(k2_xcmplx_0(A,k4_xcmplx_0(B)),0) & ~ r1_xreal_0(0,k6_xcmplx_0(B,A)) & ~ r1_xreal_0(0,k2_xcmplx_0(B,k4_xcmplx_0(A))) & ~ r1_xreal_0(k6_xcmplx_0(A,C),k2_xcmplx_0(B,k4_xcmplx_0(C))) & ~ r1_xreal_0(k2_xcmplx_0(A,k4_xcmplx_0(C)),k6_xcmplx_0(B,C)) & ~ r1_xreal_0(k6_xcmplx_0(C,B),k6_xcmplx_0(C,A)) ) => r1_xreal_0(A,B) ) ) ) ) ), file(real_2,t105_real_2), []). fof(t10_integra1,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( ( v1_integra1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m2_integra1(C,B) ) => ! [D] : ( m3_integra1(D,B,C) => ( r2_hidden(A,k4_finseq_1(D)) => r1_tarski(k2_integra1(B,C,D,A),B) ) ) ) ) ) ), file(integra1,t10_integra1), []). fof(t110_finseq_2,axiom,( ! [A,B] : ( m2_finseq_1(B,A) => m1_subset_1(B,k4_finseq_2(k3_finseq_1(B),A)) ) ), file(finseq_2,t110_finseq_2), []). fof(t112_rvsum_1,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_finseq_2(B,k1_numbers,k4_finseq_2(A,k1_numbers)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k4_finseq_2(A,k1_numbers)) => ( ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( r2_hidden(D,k2_finseq_1(A)) => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,B,D),k2_seq_1(k5_numbers,k1_numbers,C,D)) ) ) => r1_xreal_0(k15_rvsum_1(B),k15_rvsum_1(C)) ) ) ) ) ), file(rvsum_1,t112_rvsum_1), []). fof(t117_rvsum_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => k15_rvsum_1(k9_rvsum_1(A,B)) = k11_binop_2(A,k15_rvsum_1(B)) ) ) ), file(rvsum_1,t117_rvsum_1), []). fof(t11_fcont_2,axiom,( ! [A] : ( ( v1_funct_1(A) & m2_relset_1(A,k1_numbers,k1_numbers) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ( ( v1_rcomp_1(B) & r2_fcont_1(A,B) ) => r1_fcont_2(A,B) ) ) ) ), file(fcont_2,t11_fcont_2), []). fof(t11_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_seq_4(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => r1_xreal_0(0,k3_integra1(A)) ) ), file(integra1,t11_integra1), []). fof(t11_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_numbers) & m2_relset_1(B,k5_numbers,k1_numbers) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k5_numbers,k1_numbers) & m2_relset_1(C,k5_numbers,k1_numbers) ) => ( A = k6_seq_1(k5_numbers,k1_numbers,B,C) <=> ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => k2_seq_1(k5_numbers,k1_numbers,A,D) = k3_real_1(k2_seq_1(k5_numbers,k1_numbers,B,D),k2_seq_1(k5_numbers,k1_numbers,C,D)) ) ) ) ) ) ), file(seq_1,t11_seq_1), []). fof(t120_rvsum_1,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_finseq_2(B,k1_numbers,k4_finseq_2(A,k1_numbers)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k4_finseq_2(A,k1_numbers)) => k15_rvsum_1(k8_rvsum_1(A,B,C)) = k10_binop_2(k15_rvsum_1(B),k15_rvsum_1(C)) ) ) ) ), file(rvsum_1,t120_rvsum_1), []). fof(t127_real_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ( ( ~ r1_xreal_0(A,0) & ~ r1_xreal_0(B,0) ) | ( ~ r1_xreal_0(0,A) & ~ r1_xreal_0(0,B) ) ) & r1_xreal_0(k7_xcmplx_0(A,B),0) ) ) ) ), file(real_2,t127_real_2), []). fof(t12_integra4,axiom,( ! [A] : ( ( v1_integra1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k1_numbers) & m2_relset_1(B,A,k1_numbers) ) => ( r3_rfunct_1(B,A) => ( r3_integra1(A,B) <=> ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k5_numbers,k8_integra1(A)) & m2_relset_1(C,k5_numbers,k8_integra1(A)) ) => ( ( v4_seq_2(k2_integra2(A,C)) & k2_seq_2(k2_integra2(A,C)) = 0 ) => k5_real_1(k2_seq_2(k3_integra2(A,B,C)),k2_seq_2(k4_integra2(A,B,C))) = 0 ) ) ) ) ) ) ), file(integra4,t12_integra4), []). fof(t131_funct_2,axiom,( ! [A,B,C] : ( ( v1_funct_1(C) & m2_relset_1(C,A,B) ) => ( v1_partfun1(C,A,B) => ( v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) ) ) ) ), file(funct_2,t131_funct_2), []). fof(t14_integra1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m2_relset_1(B,A,k1_numbers) ) => ( v2_seq_4(k5_relset_1(A,k1_numbers,B)) => r2_rfunct_1(B,A) ) ) ) ), file(integra1,t14_integra1), []). fof(t14_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_numbers) & m2_relset_1(B,k5_numbers,k1_numbers) ) => ( A = k17_seq_1(B) <=> ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => k2_seq_1(k5_numbers,k1_numbers,A,C) = k1_real_1(k2_seq_1(k5_numbers,k1_numbers,B,C)) ) ) ) ) ), file(seq_1,t14_seq_1), []). fof(t15_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_numbers) & m2_relset_1(B,k5_numbers,k1_numbers) ) => k10_seq_1(A,B) = k9_seq_1(A,k17_seq_1(B)) ) ) ), file(seq_1,t15_seq_1), []). fof(t16_integra1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m2_relset_1(B,A,k1_numbers) ) => ( v1_seq_4(k5_relset_1(A,k1_numbers,B)) => r1_rfunct_1(B,A) ) ) ) ), file(integra1,t16_integra1), []). fof(t177_real_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xreal_0(k3_xcmplx_0(B,A),C) => ( r1_xreal_0(A,0) | r1_xreal_0(B,k7_xcmplx_0(C,A)) ) ) & ( r1_xreal_0(k3_xcmplx_0(B,A),C) => ( r1_xreal_0(0,A) | r1_xreal_0(k7_xcmplx_0(C,A),B) ) ) & ( r1_xreal_0(C,k3_xcmplx_0(B,A)) => ( r1_xreal_0(A,0) | r1_xreal_0(k7_xcmplx_0(C,A),B) ) ) & ( r1_xreal_0(C,k3_xcmplx_0(B,A)) => ( r1_xreal_0(0,A) | r1_xreal_0(B,k7_xcmplx_0(C,A)) ) ) ) ) ) ) ), file(real_2,t177_real_2), []). fof(t17_xboole_1,axiom,( ! [A,B] : r1_tarski(k3_xboole_0(A,B),A) ), file(xboole_1,t17_xboole_1), []). fof(t18_integra4,axiom,( ! [A] : ( ( v1_integra1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B,C] : ( ( v1_funct_1(C) & m2_relset_1(C,A,k1_numbers) ) => ( r1_rfunct_1(C,A) => v1_seq_4(k5_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,C,B))) ) ) ) ), file(integra4,t18_integra4), []). fof(t19_integra4,axiom,( ! [A] : ( ( v1_integra1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B,C] : ( ( v1_funct_1(C) & m2_relset_1(C,A,k1_numbers) ) => ( r2_rfunct_1(C,A) => v2_seq_4(k5_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,C,B))) ) ) ) ), file(integra4,t19_integra4), []). fof(t1_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(A,0) = A ) ), file(arithm,t1_arithm), []). fof(t1_integra2,axiom,( ! [A] : ( ( v1_integra1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) <=> ( r1_xreal_0(k4_pscomp_1(A),B) & r1_xreal_0(B,k3_pscomp_1(A)) ) ) ) ) ), file(integra2,t1_integra2), []). fof(t1_numerals,axiom,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), []). fof(t1_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & v2_xreal_0(A) ) => v2_xreal_0(B) ) ) ) ), file(real,t1_real), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t22_integra1,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( ( v1_integra1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m2_integra1(C,B) ) => ! [D] : ( m3_integra1(D,B,C) => ( r2_hidden(A,k2_finseq_1(k3_finseq_1(D))) => k3_integra1(k2_integra1(B,C,D,A)) = k1_goboard1(k4_integra1(B,k5_rfunct_1(B,B),C,D),A) ) ) ) ) ) ), file(integra1,t22_integra1), []). fof(t24_integra4,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( ( v1_integra1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k1_numbers) & m2_relset_1(C,B,k1_numbers) ) => ( ! [D] : ( m1_subset_1(D,k1_numbers) => ! [E] : ( m1_subset_1(E,k1_numbers) => ( ( r2_hidden(D,B) & r2_hidden(E,B) ) => r1_xreal_0(k18_complex1(k5_real_1(k2_seq_1(B,k1_numbers,C,D),k2_seq_1(B,k1_numbers,C,E))),A) ) ) ) => r1_xreal_0(k5_real_1(k3_pscomp_1(k5_relset_1(B,k1_numbers,C)),k4_pscomp_1(k5_relset_1(B,k1_numbers,C))),A) ) ) ) ) ), file(integra4,t24_integra4), []). fof(t26_integra1,axiom,( ! [A] : ( ( v1_integra1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_integra1(B,A) ) => ! [C] : ( m3_integra1(C,A,B) => k15_rvsum_1(k4_integra1(A,k5_rfunct_1(A,A),B,C)) = k3_integra1(A) ) ) ) ), file(integra1,t26_integra1), []). fof(t26_seq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_numbers) & m2_relset_1(B,k5_numbers,k1_numbers) ) => ( ( v4_seq_2(A) & v4_seq_2(B) ) => k2_seq_2(k10_seq_1(A,B)) = k5_real_1(k2_seq_2(A),k2_seq_2(B)) ) ) ) ), file(seq_2,t26_seq_2), []). fof(t28_rcomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v1_rcomp_1(A) => v3_seq_4(A) ) ) ), file(rcomp_1,t28_rcomp_1), []). fof(t28_xboole_1,axiom,( ! [A,B] : ( r1_tarski(A,B) => k3_xboole_0(A,B) = A ) ), file(xboole_1,t28_xboole_1), []). fof(t2_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(A,0) = 0 ) ), file(arithm,t2_arithm), []). fof(t2_boole,axiom,( ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ), file(boole,t2_boole), []). fof(t2_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & v3_xreal_0(B) ) => v3_xreal_0(A) ) ) ) ), file(real,t2_real), []). 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_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xreal_0(A,B) & r1_xreal_0(B,C) ) => r1_xreal_0(A,C) ) ) ) ) ), file(xreal_1,t2_xreal_1), []). fof(t30_fcont_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( ( v1_funct_1(B) & m2_relset_1(B,k1_numbers,k1_numbers) ) => ( ( r1_tarski(A,k4_relset_1(k1_numbers,k1_numbers,B)) & v1_rcomp_1(A) & r2_fcont_1(B,A) ) => v1_rcomp_1(k10_relset_1(k1_numbers,k1_numbers,B,A)) ) ) ) ), file(fcont_1,t30_fcont_1), []). fof(t30_integra1,axiom,( ! [A] : ( ( v1_integra1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k1_numbers) & m2_relset_1(B,A,k1_numbers) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m2_integra1(C,A) ) => ! [D] : ( m3_integra1(D,A,C) => ( r3_rfunct_1(B,A) => r1_xreal_0(k7_integra1(A,B,C,D),k6_integra1(A,B,C,D)) ) ) ) ) ) ), file(integra1,t30_integra1), []). fof(t3_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(1,A) = A ) ), file(arithm,t3_arithm), []). fof(t3_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xreal_0(A,B) & ~ v3_xreal_0(A) & v3_xreal_0(B) ) ) ) ), file(real,t3_real), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t43_partfun1,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(D) & m2_relset_1(D,A,B) ) => ( v1_funct_1(k8_relset_1(A,B,D,C)) & m2_relset_1(k8_relset_1(A,B,D,C),C,B) ) ) ), file(partfun1,t43_partfun1), []). fof(t48_rvsum_1,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_finseq_2(C,k1_numbers,k4_finseq_2(A,k1_numbers)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k4_finseq_2(A,k1_numbers)) => k2_seq_1(k5_numbers,k1_numbers,k8_rvsum_1(A,C,D),B) = k10_binop_2(k2_seq_1(k5_numbers,k1_numbers,C,B),k2_seq_1(k5_numbers,k1_numbers,D,B)) ) ) ) ) ), file(rvsum_1,t48_rvsum_1), []). fof(t4_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k6_xcmplx_0(A,0) = A ) ), file(arithm,t4_arithm), []). fof(t4_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xreal_0(A,B) & ~ v2_xreal_0(B) & v2_xreal_0(A) ) ) ) ), file(real,t4_real), []). fof(t4_subset,axiom,( ! [A,B,C] : ( ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) ) => m1_subset_1(A,C) ) ), file(subset,t4_subset), []). fof(t50_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) => r1_xreal_0(0,k6_xcmplx_0(B,A)) ) ) ) ), file(xreal_1,t50_xreal_1), []). fof(t5_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k7_xcmplx_0(0,A) = 0 ) ), file(arithm,t5_arithm), []). fof(t5_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) => ( v1_xboole_0(B) | v3_xreal_0(A) | v2_xreal_0(B) ) ) ) ) ), file(real,t5_real), []). 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(t66_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xreal_0(A,B) & r1_xreal_0(0,C) ) => r1_xreal_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,C)) ) ) ) ) ), file(xreal_1,t66_xreal_1), []). fof(t67_rvsum_1,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m1_subset_1(C,k1_numbers) => ! [D] : ( m2_finseq_2(D,k1_numbers,k4_finseq_2(A,k1_numbers)) => k2_seq_1(k5_numbers,k1_numbers,k10_rvsum_1(A,C,D),B) = k11_binop_2(C,k2_seq_1(k5_numbers,k1_numbers,D,B)) ) ) ) ) ), file(rvsum_1,t67_rvsum_1), []). fof(t68_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( B = k7_relat_1(C,A) <=> ( k1_relat_1(B) = k3_xboole_0(k1_relat_1(C),A) & ! [D] : ( r2_hidden(D,k1_relat_1(B)) => k1_funct_1(B,D) = k1_funct_1(C,D) ) ) ) ) ) ), file(funct_1,t68_funct_1), []). fof(t6_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k7_xcmplx_0(A,1) = A ) ), file(arithm,t6_arithm), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t6_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) => ( v1_xboole_0(A) | v2_xreal_0(B) | v3_xreal_0(A) ) ) ) ) ), file(real,t6_real), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t7_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v2_xreal_0(A) & ~ v3_xreal_0(B) ) ) ) ), file(real,t7_real), []). fof(t7_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(B,A) & ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xreal_0(C,A) & ~ r1_xreal_0(B,C) ) ) ) ) ) ), file(xreal_1,t7_xreal_1), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t8_integra4,axiom,( ! [A] : ( ( v1_integra1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k1_numbers) & m2_relset_1(B,A,k1_numbers) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k5_numbers,k8_integra1(A)) & m2_relset_1(C,k5_numbers,k8_integra1(A)) ) => ( ( r3_rfunct_1(B,A) & v4_seq_2(k2_integra2(A,C)) & k2_seq_2(k2_integra2(A,C)) = 0 ) => ( v4_seq_2(k4_integra2(A,B,C)) & k2_seq_2(k4_integra2(A,B,C)) = k12_integra1(A,B) ) ) ) ) ) ), file(integra4,t8_integra4), []). fof(t8_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v3_xreal_0(B) & ~ v2_xreal_0(A) ) ) ) ), file(real,t8_real), []). fof(t92_real_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( ( r1_xreal_0(A,B) & r1_xreal_0(C,D) ) => r1_xreal_0(k6_xcmplx_0(A,D),k6_xcmplx_0(B,C)) ) & ~ ( ( ( ~ r1_xreal_0(B,A) & r1_xreal_0(C,D) ) | ( r1_xreal_0(A,B) & ~ r1_xreal_0(D,C) ) ) & r1_xreal_0(k6_xcmplx_0(B,C),k6_xcmplx_0(A,D)) ) ) ) ) ) ) ), file(real_1,t92_real_1), []). fof(t9_integra4,axiom,( ! [A] : ( ( v1_integra1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k1_numbers) & m2_relset_1(B,A,k1_numbers) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k5_numbers,k8_integra1(A)) & m2_relset_1(C,k5_numbers,k8_integra1(A)) ) => ( ( r3_rfunct_1(B,A) & v4_seq_2(k2_integra2(A,C)) & k2_seq_2(k2_integra2(A,C)) = 0 ) => ( v4_seq_2(k3_integra2(A,B,C)) & k2_seq_2(k3_integra2(A,B,C)) = k11_integra1(A,B) ) ) ) ) ) ), file(integra4,t9_integra4), []).