% Mizar problem: t65_graph_3,graph_3,3442,69 fof(t65_graph_3,conjecture,( ! [A] : ( ( v2_graph_1(A) & v6_graph_1(A) & v7_graph_1(A) & l1_graph_1(A) ) => ( ~ ( ? [B] : ( v2_funct_1(B) & m2_graph_1(B,A) & ~ v1_msscyc_1(B,A) & v1_graph_3(B,A) ) & ! [B] : ( m1_subset_1(B,u1_graph_1(A)) => ! [C] : ( m1_subset_1(C,u1_graph_1(A)) => ~ ( B != C & ! [D] : ( m1_subset_1(D,u1_graph_1(A)) => ( v1_abian(k6_graph_1(A,D)) <=> ( D != B & D != C ) ) ) ) ) ) ) & ~ ( ? [B] : ( m1_subset_1(B,u1_graph_1(A)) & ? [C] : ( m1_subset_1(C,u1_graph_1(A)) & B != C & ! [D] : ( m1_subset_1(D,u1_graph_1(A)) => ( v1_abian(k6_graph_1(A,D)) <=> ( D != B & D != C ) ) ) ) ) & ! [B] : ( ( v2_funct_1(B) & m2_graph_1(B,A) ) => ~ ( ~ v1_msscyc_1(B,A) & v1_graph_3(B,A) ) ) ) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v1_graph_1,antisymmetry_r2_hidden,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_abian,cc1_card_1,cc1_finseq_1,cc1_finset_1,cc1_graph_2,cc1_membered,cc1_relset_1,cc1_xreal_0,cc20_membered,cc2_card_1,cc2_finset_1,cc2_graph_2,cc2_int_1,cc2_membered,cc2_xreal_0,cc3_card_1,cc3_int_1,cc3_membered,cc3_xreal_0,cc4_int_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,commutativity_k1_nat_1,commutativity_k2_xboole_0,commutativity_k2_xcmplx_0,commutativity_k3_xboole_0,connectedness_r1_xreal_0,d14_graph_3,d1_graph_2,d1_msscyc_1,d1_tarski,d22_graph_1,d2_cqc_lang,d2_msscyc_1,d2_xboole_0,d4_finseq_1,d5_funct_1,d5_real_1,d6_graph_3,d7_graph_2,d7_graph_3,d8_funct_1,dt_g1_graph_1,dt_k1_card_1,dt_k1_funct_1,dt_k1_funct_4,dt_k1_graph_2,dt_k1_nat_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_funcop_1,dt_k2_graph_2,dt_k2_graph_3,dt_k2_relat_1,dt_k2_xboole_0,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_cqc_lang,dt_k3_finseq_1,dt_k3_graph_3,dt_k3_xboole_0,dt_k4_card_1,dt_k4_finseq_1,dt_k4_finseq_4,dt_k4_graph_1,dt_k4_xboole_0,dt_k5_finseq_1,dt_k5_graph_1,dt_k5_numbers,dt_k5_ordinal2,dt_k6_graph_1,dt_k7_finseq_1,dt_k7_graph_3,dt_k8_graph_3,dt_k9_finseq_1,dt_l1_graph_1,dt_m1_finseq_1,dt_m1_graph_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_graph_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_graph_1,dt_u2_graph_1,dt_u3_graph_1,dt_u4_graph_1,existence_l1_graph_1,existence_m1_finseq_1,existence_m1_graph_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_graph_1,existence_m2_relset_1,existence_m2_subset_1,fc10_abian,fc10_finset_1,fc10_graph_3,fc10_membered,fc10_xreal_0,fc11_abian,fc11_finseq_1,fc11_finset_1,fc11_graph_3,fc11_membered,fc11_xreal_0,fc12_abian,fc12_finseq_1,fc12_finset_1,fc12_xreal_0,fc13_finseq_1,fc14_finseq_1,fc14_finset_1,fc17_abian,fc17_finseq_1,fc1_cqc_lang,fc1_finset_1,fc1_graph_2,fc1_int_1,fc1_ordinal2,fc1_subset_1,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc27_membered,fc28_membered,fc29_membered,fc2_abian,fc2_card_1,fc2_finseq_1,fc2_graph_3,fc2_membered,fc2_subset_1,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc37_membered,fc38_membered,fc39_membered,fc3_abian,fc3_finseq_1,fc3_graph_3,fc3_xreal_0,fc40_membered,fc41_membered,fc4_finseq_1,fc4_ordinal2,fc4_subset_1,fc5_graph_3,fc5_membered,fc6_graph_3,fc6_int_1,fc6_membered,fc7_membered,fc7_xreal_0,fc8_membered,fc8_xreal_0,fc9_abian,fc9_finset_1,fc9_membered,fc9_xreal_0,free_g1_graph_1,idempotence_k1_funct_4,idempotence_k2_xboole_0,idempotence_k3_xboole_0,l20_graph_3,rc1_abian,rc1_card_1,rc1_finseq_1,rc1_finset_1,rc1_graph_3,rc1_int_1,rc1_membered,rc1_subset_1,rc1_xreal_0,rc2_abian,rc2_card_1,rc2_finseq_1,rc2_finset_1,rc2_graph_2,rc2_int_1,rc2_subset_1,rc2_xreal_0,rc3_abian,rc3_finseq_1,rc3_finset_1,rc3_xreal_0,rc4_abian,rc4_finseq_1,rc4_finset_1,rc4_xreal_0,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,redefinition_k1_nat_1,redefinition_k2_graph_2,redefinition_k3_finseq_1,redefinition_k4_card_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_k9_finseq_1,redefinition_m2_finseq_1,redefinition_m2_graph_1,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,spc0_boole,spc1_boole,spc1_numerals,symmetry_r1_xboole_0,t11_finseq_2,t13_finseq_2,t15_graph_3,t1_arithm,t1_boole,t1_graph_2,t1_numerals,t1_real,t1_subset,t1_xreal_1,t21_xboole_1,t23_graph_3,t27_finseq_3,t29_graph_3,t29_nat_1,t2_boole,t2_graph_3,t2_real,t2_subset,t2_xreal_1,t36_graph_2,t36_graph_3,t37_nat_1,t38_nat_1,t39_graph_3,t3_boole,t3_real,t3_subset,t3_xboole_0,t44_finseq_1,t44_graph_2,t45_graph_2,t4_boole,t4_real,t4_subset,t50_graph_3,t51_graph_3,t52_graph_3,t53_graph_3,t55_graph_3,t56_finseq_1,t5_real,t5_subset,t60_relat_1,t64_graph_3,t6_boole,t6_finseq_5,t6_graph_2,t6_msscyc_1,t6_real,t72_xboole_1,t7_boole,t7_real,t8_boole,t8_graph_3,t8_real,t98_finseq_3,t9_graph_2]), [file(graph_3,t65_graph_3)]). fof(abstractness_v1_graph_1,axiom,( ! [A] : ( l1_graph_1(A) => ( v1_graph_1(A) => A = g1_graph_1(u1_graph_1(A),u2_graph_1(A),u3_graph_1(A),u4_graph_1(A)) ) ) ), file(graph_1,v1_graph_1), []). fof(antisymmetry_r2_hidden,axiom,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), []). fof(cc10_membered,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,A) => v1_xcmplx_0(B) ) ) ), file(membered,cc10_membered), []). fof(cc11_membered,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) ) ) ) ), file(membered,cc11_membered), []). fof(cc12_membered,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_rat_1(B) ) ) ) ), file(membered,cc12_membered), []). fof(cc13_membered,axiom,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc13_membered), []). fof(cc14_membered,axiom,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v4_ordinal2(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc14_membered), []). fof(cc15_membered,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc15_membered), []). fof(cc16_membered,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_membered(B) ) ) ), file(membered,cc16_membered), []). fof(cc17_membered,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) ) ) ) ), file(membered,cc17_membered), []). fof(cc18_membered,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) ) ) ) ), file(membered,cc18_membered), []). fof(cc19_membered,axiom,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) ) ) ) ), file(membered,cc19_membered), []). fof(cc1_abian,axiom,( ! [A] : ( v2_setfam_1(A) => v1_realset1(A) ) ), file(abian,cc1_abian), []). fof(cc1_card_1,axiom,( ! [A] : ( v1_card_1(A) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) ) ) ), file(card_1,cc1_card_1), []). fof(cc1_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ) ), file(finseq_1,cc1_finseq_1), []). fof(cc1_finset_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_finset_1(A) ) ), file(finset_1,cc1_finset_1), []). fof(cc1_graph_2,axiom,( ! [A] : ( ( v2_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m1_graph_1(B,A) => ( v1_xboole_0(B) => v2_funct_1(B) ) ) ) ), file(graph_2,cc1_graph_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_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_card_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_card_1(A) ) ) ), file(card_1,cc2_card_1), []). fof(cc2_finset_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_finset_1(B) ) ) ), file(finset_1,cc2_finset_1), []). fof(cc2_graph_2,axiom,( ! [A] : ( ( v2_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m1_graph_1(B,A) => ( v1_xboole_0(B) => v8_graph_1(B,A) ) ) ) ), file(graph_2,cc2_graph_2), []). fof(cc2_int_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_int_1(A) ) ) ), file(int_1,cc2_int_1), []). 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_card_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_finset_1(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_card_1(A) ) ) ), file(card_1,cc3_card_1), []). fof(cc3_int_1,axiom,( ! [A] : ( v4_ordinal2(A) => v1_int_1(A) ) ), file(int_1,cc3_int_1), []). 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_int_1,axiom,( ! [A] : ( v1_int_1(A) => ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(int_1,cc4_int_1), []). 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_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_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ), file(xboole_0,k2_xboole_0), []). fof(commutativity_k2_xcmplx_0,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ), file(xcmplx_0,k2_xcmplx_0), []). fof(commutativity_k3_xboole_0,axiom,( ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ), file(xboole_0,k3_xboole_0), []). 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(d14_graph_3,axiom,( ! [A] : ( ( v2_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( ( v2_funct_1(B) & m2_graph_1(B,A) ) => ( v1_graph_3(B,A) <=> k2_relat_1(B) = u2_graph_1(A) ) ) ) ), file(graph_3,d14_graph_3), []). fof(d1_graph_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ( ( ( r1_xreal_0(1,B) & r1_xreal_0(B,k1_nat_1(C,1)) & r1_xreal_0(C,k3_finseq_1(A)) ) => ( D = k1_graph_2(A,B,C) <=> ( k1_nat_1(k3_finseq_1(D),B) = k1_nat_1(C,1) & ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ( ~ r1_xreal_0(k3_finseq_1(D),E) => k1_funct_1(D,k1_nat_1(E,1)) = k1_funct_1(A,k1_nat_1(B,E)) ) ) ) ) ) & ( ~ ( r1_xreal_0(1,B) & r1_xreal_0(B,k1_nat_1(C,1)) & r1_xreal_0(C,k3_finseq_1(A)) ) => ( D = k1_graph_2(A,B,C) <=> D = k1_xboole_0 ) ) ) ) ) ) ) ), file(graph_2,d1_graph_2), []). fof(d1_msscyc_1,axiom,( ! [A] : ( ( v2_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( m1_graph_1(B,A) <=> ( m2_finseq_1(B,u2_graph_1(A)) & ? [C] : ( m2_finseq_1(C,u1_graph_1(A)) & r1_graph_2(A,C,B) ) ) ) ) ) ), file(msscyc_1,d1_msscyc_1), []). fof(d1_tarski,axiom,( ! [A,B] : ( B = k1_tarski(A) <=> ! [C] : ( r2_hidden(C,B) <=> C = A ) ) ), file(tarski,d1_tarski), []). fof(d22_graph_1,axiom,( ! [A] : ( ( v2_graph_1(A) & v7_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_graph_1(A)) => k6_graph_1(A,B) = k1_nat_1(k4_graph_1(A,B),k5_graph_1(A,B)) ) ) ), file(graph_1,d22_graph_1), []). fof(d2_cqc_lang,axiom,( ! [A,B] : k3_cqc_lang(A,B) = k2_funcop_1(k1_tarski(A),B) ), file(cqc_lang,d2_cqc_lang), []). fof(d2_msscyc_1,axiom,( ! [A] : ( ( v2_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m1_graph_1(B,A) => ( v1_msscyc_1(B,A) <=> ? [C] : ( m2_finseq_1(C,u1_graph_1(A)) & r1_graph_2(A,C,B) & k1_funct_1(C,1) = k1_funct_1(C,k3_finseq_1(C)) ) ) ) ) ), file(msscyc_1,d2_msscyc_1), []). fof(d2_xboole_0,axiom,( ! [A,B,C] : ( C = k2_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) | r2_hidden(D,B) ) ) ) ), file(xboole_0,d2_xboole_0), []). fof(d4_finseq_1,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( m1_finseq_1(B,A) <=> r1_tarski(k2_relat_1(B),A) ) ) ), file(finseq_1,d4_finseq_1), []). 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_real_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) <=> ~ ( r1_xreal_0(B,A) & B != A ) ) ) ) ), file(real_1,d5_real_1), []). fof(d6_graph_3,axiom,( ! [A] : ( ( v2_graph_1(A) & v7_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_graph_1(A)) => ! [C] : k7_graph_3(A,B,C) = k1_nat_1(k4_card_1(k2_graph_3(A,B,C)),k4_card_1(k3_graph_3(A,B,C))) ) ) ), file(graph_3,d6_graph_3), []). fof(d7_graph_2,axiom,( ! [A] : ( ( v2_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m2_finseq_1(B,u1_graph_1(A)) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( r1_graph_2(A,B,C) <=> ( k3_finseq_1(B) = k1_nat_1(k3_finseq_1(C),1) & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( ( r1_xreal_0(1,D) & r1_xreal_0(D,k3_finseq_1(C)) ) => r2_graph_1(A,k4_finseq_4(k5_numbers,u1_graph_1(A),B,D),k4_finseq_4(k5_numbers,u1_graph_1(A),B,k1_nat_1(D,1)),k1_funct_1(C,D)) ) ) ) ) ) ) ) ), file(graph_2,d7_graph_2), []). fof(d7_graph_3,axiom,( ! [A] : ( ( v2_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_graph_1(A)) => ! [C] : ( m1_subset_1(C,u1_graph_1(A)) => ! [D] : ( ( v1_graph_1(D) & v2_graph_1(D) & l1_graph_1(D) ) => ( D = k8_graph_3(A,B,C) <=> ( u1_graph_1(D) = u1_graph_1(A) & u2_graph_1(D) = k2_xboole_0(u2_graph_1(A),k1_tarski(u2_graph_1(A))) & u3_graph_1(D) = k1_funct_4(u3_graph_1(A),k3_cqc_lang(u2_graph_1(A),B)) & u4_graph_1(D) = k1_funct_4(u4_graph_1(A),k3_cqc_lang(u2_graph_1(A),C)) ) ) ) ) ) ) ), file(graph_3,d7_graph_3), []). fof(d8_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v2_funct_1(A) <=> ! [B,C] : ( ( r2_hidden(B,k1_relat_1(A)) & r2_hidden(C,k1_relat_1(A)) & k1_funct_1(A,B) = k1_funct_1(A,C) ) => B = C ) ) ) ), file(funct_1,d8_funct_1), []). fof(dt_g1_graph_1,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & v1_funct_2(C,B,A) & m1_relset_1(C,B,A) & v1_funct_1(D) & v1_funct_2(D,B,A) & m1_relset_1(D,B,A) ) => ( v1_graph_1(g1_graph_1(A,B,C,D)) & l1_graph_1(g1_graph_1(A,B,C,D)) ) ) ), file(graph_1,g1_graph_1), []). fof(dt_k1_card_1,axiom,( ! [A] : v1_card_1(k1_card_1(A)) ), file(card_1,k1_card_1), []). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). fof(dt_k1_funct_4,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => ( v1_relat_1(k1_funct_4(A,B)) & v1_funct_1(k1_funct_4(A,B)) ) ) ), file(funct_4,k1_funct_4), []). fof(dt_k1_graph_2,axiom,( ! [A,B,C] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & m1_subset_1(B,k5_numbers) & m1_subset_1(C,k5_numbers) ) => ( v1_relat_1(k1_graph_2(A,B,C)) & v1_funct_1(k1_graph_2(A,B,C)) & v1_finseq_1(k1_graph_2(A,B,C)) ) ) ), file(graph_2,k1_graph_2), []). 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_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_graph_2,axiom,( ! [A,B,C,D] : ( ( m1_finseq_1(B,A) & m1_subset_1(C,k5_numbers) & m1_subset_1(D,k5_numbers) ) => m2_finseq_1(k2_graph_2(A,B,C,D),A) ) ), file(graph_2,k2_graph_2), []). fof(dt_k2_graph_3,axiom,( ! [A,B,C] : ( ( v2_graph_1(A) & l1_graph_1(A) & m1_subset_1(B,u1_graph_1(A)) ) => m1_subset_1(k2_graph_3(A,B,C),k1_zfmisc_1(u2_graph_1(A))) ) ), file(graph_3,k2_graph_3), []). fof(dt_k2_relat_1,axiom,( $true ), file(relat_1,k2_relat_1), []). fof(dt_k2_xboole_0,axiom,( $true ), file(xboole_0,k2_xboole_0), []). fof(dt_k2_xcmplx_0,axiom,( $true ), file(xcmplx_0,k2_xcmplx_0), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). fof(dt_k3_cqc_lang,axiom,( $true ), file(cqc_lang,k3_cqc_lang), []). 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_graph_3,axiom,( ! [A,B,C] : ( ( v2_graph_1(A) & l1_graph_1(A) & m1_subset_1(B,u1_graph_1(A)) ) => m1_subset_1(k3_graph_3(A,B,C),k1_zfmisc_1(u2_graph_1(A))) ) ), file(graph_3,k3_graph_3), []). fof(dt_k3_xboole_0,axiom,( $true ), file(xboole_0,k3_xboole_0), []). fof(dt_k4_card_1,axiom,( ! [A] : ( v1_finset_1(A) => m2_subset_1(k4_card_1(A),k1_numbers,k5_numbers) ) ), file(card_1,k4_card_1), []). fof(dt_k4_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m1_subset_1(k4_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ), file(finseq_1,k4_finseq_1), []). fof(dt_k4_finseq_4,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & m1_relset_1(C,A,B) ) => m1_subset_1(k4_finseq_4(A,B,C,D),B) ) ), file(finseq_4,k4_finseq_4), []). fof(dt_k4_graph_1,axiom,( ! [A,B] : ( ( v2_graph_1(A) & v7_graph_1(A) & l1_graph_1(A) & m1_subset_1(B,u1_graph_1(A)) ) => m2_subset_1(k4_graph_1(A,B),k1_numbers,k5_numbers) ) ), file(graph_1,k4_graph_1), []). fof(dt_k4_xboole_0,axiom,( $true ), file(xboole_0,k4_xboole_0), []). fof(dt_k5_finseq_1,axiom,( $true ), file(finseq_1,k5_finseq_1), []). fof(dt_k5_graph_1,axiom,( ! [A,B] : ( ( v2_graph_1(A) & v7_graph_1(A) & l1_graph_1(A) & m1_subset_1(B,u1_graph_1(A)) ) => m2_subset_1(k5_graph_1(A,B),k1_numbers,k5_numbers) ) ), file(graph_1,k5_graph_1), []). fof(dt_k5_numbers,axiom,( m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ), file(numbers,k5_numbers), []). fof(dt_k5_ordinal2,axiom,( $true ), file(ordinal2,k5_ordinal2), []). fof(dt_k6_graph_1,axiom,( ! [A,B] : ( ( v2_graph_1(A) & v7_graph_1(A) & l1_graph_1(A) & m1_subset_1(B,u1_graph_1(A)) ) => m2_subset_1(k6_graph_1(A,B),k1_numbers,k5_numbers) ) ), file(graph_1,k6_graph_1), []). fof(dt_k7_finseq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( v1_relat_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) ) ) ), file(finseq_1,k7_finseq_1), []). fof(dt_k7_graph_3,axiom,( ! [A,B,C] : ( ( v2_graph_1(A) & v7_graph_1(A) & l1_graph_1(A) & m1_subset_1(B,u1_graph_1(A)) ) => m2_subset_1(k7_graph_3(A,B,C),k1_numbers,k5_numbers) ) ), file(graph_3,k7_graph_3), []). fof(dt_k8_graph_3,axiom,( ! [A,B,C] : ( ( v2_graph_1(A) & l1_graph_1(A) & m1_subset_1(B,u1_graph_1(A)) & m1_subset_1(C,u1_graph_1(A)) ) => ( v1_graph_1(k8_graph_3(A,B,C)) & v2_graph_1(k8_graph_3(A,B,C)) & l1_graph_1(k8_graph_3(A,B,C)) ) ) ), file(graph_3,k8_graph_3), []). fof(dt_k9_finseq_1,axiom,( ! [A] : ( v1_relat_1(k9_finseq_1(A)) & v1_funct_1(k9_finseq_1(A)) ) ), file(finseq_1,k9_finseq_1), []). fof(dt_l1_graph_1,axiom,( $true ), file(graph_1,l1_graph_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_graph_1,axiom,( ! [A] : ( ( v2_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m1_graph_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) ) ) ), file(graph_1,m1_graph_1), []). 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_graph_1,axiom,( ! [A] : ( ( v2_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m2_graph_1(B,A) => m2_finseq_1(B,u2_graph_1(A)) ) ) ), file(graph_1,m2_graph_1), []). 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_u1_graph_1,axiom,( $true ), file(graph_1,u1_graph_1), []). fof(dt_u2_graph_1,axiom,( $true ), file(graph_1,u2_graph_1), []). fof(dt_u3_graph_1,axiom,( ! [A] : ( l1_graph_1(A) => ( v1_funct_1(u3_graph_1(A)) & v1_funct_2(u3_graph_1(A),u2_graph_1(A),u1_graph_1(A)) & m2_relset_1(u3_graph_1(A),u2_graph_1(A),u1_graph_1(A)) ) ) ), file(graph_1,u3_graph_1), []). fof(dt_u4_graph_1,axiom,( ! [A] : ( l1_graph_1(A) => ( v1_funct_1(u4_graph_1(A)) & v1_funct_2(u4_graph_1(A),u2_graph_1(A),u1_graph_1(A)) & m2_relset_1(u4_graph_1(A),u2_graph_1(A),u1_graph_1(A)) ) ) ), file(graph_1,u4_graph_1), []). fof(existence_l1_graph_1,axiom,( ? [A] : l1_graph_1(A) ), file(graph_1,l1_graph_1), []). fof(existence_m1_finseq_1,axiom,( ! [A] : ? [B] : m1_finseq_1(B,A) ), file(finseq_1,m1_finseq_1), []). fof(existence_m1_graph_1,axiom,( ! [A] : ( ( v2_graph_1(A) & l1_graph_1(A) ) => ? [B] : m1_graph_1(B,A) ) ), file(graph_1,m1_graph_1), []). 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_graph_1,axiom,( ! [A] : ( ( v2_graph_1(A) & l1_graph_1(A) ) => ? [B] : m2_graph_1(B,A) ) ), file(graph_1,m2_graph_1), []). 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_abian,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_abian(A) & v1_int_1(B) & ~ v1_abian(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_int_1(k2_xcmplx_0(A,B)) & ~ v1_abian(k2_xcmplx_0(A,B)) ) ) ), file(abian,fc10_abian), []). fof(fc10_finset_1,axiom,( ! [A,B] : ( v1_finset_1(B) => v1_finset_1(k3_xboole_0(A,B)) ) ), file(finset_1,fc10_finset_1), []). fof(fc10_graph_3,axiom,( ! [A,B,C] : ( ( v2_graph_1(A) & v7_graph_1(A) & l1_graph_1(A) & m1_subset_1(B,u1_graph_1(A)) & m1_subset_1(C,u1_graph_1(A)) ) => ( v1_graph_1(k8_graph_3(A,B,C)) & v2_graph_1(k8_graph_3(A,B,C)) & v7_graph_1(k8_graph_3(A,B,C)) ) ) ), file(graph_3,fc10_graph_3), []). 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(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_abian,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_abian(A) & v1_int_1(B) & ~ v1_abian(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v1_int_1(k2_xcmplx_0(B,A)) & ~ v1_abian(k2_xcmplx_0(B,A)) ) ) ), file(abian,fc11_abian), []). fof(fc11_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_finset_1(A) ) => v1_finset_1(k2_relat_1(A)) ) ), file(finseq_1,fc11_finseq_1), []). fof(fc11_finset_1,axiom,( ! [A,B] : ( v1_finset_1(A) => v1_finset_1(k3_xboole_0(A,B)) ) ), file(finset_1,fc11_finset_1), []). fof(fc11_graph_3,axiom,( ! [A,B,C] : ( ( v2_graph_1(A) & v6_graph_1(A) & l1_graph_1(A) & m1_subset_1(B,u1_graph_1(A)) & m1_subset_1(C,u1_graph_1(A)) ) => ( v1_graph_1(k8_graph_3(A,B,C)) & v2_graph_1(k8_graph_3(A,B,C)) & v6_graph_1(k8_graph_3(A,B,C)) ) ) ), file(graph_3,fc11_graph_3), []). 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(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_abian,axiom,( ! [A,B] : ( ( v1_int_1(A) & ~ v1_abian(A) & v1_int_1(B) & ~ v1_abian(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_int_1(k2_xcmplx_0(A,B)) & v1_abian(k2_xcmplx_0(A,B)) ) ) ), file(abian,fc12_abian), []). fof(fc12_finseq_1,axiom,( ! [A] : ( ~ v1_xboole_0(k5_finseq_1(A)) & v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) ) ), file(finseq_1,fc12_finseq_1), []). fof(fc12_finset_1,axiom,( ! [A,B] : ( v1_finset_1(A) => v1_finset_1(k4_xboole_0(A,B)) ) ), file(finset_1,fc12_finset_1), []). 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_finseq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ~ v1_xboole_0(k7_finseq_1(A,B)) & v1_relat_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finset_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) ) ) ), file(finseq_1,fc13_finseq_1), []). fof(fc14_finseq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ~ v1_xboole_0(k7_finseq_1(B,A)) & v1_relat_1(k7_finseq_1(B,A)) & v1_funct_1(k7_finseq_1(B,A)) & v1_finset_1(k7_finseq_1(B,A)) & v1_finseq_1(k7_finseq_1(B,A)) ) ) ), file(finseq_1,fc14_finseq_1), []). fof(fc14_finset_1,axiom,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_zfmisc_1(A,B)) ) ), file(finset_1,fc14_finset_1), []). fof(fc17_abian,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ v1_xboole_0(k1_zfmisc_1(A)) & ~ v2_setfam_1(k1_zfmisc_1(A)) ) ) ), file(abian,fc17_abian), []). fof(fc17_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) => v1_finset_1(k1_relat_1(A)) ) ), file(finseq_1,fc17_finseq_1), []). fof(fc1_cqc_lang,axiom,( ! [A,B] : ( v1_relat_1(k3_cqc_lang(A,B)) & v1_funct_1(k3_cqc_lang(A,B)) ) ), file(cqc_lang,fc1_cqc_lang), []). fof(fc1_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)) ) ), file(finset_1,fc1_finset_1), []). fof(fc1_graph_2,axiom,( ! [A] : ( ( v2_graph_1(A) & l1_graph_1(A) ) => ~ v1_xboole_0(u1_graph_1(A)) ) ), file(graph_2,fc1_graph_2), []). fof(fc1_int_1,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_int_1(k2_xcmplx_0(A,B)) ) ) ), file(int_1,fc1_int_1), []). 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(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(fc27_membered,axiom,( ! [A,B] : ( v1_membered(A) => v1_membered(k3_xboole_0(A,B)) ) ), file(membered,fc27_membered), []). fof(fc28_membered,axiom,( ! [A,B] : ( v1_membered(A) => v1_membered(k3_xboole_0(B,A)) ) ), file(membered,fc28_membered), []). 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(fc2_abian,axiom,( ! [A] : ( ( v1_int_1(A) & v1_abian(A) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,1)) & v1_xreal_0(k2_xcmplx_0(A,1)) & v1_int_1(k2_xcmplx_0(A,1)) & ~ v1_abian(k2_xcmplx_0(A,1)) ) ) ), file(abian,fc2_abian), []). fof(fc2_card_1,axiom,( ! [A] : ( v1_finset_1(A) => ( v1_ordinal1(k1_card_1(A)) & v2_ordinal1(k1_card_1(A)) & v3_ordinal1(k1_card_1(A)) & v1_finset_1(k1_card_1(A)) & v1_card_1(k1_card_1(A)) ) ) ), file(card_1,fc2_card_1), []). fof(fc2_finseq_1,axiom, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) & v1_funct_1(k1_xboole_0) & v2_funct_1(k1_xboole_0) & v1_finset_1(k1_xboole_0) & v1_finseq_1(k1_xboole_0) ), file(finseq_1,fc2_finseq_1), []). fof(fc2_graph_3,axiom,( ! [A,B,C] : ( ( v2_graph_1(A) & v7_graph_1(A) & l1_graph_1(A) & m1_subset_1(B,u1_graph_1(A)) ) => v1_finset_1(k2_graph_3(A,B,C)) ) ), file(graph_3,fc2_graph_3), []). 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(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(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(fc37_membered,axiom,( ! [A,B] : ( v1_membered(A) => v1_membered(k4_xboole_0(A,B)) ) ), file(membered,fc37_membered), []). fof(fc38_membered,axiom,( ! [A,B] : ( v2_membered(A) => ( v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) ) ) ), file(membered,fc38_membered), []). fof(fc39_membered,axiom,( ! [A,B] : ( v3_membered(A) => ( v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) ) ) ), file(membered,fc39_membered), []). fof(fc3_abian,axiom,( ! [A] : ( ( v1_int_1(A) & ~ v1_abian(A) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,1)) & v1_xreal_0(k2_xcmplx_0(A,1)) & v1_int_1(k2_xcmplx_0(A,1)) & v1_abian(k2_xcmplx_0(A,1)) ) ) ), file(abian,fc3_abian), []). fof(fc3_finseq_1,axiom,( ! [A] : ( v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) ) ), file(finseq_1,fc3_finseq_1), []). fof(fc3_graph_3,axiom,( ! [A,B,C] : ( ( v2_graph_1(A) & v7_graph_1(A) & l1_graph_1(A) & m1_subset_1(B,u1_graph_1(A)) ) => v1_finset_1(k3_graph_3(A,B,C)) ) ), file(graph_3,fc3_graph_3), []). 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(fc40_membered,axiom,( ! [A,B] : ( v4_membered(A) => ( v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) & v4_membered(k4_xboole_0(A,B)) ) ) ), file(membered,fc40_membered), []). fof(fc41_membered,axiom,( ! [A,B] : ( v5_membered(A) => ( v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) & v4_membered(k4_xboole_0(A,B)) & v5_membered(k4_xboole_0(A,B)) ) ) ), file(membered,fc41_membered), []). fof(fc4_finseq_1,axiom,( ! [A] : ( v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) ) ), file(finseq_1,fc4_finseq_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_graph_3,axiom,( ! [A,B,C] : ( ( v2_graph_1(A) & l1_graph_1(A) & m1_subset_1(B,u1_graph_1(A)) & v1_xboole_0(C) ) => ( v1_xboole_0(k2_graph_3(A,B,C)) & v1_finset_1(k2_graph_3(A,B,C)) & v1_membered(k2_graph_3(A,B,C)) & v2_membered(k2_graph_3(A,B,C)) & v3_membered(k2_graph_3(A,B,C)) & v4_membered(k2_graph_3(A,B,C)) & v5_membered(k2_graph_3(A,B,C)) ) ) ), file(graph_3,fc5_graph_3), []). 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_graph_3,axiom,( ! [A,B,C] : ( ( v2_graph_1(A) & l1_graph_1(A) & m1_subset_1(B,u1_graph_1(A)) & v1_xboole_0(C) ) => ( v1_xboole_0(k3_graph_3(A,B,C)) & v1_finset_1(k3_graph_3(A,B,C)) & v1_membered(k3_graph_3(A,B,C)) & v2_membered(k3_graph_3(A,B,C)) & v3_membered(k3_graph_3(A,B,C)) & v4_membered(k3_graph_3(A,B,C)) & v5_membered(k3_graph_3(A,B,C)) ) ) ), file(graph_3,fc6_graph_3), []). fof(fc6_int_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & v1_int_1(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v1_int_1(k2_xcmplx_0(B,A)) ) ) ), file(int_1,fc6_int_1), []). 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(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_membered,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) ) ) ), file(membered,fc8_membered), []). 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_abian,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_abian(A) & v1_int_1(B) & v1_abian(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_int_1(k2_xcmplx_0(A,B)) & v1_abian(k2_xcmplx_0(A,B)) ) ) ), file(abian,fc9_abian), []). fof(fc9_finset_1,axiom,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_xboole_0(A,B)) ) ), file(finset_1,fc9_finset_1), []). fof(fc9_membered,axiom,( ! [A] : ( v1_rat_1(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) ) ) ), file(membered,fc9_membered), []). fof(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(free_g1_graph_1,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & v1_funct_2(C,B,A) & m1_relset_1(C,B,A) & v1_funct_1(D) & v1_funct_2(D,B,A) & m1_relset_1(D,B,A) ) => ! [E,F,G,H] : ( g1_graph_1(A,B,C,D) = g1_graph_1(E,F,G,H) => ( A = E & B = F & C = G & D = H ) ) ) ), file(graph_1,g1_graph_1), []). fof(idempotence_k1_funct_4,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => k1_funct_4(A,A) = A ) ), file(funct_4,k1_funct_4), []). fof(idempotence_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,A) = A ), file(xboole_0,k2_xboole_0), []). fof(idempotence_k3_xboole_0,axiom,( ! [A,B] : k3_xboole_0(A,A) = A ), file(xboole_0,k3_xboole_0), []). fof(l20_graph_3,axiom,( ! [A] : ( ( v2_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m1_graph_1(B,A) => ! [C] : ( m2_finseq_1(C,u1_graph_1(A)) => ( r1_graph_2(A,C,B) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( ( r1_xreal_0(1,D) & r1_xreal_0(D,k3_finseq_1(B)) ) => ( r1_xreal_0(1,D) & r1_xreal_0(D,k3_finseq_1(C)) & r1_xreal_0(1,k1_nat_1(D,1)) & r1_xreal_0(k1_nat_1(D,1),k3_finseq_1(C)) & ( ( k1_funct_1(C,D) = k1_funct_1(u4_graph_1(A),k1_funct_1(B,D)) & k1_funct_1(C,k1_nat_1(D,1)) = k1_funct_1(u3_graph_1(A),k1_funct_1(B,D)) ) | ( k1_funct_1(C,D) = k1_funct_1(u3_graph_1(A),k1_funct_1(B,D)) & k1_funct_1(C,k1_nat_1(D,1)) = k1_funct_1(u4_graph_1(A),k1_funct_1(B,D)) ) ) ) ) ) ) ) ) ) ), file(graph_3,l20_graph_3), []). fof(rc1_abian,axiom,( ? [A] : ( m1_subset_1(A,k5_numbers) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_int_1(A) & v1_abian(A) ) ), file(abian,rc1_abian), []). fof(rc1_card_1,axiom,( ? [A] : v1_card_1(A) ), file(card_1,rc1_card_1), []). fof(rc1_finseq_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc1_finseq_1), []). fof(rc1_finset_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) ) ), file(finset_1,rc1_finset_1), []). fof(rc1_graph_3,axiom,( ! [A] : ( ( v2_graph_1(A) & l1_graph_1(A) ) => ? [B] : ( m1_graph_1(B,A) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v1_msscyc_1(B,A) ) ) ), file(graph_3,rc1_graph_3), []). fof(rc1_int_1,axiom,( ? [A] : ( m1_subset_1(A,k1_numbers) & v1_xcmplx_0(A) & v1_xreal_0(A) & v1_int_1(A) ) ), file(int_1,rc1_int_1), []). 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(rc1_xreal_0,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(xreal_0,rc1_xreal_0), []). fof(rc2_abian,axiom,( ? [A] : ( m1_subset_1(A,k5_numbers) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_int_1(A) & ~ v1_abian(A) ) ), file(abian,rc2_abian), []). fof(rc2_card_1,axiom,( ? [A] : ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v1_finset_1(A) & v1_card_1(A) ) ), file(card_1,rc2_card_1), []). fof(rc2_finseq_1,axiom,( ! [A] : ? [B] : ( m1_relset_1(B,k5_numbers,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc2_finseq_1), []). fof(rc2_finset_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_ordinal1(B) & v2_ordinal1(B) & v3_ordinal1(B) & v4_ordinal2(B) & v1_finset_1(B) ) ), file(finset_1,rc2_finset_1), []). fof(rc2_graph_2,axiom,( ! [A] : ( ( v2_graph_1(A) & l1_graph_1(A) ) => ? [B] : ( m1_graph_1(B,A) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_xboole_0(B) & v1_finset_1(B) & v1_finseq_1(B) ) ) ), file(graph_2,rc2_graph_2), []). fof(rc2_int_1,axiom,( ? [A] : v1_int_1(A) ), file(int_1,rc2_int_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(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_abian,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) & v1_int_1(A) & v1_abian(A) ) ), file(abian,rc3_abian), []). fof(rc3_finseq_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc3_finseq_1), []). fof(rc3_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc3_finset_1), []). 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_abian,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) & v1_int_1(A) & ~ v1_abian(A) ) ), file(abian,rc4_abian), []). fof(rc4_finseq_1,axiom,( ! [A] : ? [B] : ( m1_finseq_1(B,A) & v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc4_finseq_1), []). fof(rc4_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc4_finset_1), []). 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(rc6_finseq_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc6_finseq_1), []). fof(rc7_finseq_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc7_finseq_1), []). fof(rc8_finseq_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc8_finseq_1), []). fof(redefinition_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_k2_graph_2,axiom,( ! [A,B,C,D] : ( ( m1_finseq_1(B,A) & m1_subset_1(C,k5_numbers) & m1_subset_1(D,k5_numbers) ) => k2_graph_2(A,B,C,D) = k1_graph_2(B,C,D) ) ), file(graph_2,k2_graph_2), []). fof(redefinition_k3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k3_finseq_1(A) = k1_card_1(A) ) ), file(finseq_1,k3_finseq_1), []). fof(redefinition_k4_card_1,axiom,( ! [A] : ( v1_finset_1(A) => k4_card_1(A) = k1_card_1(A) ) ), file(card_1,k4_card_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_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_k9_finseq_1,axiom,( ! [A] : k9_finseq_1(A) = k5_finseq_1(A) ), file(finseq_1,k9_finseq_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_graph_1,axiom,( ! [A] : ( ( v2_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m2_graph_1(B,A) <=> m1_graph_1(B,A) ) ) ), file(graph_1,m2_graph_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_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(symmetry_r1_xboole_0,axiom,( ! [A,B] : ( r1_xboole_0(A,B) => r1_xboole_0(B,A) ) ), file(xboole_0,r1_xboole_0), []). fof(t11_finseq_2,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ~ ( r2_hidden(A,k2_relat_1(B)) & ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ~ ( r2_hidden(C,k4_finseq_1(B)) & k1_funct_1(B,C) = A ) ) ) ) ), file(finseq_2,t11_finseq_2), []). fof(t13_finseq_2,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B,C] : ( m2_finseq_1(C,B) => ( r2_hidden(A,k4_finseq_1(C)) => r2_hidden(k1_funct_1(C,A),B) ) ) ) ), file(finseq_2,t13_finseq_2), []). fof(t15_graph_3,axiom,( ! [A] : ( ( v2_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( ( v2_funct_1(C) & v1_msscyc_1(C,A) & m2_graph_1(C,A) ) => ~ ( r2_hidden(B,k4_finseq_1(C)) & ! [D] : ( ( v2_funct_1(D) & v1_msscyc_1(D,A) & m2_graph_1(D,A) ) => ~ ( k1_funct_1(D,1) = k1_funct_1(C,B) & k3_finseq_1(D) = k3_finseq_1(C) & k2_relat_1(D) = k2_relat_1(C) ) ) ) ) ) ) ), file(graph_3,t15_graph_3), []). 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_graph_2,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( ( r1_xreal_0(k1_nat_1(A,1),B) & r1_xreal_0(B,C) ) <=> ? [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) & r1_xreal_0(A,D) & ~ r1_xreal_0(C,D) & B = k1_nat_1(D,1) ) ) ) ) ) ), file(graph_2,t1_graph_2), []). 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(t1_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & r1_xreal_0(B,A) ) => A = B ) ) ) ), file(xreal_1,t1_xreal_1), []). fof(t21_xboole_1,axiom,( ! [A,B] : k3_xboole_0(A,k2_xboole_0(A,B)) = A ), file(xboole_1,t21_xboole_1), []). fof(t23_graph_3,axiom,( ! [A] : ( ( v2_graph_1(A) & l1_graph_1(A) ) => ( v6_graph_1(A) <=> ! [B] : ( m1_subset_1(B,u1_graph_1(A)) => ! [C] : ( m1_subset_1(C,u1_graph_1(A)) => ~ ( B != C & ! [D] : ( m1_graph_1(D,A) => ! [E] : ( m2_finseq_1(E,u1_graph_1(A)) => ~ ( ~ v1_xboole_0(D) & r1_graph_2(A,E,D) & k1_funct_1(E,1) = B & k1_funct_1(E,k3_finseq_1(E)) = C ) ) ) ) ) ) ) ) ), file(graph_3,t23_graph_3), []). fof(t27_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v4_ordinal2(B) => ( r2_hidden(B,k4_finseq_1(A)) <=> ( r1_xreal_0(1,B) & r1_xreal_0(B,k3_finseq_1(A)) ) ) ) ) ), file(finseq_3,t27_finseq_3), []). fof(t29_graph_3,axiom,( ! [A] : ( ( v2_graph_1(A) & v7_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_graph_1(A)) => k6_graph_1(A,B) = k7_graph_3(A,B,u2_graph_1(A)) ) ) ), file(graph_3,t29_graph_3), []). fof(t29_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => r1_xreal_0(A,k2_xcmplx_0(A,B)) ) ) ), file(nat_1,t29_nat_1), []). fof(t2_boole,axiom,( ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ), file(boole,t2_boole), []). fof(t2_graph_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ~ ( r2_hidden(D,k4_finseq_1(k1_graph_2(A,B,C))) & ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ~ ( r2_hidden(E,k4_finseq_1(A)) & k1_funct_1(A,E) = k1_funct_1(k1_graph_2(A,B,C),D) & k1_nat_1(E,1) = k1_nat_1(B,D) & r1_xreal_0(B,E) & r1_xreal_0(E,C) ) ) ) ) ) ) ) ), file(graph_3,t2_graph_3), []). 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(t36_graph_2,axiom,( ! [A] : ( ( v2_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m2_graph_1(B,A) => ? [C] : ( m2_finseq_1(C,u1_graph_1(A)) & r1_graph_2(A,C,B) ) ) ) ), file(graph_2,t36_graph_2), []). fof(t36_graph_3,axiom,( ! [A,B] : ( ( v2_graph_1(B) & v7_graph_1(B) & l1_graph_1(B) ) => ! [C] : ( m1_subset_1(C,u1_graph_1(B)) => k7_graph_3(B,C,A) = k7_graph_3(B,C,k3_xboole_0(A,u2_graph_1(B))) ) ) ), file(graph_3,t36_graph_3), []). fof(t37_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ! [C] : ( v4_ordinal2(C) => ( r1_xreal_0(A,B) => r1_xreal_0(A,k2_xcmplx_0(B,C)) ) ) ) ) ), file(nat_1,t37_nat_1), []). fof(t38_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ( ~ r1_xreal_0(k2_xcmplx_0(B,1),A) <=> r1_xreal_0(A,B) ) ) ) ), file(nat_1,t38_nat_1), []). fof(t39_graph_3,axiom,( ! [A] : ( ( v2_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_graph_1(A)) => ! [C] : ( m1_subset_1(C,u1_graph_1(A)) => ( r2_hidden(u2_graph_1(A),u2_graph_1(k8_graph_3(A,B,C))) & u2_graph_1(A) = k4_xboole_0(u2_graph_1(k8_graph_3(A,B,C)),k1_tarski(u2_graph_1(A))) & k1_funct_1(u3_graph_1(k8_graph_3(A,B,C)),u2_graph_1(A)) = B & k1_funct_1(u4_graph_1(k8_graph_3(A,B,C)),u2_graph_1(A)) = C ) ) ) ) ), file(graph_3,t39_graph_3), []). fof(t3_boole,axiom,( ! [A] : k4_xboole_0(A,k1_xboole_0) = A ), file(boole,t3_boole), []). 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(t3_xboole_0,axiom,( ! [A,B] : ( ~ ( ~ r1_xboole_0(A,B) & ! [C] : ~ ( r2_hidden(C,A) & r2_hidden(C,B) ) ) & ~ ( ? [C] : ( r2_hidden(C,A) & r2_hidden(C,B) ) & r1_xboole_0(A,B) ) ) ), file(xboole_0,t3_xboole_0), []). fof(t44_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => k2_relat_1(k7_finseq_1(A,B)) = k2_xboole_0(k2_relat_1(A),k2_relat_1(B)) ) ) ), file(finseq_1,t44_finseq_1), []). fof(t44_graph_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( ( v2_graph_1(D) & l1_graph_1(D) ) => ! [E] : ( m2_graph_1(E,D) => ( ( r1_xreal_0(1,B) & r1_xreal_0(B,C) & r1_xreal_0(C,k3_finseq_1(E)) & A = k2_graph_2(u2_graph_1(D),E,B,C) ) => m2_graph_1(A,D) ) ) ) ) ) ) ), file(graph_2,t44_graph_2), []). fof(t45_graph_2,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( ( v2_graph_1(C) & l1_graph_1(C) ) => ! [D] : ( m2_finseq_1(D,u1_graph_1(C)) => ! [E] : ( m2_finseq_1(E,u1_graph_1(C)) => ! [F] : ( m2_graph_1(F,C) => ! [G] : ( m2_graph_1(G,C) => ( ( r1_xreal_0(1,A) & r1_xreal_0(A,B) & r1_xreal_0(B,k3_finseq_1(F)) & G = k2_graph_2(u2_graph_1(C),F,A,B) & r1_graph_2(C,D,F) & E = k2_graph_2(u1_graph_1(C),D,A,k1_nat_1(B,1)) ) => r1_graph_2(C,E,G) ) ) ) ) ) ) ) ) ), file(graph_2,t45_graph_2), []). fof(t4_boole,axiom,( ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ), file(boole,t4_boole), []). 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_graph_3,axiom,( ! [A] : ( ( v2_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_graph_1(A)) => ! [C] : ( m1_subset_1(C,u1_graph_1(A)) => ! [D] : ( ( v2_funct_1(D) & m2_graph_1(D,k8_graph_3(A,B,C)) ) => ( ~ r2_hidden(u2_graph_1(A),k2_relat_1(D)) => ( v2_funct_1(D) & m2_graph_1(D,A) ) ) ) ) ) ) ), file(graph_3,t50_graph_3), []). fof(t51_graph_3,axiom,( ! [A] : ( ( v2_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_graph_1(A)) => ! [C] : ( m1_subset_1(C,u1_graph_1(A)) => ! [D] : ( m2_finseq_1(D,u1_graph_1(A)) => ! [E] : ( ( v2_funct_1(E) & m2_graph_1(E,k8_graph_3(A,B,C)) ) => ! [F] : ( m2_finseq_1(F,u1_graph_1(k8_graph_3(A,B,C))) => ( ( D = F & r1_graph_2(k8_graph_3(A,B,C),F,E) ) => ( r2_hidden(u2_graph_1(A),k2_relat_1(E)) | r1_graph_2(A,D,E) ) ) ) ) ) ) ) ) ), file(graph_3,t51_graph_3), []). fof(t52_graph_3,axiom,( ! [A,B] : ( ( v2_graph_1(B) & v7_graph_1(B) & l1_graph_1(B) ) => ! [C] : ( m1_subset_1(C,u1_graph_1(B)) => ! [D] : ( m1_subset_1(D,u1_graph_1(B)) => ! [E] : ( m1_subset_1(E,u1_graph_1(B)) => ! [F] : ( m1_subset_1(F,u1_graph_1(k8_graph_3(B,D,E))) => ( ( F = C & r2_hidden(u2_graph_1(B),A) ) => ( D = E | ( C != D & C != E ) | k7_graph_3(k8_graph_3(B,D,E),F,A) = k1_nat_1(k7_graph_3(B,C,A),1) ) ) ) ) ) ) ) ), file(graph_3,t52_graph_3), []). fof(t53_graph_3,axiom,( ! [A,B] : ( ( v2_graph_1(B) & v7_graph_1(B) & l1_graph_1(B) ) => ! [C] : ( m1_subset_1(C,u1_graph_1(B)) => ! [D] : ( m1_subset_1(D,u1_graph_1(B)) => ! [E] : ( m1_subset_1(E,u1_graph_1(B)) => ! [F] : ( m1_subset_1(F,u1_graph_1(k8_graph_3(B,D,E))) => ( F = C => ( C = D | C = E | k7_graph_3(k8_graph_3(B,D,E),F,A) = k7_graph_3(B,C,A) ) ) ) ) ) ) ) ), file(graph_3,t53_graph_3), []). fof(t55_graph_3,axiom,( ! [A] : ( ( v2_graph_1(A) & v7_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_graph_1(A)) => ! [C] : ( m2_finseq_1(C,u1_graph_1(A)) => ! [D] : ( ( v2_funct_1(D) & m2_graph_1(D,A) ) => ( r1_graph_2(A,C,D) => ( v1_msscyc_1(D,A) | ( v1_abian(k7_graph_3(A,B,k2_relat_1(D))) <=> ( B != k1_funct_1(C,1) & B != k1_funct_1(C,k3_finseq_1(C)) ) ) ) ) ) ) ) ) ), file(graph_3,t55_graph_3), []). fof(t56_finseq_1,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( B = k9_finseq_1(A) <=> ( k3_finseq_1(B) = 1 & k2_relat_1(B) = k1_tarski(A) ) ) ) ), file(finseq_1,t56_finseq_1), []). 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(t60_relat_1,axiom, ( k1_relat_1(k1_xboole_0) = k1_xboole_0 & k2_relat_1(k1_xboole_0) = k1_xboole_0 ), file(relat_1,t60_relat_1), []). fof(t64_graph_3,axiom,( ! [A] : ( ( v2_graph_1(A) & v6_graph_1(A) & v7_graph_1(A) & l1_graph_1(A) ) => ( ? [B] : ( v2_funct_1(B) & v1_msscyc_1(B,A) & m2_graph_1(B,A) & v1_graph_3(B,A) ) <=> ! [B] : ( m1_subset_1(B,u1_graph_1(A)) => v1_abian(k6_graph_1(A,B)) ) ) ) ), file(graph_3,t64_graph_3), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t6_finseq_5,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( r2_hidden(1,k4_finseq_1(A)) & r2_hidden(k3_finseq_1(A),k4_finseq_1(A)) ) ) ), file(finseq_5,t6_finseq_5), []). fof(t6_graph_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( ( r1_xreal_0(1,B) & r1_xreal_0(B,k3_finseq_1(A)) ) => k1_graph_2(A,B,B) = k9_finseq_1(k1_funct_1(A,B)) ) ) ) ), file(graph_2,t6_graph_2), []). fof(t6_msscyc_1,axiom,( ! [A] : ( ( v2_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m1_graph_1(B,A) => ! [C] : ( m2_finseq_1(C,u1_graph_1(A)) => ( ( v1_msscyc_1(B,A) & r1_graph_2(A,C,B) ) => k1_funct_1(C,1) = k1_funct_1(C,k3_finseq_1(C)) ) ) ) ) ), file(msscyc_1,t6_msscyc_1), []). 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(t72_xboole_1,axiom,( ! [A,B,C,D] : ( ( k2_xboole_0(A,B) = k2_xboole_0(C,D) & r1_xboole_0(C,A) & r1_xboole_0(D,B) ) => C = B ) ), file(xboole_1,t72_xboole_1), []). 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(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t8_graph_3,axiom,( ! [A] : ( ( v2_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( ( v2_funct_1(B) & m2_graph_1(B,A) ) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( v2_funct_1(k2_graph_2(u2_graph_1(A),B,C,D)) & m2_graph_1(k2_graph_2(u2_graph_1(A),B,C,D),A) ) ) ) ) ) ), file(graph_3,t8_graph_3), []). 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(t98_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ( r1_xboole_0(k2_relat_1(A),k2_relat_1(B)) & v2_funct_1(A) & v2_funct_1(B) ) <=> v2_funct_1(k7_finseq_1(A,B)) ) ) ) ), file(finseq_3,t98_finseq_3), []). fof(t9_graph_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( r1_xreal_0(B,k3_finseq_1(A)) => k7_finseq_1(k1_graph_2(A,1,B),k1_graph_2(A,k1_nat_1(B,1),k3_finseq_1(A))) = A ) ) ) ), file(graph_2,t9_graph_2), []).