% Mizar problem: t61_scmring4,scmring4,2988,33 fof(t61_scmring4,conjecture,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( ( ~ v3_struct_0(B) & v4_group_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v6_vectsp_1(B) & v7_vectsp_1(B) & v8_vectsp_1(B) & v1_scmring1(B) & l3_vectsp_1(B) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B)))) => ( ~ v3_realset2(B) => ! [D] : ( ( v11_ami_1(D,k1_tarski(u1_struct_0(B)),k1_scmring2(B)) & m1_ami_1(D,k1_tarski(u1_struct_0(B)),k1_scmring2(B)) ) => ( ( r2_hidden(k2_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B)),k1_relat_1(D)) & r1_tarski(D,C) ) => ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => k11_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k10_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k8_ami_5(k1_tarski(u1_struct_0(B)),k1_scmring2(B),C,k3_scmring4(k1_tarski(u1_struct_0(B)),k1_scmring2(B),A,D))),E) = k8_ami_5(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k8_ami_5(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k11_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k10_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),C),E),k12_ami_3(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k8_amistd_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k6_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k11_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k10_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),C),E)),A))),k6_ami_5(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k3_scmring4(k1_tarski(u1_struct_0(B)),k1_scmring2(B),A,D))) ) ) ) ) ) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v1_ami_1,antisymmetry_r2_hidden,cc13_amistd_2,cc14_amistd_2,cc1_amistd_1,cc1_amistd_2,cc1_finseq_1,cc1_finset_1,cc1_fraenkel,cc1_funct_1,cc1_nat_1,cc1_relset_1,cc1_scmfsa_4,cc1_scmring1,cc1_setfam_1,cc1_xreal_0,cc2_amistd_1,cc2_finset_1,cc2_funct_1,cc2_nat_1,cc2_xreal_0,cc3_amistd_1,cc3_amistd_2,cc3_nat_1,cc3_scmring1,cc3_xreal_0,cc4_amistd_1,cc4_amistd_2,cc4_scmring1,cc4_xreal_0,cc5_amistd_2,cc5_scmring1,cc5_xreal_0,cc6_amistd_2,cc6_scmring1,cc6_xreal_0,cc7_amistd_2,cc7_xreal_0,cc8_amistd_1,cc8_xreal_0,commutativity_k1_nat_1,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k2_xcmplx_0,commutativity_k3_xboole_0,d15_ami_1,d15_amistd_2,d16_ami_3,d17_ami_1,d18_ami_1,d19_ami_1,d1_funct_4,d1_tarski,d2_scmring4,d5_ami_1,d5_ami_5,d7_ami_1,d7_xboole_0,dt_g1_ami_1,dt_k10_ami_1,dt_k10_amistd_2,dt_k11_ami_1,dt_k12_ami_3,dt_k13_ami_1,dt_k13_ami_3,dt_k13_finseq_1,dt_k17_ami_1,dt_k1_funct_1,dt_k1_funct_2,dt_k1_funct_4,dt_k1_nat_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_scmring2,dt_k1_struct_0,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_ami_1,dt_k2_ami_2,dt_k2_tarski,dt_k2_xboole_0,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_ami_2,dt_k3_scmring4,dt_k3_tarski,dt_k3_xboole_0,dt_k4_ami_1,dt_k4_card_3,dt_k5_ami_5,dt_k5_amistd_1,dt_k5_numbers,dt_k5_ordinal2,dt_k6_ami_1,dt_k6_ami_5,dt_k7_ami_1,dt_k7_ami_5,dt_k8_ami_1,dt_k8_ami_5,dt_k8_amistd_1,dt_k8_amistd_2,dt_k8_funct_2,dt_k9_ami_1,dt_k9_amistd_2,dt_l1_ami_1,dt_l1_group_1,dt_l1_rlvect_1,dt_l1_struct_0,dt_l1_vectsp_1,dt_l2_struct_0,dt_l2_vectsp_1,dt_l3_vectsp_1,dt_m1_ami_1,dt_m1_relset_1,dt_m1_struct_0,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_ami_1,dt_u1_struct_0,dt_u2_ami_1,dt_u3_ami_1,dt_u4_ami_1,dt_u5_ami_1,dt_u6_ami_1,existence_l1_ami_1,existence_l1_group_1,existence_l1_rlvect_1,existence_l1_struct_0,existence_l1_vectsp_1,existence_l2_struct_0,existence_l2_vectsp_1,existence_l3_vectsp_1,existence_m1_ami_1,existence_m1_relset_1,existence_m1_struct_0,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,fc10_ami_1,fc10_finset_1,fc10_xreal_0,fc11_finset_1,fc11_xreal_0,fc12_scmring3,fc12_xreal_0,fc14_finset_1,fc16_finseq_1,fc17_finseq_1,fc1_ami_5,fc1_amistd_2,fc1_card_4,fc1_finset_1,fc1_fraenkel,fc1_nat_1,fc1_scmring4,fc1_struct_0,fc1_xboole_0,fc20_amistd_2,fc21_amistd_2,fc22_amistd_2,fc23_amistd_2,fc24_amistd_2,fc25_amistd_2,fc26_amistd_2,fc2_ami_1,fc2_amistd_2,fc2_finseq_1,fc2_finset_1,fc2_fraenkel,fc2_scmring1,fc2_setfam_1,fc2_xboole_0,fc38_scmring3,fc39_scmring3,fc3_ami_1,fc3_amistd_2,fc3_nat_1,fc3_setfam_1,fc3_xboole_0,fc3_xreal_0,fc40_scmring3,fc4_ami_1,fc4_amistd_1,fc4_nat_1,fc4_setfam_1,fc5_amistd_2,fc7_xreal_0,fc8_xreal_0,fc9_amistd_2,fc9_finseq_1,fc9_finset_1,fc9_xreal_0,free_g1_ami_1,idempotence_k17_ami_1,idempotence_k1_funct_4,idempotence_k2_xboole_0,idempotence_k3_xboole_0,idempotence_k8_ami_5,irreflexivity_r1_subset_1,l1_scmring4,rc10_ami_1,rc11_ami_1,rc1_ami_1,rc1_ami_3,rc1_amistd_1,rc1_amistd_2,rc1_finseq_1,rc1_finset_1,rc1_fraenkel,rc1_funct_1,rc1_nat_1,rc1_scmfsa_4,rc1_scmring4,rc1_setfam_1,rc1_xboole_0,rc1_xreal_0,rc2_ami_1,rc2_amistd_1,rc2_finseq_1,rc2_finset_1,rc2_funct_1,rc2_nat_1,rc2_xboole_0,rc2_xreal_0,rc3_ami_1,rc3_amistd_1,rc3_amistd_2,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc3_nat_1,rc3_struct_0,rc3_xreal_0,rc4_amistd_1,rc4_amistd_2,rc4_finset_1,rc4_funct_1,rc4_struct_0,rc4_xreal_0,rc5_ami_1,rc5_amistd_1,rc5_amistd_2,rc5_struct_0,rc6_ami_1,rc6_amistd_1,rc6_amistd_2,rc6_finseq_1,rc7_ami_1,rc7_finseq_1,rc8_ami_1,rc8_finseq_1,rc9_ami_1,redefinition_k11_ami_1,redefinition_k13_ami_1,redefinition_k17_ami_1,redefinition_k1_nat_1,redefinition_k1_struct_0,redefinition_k5_numbers,redefinition_k8_ami_5,redefinition_k8_funct_2,redefinition_m1_struct_0,redefinition_m2_relset_1,redefinition_m2_subset_1,redefinition_r1_subset_1,reflexivity_r1_tarski,s1_nat_1__e16_72__scmring4,spc0_boole,spc1_boole,spc1_numerals,symmetry_r1_subset_1,symmetry_r1_xboole_0,t11_scmring4,t12_funct_4,t13_scmring4,t14_funct_4,t15_funct_4,t1_arithm,t1_boole,t1_numerals,t1_subset,t1_xboole_1,t23_xboole_1,t26_scmring4,t29_scmring4,t2_boole,t2_subset,t33_ami_5,t34_ami_3,t35_scmring4,t36_funct_4,t3_subset,t40_scmring4,t48_scmring4,t4_subset,t50_ami_3,t50_scmring4,t53_scmring4,t54_scmring4,t5_subset,t62_ami_5,t63_ami_5,t63_xboole_1,t64_ami_5,t65_ami_5,t66_ami_5,t6_boole,t73_ami_5,t76_ami_5,t79_funct_4,t7_boole,t8_boole,t8_grfunc_1]), [file(scmring4,t61_scmring4)]). fof(abstractness_v1_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ( v1_ami_1(B,A) => B = g1_ami_1(A,u1_struct_0(B),u1_ami_1(A,B),u2_ami_1(A,B),u3_ami_1(A,B),u4_ami_1(A,B),u5_ami_1(A,B),u6_ami_1(A,B)) ) ) ), file(ami_1,v1_ami_1), []). fof(antisymmetry_r2_hidden,axiom,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), []). fof(cc13_amistd_2,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & v8_amistd_2(B,A) & v11_amistd_2(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_subset_1(C,u4_ami_1(A,B)) => ( ~ v1_xboole_0(C) & v10_amistd_2(C,A,B) ) ) ) ), file(amistd_2,cc13_amistd_2), []). fof(cc14_amistd_2,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v2_ami_1(B,A) & v13_amistd_2(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_subset_1(C,u4_ami_1(A,B)) => ( ~ v1_xboole_0(C) & v12_amistd_2(C,A,B) ) ) ) ), file(amistd_2,cc14_amistd_2), []). fof(cc1_amistd_1,axiom,( ! [A] : ( v1_relat_1(A) => ( v1_relat_1(A) & v1_setfam_1(A) ) ) ), file(amistd_1,cc1_amistd_1), []). fof(cc1_amistd_2,axiom,( ! [A] : ( v1_amistd_2(A) => ( v1_fraenkel(A) & v1_pralg_2(A) ) ) ), file(amistd_2,cc1_amistd_2), []). 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_nat_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) ) ) ), file(nat_1,cc1_nat_1), []). 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_scmfsa_4,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ! [C] : ( m1_ami_1(C,A,B) => ( v1_relat_1(C) & v1_funct_1(C) & v1_finset_1(C) ) ) ) ), file(scmfsa_4,cc1_scmfsa_4), []). fof(cc1_scmring1,axiom,( ! [A] : ( ~ v1_finset_1(A) => ( ~ v1_xboole_0(A) & ~ v1_realset1(A) ) ) ), file(scmring1,cc1_scmring1), []). fof(cc1_setfam_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_setfam_1(A) ) => ! [B] : ( m1_subset_1(B,A) => ~ v1_xboole_0(B) ) ) ), file(setfam_1,cc1_setfam_1), []). fof(cc1_xreal_0,axiom,( ! [A] : ( v4_ordinal2(A) => v1_xreal_0(A) ) ), file(xreal_0,cc1_xreal_0), []). fof(cc2_amistd_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ! [C] : ( m1_ami_1(C,A,B) => ( v1_xboole_0(C) => ( v1_relat_1(C) & v1_funct_1(C) & v1_finset_1(C) & v1_setfam_1(C) & v1_ami_3(C,A,B) ) ) ) ) ), file(amistd_1,cc2_amistd_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_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_nat_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) ) ) ), file(nat_1,cc2_nat_1), []). fof(cc2_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xcmplx_0(A) ) ), file(xreal_0,cc2_xreal_0), []). fof(cc3_amistd_1,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( l1_ami_1(B,A) => ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v7_ami_1(B,A) & v8_ami_1(B,A) ) => ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v13_ami_1(B,A) ) ) ) ) ), file(amistd_1,cc3_amistd_1), []). fof(cc3_amistd_2,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( l1_ami_1(B,A) => ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) ) => ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v7_amistd_2(B,A) ) ) ) ) ), file(amistd_2,cc3_amistd_2), []). fof(cc3_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ( v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(nat_1,cc3_nat_1), []). fof(cc3_scmring1,axiom,( ! [A] : ( l1_rlvect_1(A) => ( ( ~ v3_struct_0(A) & v3_realset2(A) ) => ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) ) ) ) ), file(scmring1,cc3_scmring1), []). 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_amistd_1,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( l1_ami_1(B,A) => ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) ) => ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v3_amistd_1(B,A) ) ) ) ) ), file(amistd_1,cc4_amistd_1), []). fof(cc4_amistd_2,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ( v8_amistd_2(B,A) => v2_amistd_2(B,A) ) ) ), file(amistd_2,cc4_amistd_2), []). fof(cc4_scmring1,axiom,( ! [A] : ( l3_vectsp_1(A) => ( ( ~ v3_struct_0(A) & v3_realset2(A) ) => ( ~ v3_struct_0(A) & v4_vectsp_1(A) & v6_vectsp_1(A) ) ) ) ), file(scmring1,cc4_scmring1), []). 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_amistd_2,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v5_amistd_2(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_subset_1(C,u4_ami_1(A,B)) => ( ~ v1_xboole_0(C) & v3_amistd_2(C,A,B) ) ) ) ), file(amistd_2,cc5_amistd_2), []). fof(cc5_scmring1,axiom,( ! [A] : ( m1_subset_1(A,k2_ami_2) => ( v4_ordinal2(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xcmplx_0(A) ) ) ), file(scmring1,cc5_scmring1), []). 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_amistd_2,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v6_amistd_2(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_subset_1(C,u4_ami_1(A,B)) => ( ~ v1_xboole_0(C) & v4_amistd_2(C,A,B) ) ) ) ), file(amistd_2,cc6_amistd_2), []). fof(cc6_scmring1,axiom,( ! [A] : ( l1_struct_0(A) => ( ( ~ v3_struct_0(A) & v3_realset2(A) ) => ( ~ v3_struct_0(A) & v1_scmring1(A) ) ) ) ), file(scmring1,cc6_scmring1), []). 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_amistd_2,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_ami_1(C,A,B) => ( ( ~ v1_xboole_0(C) & v1_ami_3(C,A,B) & v1_realset1(C) ) => ( v1_relat_1(C) & v1_funct_1(C) & ~ v1_xboole_0(C) & v1_finset_1(C) & v1_setfam_1(C) & v1_ami_3(C,A,B) & v11_amistd_1(C,A,B) ) ) ) ) ), file(amistd_2,cc7_amistd_2), []). 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_amistd_1,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_ami_1(C,A,B) => ( v1_xboole_0(C) => ( v1_relat_1(C) & v1_funct_1(C) & v1_finset_1(C) & v1_setfam_1(C) & v9_amistd_1(C,A,B) ) ) ) ) ), file(amistd_1,cc8_amistd_1), []). 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(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_tarski,axiom,( ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ), file(tarski,k2_tarski), []). fof(commutativity_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ), file(xboole_0,k2_xboole_0), []). fof(commutativity_k2_xcmplx_0,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ), file(xcmplx_0,k2_xcmplx_0), []). fof(commutativity_k3_xboole_0,axiom,( ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ), file(xboole_0,k3_xboole_0), []). fof(d15_ami_1,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) => k6_ami_1(A,B,C) = k1_funct_1(C,k2_ami_1(A,B)) ) ) ) ), file(ami_1,d15_ami_1), []). fof(d15_amistd_2,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & v8_amistd_2(B,A) & l1_ami_1(B,A) ) => ! [C] : ( ( v1_ami_3(C,A,B) & m1_ami_1(C,A,B) ) => ! [D] : ( v4_ordinal2(D) => ! [E] : ( m1_ami_1(E,A,B) => ( E = k9_amistd_2(A,B,C,D) <=> ( k1_relat_1(E) = k1_relat_1(C) & ! [F] : ( v4_ordinal2(F) => ( r2_hidden(k5_amistd_1(A,B,F),k1_relat_1(C)) => k1_funct_1(E,k5_amistd_1(A,B,F)) = k8_amistd_2(A,B,k5_ami_5(A,B,C,k5_amistd_1(A,B,F)),D) ) ) ) ) ) ) ) ) ) ), file(amistd_2,d15_amistd_2), []). fof(d16_ami_3,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_ami_1(C,A,B) => ( r2_hidden(k2_ami_1(A,B),k1_relat_1(C)) => k13_ami_3(A,B,C) = k1_funct_1(C,k2_ami_1(A,B)) ) ) ) ) ), file(ami_3,d16_ami_3), []). fof(d17_ami_1,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) => k8_ami_1(A,B,C) = k1_funct_1(C,k6_ami_1(A,B,C)) ) ) ) ), file(ami_1,d17_ami_1), []). fof(d18_ami_1,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) => k9_ami_1(A,B,C) = k4_ami_1(A,B,k8_ami_1(A,B,C),C) ) ) ) ), file(ami_1,d18_ami_1), []). fof(d19_ami_1,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k5_numbers,k4_card_3(u5_ami_1(A,B))) & m2_relset_1(D,k5_numbers,k4_card_3(u5_ami_1(A,B))) ) => ( D = k10_ami_1(A,B,C) <=> ( k8_funct_2(k5_numbers,k4_card_3(u5_ami_1(A,B)),D,0) = C & ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => k8_funct_2(k5_numbers,k4_card_3(u5_ami_1(A,B)),D,k1_nat_1(E,1)) = k9_ami_1(A,B,k8_funct_2(k5_numbers,k4_card_3(u5_ami_1(A,B)),D,E)) ) ) ) ) ) ) ) ), file(ami_1,d19_ami_1), []). fof(d1_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( C = k1_funct_4(A,B) <=> ( k1_relat_1(C) = k2_xboole_0(k1_relat_1(A),k1_relat_1(B)) & ! [D] : ( r2_hidden(D,k2_xboole_0(k1_relat_1(A),k1_relat_1(B))) => ( ( r2_hidden(D,k1_relat_1(B)) => k1_funct_1(C,D) = k1_funct_1(B,D) ) & ( ~ r2_hidden(D,k1_relat_1(B)) => k1_funct_1(C,D) = k1_funct_1(A,D) ) ) ) ) ) ) ) ) ), file(funct_4,d1_funct_4), []). fof(d1_tarski,axiom,( ! [A,B] : ( B = k1_tarski(A) <=> ! [C] : ( r2_hidden(C,B) <=> C = A ) ) ), file(tarski,d1_tarski), []). fof(d2_scmring4,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & v8_amistd_2(B,A) & l1_ami_1(B,A) ) => ! [C] : ( v4_ordinal2(C) => ! [D] : ( m1_ami_1(D,A,B) => k3_scmring4(A,B,C,D) = k17_ami_1(A,B,k17_ami_1(A,B,k12_ami_3(A,B,k8_amistd_1(A,B,k13_ami_3(A,B,D),C)),k9_amistd_2(A,B,k10_amistd_2(A,B,k6_ami_5(A,B,D),C),C)),k7_ami_5(A,B,D)) ) ) ) ) ), file(scmring4,d2_scmring4), []). fof(d5_ami_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & l1_ami_1(B,A) ) => k2_ami_1(A,B) = u1_ami_1(A,B) ) ), file(ami_1,d5_ami_1), []). fof(d5_ami_5,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_ami_1(C,A,B) => ! [D] : ( m1_struct_0(D,B,u2_ami_1(A,B)) => ( r2_hidden(D,k1_relat_1(C)) => k5_ami_5(A,B,C,D) = k1_funct_1(C,D) ) ) ) ) ) ), file(ami_5,d5_ami_5), []). fof(d7_ami_1,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v2_ami_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B)) => ! [D] : ( m1_subset_1(D,k4_card_3(u5_ami_1(A,B))) => k4_ami_1(A,B,C,D) = k1_funct_1(k8_funct_2(u4_ami_1(A,B),k1_funct_2(k4_card_3(u5_ami_1(A,B)),k4_card_3(u5_ami_1(A,B))),u6_ami_1(A,B),C),D) ) ) ) ) ), file(ami_1,d7_ami_1), []). fof(d7_xboole_0,axiom,( ! [A,B] : ( r1_xboole_0(A,B) <=> k3_xboole_0(A,B) = k1_xboole_0 ) ), file(xboole_0,d7_xboole_0), []). fof(dt_g1_ami_1,axiom,( ! [A,B,C,D,E,F,G,H] : ( ( m1_subset_1(C,B) & m1_subset_1(D,k1_zfmisc_1(B)) & ~ v1_xboole_0(E) & ~ v1_xboole_0(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(E,k13_finseq_1(k2_xboole_0(k3_tarski(A),B))))) & v1_funct_1(G) & v1_funct_2(G,B,k2_xboole_0(A,k2_tarski(F,D))) & m1_relset_1(G,B,k2_xboole_0(A,k2_tarski(F,D))) & v1_funct_1(H) & v1_funct_2(H,F,k1_funct_2(k4_card_3(G),k4_card_3(G))) & m1_relset_1(H,F,k1_funct_2(k4_card_3(G),k4_card_3(G))) ) => ( v1_ami_1(g1_ami_1(A,B,C,D,E,F,G,H),A) & l1_ami_1(g1_ami_1(A,B,C,D,E,F,G,H),A) ) ) ), file(ami_1,g1_ami_1), []). fof(dt_k10_ami_1,axiom,( ! [A,B,C] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) ) => ( v1_funct_1(k10_ami_1(A,B,C)) & v1_funct_2(k10_ami_1(A,B,C),k5_numbers,k4_card_3(u5_ami_1(A,B))) & m2_relset_1(k10_ami_1(A,B,C),k5_numbers,k4_card_3(u5_ami_1(A,B))) ) ) ), file(ami_1,k10_ami_1), []). fof(dt_k10_amistd_2,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) & m1_ami_1(C,A,B) & v4_ordinal2(D) ) => m1_ami_1(k10_amistd_2(A,B,C,D),A,B) ) ), file(amistd_2,k10_amistd_2), []). fof(dt_k11_ami_1,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v2_ami_1(B,A) & l1_ami_1(B,A) & v1_funct_1(C) & v1_funct_2(C,k5_numbers,k4_card_3(u5_ami_1(A,B))) & m1_relset_1(C,k5_numbers,k4_card_3(u5_ami_1(A,B))) & m1_subset_1(D,k5_numbers) ) => m1_subset_1(k11_ami_1(A,B,C,D),k4_card_3(u5_ami_1(A,B))) ) ), file(ami_1,k11_ami_1), []). fof(dt_k12_ami_3,axiom,( ! [A,B,C] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,u2_ami_1(A,B)) ) => m1_ami_1(k12_ami_3(A,B,C),A,B) ) ), file(ami_3,k12_ami_3), []). fof(dt_k13_ami_1,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) & m1_subset_1(D,u2_ami_1(A,B)) ) => m2_subset_1(k13_ami_1(A,B,C,D),k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B)) ) ), file(ami_1,k13_ami_1), []). fof(dt_k13_ami_3,axiom,( ! [A,B,C] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) & m1_ami_1(C,A,B) ) => m1_struct_0(k13_ami_3(A,B,C),B,u2_ami_1(A,B)) ) ), file(ami_3,k13_ami_3), []). fof(dt_k13_finseq_1,axiom,( $true ), file(finseq_1,k13_finseq_1), []). fof(dt_k17_ami_1,axiom,( ! [A,B,C,D] : ( ( l1_ami_1(B,A) & m1_ami_1(C,A,B) & m1_ami_1(D,A,B) ) => m1_ami_1(k17_ami_1(A,B,C,D),A,B) ) ), file(ami_1,k17_ami_1), []). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). fof(dt_k1_funct_2,axiom,( $true ), file(funct_2,k1_funct_2), []). fof(dt_k1_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_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_scmring2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v1_scmring1(A) & l3_vectsp_1(A) ) => ( v1_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & l1_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A))) ) ) ), file(scmring2,k1_scmring2), []). fof(dt_k1_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) ) => m1_subset_1(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ), file(struct_0,k1_struct_0), []). 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_ami_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & l1_ami_1(B,A) ) => m1_subset_1(k2_ami_1(A,B),u1_struct_0(B)) ) ), file(ami_1,k2_ami_1), []). fof(dt_k2_ami_2,axiom,( m1_subset_1(k2_ami_2,k1_zfmisc_1(k5_numbers)) ), file(ami_2,k2_ami_2), []). fof(dt_k2_tarski,axiom,( $true ), file(tarski,k2_tarski), []). fof(dt_k2_xboole_0,axiom,( $true ), file(xboole_0,k2_xboole_0), []). fof(dt_k2_xcmplx_0,axiom,( $true ), file(xcmplx_0,k2_xcmplx_0), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). fof(dt_k3_ami_2,axiom,( m1_subset_1(k3_ami_2,k1_zfmisc_1(k5_numbers)) ), file(ami_2,k3_ami_2), []). fof(dt_k3_scmring4,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & v8_amistd_2(B,A) & l1_ami_1(B,A) & v4_ordinal2(C) & m1_ami_1(D,A,B) ) => m1_ami_1(k3_scmring4(A,B,C,D),A,B) ) ), file(scmring4,k3_scmring4), []). fof(dt_k3_tarski,axiom,( $true ), file(tarski,k3_tarski), []). fof(dt_k3_xboole_0,axiom,( $true ), file(xboole_0,k3_xboole_0), []). fof(dt_k4_ami_1,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v2_ami_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,u4_ami_1(A,B)) & m1_subset_1(D,k4_card_3(u5_ami_1(A,B))) ) => m1_subset_1(k4_ami_1(A,B,C,D),k4_card_3(u5_ami_1(A,B))) ) ), file(ami_1,k4_ami_1), []). fof(dt_k4_card_3,axiom,( $true ), file(card_3,k4_card_3), []). fof(dt_k5_ami_5,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) & m1_ami_1(C,A,B) & m1_subset_1(D,u2_ami_1(A,B)) ) => m2_subset_1(k5_ami_5(A,B,C,D),k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B)) ) ), file(ami_5,k5_ami_5), []). fof(dt_k5_amistd_1,axiom,( ! [A,B,C] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) & v4_ordinal2(C) ) => m1_struct_0(k5_amistd_1(A,B,C),B,u2_ami_1(A,B)) ) ), file(amistd_1,k5_amistd_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_ami_1,axiom,( ! [A,B,C] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) ) => m1_struct_0(k6_ami_1(A,B,C),B,u2_ami_1(A,B)) ) ), file(ami_1,k6_ami_1), []). fof(dt_k6_ami_5,axiom,( ! [A,B,C] : ( ( l1_ami_1(B,A) & m1_ami_1(C,A,B) ) => ( v1_ami_3(k6_ami_5(A,B,C),A,B) & m1_ami_1(k6_ami_5(A,B,C),A,B) ) ) ), file(ami_5,k6_ami_5), []). fof(dt_k7_ami_1,axiom,( $true ), file(ami_1,k7_ami_1), []). fof(dt_k7_ami_5,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(B) & l1_ami_1(B,A) & m1_ami_1(C,A,B) ) => m1_ami_1(k7_ami_5(A,B,C),A,B) ) ), file(ami_5,k7_ami_5), []). fof(dt_k8_ami_1,axiom,( ! [A,B,C] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) ) => m2_subset_1(k8_ami_1(A,B,C),k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B)) ) ), file(ami_1,k8_ami_1), []). fof(dt_k8_ami_5,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v2_ami_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) & m1_ami_1(D,A,B) ) => m1_subset_1(k8_ami_5(A,B,C,D),k4_card_3(u5_ami_1(A,B))) ) ), file(ami_5,k8_ami_5), []). fof(dt_k8_amistd_1,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,u2_ami_1(A,B)) & v4_ordinal2(D) ) => m1_struct_0(k8_amistd_1(A,B,C,D),B,u2_ami_1(A,B)) ) ), file(amistd_1,k8_amistd_1), []). fof(dt_k8_amistd_2,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & v8_amistd_2(B,A) & l1_ami_1(B,A) & m1_subset_1(C,u4_ami_1(A,B)) & v4_ordinal2(D) ) => m2_subset_1(k8_amistd_2(A,B,C,D),k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B)) ) ), file(amistd_2,k8_amistd_2), []). 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_ami_1,axiom,( ! [A,B,C] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) ) => m1_subset_1(k9_ami_1(A,B,C),k4_card_3(u5_ami_1(A,B))) ) ), file(ami_1,k9_ami_1), []). fof(dt_k9_amistd_2,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & v8_amistd_2(B,A) & l1_ami_1(B,A) & v1_ami_3(C,A,B) & m1_ami_1(C,A,B) & v4_ordinal2(D) ) => m1_ami_1(k9_amistd_2(A,B,C,D),A,B) ) ), file(amistd_2,k9_amistd_2), []). fof(dt_l1_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => l1_struct_0(B) ) ), file(ami_1,l1_ami_1), []). fof(dt_l1_group_1,axiom,( ! [A] : ( l1_group_1(A) => l1_struct_0(A) ) ), file(group_1,l1_group_1), []). fof(dt_l1_rlvect_1,axiom,( ! [A] : ( l1_rlvect_1(A) => l2_struct_0(A) ) ), file(rlvect_1,l1_rlvect_1), []). fof(dt_l1_struct_0,axiom,( $true ), file(struct_0,l1_struct_0), []). fof(dt_l1_vectsp_1,axiom,( ! [A] : ( l1_vectsp_1(A) => l1_group_1(A) ) ), file(vectsp_1,l1_vectsp_1), []). fof(dt_l2_struct_0,axiom,( ! [A] : ( l2_struct_0(A) => l1_struct_0(A) ) ), file(struct_0,l2_struct_0), []). fof(dt_l2_vectsp_1,axiom,( ! [A] : ( l2_vectsp_1(A) => ( l1_vectsp_1(A) & l2_struct_0(A) ) ) ), file(vectsp_1,l2_vectsp_1), []). fof(dt_l3_vectsp_1,axiom,( ! [A] : ( l3_vectsp_1(A) => ( l1_rlvect_1(A) & l2_vectsp_1(A) ) ) ), file(vectsp_1,l3_vectsp_1), []). fof(dt_m1_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ! [C] : ( m1_ami_1(C,A,B) => m1_subset_1(C,k7_ami_1(u5_ami_1(A,B))) ) ) ), file(ami_1,m1_ami_1), []). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), []). fof(dt_m1_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_struct_0(C,A,B) => m1_subset_1(C,u1_struct_0(A)) ) ) ), file(struct_0,m1_struct_0), []). 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_u1_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => m1_subset_1(u1_ami_1(A,B),u1_struct_0(B)) ) ), file(ami_1,u1_ami_1), []). fof(dt_u1_struct_0,axiom,( $true ), file(struct_0,u1_struct_0), []). fof(dt_u2_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => m1_subset_1(u2_ami_1(A,B),k1_zfmisc_1(u1_struct_0(B))) ) ), file(ami_1,u2_ami_1), []). fof(dt_u3_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ~ v1_xboole_0(u3_ami_1(A,B)) ) ), file(ami_1,u3_ami_1), []). fof(dt_u4_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ( ~ v1_xboole_0(u4_ami_1(A,B)) & m1_subset_1(u4_ami_1(A,B),k1_zfmisc_1(k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))))) ) ) ), file(ami_1,u4_ami_1), []). fof(dt_u5_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ( v1_funct_1(u5_ami_1(A,B)) & v1_funct_2(u5_ami_1(A,B),u1_struct_0(B),k2_xboole_0(A,k2_tarski(u4_ami_1(A,B),u2_ami_1(A,B)))) & m2_relset_1(u5_ami_1(A,B),u1_struct_0(B),k2_xboole_0(A,k2_tarski(u4_ami_1(A,B),u2_ami_1(A,B)))) ) ) ), file(ami_1,u5_ami_1), []). fof(dt_u6_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ( v1_funct_1(u6_ami_1(A,B)) & v1_funct_2(u6_ami_1(A,B),u4_ami_1(A,B),k1_funct_2(k4_card_3(u5_ami_1(A,B)),k4_card_3(u5_ami_1(A,B)))) & m2_relset_1(u6_ami_1(A,B),u4_ami_1(A,B),k1_funct_2(k4_card_3(u5_ami_1(A,B)),k4_card_3(u5_ami_1(A,B)))) ) ) ), file(ami_1,u6_ami_1), []). fof(existence_l1_ami_1,axiom,( ! [A] : ? [B] : l1_ami_1(B,A) ), file(ami_1,l1_ami_1), []). fof(existence_l1_group_1,axiom,( ? [A] : l1_group_1(A) ), file(group_1,l1_group_1), []). fof(existence_l1_rlvect_1,axiom,( ? [A] : l1_rlvect_1(A) ), file(rlvect_1,l1_rlvect_1), []). fof(existence_l1_struct_0,axiom,( ? [A] : l1_struct_0(A) ), file(struct_0,l1_struct_0), []). fof(existence_l1_vectsp_1,axiom,( ? [A] : l1_vectsp_1(A) ), file(vectsp_1,l1_vectsp_1), []). fof(existence_l2_struct_0,axiom,( ? [A] : l2_struct_0(A) ), file(struct_0,l2_struct_0), []). fof(existence_l2_vectsp_1,axiom,( ? [A] : l2_vectsp_1(A) ), file(vectsp_1,l2_vectsp_1), []). fof(existence_l3_vectsp_1,axiom,( ? [A] : l3_vectsp_1(A) ), file(vectsp_1,l3_vectsp_1), []). fof(existence_m1_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ? [C] : m1_ami_1(C,A,B) ) ), file(ami_1,m1_ami_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_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ? [C] : m1_struct_0(C,A,B) ) ), file(struct_0,m1_struct_0), []). 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(fc10_ami_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( ~ v1_xboole_0(k7_ami_1(A)) & v1_fraenkel(k7_ami_1(A)) ) ) ), file(ami_1,fc10_ami_1), []). 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_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_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_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_scmring3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_group_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v1_scmring1(A) & l3_vectsp_1(A) ) => ( ~ v3_struct_0(k1_scmring2(A)) & v1_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & ~ v2_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v4_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v5_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v6_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v7_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v8_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v10_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v4_amistd_1(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v7_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A))) ) ) ), file(scmring3,fc12_scmring3), []). 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(fc16_finseq_1,axiom,( ! [A] : ( ~ v1_xboole_0(k13_finseq_1(A)) & v1_fraenkel(k13_finseq_1(A)) ) ), file(finseq_1,fc16_finseq_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_ami_5,axiom, ( ~ v1_xboole_0(k2_ami_2) & ~ v1_finset_1(k2_ami_2) & v1_membered(k2_ami_2) & v2_membered(k2_ami_2) & v3_membered(k2_ami_2) & v4_membered(k2_ami_2) & v5_membered(k2_ami_2) ), file(ami_5,fc1_ami_5), []). fof(fc1_amistd_2,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) & ~ v1_xboole_0(B) ) => ( v1_relat_1(k1_funct_4(A,B)) & v1_funct_1(k1_funct_4(A,B)) & ~ v1_xboole_0(k1_funct_4(A,B)) & v1_setfam_1(k1_funct_4(A,B)) ) ) ), file(amistd_2,fc1_amistd_2), []). fof(fc1_card_4,axiom, ( ~ v1_xboole_0(k5_ordinal2) & v1_ordinal1(k5_ordinal2) & v2_ordinal1(k5_ordinal2) & v3_ordinal1(k5_ordinal2) & ~ v1_finset_1(k5_ordinal2) & v1_membered(k5_ordinal2) & v2_membered(k5_ordinal2) & v3_membered(k5_ordinal2) & v4_membered(k5_ordinal2) & v5_membered(k5_ordinal2) ), file(card_4,fc1_card_4), []). 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_fraenkel,axiom,( ! [A,B] : v1_fraenkel(k1_funct_2(A,B)) ), file(fraenkel,fc1_fraenkel), []). fof(fc1_nat_1,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => ( v4_ordinal2(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(nat_1,fc1_nat_1), []). fof(fc1_scmring4,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => ( ~ v1_xboole_0(u2_ami_1(A,B)) & ~ v1_finset_1(u2_ami_1(A,B)) & ~ v1_realset1(u2_ami_1(A,B)) ) ) ), file(scmring4,fc1_scmring4), []). 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(fc1_xboole_0,axiom,( v1_xboole_0(k1_xboole_0) ), file(xboole_0,fc1_xboole_0), []). fof(fc20_amistd_2,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & v8_amistd_2(B,A) & l1_ami_1(B,A) & v1_ami_3(C,A,B) & m1_ami_1(C,A,B) & v4_ordinal2(D) ) => ( v1_relat_1(k9_amistd_2(A,B,C,D)) & v1_funct_1(k9_amistd_2(A,B,C,D)) & v1_finset_1(k9_amistd_2(A,B,C,D)) & v1_setfam_1(k9_amistd_2(A,B,C,D)) & v1_ami_3(k9_amistd_2(A,B,C,D),A,B) ) ) ), file(amistd_2,fc20_amistd_2), []). fof(fc21_amistd_2,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & v8_amistd_2(B,A) & l1_ami_1(B,A) & v1_xboole_0(C) & v1_ami_3(C,A,B) & m1_ami_1(C,A,B) & v4_ordinal2(D) ) => ( v1_relat_1(k9_amistd_2(A,B,C,D)) & v1_funct_1(k9_amistd_2(A,B,C,D)) & v1_xboole_0(k9_amistd_2(A,B,C,D)) & v1_finset_1(k9_amistd_2(A,B,C,D)) & v1_setfam_1(k9_amistd_2(A,B,C,D)) & v1_ami_3(k9_amistd_2(A,B,C,D),A,B) & v1_membered(k9_amistd_2(A,B,C,D)) & v2_membered(k9_amistd_2(A,B,C,D)) & v3_membered(k9_amistd_2(A,B,C,D)) & v4_membered(k9_amistd_2(A,B,C,D)) & v5_membered(k9_amistd_2(A,B,C,D)) & v9_amistd_1(k9_amistd_2(A,B,C,D),A,B) ) ) ), file(amistd_2,fc21_amistd_2), []). fof(fc22_amistd_2,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & v8_amistd_2(B,A) & l1_ami_1(B,A) & ~ v1_xboole_0(C) & v1_ami_3(C,A,B) & m1_ami_1(C,A,B) & v4_ordinal2(D) ) => ( v1_relat_1(k9_amistd_2(A,B,C,D)) & v1_funct_1(k9_amistd_2(A,B,C,D)) & ~ v1_xboole_0(k9_amistd_2(A,B,C,D)) & v1_finset_1(k9_amistd_2(A,B,C,D)) & v1_setfam_1(k9_amistd_2(A,B,C,D)) & v1_ami_3(k9_amistd_2(A,B,C,D),A,B) ) ) ), file(amistd_2,fc22_amistd_2), []). fof(fc23_amistd_2,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & v8_amistd_2(B,A) & l1_ami_1(B,A) & v1_ami_3(C,A,B) & v9_amistd_1(C,A,B) & m1_ami_1(C,A,B) & v4_ordinal2(D) ) => ( v1_relat_1(k9_amistd_2(A,B,C,D)) & v1_funct_1(k9_amistd_2(A,B,C,D)) & v1_finset_1(k9_amistd_2(A,B,C,D)) & v1_setfam_1(k9_amistd_2(A,B,C,D)) & v1_ami_3(k9_amistd_2(A,B,C,D),A,B) & v9_amistd_1(k9_amistd_2(A,B,C,D),A,B) ) ) ), file(amistd_2,fc23_amistd_2), []). fof(fc24_amistd_2,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) & m1_ami_1(C,A,B) & v4_ordinal2(D) ) => ( v1_relat_1(k10_amistd_2(A,B,C,D)) & v1_funct_1(k10_amistd_2(A,B,C,D)) & v1_finset_1(k10_amistd_2(A,B,C,D)) & v1_setfam_1(k10_amistd_2(A,B,C,D)) & v1_ami_3(k10_amistd_2(A,B,C,D),A,B) ) ) ), file(amistd_2,fc24_amistd_2), []). fof(fc25_amistd_2,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) & v1_xboole_0(C) & m1_ami_1(C,A,B) & v4_ordinal2(D) ) => ( v1_relat_1(k10_amistd_2(A,B,C,D)) & v1_funct_1(k10_amistd_2(A,B,C,D)) & v1_xboole_0(k10_amistd_2(A,B,C,D)) & v1_finset_1(k10_amistd_2(A,B,C,D)) & v1_setfam_1(k10_amistd_2(A,B,C,D)) & v1_ami_3(k10_amistd_2(A,B,C,D),A,B) & v1_membered(k10_amistd_2(A,B,C,D)) & v2_membered(k10_amistd_2(A,B,C,D)) & v3_membered(k10_amistd_2(A,B,C,D)) & v4_membered(k10_amistd_2(A,B,C,D)) & v5_membered(k10_amistd_2(A,B,C,D)) & v9_amistd_1(k10_amistd_2(A,B,C,D),A,B) ) ) ), file(amistd_2,fc25_amistd_2), []). fof(fc26_amistd_2,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) & ~ v1_xboole_0(C) & v1_ami_3(C,A,B) & m1_ami_1(C,A,B) & v4_ordinal2(D) ) => ( v1_relat_1(k10_amistd_2(A,B,C,D)) & v1_funct_1(k10_amistd_2(A,B,C,D)) & ~ v1_xboole_0(k10_amistd_2(A,B,C,D)) & v1_finset_1(k10_amistd_2(A,B,C,D)) & v1_setfam_1(k10_amistd_2(A,B,C,D)) & v1_ami_3(k10_amistd_2(A,B,C,D),A,B) ) ) ), file(amistd_2,fc26_amistd_2), []). fof(fc2_ami_1,axiom,( ! [A,B] : ( ( ~ v2_ami_1(B,A) & l1_ami_1(B,A) ) => ~ v1_xboole_0(u2_ami_1(A,B)) ) ), file(ami_1,fc2_ami_1), []). fof(fc2_amistd_2,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) & ~ v1_xboole_0(B) ) => ( v1_relat_1(k1_funct_4(B,A)) & v1_funct_1(k1_funct_4(B,A)) & ~ v1_xboole_0(k1_funct_4(B,A)) & v1_setfam_1(k1_funct_4(B,A)) ) ) ), file(amistd_2,fc2_amistd_2), []). 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_finset_1,axiom,( ! [A,B] : ( ~ v1_xboole_0(k2_tarski(A,B)) & v1_finset_1(k2_tarski(A,B)) ) ), file(finset_1,fc2_finset_1), []). fof(fc2_fraenkel,axiom,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => ( v1_finset_1(k1_funct_2(A,B)) & v1_fraenkel(k1_funct_2(A,B)) ) ) ), file(fraenkel,fc2_fraenkel), []). fof(fc2_scmring1,axiom, ( ~ v1_xboole_0(k3_ami_2) & ~ v1_finset_1(k3_ami_2) & ~ v1_realset1(k3_ami_2) & v1_membered(k3_ami_2) & v2_membered(k3_ami_2) & v3_membered(k3_ami_2) & v4_membered(k3_ami_2) & v5_membered(k3_ami_2) ), file(scmring1,fc2_scmring1), []). fof(fc2_setfam_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ v1_xboole_0(k1_tarski(A)) & v1_setfam_1(k1_tarski(A)) ) ) ), file(setfam_1,fc2_setfam_1), []). fof(fc2_xboole_0,axiom,( ! [A,B] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k2_xboole_0(A,B)) ) ), file(xboole_0,fc2_xboole_0), []). fof(fc38_scmring3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_group_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v1_scmring1(A) & l3_vectsp_1(A) ) => ( ~ v3_struct_0(k1_scmring2(A)) & v1_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & ~ v2_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v4_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v5_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v6_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v7_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v8_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v10_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v4_amistd_1(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v2_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v5_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v6_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v7_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A))) ) ) ), file(scmring3,fc38_scmring3), []). fof(fc39_scmring3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_group_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v1_scmring1(A) & l3_vectsp_1(A) ) => ( ~ v3_struct_0(k1_scmring2(A)) & v1_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & ~ v2_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v4_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v5_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v6_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v7_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v8_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v10_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v4_amistd_1(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v2_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v5_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v6_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v7_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v8_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A))) ) ) ), file(scmring3,fc39_scmring3), []). fof(fc3_ami_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => v1_fraenkel(k4_card_3(A)) ) ), file(ami_1,fc3_ami_1), []). fof(fc3_amistd_2,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ( v1_relat_1(k1_funct_4(A,B)) & v1_funct_1(k1_funct_4(A,B)) & v1_finset_1(k1_funct_4(A,B)) & v1_setfam_1(k1_funct_4(A,B)) ) ) ), file(amistd_2,fc3_amistd_2), []). fof(fc3_nat_1,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & ~ v1_xboole_0(B) & v4_ordinal2(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v4_ordinal2(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(nat_1,fc3_nat_1), []). fof(fc3_setfam_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ( ~ v1_xboole_0(k2_tarski(A,B)) & v1_setfam_1(k2_tarski(A,B)) ) ) ), file(setfam_1,fc3_setfam_1), []). fof(fc3_xboole_0,axiom,( ! [A,B] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k2_xboole_0(B,A)) ) ), file(xboole_0,fc3_xboole_0), []). 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_scmring3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_group_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v1_scmring1(A) & l3_vectsp_1(A) ) => ( ~ v3_struct_0(k1_scmring2(A)) & v1_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & ~ v2_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v4_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v5_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v6_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v7_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v8_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v10_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v4_amistd_1(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v2_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v5_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v6_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v7_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v8_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v11_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A))) & v13_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A))) ) ) ), file(scmring3,fc40_scmring3), []). fof(fc4_ami_1,axiom,( ! [A,B,C] : ( ( v1_setfam_1(B) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) ) => ( ~ v1_xboole_0(k4_card_3(C)) & v1_fraenkel(k4_card_3(C)) ) ) ), file(ami_1,fc4_ami_1), []). fof(fc4_amistd_1,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v2_ami_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,u4_ami_1(A,B)) & m1_subset_1(D,k4_card_3(u5_ami_1(A,B))) ) => ( v1_relat_1(k1_funct_1(k8_funct_2(u4_ami_1(A,B),k1_funct_2(k4_card_3(u5_ami_1(A,B)),k4_card_3(u5_ami_1(A,B))),u6_ami_1(A,B),C),D)) & v1_funct_1(k1_funct_1(k8_funct_2(u4_ami_1(A,B),k1_funct_2(k4_card_3(u5_ami_1(A,B)),k4_card_3(u5_ami_1(A,B))),u6_ami_1(A,B),C),D)) & v1_setfam_1(k1_funct_1(k8_funct_2(u4_ami_1(A,B),k1_funct_2(k4_card_3(u5_ami_1(A,B)),k4_card_3(u5_ami_1(A,B))),u6_ami_1(A,B),C),D)) ) ) ), file(amistd_1,fc4_amistd_1), []). fof(fc4_nat_1,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & ~ v1_xboole_0(B) & v4_ordinal2(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v4_ordinal2(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(nat_1,fc4_nat_1), []). fof(fc4_setfam_1,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & v1_setfam_1(B) ) => v1_setfam_1(k2_xboole_0(A,B)) ) ), file(setfam_1,fc4_setfam_1), []). fof(fc5_amistd_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_fraenkel(k4_card_3(A)) & v1_amistd_2(k4_card_3(A)) ) ) ), file(amistd_2,fc5_amistd_2), []). 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_amistd_2,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & v7_amistd_2(B,A) & l1_ami_1(B,A) ) => ~ v1_realset1(u2_ami_1(A,B)) ) ), file(amistd_2,fc9_amistd_2), []). fof(fc9_finseq_1,axiom,( ! [A] : ~ v1_xboole_0(k13_finseq_1(A)) ), file(finseq_1,fc9_finseq_1), []). 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_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_ami_1,axiom,( ! [A,B,C,D,E,F,G,H] : ( ( m1_subset_1(C,B) & m1_subset_1(D,k1_zfmisc_1(B)) & ~ v1_xboole_0(E) & ~ v1_xboole_0(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(E,k13_finseq_1(k2_xboole_0(k3_tarski(A),B))))) & v1_funct_1(G) & v1_funct_2(G,B,k2_xboole_0(A,k2_tarski(F,D))) & m1_relset_1(G,B,k2_xboole_0(A,k2_tarski(F,D))) & v1_funct_1(H) & v1_funct_2(H,F,k1_funct_2(k4_card_3(G),k4_card_3(G))) & m1_relset_1(H,F,k1_funct_2(k4_card_3(G),k4_card_3(G))) ) => ! [I,J,K,L,M,N,O,P] : ( g1_ami_1(A,B,C,D,E,F,G,H) = g1_ami_1(I,J,K,L,M,N,O,P) => ( A = I & B = J & C = K & D = L & E = M & F = N & G = O & H = P ) ) ) ), file(ami_1,g1_ami_1), []). fof(idempotence_k17_ami_1,axiom,( ! [A,B,C,D] : ( ( l1_ami_1(B,A) & m1_ami_1(C,A,B) & m1_ami_1(D,A,B) ) => k17_ami_1(A,B,C,C) = C ) ), file(ami_1,k17_ami_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(idempotence_k8_ami_5,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v2_ami_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) & m1_ami_1(D,A,B) ) => k8_ami_5(A,B,C,C) = C ) ), file(ami_5,k8_ami_5), []). fof(irreflexivity_r1_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ r1_subset_1(A,A) ) ), file(subset_1,r1_subset_1), []). fof(l1_scmring4,axiom,( ! [A,B] : ( k3_xboole_0(B,k1_tarski(A)) != k1_xboole_0 => r2_hidden(A,B) ) ), file(scmring4,l1_scmring4), []). fof(rc10_ami_1,axiom,( ! [A] : ( v1_setfam_1(A) => ? [B] : ( l1_ami_1(B,A) & ~ v3_struct_0(B) & v1_ami_1(B,A) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & v5_ami_1(B,A) & v6_ami_1(B,A) & v7_ami_1(B,A) & v8_ami_1(B,A) & v10_ami_1(B,A) & v13_ami_1(B,A) ) ) ), file(ami_1,rc10_ami_1), []). fof(rc11_ami_1,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v13_ami_1(B,A) & l1_ami_1(B,A) ) => ? [C] : ( m1_ami_1(C,A,B) & ~ v1_xboole_0(C) & v1_relat_1(C) & v1_funct_1(C) & v11_ami_1(C,A,B) ) ) ), file(ami_1,rc11_ami_1), []). fof(rc1_ami_1,axiom,( ! [A] : ? [B] : ( l1_ami_1(B,A) & v1_ami_1(B,A) ) ), file(ami_1,rc1_ami_1), []). fof(rc1_ami_3,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ? [C] : ( m1_ami_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C) & v1_ami_3(C,A,B) ) ) ), file(ami_3,rc1_ami_3), []). fof(rc1_amistd_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & ~ v1_realset1(A) ) ), file(amistd_1,rc1_amistd_1), []). fof(rc1_amistd_2,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_fraenkel(A) & v1_pralg_2(A) & v1_amistd_2(A) ) ), file(amistd_2,rc1_amistd_2), []). 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_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc1_funct_1), []). fof(rc1_nat_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(nat_1,rc1_nat_1), []). fof(rc1_scmfsa_4,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ? [C] : ( m1_ami_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C) & v1_finset_1(C) & v1_ami_3(C,A,B) ) ) ), file(scmfsa_4,rc1_scmfsa_4), []). fof(rc1_scmring4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_group_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v1_scmring1(A) & l3_vectsp_1(A) ) => ? [B] : ( m1_ami_1(B,k1_tarski(u1_struct_0(A)),k1_scmring2(A)) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_setfam_1(B) & v11_ami_1(B,k1_tarski(u1_struct_0(A)),k1_scmring2(A)) & ~ v1_ami_3(B,k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) ), file(scmring4,rc1_scmring4), []). fof(rc1_setfam_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_setfam_1(A) ) ), file(setfam_1,rc1_setfam_1), []). fof(rc1_xboole_0,axiom,( ? [A] : v1_xboole_0(A) ), file(xboole_0,rc1_xboole_0), []). fof(rc1_xreal_0,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(xreal_0,rc1_xreal_0), []). fof(rc2_ami_1,axiom,( ! [A] : ? [B] : ( l1_ami_1(B,A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) ) ), file(ami_1,rc2_ami_1), []). fof(rc2_amistd_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ? [C] : ( m1_ami_1(C,A,B) & v1_xboole_0(C) & v1_relat_1(C) & v1_funct_1(C) & v2_funct_1(C) & v1_finset_1(C) & v1_realset1(C) & v1_setfam_1(C) & v1_ami_3(C,A,B) & v1_membered(C) & v2_membered(C) & v3_membered(C) & v4_membered(C) & v5_membered(C) ) ) ), file(amistd_1,rc2_amistd_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_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) ), file(funct_1,rc2_funct_1), []). fof(rc2_nat_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(A) & v3_ordinal1(A) ) ), file(nat_1,rc2_nat_1), []). fof(rc2_xboole_0,axiom,( ? [A] : ~ v1_xboole_0(A) ), file(xboole_0,rc2_xboole_0), []). 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_ami_1,axiom,( ! [A] : ( v1_setfam_1(A) => ? [B] : ( l1_ami_1(B,A) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) ) ) ), file(ami_1,rc3_ami_1), []). fof(rc3_amistd_1,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) ) => ? [C] : ( m1_ami_1(C,A,B) & ~ v1_xboole_0(C) & v1_relat_1(C) & v1_funct_1(C) & v1_finset_1(C) & v1_realset1(C) & v1_setfam_1(C) & v1_ami_3(C,A,B) ) ) ), file(amistd_1,rc3_amistd_1), []). fof(rc3_amistd_2,axiom,( ! [A] : ( v1_setfam_1(A) => ? [B] : ( l1_ami_1(B,A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v3_amistd_1(B,A) & v4_amistd_1(B,A) & v7_amistd_2(B,A) ) ) ), file(amistd_2,rc3_amistd_2), []). 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_nat_1,axiom,( ? [A] : ( m1_subset_1(A,k5_numbers) & ~ v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(nat_1,rc3_nat_1), []). 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_amistd_1,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v7_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) ) => ? [C] : ( m1_ami_1(C,A,B) & ~ v1_xboole_0(C) & v1_relat_1(C) & v1_funct_1(C) & v1_finset_1(C) & v1_realset1(C) & v1_setfam_1(C) & v11_ami_1(C,A,B) & v1_ami_3(C,A,B) ) ) ), file(amistd_1,rc4_amistd_1), []). fof(rc4_amistd_2,axiom,( ! [A] : ( v1_setfam_1(A) => ? [B] : ( l1_ami_1(B,A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & v5_ami_1(B,A) & v7_ami_1(B,A) & v8_ami_1(B,A) & v10_ami_1(B,A) & v13_ami_1(B,A) & v3_amistd_1(B,A) & v4_amistd_1(B,A) & v2_amistd_2(B,A) & v5_amistd_2(B,A) & v6_amistd_2(B,A) & v7_amistd_2(B,A) & v8_amistd_2(B,A) ) ) ), file(amistd_2,rc4_amistd_2), []). 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_struct_0,axiom,( ? [A] : ( l2_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc4_struct_0), []). fof(rc4_xreal_0,axiom,( ? [A] : ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc4_xreal_0), []). fof(rc5_ami_1,axiom,( ! [A] : ? [B] : ( l1_ami_1(B,A) & v1_ami_1(B,A) & v6_ami_1(B,A) ) ), file(ami_1,rc5_ami_1), []). fof(rc5_amistd_1,axiom,( ! [A] : ( v1_setfam_1(A) => ? [B] : ( l1_ami_1(B,A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & v5_ami_1(B,A) & v7_ami_1(B,A) & v8_ami_1(B,A) & v10_ami_1(B,A) & v13_ami_1(B,A) & v4_amistd_1(B,A) ) ) ), file(amistd_1,rc5_amistd_1), []). fof(rc5_amistd_2,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v7_amistd_2(B,A) & l1_ami_1(B,A) ) => ? [C] : ( m1_ami_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C) & v1_finset_1(C) & v1_setfam_1(C) & v1_ami_3(C,A,B) & ~ v1_realset1(C) ) ) ), file(amistd_2,rc5_amistd_2), []). 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_ami_1,axiom,( ! [A] : ? [B] : ( l1_ami_1(B,A) & ~ v3_struct_0(B) & v1_ami_1(B,A) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v6_ami_1(B,A) & v8_ami_1(B,A) ) ), file(ami_1,rc6_ami_1), []). fof(rc6_amistd_1,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => ? [C] : ( m1_ami_1(C,A,B) & ~ v1_xboole_0(C) & v1_relat_1(C) & v1_funct_1(C) & v1_finset_1(C) & v1_realset1(C) & v1_setfam_1(C) & v1_ami_3(C,A,B) & v9_amistd_1(C,A,B) ) ) ), file(amistd_1,rc6_amistd_1), []). fof(rc6_amistd_2,axiom,( ! [A] : ( v1_setfam_1(A) => ? [B] : ( l1_ami_1(B,A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & v5_ami_1(B,A) & v7_ami_1(B,A) & v8_ami_1(B,A) & v10_ami_1(B,A) & v13_ami_1(B,A) & v3_amistd_1(B,A) & v4_amistd_1(B,A) & v2_amistd_2(B,A) & v5_amistd_2(B,A) & v6_amistd_2(B,A) & v7_amistd_2(B,A) & v8_amistd_2(B,A) & v11_amistd_2(B,A) & v13_amistd_2(B,A) ) ) ), file(amistd_2,rc6_amistd_2), []). 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_ami_1,axiom,( ! [A] : ( v1_setfam_1(A) => ? [B] : ( l1_ami_1(B,A) & ~ v3_struct_0(B) & v1_ami_1(B,A) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & v5_ami_1(B,A) & v6_ami_1(B,A) & v7_ami_1(B,A) & v8_ami_1(B,A) ) ) ), file(ami_1,rc7_ami_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_ami_1,axiom,( ! [A] : ? [B] : ( l1_ami_1(B,A) & v1_ami_1(B,A) & v6_ami_1(B,A) & v10_ami_1(B,A) ) ), file(ami_1,rc8_ami_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(rc9_ami_1,axiom,( ! [A] : ? [B] : ( l1_ami_1(B,A) & ~ v3_struct_0(B) & v1_ami_1(B,A) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v6_ami_1(B,A) & v8_ami_1(B,A) & v10_ami_1(B,A) ) ), file(ami_1,rc9_ami_1), []). fof(redefinition_k11_ami_1,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v2_ami_1(B,A) & l1_ami_1(B,A) & v1_funct_1(C) & v1_funct_2(C,k5_numbers,k4_card_3(u5_ami_1(A,B))) & m1_relset_1(C,k5_numbers,k4_card_3(u5_ami_1(A,B))) & m1_subset_1(D,k5_numbers) ) => k11_ami_1(A,B,C,D) = k1_funct_1(C,D) ) ), file(ami_1,k11_ami_1), []). fof(redefinition_k13_ami_1,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) & m1_subset_1(D,u2_ami_1(A,B)) ) => k13_ami_1(A,B,C,D) = k1_funct_1(C,D) ) ), file(ami_1,k13_ami_1), []). fof(redefinition_k17_ami_1,axiom,( ! [A,B,C,D] : ( ( l1_ami_1(B,A) & m1_ami_1(C,A,B) & m1_ami_1(D,A,B) ) => k17_ami_1(A,B,C,D) = k1_funct_4(C,D) ) ), file(ami_1,k17_ami_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_k1_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) ) => k1_struct_0(A,B) = k1_tarski(B) ) ), file(struct_0,k1_struct_0), []). fof(redefinition_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_k8_ami_5,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v2_ami_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) & m1_ami_1(D,A,B) ) => k8_ami_5(A,B,C,D) = k1_funct_4(C,D) ) ), file(ami_5,k8_ami_5), []). 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_m1_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_struct_0(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(struct_0,m1_struct_0), []). fof(redefinition_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) <=> m1_relset_1(C,A,B) ) ), file(relset_1,m2_relset_1), []). fof(redefinition_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(subset_1,m2_subset_1), []). fof(redefinition_r1_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ( r1_subset_1(A,B) <=> r1_xboole_0(A,B) ) ) ), file(subset_1,r1_subset_1), []). fof(reflexivity_r1_tarski,axiom,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), []). fof(s1_nat_1__e16_72__scmring4,axiom,( ! [A,B,C,D] : ( ( v4_ordinal2(A) & ~ v3_struct_0(B) & v4_group_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v6_vectsp_1(B) & v7_vectsp_1(B) & v8_vectsp_1(B) & v1_scmring1(B) & l3_vectsp_1(B) & m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B)))) & v11_ami_1(D,k1_tarski(u1_struct_0(B)),k1_scmring2(B)) & m1_ami_1(D,k1_tarski(u1_struct_0(B)),k1_scmring2(B)) ) => ( ( k11_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k10_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k8_ami_5(k1_tarski(u1_struct_0(B)),k1_scmring2(B),C,k3_scmring4(k1_tarski(u1_struct_0(B)),k1_scmring2(B),A,D))),0) = k8_ami_5(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k8_ami_5(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k11_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k10_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),C),0),k12_ami_3(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k8_amistd_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k6_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k11_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k10_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),C),0)),A))),k6_ami_5(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k3_scmring4(k1_tarski(u1_struct_0(B)),k1_scmring2(B),A,D))) & ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ( k11_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k10_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k8_ami_5(k1_tarski(u1_struct_0(B)),k1_scmring2(B),C,k3_scmring4(k1_tarski(u1_struct_0(B)),k1_scmring2(B),A,D))),E) = k8_ami_5(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k8_ami_5(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k11_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k10_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),C),E),k12_ami_3(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k8_amistd_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k6_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k11_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k10_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),C),E)),A))),k6_ami_5(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k3_scmring4(k1_tarski(u1_struct_0(B)),k1_scmring2(B),A,D))) => k11_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k10_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k8_ami_5(k1_tarski(u1_struct_0(B)),k1_scmring2(B),C,k3_scmring4(k1_tarski(u1_struct_0(B)),k1_scmring2(B),A,D))),k1_nat_1(E,1)) = k8_ami_5(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k8_ami_5(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k11_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k10_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),C),k1_nat_1(E,1)),k12_ami_3(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k8_amistd_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k6_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k11_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k10_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),C),k1_nat_1(E,1))),A))),k6_ami_5(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k3_scmring4(k1_tarski(u1_struct_0(B)),k1_scmring2(B),A,D))) ) ) ) => ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => k11_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k10_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k8_ami_5(k1_tarski(u1_struct_0(B)),k1_scmring2(B),C,k3_scmring4(k1_tarski(u1_struct_0(B)),k1_scmring2(B),A,D))),E) = k8_ami_5(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k8_ami_5(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k11_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k10_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),C),E),k12_ami_3(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k8_amistd_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k6_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k11_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k10_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),C),E)),A))),k6_ami_5(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k3_scmring4(k1_tarski(u1_struct_0(B)),k1_scmring2(B),A,D))) ) ) ) ), file(scmring4,s1_nat_1__e16_72__scmring4), []). 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_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ( r1_subset_1(A,B) => r1_subset_1(B,A) ) ) ), file(subset_1,r1_subset_1), []). 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_scmring4,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v1_setfam_1(B) => ! [C] : ( ( ~ v3_struct_0(C) & ~ v2_ami_1(C,B) & v5_ami_1(C,B) & v8_ami_1(C,B) & v4_amistd_1(C,B) & l1_ami_1(C,B) ) => ! [D] : ( m1_struct_0(D,C,u2_ami_1(B,C)) => ! [E] : ( m1_ami_1(E,B,C) => ( r2_hidden(D,k1_relat_1(E)) => k1_funct_1(k10_amistd_2(B,C,E,A),k8_amistd_1(B,C,D,A)) = k1_funct_1(E,D) ) ) ) ) ) ) ), file(scmring4,t11_scmring4), []). fof(t12_funct_4,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ~ r2_hidden(A,k1_relat_1(B)) => k1_funct_1(k1_funct_4(C,B),A) = k1_funct_1(C,A) ) ) ) ), file(funct_4,t12_funct_4), []). fof(t13_scmring4,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v7_ami_1(B,A) & v8_ami_1(B,A) & v10_ami_1(B,A) & v13_amistd_2(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) => ! [D] : ( m2_subset_1(D,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B)) => ! [E] : ( ( v1_ami_3(E,A,B) & m1_ami_1(E,A,B) ) => k4_ami_1(A,B,D,k8_ami_5(A,B,C,E)) = k8_ami_5(A,B,k4_ami_1(A,B,D,C),E) ) ) ) ) ) ), file(scmring4,t13_scmring4), []). fof(t14_funct_4,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(A,k1_relat_1(B)) => k1_funct_1(k1_funct_4(C,B),A) = k1_funct_1(B,A) ) ) ) ), file(funct_4,t14_funct_4), []). fof(t15_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => k1_funct_4(k1_funct_4(A,B),C) = k1_funct_4(A,k1_funct_4(B,C)) ) ) ) ), file(funct_4,t15_funct_4), []). 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_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(t1_xboole_1,axiom,( ! [A,B,C] : ( ( r1_tarski(A,B) & r1_tarski(B,C) ) => r1_tarski(A,C) ) ), file(xboole_1,t1_xboole_1), []). fof(t23_xboole_1,axiom,( ! [A,B,C] : k3_xboole_0(A,k2_xboole_0(B,C)) = k2_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C)) ), file(xboole_1,t23_xboole_1), []). fof(t26_scmring4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_group_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v1_scmring1(A) & l3_vectsp_1(A) ) => ! [B] : ( m1_ami_1(B,k1_tarski(u1_struct_0(A)),k1_scmring2(A)) => r1_tarski(k1_relat_1(k7_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B)),k2_ami_2) ) ) ), file(scmring4,t26_scmring4), []). fof(t29_scmring4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_group_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v1_scmring1(A) & l3_vectsp_1(A) ) => ! [B] : ( m1_ami_1(B,k1_tarski(u1_struct_0(A)),k1_scmring2(A)) => r1_tarski(k1_relat_1(k6_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B)),k3_ami_2) ) ) ), file(scmring4,t29_scmring4), []). fof(t2_boole,axiom,( ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ), file(boole,t2_boole), []). fof(t2_subset,axiom,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), []). fof(t33_ami_5,axiom,( r1_subset_1(k2_ami_2,k3_ami_2) ), file(ami_5,t33_ami_5), []). fof(t34_ami_3,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_struct_0(C,B,u2_ami_1(A,B)) => k1_relat_1(k12_ami_3(A,B,C)) = k1_struct_0(B,k2_ami_1(A,B)) ) ) ) ), file(ami_3,t34_ami_3), []). fof(t35_scmring4,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( ( ~ v3_struct_0(B) & v4_group_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v6_vectsp_1(B) & v7_vectsp_1(B) & v8_vectsp_1(B) & v1_scmring1(B) & l3_vectsp_1(B) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B)))) => k4_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k8_amistd_2(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k8_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),C),A),k8_ami_5(k1_tarski(u1_struct_0(B)),k1_scmring2(B),C,k12_ami_3(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k8_amistd_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k6_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),C),A)))) = k8_ami_5(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k9_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),C),k12_ami_3(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k8_amistd_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k6_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k9_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),C)),A))) ) ) ) ), file(scmring4,t35_scmring4), []). fof(t36_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) => k1_funct_4(A,B) = k1_funct_4(B,A) ) ) ) ), file(funct_4,t36_funct_4), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t40_scmring4,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( ( ~ v3_struct_0(B) & v4_group_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v6_vectsp_1(B) & v7_vectsp_1(B) & v8_vectsp_1(B) & v1_scmring1(B) & l3_vectsp_1(B) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B)))) => ( ~ v3_realset2(B) => ! [D] : ( ( v11_ami_1(D,k1_tarski(u1_struct_0(B)),k1_scmring2(B)) & ~ v1_ami_3(D,k1_tarski(u1_struct_0(B)),k1_scmring2(B)) & m1_ami_1(D,k1_tarski(u1_struct_0(B)),k1_scmring2(B)) ) => ( r1_tarski(D,C) => r2_hidden(k6_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k11_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),k10_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B),C),A)),k1_relat_1(k6_ami_5(k1_tarski(u1_struct_0(B)),k1_scmring2(B),D))) ) ) ) ) ) ) ), file(scmring4,t40_scmring4), []). fof(t48_scmring4,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v1_setfam_1(B) => ! [C] : ( ( ~ v3_struct_0(C) & ~ v2_ami_1(C,B) & v5_ami_1(C,B) & v8_ami_1(C,B) & v4_amistd_1(C,B) & v8_amistd_2(C,B) & l1_ami_1(C,B) ) => ! [D] : ( m1_ami_1(D,B,C) => ( v10_ami_1(C,B) => k6_ami_5(B,C,k3_scmring4(B,C,A,D)) = k9_amistd_2(B,C,k10_amistd_2(B,C,k6_ami_5(B,C,D),A),A) ) ) ) ) ) ), file(scmring4,t48_scmring4), []). 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_ami_3,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_struct_0(C,B,u2_ami_1(A,B)) => k1_funct_1(k12_ami_3(A,B,C),k2_ami_1(A,B)) = C ) ) ) ), file(ami_3,t50_ami_3), []). fof(t50_scmring4,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v1_setfam_1(B) => ! [C] : ( ( ~ v3_struct_0(C) & ~ v2_ami_1(C,B) & v5_ami_1(C,B) & v8_ami_1(C,B) & v4_amistd_1(C,B) & v8_amistd_2(C,B) & l1_ami_1(C,B) ) => ! [D] : ( m1_ami_1(D,B,C) => ! [E] : ( m1_struct_0(E,C,u2_ami_1(B,C)) => ( v10_ami_1(C,B) => ( r2_hidden(E,k1_relat_1(D)) <=> r2_hidden(k8_amistd_1(B,C,E,A),k1_relat_1(k3_scmring4(B,C,A,D))) ) ) ) ) ) ) ) ), file(scmring4,t50_scmring4), []). fof(t53_scmring4,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v1_setfam_1(B) => ! [C] : ( ( ~ v3_struct_0(C) & ~ v2_ami_1(C,B) & v5_ami_1(C,B) & v8_ami_1(C,B) & v4_amistd_1(C,B) & v8_amistd_2(C,B) & l1_ami_1(C,B) ) => ! [D] : ( ( v1_ami_3(D,B,C) & m1_ami_1(D,B,C) ) => ! [E] : ( m1_struct_0(E,C,u2_ami_1(B,C)) => ( r2_hidden(E,k1_relat_1(D)) => k1_funct_1(k9_amistd_2(B,C,D,A),E) = k8_amistd_2(B,C,k5_ami_5(B,C,D,E),A) ) ) ) ) ) ) ), file(scmring4,t53_scmring4), []). fof(t54_scmring4,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v1_setfam_1(B) => ! [C] : ( ( ~ v3_struct_0(C) & ~ v2_ami_1(C,B) & v5_ami_1(C,B) & v8_ami_1(C,B) & v4_amistd_1(C,B) & v8_amistd_2(C,B) & l1_ami_1(C,B) ) => ! [D] : ( ( v1_ami_3(D,B,C) & m1_ami_1(D,B,C) ) => k10_amistd_2(B,C,k9_amistd_2(B,C,D,A),A) = k9_amistd_2(B,C,k10_amistd_2(B,C,D,A),A) ) ) ) ) ), file(scmring4,t54_scmring4), []). 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(t62_ami_5,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & l1_ami_1(B,A) ) => ! [C] : ( m1_ami_1(C,A,B) => r1_tarski(k7_ami_5(A,B,C),C) ) ) ), file(ami_5,t62_ami_5), []). fof(t63_ami_5,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ! [C] : ( m1_ami_1(C,A,B) => r1_tarski(k6_ami_5(A,B,C),C) ) ) ), file(ami_5,t63_ami_5), []). fof(t63_xboole_1,axiom,( ! [A,B,C] : ( ( r1_tarski(A,B) & r1_xboole_0(B,C) ) => r1_xboole_0(A,C) ) ), file(xboole_1,t63_xboole_1), []). fof(t64_ami_5,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v7_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_ami_1(C,A,B) => ! [D] : ( m1_subset_1(D,k4_card_3(u5_ami_1(A,B))) => ( r1_tarski(C,D) => ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => r1_tarski(k6_ami_5(A,B,C),k11_ami_1(A,B,k10_ami_1(A,B,D),E)) ) ) ) ) ) ) ), file(ami_5,t64_ami_5), []). fof(t65_ami_5,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & l1_ami_1(B,A) ) => ! [C] : ( m1_ami_1(C,A,B) => ~ r2_hidden(k2_ami_1(A,B),k1_relat_1(k7_ami_5(A,B,C))) ) ) ), file(ami_5,t65_ami_5), []). fof(t66_ami_5,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v10_ami_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_ami_1(C,A,B) => ~ r2_hidden(k2_ami_1(A,B),k1_relat_1(k6_ami_5(A,B,C))) ) ) ) ), file(ami_5,t66_ami_5), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t73_ami_5,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_ami_1(C,A,B) => ! [D] : ( m1_struct_0(D,B,u2_ami_1(A,B)) => ( r2_hidden(D,k1_relat_1(C)) => r2_hidden(D,k1_relat_1(k6_ami_5(A,B,C))) ) ) ) ) ) ), file(ami_5,t73_ami_5), []). fof(t76_ami_5,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v10_ami_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_ami_1(C,A,B) => ~ ( r2_hidden(k2_ami_1(A,B),k1_relat_1(C)) & v1_ami_3(C,A,B) ) ) ) ) ), file(ami_5,t76_ami_5), []). 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_grfunc_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_tarski(A,B) <=> ( r1_tarski(k1_relat_1(A),k1_relat_1(B)) & ! [C] : ( r2_hidden(C,k1_relat_1(A)) => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) ) ) ) ), file(grfunc_1,t8_grfunc_1), []).