% Mizar problem: t15_circuit2,circuit2,1826,49 fof(t15_circuit2,conjecture,( ! [A] : ( ( ~ v3_struct_0(A) & v6_group_1(A) & ~ v2_msualg_1(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v5_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m3_pboole(C,k2_msafree2(A),k2_pre_circ(k2_msafree2(A),k5_numbers),k3_pre_circ(u1_struct_0(A),u4_msualg_1(A,B),k2_msafree2(A))) => ! [D] : ( m1_subset_1(D,k4_card_3(u4_msualg_1(A,B))) => ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ( ( v5_seqm_3(k10_funct_6(C)) & v1_circuit2(k8_funct_2(k5_numbers,k4_card_3(u4_msualg_1(A,B)),k9_circuit2(A,B,C,D),E),A,B) ) => ( v1_xboole_0(k2_msafree2(A)) | ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ( r1_xreal_0(E,F) => k8_funct_2(k5_numbers,k4_card_3(u4_msualg_1(A,B)),k9_circuit2(A,B,C,D),E) = k8_funct_2(k5_numbers,k4_card_3(u4_msualg_1(A,B)),k9_circuit2(A,B,C,D),F) ) ) ) ) ) ) ) ) ) ), inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_arytm_3,cc1_finseq_1,cc1_finset_1,cc1_fraenkel,cc1_funct_1,cc1_membered,cc1_msafree2,cc1_pboole,cc1_relset_1,cc1_xreal_0,cc20_membered,cc2_arytm_3,cc2_finset_1,cc2_funct_1,cc2_membered,cc2_msafree2,cc2_pboole,cc2_xreal_0,cc3_arytm_3,cc3_membered,cc3_pboole,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_k1_nat_1,commutativity_k2_xcmplx_0,connectedness_r1_xreal_0,d2_circuit1,d4_msafree2,d5_seqm_3,d6_circuit2,d7_circuit2,d8_circuit2,d9_circuit2,dt_k10_funct_6,dt_k1_circuit1,dt_k1_circuit2,dt_k1_funct_1,dt_k1_funct_4,dt_k1_msafree2,dt_k1_nat_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_circuit1,dt_k2_funcop_1,dt_k2_msafree2,dt_k2_pre_circ,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_pre_circ,dt_k4_card_3,dt_k5_numbers,dt_k5_ordinal2,dt_k6_circuit2,dt_k7_circuit2,dt_k7_relat_1,dt_k8_circuit2,dt_k8_funct_2,dt_k9_circuit2,dt_l1_msualg_1,dt_l1_struct_0,dt_l2_msualg_1,dt_l3_msualg_1,dt_m1_msafree2,dt_m1_pboole,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,dt_m3_pboole,dt_u1_struct_0,dt_u4_msualg_1,existence_l1_msualg_1,existence_l1_struct_0,existence_l2_msualg_1,existence_l3_msualg_1,existence_m1_msafree2,existence_m1_pboole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,existence_m3_pboole,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc14_finset_1,fc17_finseq_1,fc1_funcop_1,fc1_msafree2,fc1_msualg_1,fc1_ordinal2,fc1_struct_0,fc2_finseq_1,fc2_funcop_1,fc2_membered,fc2_pboole,fc2_pre_circ,fc3_funcop_1,fc3_pralg_1,fc3_xreal_0,fc4_funct_1,fc4_ordinal2,fc5_membered,fc6_membered,fc7_funcop_1,fc7_xreal_0,fc8_xreal_0,fc9_funcop_1,fc9_xreal_0,idempotence_k1_circuit2,idempotence_k1_funct_4,rc1_arytm_3,rc1_finseq_1,rc1_finset_1,rc1_fraenkel,rc1_funcop_1,rc1_funct_1,rc1_membered,rc1_msafree2,rc1_pboole,rc1_pre_circ,rc1_xreal_0,rc2_finseq_1,rc2_finset_1,rc2_funct_1,rc2_pboole,rc2_xreal_0,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc3_pboole,rc3_struct_0,rc3_xreal_0,rc4_finset_1,rc4_funct_1,rc4_msafree2,rc4_pboole,rc4_xreal_0,rc5_funct_1,rc5_struct_0,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,redefinition_k1_circuit2,redefinition_k1_nat_1,redefinition_k2_pre_circ,redefinition_k3_pre_circ,redefinition_k5_numbers,redefinition_k8_funct_2,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,s1_nat_1__e4_25__circuit2,spc0_boole,spc1_boole,spc1_numerals,t14_circuit2,t19_nat_1,t1_numerals,t1_subset,t26_nat_1,t2_circuit1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t79_funct_4,t7_boole,t8_boole,t8_pre_circ]), [file(circuit2,t15_circuit2)]). fof(antisymmetry_r2_hidden,axiom,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), []). fof(cc10_membered,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,A) => v1_xcmplx_0(B) ) ) ), file(membered,cc10_membered), []). fof(cc11_membered,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) ) ) ) ), file(membered,cc11_membered), []). fof(cc12_membered,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_rat_1(B) ) ) ) ), file(membered,cc12_membered), []). fof(cc13_membered,axiom,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc13_membered), []). fof(cc14_membered,axiom,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v4_ordinal2(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc14_membered), []). fof(cc15_membered,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc15_membered), []). fof(cc16_membered,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_membered(B) ) ) ), file(membered,cc16_membered), []). fof(cc17_membered,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) ) ) ) ), file(membered,cc17_membered), []). fof(cc18_membered,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) ) ) ) ), file(membered,cc18_membered), []). fof(cc19_membered,axiom,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) ) ) ) ), file(membered,cc19_membered), []). fof(cc1_arytm_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_ordinal1(B) & v2_ordinal1(B) & v3_ordinal1(B) ) ) ) ), file(arytm_3,cc1_arytm_3), []). fof(cc1_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ) ), file(finseq_1,cc1_finseq_1), []). fof(cc1_finset_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_finset_1(A) ) ), file(finset_1,cc1_finset_1), []). fof(cc1_fraenkel,axiom,( ! [A] : ( v1_fraenkel(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ) ), file(fraenkel,cc1_fraenkel), []). fof(cc1_funct_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_funct_1(A) ) ), file(funct_1,cc1_funct_1), []). fof(cc1_membered,axiom,( ! [A] : ( v5_membered(A) => v4_membered(A) ) ), file(membered,cc1_membered), []). fof(cc1_msafree2,axiom,( ! [A] : ( l1_msualg_1(A) => ( ( ~ v3_struct_0(A) & v2_msualg_1(A) ) => ( ~ v3_struct_0(A) & v2_msafree2(A) ) ) ) ), file(msafree2,cc1_msafree2), []). fof(cc1_pboole,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_pboole(B,A) => ( v2_relat_1(B) => ~ v3_relat_1(B) ) ) ) ), file(pboole,cc1_pboole), []). 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_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_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_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ) ), file(funct_1,cc2_funct_1), []). fof(cc2_membered,axiom,( ! [A] : ( v4_membered(A) => v3_membered(A) ) ), file(membered,cc2_membered), []). fof(cc2_msafree2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ( ( v5_msualg_1(B,A) & v4_msafree2(B,A) ) => ( v5_msualg_1(B,A) & v3_msafree2(B,A) ) ) ) ) ), file(msafree2,cc2_msafree2), []). fof(cc2_pboole,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_pboole(B,A) => ( v3_relat_1(B) => ~ v2_relat_1(B) ) ) ) ), file(pboole,cc2_pboole), []). 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_pboole,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => ! [D] : ( m3_pboole(D,A,B,C) => v1_funcop_1(D) ) ) ), file(pboole,cc3_pboole), []). 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_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_xcmplx_0,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ), file(xcmplx_0,k2_xcmplx_0), []). fof(connectedness_r1_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(d2_circuit1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ( v1_msafree2(A) => ! [B] : ( ( v5_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m3_pboole(C,k2_msafree2(A),k2_pre_circ(k2_msafree2(A),k5_numbers),k3_pre_circ(u1_struct_0(A),u4_msualg_1(A,B),k2_msafree2(A))) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => k2_circuit1(A,B,C,D) = k1_funct_1(k10_funct_6(C),D) ) ) ) ) ) ), file(circuit1,d2_circuit1), []). fof(d4_msafree2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) ) => ( v1_msafree2(A) <=> k2_msafree2(A) != k1_xboole_0 ) ) ), file(msafree2,d4_msafree2), []). fof(d5_seqm_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v5_seqm_3(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) ) ) ) ), file(seqm_3,d5_seqm_3), []). fof(d6_circuit2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v5_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u4_msualg_1(A,B))) => ( v1_circuit2(C,A,B) <=> C = k6_circuit2(A,B,C) ) ) ) ) ), file(circuit2,d6_circuit2), []). fof(d7_circuit2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v5_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u4_msualg_1(A,B))) => ! [D] : ( m1_msafree2(D,A,B) => k7_circuit2(A,B,C,D) = k6_circuit2(A,B,k1_circuit2(A,B,C,D)) ) ) ) ) ), file(circuit2,d7_circuit2), []). fof(d8_circuit2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v5_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m3_pboole(C,k2_msafree2(A),k2_pre_circ(k2_msafree2(A),k5_numbers),k3_pre_circ(u1_struct_0(A),u4_msualg_1(A,B),k2_msafree2(A))) => ! [D] : ( m1_subset_1(D,k4_card_3(u4_msualg_1(A,B))) => k8_circuit2(A,B,C,D) = k1_funct_4(k1_circuit2(A,B,D,k2_circuit1(A,B,C,0)),k1_circuit1(A,B)) ) ) ) ) ), file(circuit2,d8_circuit2), []). fof(d9_circuit2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v5_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m3_pboole(C,k2_msafree2(A),k2_pre_circ(k2_msafree2(A),k5_numbers),k3_pre_circ(u1_struct_0(A),u4_msualg_1(A,B),k2_msafree2(A))) => ! [D] : ( m1_subset_1(D,k4_card_3(u4_msualg_1(A,B))) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k5_numbers,k4_card_3(u4_msualg_1(A,B))) & m2_relset_1(E,k5_numbers,k4_card_3(u4_msualg_1(A,B))) ) => ( E = k9_circuit2(A,B,C,D) <=> ( k8_funct_2(k5_numbers,k4_card_3(u4_msualg_1(A,B)),E,0) = k8_circuit2(A,B,C,D) & ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => k8_funct_2(k5_numbers,k4_card_3(u4_msualg_1(A,B)),E,k1_nat_1(F,1)) = k7_circuit2(A,B,k8_funct_2(k5_numbers,k4_card_3(u4_msualg_1(A,B)),E,F),k2_circuit1(A,B,C,k1_nat_1(F,1))) ) ) ) ) ) ) ) ) ), file(circuit2,d9_circuit2), []). fof(dt_k10_funct_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k10_funct_6(A)) & v1_funct_1(k10_funct_6(A)) & v1_funcop_1(k10_funct_6(A)) ) ) ), file(funct_6,k10_funct_6), []). fof(dt_k1_circuit1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v2_msafree2(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => m1_pboole(k1_circuit1(A,B),k1_msafree2(A)) ) ), file(circuit1,k1_circuit1), []). fof(dt_k1_circuit2,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) & m1_subset_1(C,k4_card_3(u4_msualg_1(A,B))) & m1_msafree2(D,A,B) ) => m1_subset_1(k1_circuit2(A,B,C,D),k4_card_3(u4_msualg_1(A,B))) ) ), file(circuit2,k1_circuit2), []). 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_msafree2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) ) => m1_subset_1(k1_msafree2(A),k1_zfmisc_1(u1_struct_0(A))) ) ), file(msafree2,k1_msafree2), []). 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_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_circuit1,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v2_msafree2(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) & m3_pboole(C,k2_msafree2(A),k2_pre_circ(k2_msafree2(A),k5_numbers),k3_pre_circ(u1_struct_0(A),u4_msualg_1(A,B),k2_msafree2(A))) & m1_subset_1(D,k5_numbers) ) => m1_msafree2(k2_circuit1(A,B,C,D),A,B) ) ), file(circuit1,k2_circuit1), []). fof(dt_k2_funcop_1,axiom,( $true ), file(funcop_1,k2_funcop_1), []). fof(dt_k2_msafree2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) ) => m1_subset_1(k2_msafree2(A),k1_zfmisc_1(u1_struct_0(A))) ) ), file(msafree2,k2_msafree2), []). fof(dt_k2_pre_circ,axiom,( ! [A,B] : m1_pboole(k2_pre_circ(A,B),A) ), file(pre_circ,k2_pre_circ), []). 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_pre_circ,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_subset_1(C,k1_zfmisc_1(A)) ) => m1_pboole(k3_pre_circ(A,B,C),C) ) ), file(pre_circ,k3_pre_circ), []). fof(dt_k4_card_3,axiom,( $true ), file(card_3,k4_card_3), []). 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_circuit2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v2_msafree2(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) & m1_subset_1(C,k4_card_3(u4_msualg_1(A,B))) ) => m1_subset_1(k6_circuit2(A,B,C),k4_card_3(u4_msualg_1(A,B))) ) ), file(circuit2,k6_circuit2), []). fof(dt_k7_circuit2,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) & m1_subset_1(C,k4_card_3(u4_msualg_1(A,B))) & m1_msafree2(D,A,B) ) => m1_subset_1(k7_circuit2(A,B,C,D),k4_card_3(u4_msualg_1(A,B))) ) ), file(circuit2,k7_circuit2), []). 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_k8_circuit2,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) & m3_pboole(C,k2_msafree2(A),k2_pre_circ(k2_msafree2(A),k5_numbers),k3_pre_circ(u1_struct_0(A),u4_msualg_1(A,B),k2_msafree2(A))) & m1_subset_1(D,k4_card_3(u4_msualg_1(A,B))) ) => m1_subset_1(k8_circuit2(A,B,C,D),k4_card_3(u4_msualg_1(A,B))) ) ), file(circuit2,k8_circuit2), []). 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_k9_circuit2,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) & m3_pboole(C,k2_msafree2(A),k2_pre_circ(k2_msafree2(A),k5_numbers),k3_pre_circ(u1_struct_0(A),u4_msualg_1(A,B),k2_msafree2(A))) & m1_subset_1(D,k4_card_3(u4_msualg_1(A,B))) ) => ( v1_funct_1(k9_circuit2(A,B,C,D)) & v1_funct_2(k9_circuit2(A,B,C,D),k5_numbers,k4_card_3(u4_msualg_1(A,B))) & m2_relset_1(k9_circuit2(A,B,C,D),k5_numbers,k4_card_3(u4_msualg_1(A,B))) ) ) ), file(circuit2,k9_circuit2), []). fof(dt_l1_msualg_1,axiom,( ! [A] : ( l1_msualg_1(A) => l1_struct_0(A) ) ), file(msualg_1,l1_msualg_1), []). fof(dt_l1_struct_0,axiom,( $true ), file(struct_0,l1_struct_0), []). fof(dt_l2_msualg_1,axiom,( $true ), file(msualg_1,l2_msualg_1), []). fof(dt_l3_msualg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => l2_msualg_1(B,A) ) ) ), file(msualg_1,l3_msualg_1), []). fof(dt_m1_msafree2,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_msafree2(C,A,B) => m1_pboole(C,k2_msafree2(A)) ) ) ), file(msafree2,m1_msafree2), []). fof(dt_m1_pboole,axiom,( ! [A,B] : ( m1_pboole(B,A) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ), file(pboole,m1_pboole), []). 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_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_pboole,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => ! [D] : ( m3_pboole(D,A,B,C) => m1_pboole(D,A) ) ) ), file(pboole,m3_pboole), []). fof(dt_u1_struct_0,axiom,( $true ), file(struct_0,u1_struct_0), []). fof(dt_u4_msualg_1,axiom,( ! [A,B] : ( ( l1_struct_0(A) & l2_msualg_1(B,A) ) => m1_pboole(u4_msualg_1(A,B),u1_struct_0(A)) ) ), file(msualg_1,u4_msualg_1), []). fof(existence_l1_msualg_1,axiom,( ? [A] : l1_msualg_1(A) ), file(msualg_1,l1_msualg_1), []). fof(existence_l1_struct_0,axiom,( ? [A] : l1_struct_0(A) ), file(struct_0,l1_struct_0), []). fof(existence_l2_msualg_1,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : l2_msualg_1(B,A) ) ), file(msualg_1,l2_msualg_1), []). fof(existence_l3_msualg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) ) => ? [B] : l3_msualg_1(B,A) ) ), file(msualg_1,l3_msualg_1), []). fof(existence_m1_msafree2,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) ) => ? [C] : m1_msafree2(C,A,B) ) ), file(msafree2,m1_msafree2), []). fof(existence_m1_pboole,axiom,( ! [A] : ? [B] : m1_pboole(B,A) ), file(pboole,m1_pboole), []). 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_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_pboole,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => ? [D] : m3_pboole(D,A,B,C) ) ), file(pboole,m3_pboole), []). 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(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_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_funcop_1,axiom,( ! [A,B] : ( v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) ) ), file(funcop_1,fc1_funcop_1), []). fof(fc1_msafree2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v1_msafree2(A) & l1_msualg_1(A) ) => ~ v1_xboole_0(k2_msafree2(A)) ) ), file(msafree2,fc1_msafree2), []). fof(fc1_msualg_1,axiom,( ! [A,B] : ( ( l1_struct_0(A) & v5_msualg_1(B,A) & l2_msualg_1(B,A) ) => ( v1_relat_1(u4_msualg_1(A,B)) & v2_relat_1(u4_msualg_1(A,B)) & v1_funct_1(u4_msualg_1(A,B)) ) ) ), file(msualg_1,fc1_msualg_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_struct_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ~ v1_xboole_0(u1_struct_0(A)) ) ), file(struct_0,fc1_struct_0), []). 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_funcop_1,axiom,( ! [A] : ( v1_xboole_0(k2_funcop_1(k1_xboole_0,A)) & v1_relat_1(k2_funcop_1(k1_xboole_0,A)) & v1_funct_1(k2_funcop_1(k1_xboole_0,A)) & v2_funct_1(k2_funcop_1(k1_xboole_0,A)) ) ), file(funcop_1,fc2_funcop_1), []). fof(fc2_membered,axiom, ( ~ v1_xboole_0(k1_numbers) & v1_membered(k1_numbers) & v2_membered(k1_numbers) ), file(membered,fc2_membered), []). fof(fc2_pboole,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v2_relat_1(B) & m1_pboole(B,A) & m1_subset_1(C,A) ) => ~ v1_xboole_0(k1_funct_1(B,C)) ) ), file(pboole,fc2_pboole), []). fof(fc2_pre_circ,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k7_relat_1(A,B)) & v2_relat_1(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)) ) ) ), file(pre_circ,fc2_pre_circ), []). fof(fc3_funcop_1,axiom,( ! [A,B] : ( v1_xboole_0(B) => ( v1_xboole_0(k2_funcop_1(B,A)) & v1_relat_1(k2_funcop_1(B,A)) & v1_funct_1(k2_funcop_1(B,A)) & v2_funct_1(k2_funcop_1(B,A)) ) ) ), file(funcop_1,fc3_funcop_1), []). fof(fc3_pralg_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v2_relat_1(B) & m1_pboole(B,A) ) => ( ~ v1_xboole_0(k4_card_3(B)) & v1_fraenkel(k4_card_3(B)) ) ) ), file(pralg_1,fc3_pralg_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_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)) ) ) ), file(funct_1,fc4_funct_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(fc5_membered,axiom, ( v1_membered(k5_ordinal2) & v2_membered(k5_ordinal2) & v3_membered(k5_ordinal2) & v4_membered(k5_ordinal2) & v5_membered(k5_ordinal2) ), file(membered,fc5_membered), []). fof(fc6_membered,axiom, ( v1_xboole_0(k1_xboole_0) & v1_membered(k1_xboole_0) & v2_membered(k1_xboole_0) & v3_membered(k1_xboole_0) & v4_membered(k1_xboole_0) & v5_membered(k1_xboole_0) ), file(membered,fc6_membered), []). fof(fc7_funcop_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => ( v1_relat_1(k1_funct_1(A,B)) & v1_funct_1(k1_funct_1(A,B)) ) ) ), file(funcop_1,fc7_funcop_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_funcop_1,axiom,( ! [A,B] : ( ~ v1_xboole_0(B) => ( v1_relat_1(k2_funcop_1(A,B)) & v2_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) ) ) ), file(funcop_1,fc9_funcop_1), []). fof(fc9_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_k1_circuit2,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) & m1_subset_1(C,k4_card_3(u4_msualg_1(A,B))) & m1_msafree2(D,A,B) ) => k1_circuit2(A,B,C,C) = C ) ), file(circuit2,k1_circuit2), []). 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(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_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_fraenkel,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_fraenkel(A) ) ), file(fraenkel,rc1_fraenkel), []). fof(rc1_funcop_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) ), file(funcop_1,rc1_funcop_1), []). fof(rc1_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc1_funct_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_msafree2,axiom,( ? [A] : ( l1_msualg_1(A) & ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v1_msafree2(A) ) ), file(msafree2,rc1_msafree2), []). fof(rc1_pboole,axiom,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A) ) ), file(pboole,rc1_pboole), []). fof(rc1_pre_circ,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ), file(pre_circ,rc1_pre_circ), []). fof(rc1_xreal_0,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(xreal_0,rc1_xreal_0), []). 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_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) ), file(funct_1,rc2_funct_1), []). fof(rc2_pboole,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v3_relat_1(B) & v1_funct_1(B) ) ), file(pboole,rc2_pboole), []). 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_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_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ), file(funct_1,rc3_funct_1), []). fof(rc3_pboole,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v2_relat_1(B) & v1_funct_1(B) ) ), file(pboole,rc3_pboole), []). fof(rc3_struct_0,axiom,( ? [A] : ( l1_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc3_struct_0), []). 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_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_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc4_funct_1), []). fof(rc4_msafree2,axiom,( ? [A] : ( l1_msualg_1(A) & ~ v3_struct_0(A) & v6_group_1(A) & ~ v2_msualg_1(A) & v2_msafree2(A) & v5_msafree2(A) ) ), file(msafree2,rc4_msafree2), []). fof(rc4_pboole,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_funcop_1(B) ) ), file(pboole,rc4_pboole), []). 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(rc5_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc5_funct_1), []). fof(rc5_struct_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) ) ) ), file(struct_0,rc5_struct_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_circuit2,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) & m1_subset_1(C,k4_card_3(u4_msualg_1(A,B))) & m1_msafree2(D,A,B) ) => k1_circuit2(A,B,C,D) = k1_funct_4(C,D) ) ), file(circuit2,k1_circuit2), []). 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_pre_circ,axiom,( ! [A,B] : k2_pre_circ(A,B) = k2_funcop_1(A,B) ), file(pre_circ,k2_pre_circ), []). fof(redefinition_k3_pre_circ,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k3_pre_circ(A,B,C) = k7_relat_1(B,C) ) ), file(pre_circ,k3_pre_circ), []). fof(redefinition_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). 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_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) <=> m1_relset_1(C,A,B) ) ), file(relset_1,m2_relset_1), []). fof(redefinition_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(subset_1,m2_subset_1), []). fof(reflexivity_r1_tarski,axiom,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), []). fof(reflexivity_r1_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => r1_xreal_0(A,A) ) ), file(xreal_0,r1_xreal_0), []). fof(s1_nat_1__e4_25__circuit2,axiom,( ! [A,B,C,D,E] : ( ( ~ v3_struct_0(A) & v6_group_1(A) & ~ v2_msualg_1(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) & m3_pboole(C,k2_msafree2(A),k2_pre_circ(k2_msafree2(A),k5_numbers),k3_pre_circ(u1_struct_0(A),u4_msualg_1(A,B),k2_msafree2(A))) & m1_subset_1(D,k4_card_3(u4_msualg_1(A,B))) & m2_subset_1(E,k1_numbers,k5_numbers) ) => ( ( ( r1_xreal_0(E,0) => k8_funct_2(k5_numbers,k4_card_3(u4_msualg_1(A,B)),k9_circuit2(A,B,C,D),E) = k8_funct_2(k5_numbers,k4_card_3(u4_msualg_1(A,B)),k9_circuit2(A,B,C,D),0) ) & ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ( ( r1_xreal_0(E,F) => k8_funct_2(k5_numbers,k4_card_3(u4_msualg_1(A,B)),k9_circuit2(A,B,C,D),E) = k8_funct_2(k5_numbers,k4_card_3(u4_msualg_1(A,B)),k9_circuit2(A,B,C,D),F) ) => ( r1_xreal_0(E,k1_nat_1(F,1)) => k8_funct_2(k5_numbers,k4_card_3(u4_msualg_1(A,B)),k9_circuit2(A,B,C,D),E) = k8_funct_2(k5_numbers,k4_card_3(u4_msualg_1(A,B)),k9_circuit2(A,B,C,D),k1_nat_1(F,1)) ) ) ) ) => ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ( r1_xreal_0(E,F) => k8_funct_2(k5_numbers,k4_card_3(u4_msualg_1(A,B)),k9_circuit2(A,B,C,D),E) = k8_funct_2(k5_numbers,k4_card_3(u4_msualg_1(A,B)),k9_circuit2(A,B,C,D),F) ) ) ) ) ), file(circuit2,s1_nat_1__e4_25__circuit2), []). 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(t14_circuit2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v6_group_1(A) & ~ v2_msualg_1(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v5_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m3_pboole(C,k2_msafree2(A),k2_pre_circ(k2_msafree2(A),k5_numbers),k3_pre_circ(u1_struct_0(A),u4_msualg_1(A,B),k2_msafree2(A))) => ( v5_seqm_3(k10_funct_6(C)) => ( v1_xboole_0(k2_msafree2(A)) | ! [D] : ( m1_subset_1(D,k4_card_3(u4_msualg_1(A,B))) => ! [E] : ( m1_msafree2(E,A,B) => ( E = k1_funct_1(k10_funct_6(C),0) => ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => r1_tarski(E,k8_funct_2(k5_numbers,k4_card_3(u4_msualg_1(A,B)),k9_circuit2(A,B,C,D),F)) ) ) ) ) ) ) ) ) ) ), file(circuit2,t14_circuit2), []). fof(t19_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ~ ( 0 != A & r1_xreal_0(A,0) ) ) ), file(nat_1,t19_nat_1), []). fof(t1_numerals,axiom,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t26_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ~ ( r1_xreal_0(A,k2_xcmplx_0(B,1)) & ~ r1_xreal_0(A,B) & A != k2_xcmplx_0(B,1) ) ) ) ), file(nat_1,t26_nat_1), []). fof(t2_circuit1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v5_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m3_pboole(C,k2_msafree2(A),k2_pre_circ(k2_msafree2(A),k5_numbers),k3_pre_circ(u1_struct_0(A),u4_msualg_1(A,B),k2_msafree2(A))) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( v1_msafree2(A) => m1_msafree2(k1_funct_1(k10_funct_6(C),D),A,B) ) ) ) ) ) ), file(circuit1,t2_circuit1), []). fof(t2_subset,axiom,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t4_subset,axiom,( ! [A,B,C] : ( ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) ) => m1_subset_1(A,C) ) ), file(subset,t4_subset), []). fof(t5_subset,axiom,( ! [A,B,C] : ~ ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C) ) ), file(subset,t5_subset), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t79_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_tarski(A,B) => ( k1_funct_4(A,B) = B & k1_funct_4(B,A) = B ) ) ) ) ), file(funct_4,t79_funct_4), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t8_pre_circ,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B,C] : ( ( v2_relat_1(C) & m1_pboole(C,A) ) => ! [D] : ( m3_pboole(D,A,k2_pre_circ(A,B),C) => k1_relat_1(k10_funct_6(D)) = B ) ) ) ), file(pre_circ,t8_pre_circ), []).