% Mizar problem: t93_ami_5,ami_5,2635,67 fof(t93_ami_5,conjecture,( ! [A] : ( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) & ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3) & m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) ) => ! [B] : ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ! [C] : ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ( ( r1_tarski(A,B) & r1_tarski(A,C) ) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ! [E] : ( m1_ami_3(E) => ! [F] : ( m1_ami_3(F) => ! [G] : ( m2_subset_1(G,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)) => ( ( G = k8_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D)) & G = k7_ami_3(E,F) & r2_hidden(F,k1_relat_1(A)) ) => ( E = F | k6_int_1(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),E),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),F)) = k6_int_1(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),E),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),F)) ) ) ) ) ) ) ) ) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v1_ami_1,antisymmetry_r2_hidden,cc1_arytm_3,cc1_finseq_1,cc1_fraenkel,cc1_funct_1,cc1_int_1,cc1_relset_1,cc1_setfam_1,cc2_arytm_3,cc2_funct_1,cc2_int_1,cc3_arytm_3,cc3_int_1,cc4_int_1,commutativity_k1_nat_1,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k2_xcmplx_0,d15_ami_1,d17_ami_1,d18_ami_1,d19_ami_1,d1_ami_3,d25_ami_1,d5_ami_1,d5_tarski,d7_ami_1,d7_ami_3,dt_g1_ami_1,dt_k10_ami_1,dt_k10_finseq_1,dt_k11_ami_1,dt_k11_ami_3,dt_k13_finseq_1,dt_k17_ami_2,dt_k1_ami_3,dt_k1_fraenkel,dt_k1_funct_1,dt_k1_funct_2,dt_k1_gr_cy_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_ami_1,dt_k2_ami_3,dt_k2_tarski,dt_k2_xboole_0,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_ami_2,dt_k3_tarski,dt_k4_ami_1,dt_k4_ami_2,dt_k4_card_3,dt_k4_numbers,dt_k4_tarski,dt_k5_ami_2,dt_k5_int_1,dt_k5_numbers,dt_k5_ordinal2,dt_k6_ami_1,dt_k6_int_1,dt_k7_ami_1,dt_k7_ami_3,dt_k7_relat_1,dt_k8_ami_1,dt_k8_funct_2,dt_k9_ami_1,dt_l1_ami_1,dt_l1_struct_0,dt_m1_ami_1,dt_m1_ami_3,dt_m1_fraenkel,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_struct_0,existence_m1_ami_1,existence_m1_ami_3,existence_m1_fraenkel,existence_m1_relset_1,existence_m1_struct_0,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,fc10_ami_1,fc16_finseq_1,fc17_finseq_1,fc1_ami_3,fc1_fraenkel,fc1_int_1,fc1_numbers,fc1_ordinal2,fc1_struct_0,fc1_xboole_0,fc2_ami_1,fc2_ami_2,fc2_ami_3,fc2_ami_5,fc2_finseq_1,fc2_fraenkel,fc2_setfam_1,fc2_xboole_0,fc3_ami_1,fc3_ami_2,fc3_ami_3,fc3_setfam_1,fc3_xboole_0,fc4_ami_1,fc4_funct_1,fc4_numbers,fc4_setfam_1,fc5_ami_3,fc5_finseq_1,fc6_int_1,fc7_finseq_1,fc9_finseq_1,free_g1_ami_1,idempotence_k2_xboole_0,rc1_ami_1,rc1_ami_3,rc1_arytm_3,rc1_finseq_1,rc1_fraenkel,rc1_funct_1,rc1_int_1,rc1_setfam_1,rc1_xboole_0,rc2_ami_1,rc2_ami_5,rc2_finseq_1,rc2_funct_1,rc2_int_1,rc2_xboole_0,rc3_ami_1,rc3_finseq_1,rc3_funct_1,rc3_struct_0,rc4_funct_1,rc5_ami_1,rc5_struct_0,rc6_ami_1,rc6_finseq_1,rc7_ami_1,rc7_finseq_1,rc8_ami_1,rc8_finseq_1,rc9_ami_1,redefinition_k11_ami_1,redefinition_k1_fraenkel,redefinition_k1_nat_1,redefinition_k2_ami_3,redefinition_k5_numbers,redefinition_k8_funct_2,redefinition_m1_struct_0,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,spc0_boole,spc1_boole,spc1_numerals,spc5_boole,spc5_numerals,spc9_boole,spc9_numerals,t12_ami_3,t1_arithm,t1_boole,t1_numerals,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t72_funct_1,t7_boole,t87_ami_5,t8_boole]), [file(ami_5,t93_ami_5)]). 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(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_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_int_1,axiom,( ! [A] : ( m1_subset_1(A,k4_numbers) => v1_int_1(A) ) ), file(int_1,cc1_int_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_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(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_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_int_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_int_1(A) ) ) ), file(int_1,cc2_int_1), []). fof(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_int_1,axiom,( ! [A] : ( v4_ordinal2(A) => v1_int_1(A) ) ), file(int_1,cc3_int_1), []). fof(cc4_int_1,axiom,( ! [A] : ( v1_int_1(A) => ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(int_1,cc4_int_1), []). fof(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(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(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_ami_3,axiom,( k1_ami_3 = g1_ami_1(k1_tarski(k4_numbers),k5_numbers,0,k3_ami_2,k1_gr_cy_1(9),k4_ami_2,k5_ami_2,k17_ami_2) ), file(ami_3,d1_ami_3), []). fof(d25_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_ami_1(C,A,B) => ( v11_ami_1(C,A,B) <=> ! [D] : ( m1_subset_1(D,k4_card_3(u5_ami_1(A,B))) => ! [E] : ( m1_subset_1(E,k4_card_3(u5_ami_1(A,B))) => ( ( r1_tarski(C,D) & r1_tarski(C,E) ) => ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => k7_relat_1(k11_ami_1(A,B,k10_ami_1(A,B,D),F),k1_relat_1(C)) = k7_relat_1(k11_ami_1(A,B,k10_ami_1(A,B,E),F),k1_relat_1(C)) ) ) ) ) ) ) ) ) ), file(ami_1,d25_ami_1), []). 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_tarski,axiom,( ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ), file(tarski,d5_tarski), []). 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_ami_3,axiom,( ! [A] : ( m1_ami_3(A) => ! [B] : ( m1_ami_3(B) => k7_ami_3(A,B) = k4_tarski(5,k10_finseq_1(A,B)) ) ) ), file(ami_3,d7_ami_3), []). 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_finseq_1,axiom,( $true ), file(finseq_1,k10_finseq_1), []). 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_k11_ami_3,axiom,( ! [A] : ( m1_subset_1(A,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) => m1_struct_0(k11_ami_3(A),k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ), file(ami_3,k11_ami_3), []). fof(dt_k13_finseq_1,axiom,( $true ), file(finseq_1,k13_finseq_1), []). fof(dt_k17_ami_2,axiom, ( v1_funct_1(k17_ami_2) & v1_funct_2(k17_ami_2,k4_ami_2,k1_fraenkel(k4_card_3(k5_ami_2),k4_card_3(k5_ami_2))) & m2_relset_1(k17_ami_2,k4_ami_2,k1_fraenkel(k4_card_3(k5_ami_2),k4_card_3(k5_ami_2))) ), file(ami_2,k17_ami_2), []). fof(dt_k1_ami_3,axiom, ( v1_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & l1_ami_1(k1_ami_3,k1_tarski(k4_numbers)) ), file(ami_3,k1_ami_3), []). fof(dt_k1_fraenkel,axiom,( ! [A,B] : ( ~ v1_xboole_0(B) => m1_fraenkel(k1_fraenkel(A,B),A,B) ) ), file(fraenkel,k1_fraenkel), []). 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_gr_cy_1,axiom,( ! [A] : ( v4_ordinal2(A) => ( ~ v1_xboole_0(k1_gr_cy_1(A)) & m1_subset_1(k1_gr_cy_1(A),k1_zfmisc_1(k5_numbers)) ) ) ), file(gr_cy_1,k1_gr_cy_1), []). fof(dt_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => m2_subset_1(k1_nat_1(A,B),k1_numbers,k5_numbers) ) ), file(nat_1,k1_nat_1), []). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), []). fof(dt_k1_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), []). fof(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), []). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), []). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), []). fof(dt_k2_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_3,axiom,( ! [A,B] : ( ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) & m1_ami_3(B) ) => v1_int_1(k2_ami_3(A,B)) ) ), file(ami_3,k2_ami_3), []). 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_tarski,axiom,( $true ), file(tarski,k3_tarski), []). 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_ami_2,axiom,( m1_subset_1(k4_ami_2,k1_zfmisc_1(k2_zfmisc_1(k1_gr_cy_1(9),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),k5_numbers))))) ), file(ami_2,k4_ami_2), []). fof(dt_k4_card_3,axiom,( $true ), file(card_3,k4_card_3), []). fof(dt_k4_numbers,axiom,( $true ), file(numbers,k4_numbers), []). fof(dt_k4_tarski,axiom,( $true ), file(tarski,k4_tarski), []). fof(dt_k5_ami_2,axiom, ( v1_funct_1(k5_ami_2) & v1_funct_2(k5_ami_2,k5_numbers,k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(k4_ami_2,k3_ami_2))) & m2_relset_1(k5_ami_2,k5_numbers,k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(k4_ami_2,k3_ami_2))) ), file(ami_2,k5_ami_2), []). fof(dt_k5_int_1,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => v1_int_1(k5_int_1(A,B)) ) ), file(int_1,k5_int_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_int_1,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => v1_int_1(k6_int_1(A,B)) ) ), file(int_1,k6_int_1), []). fof(dt_k7_ami_1,axiom,( $true ), file(ami_1,k7_ami_1), []). fof(dt_k7_ami_3,axiom,( ! [A,B] : ( ( m1_ami_3(A) & m1_ami_3(B) ) => m2_subset_1(k7_ami_3(A,B),k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ), file(ami_3,k7_ami_3), []). 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_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_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_l1_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => l1_struct_0(B) ) ), file(ami_1,l1_ami_1), []). fof(dt_l1_struct_0,axiom,( $true ), file(struct_0,l1_struct_0), []). 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_ami_3,axiom,( ! [A] : ( m1_ami_3(A) => m1_subset_1(A,u1_struct_0(k1_ami_3)) ) ), file(ami_3,m1_ami_3), []). fof(dt_m1_fraenkel,axiom,( ! [A,B,C] : ( m1_fraenkel(C,A,B) => ( ~ v1_xboole_0(C) & v1_fraenkel(C) ) ) ), file(fraenkel,m1_fraenkel), []). 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_struct_0,axiom,( ? [A] : l1_struct_0(A) ), file(struct_0,l1_struct_0), []). 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_ami_3,axiom,( ? [A] : m1_ami_3(A) ), file(ami_3,m1_ami_3), []). fof(existence_m1_fraenkel,axiom,( ! [A,B] : ? [C] : m1_fraenkel(C,A,B) ), file(fraenkel,m1_fraenkel), []). 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(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_3,axiom, ( ~ v3_struct_0(k1_ami_3) & v1_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & ~ v2_ami_1(k1_ami_3,k1_tarski(k4_numbers)) ), file(ami_3,fc1_ami_3), []). fof(fc1_fraenkel,axiom,( ! [A,B] : v1_fraenkel(k1_funct_2(A,B)) ), file(fraenkel,fc1_fraenkel), []). fof(fc1_int_1,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_int_1(k2_xcmplx_0(A,B)) ) ) ), file(int_1,fc1_int_1), []). fof(fc1_numbers,axiom,( ~ v1_xboole_0(k1_numbers) ), file(numbers,fc1_numbers), []). 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(fc1_xboole_0,axiom,( v1_xboole_0(k1_xboole_0) ), file(xboole_0,fc1_xboole_0), []). 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_ami_2,axiom, ( ~ v1_xboole_0(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(ami_2,fc2_ami_2), []). fof(fc2_ami_3,axiom, ( ~ v3_struct_0(k1_ami_3) & v1_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & ~ v2_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & v5_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & v6_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & v8_ami_1(k1_ami_3,k1_tarski(k4_numbers)) ), file(ami_3,fc2_ami_3), []). fof(fc2_ami_5,axiom, ( ~ v1_xboole_0(u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) & ~ v1_finset_1(u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ), file(ami_5,fc2_ami_5), []). 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_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_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(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_ami_2,axiom, ( v1_relat_1(k4_ami_2) & ~ v1_xboole_0(k4_ami_2) ), file(ami_2,fc3_ami_2), []). fof(fc3_ami_3,axiom, ( ~ v3_struct_0(k1_ami_3) & v1_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & ~ v2_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & v4_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & v5_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & v6_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & v8_ami_1(k1_ami_3,k1_tarski(k4_numbers)) ), file(ami_3,fc3_ami_3), []). 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(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_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_numbers,axiom,( ~ v1_xboole_0(k4_numbers) ), file(numbers,fc4_numbers), []). 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_ami_3,axiom, ( ~ v3_struct_0(k1_ami_3) & v1_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & ~ v2_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & v4_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & v5_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & v6_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & v7_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & v8_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & v10_ami_1(k1_ami_3,k1_tarski(k4_numbers)) ), file(ami_3,fc5_ami_3), []). fof(fc5_finseq_1,axiom,( ! [A,B] : ( v1_relat_1(k10_finseq_1(A,B)) & v1_funct_1(k10_finseq_1(A,B)) ) ), file(finseq_1,fc5_finseq_1), []). fof(fc6_int_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & v1_int_1(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v1_int_1(k2_xcmplx_0(B,A)) ) ) ), file(int_1,fc6_int_1), []). fof(fc7_finseq_1,axiom,( ! [A,B] : ( v1_relat_1(k10_finseq_1(A,B)) & v1_funct_1(k10_finseq_1(A,B)) & v1_finset_1(k10_finseq_1(A,B)) & v1_finseq_1(k10_finseq_1(A,B)) ) ), file(finseq_1,fc7_finseq_1), []). fof(fc9_finseq_1,axiom,( ! [A] : ~ v1_xboole_0(k13_finseq_1(A)) ), file(finseq_1,fc9_finseq_1), []). 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_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,A) = A ), file(xboole_0,k2_xboole_0), []). 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_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_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_int_1,axiom,( ? [A] : ( m1_subset_1(A,k1_numbers) & v1_xcmplx_0(A) & v1_xreal_0(A) & v1_int_1(A) ) ), file(int_1,rc1_int_1), []). fof(rc1_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(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_ami_5,axiom,( ? [A] : ( m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) & v1_relat_1(A) & v1_funct_1(A) & v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) & ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3) ) ), file(ami_5,rc2_ami_5), []). 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_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) ), file(funct_1,rc2_funct_1), []). fof(rc2_int_1,axiom,( ? [A] : v1_int_1(A) ), file(int_1,rc2_int_1), []). fof(rc2_xboole_0,axiom,( ? [A] : ~ v1_xboole_0(A) ), file(xboole_0,rc2_xboole_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_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_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ), file(funct_1,rc3_funct_1), []). fof(rc3_struct_0,axiom,( ? [A] : ( l1_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc3_struct_0), []). 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(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_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_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_k1_fraenkel,axiom,( ! [A,B] : ( ~ v1_xboole_0(B) => k1_fraenkel(A,B) = k1_funct_2(A,B) ) ), file(fraenkel,k1_fraenkel), []). 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_ami_3,axiom,( ! [A,B] : ( ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) & m1_ami_3(B) ) => k2_ami_3(A,B) = k1_funct_1(A,B) ) ), file(ami_3,k2_ami_3), []). 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_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(reflexivity_r1_tarski,axiom,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), []). 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(spc5_boole,axiom,( ~ v1_xboole_0(5) ), file(boole,spc5_boole), []). fof(spc5_numerals,axiom, ( v2_xreal_0(5) & m1_subset_1(5,k5_numbers) ), file(numerals,spc5_numerals), []). fof(spc9_boole,axiom,( ~ v1_xboole_0(9) ), file(boole,spc9_boole), []). fof(spc9_numerals,axiom, ( v2_xreal_0(9) & m1_subset_1(9,k5_numbers) ), file(numerals,spc9_numerals), []). fof(t12_ami_3,axiom,( ! [A] : ( m1_ami_3(A) => ! [B] : ( m1_ami_3(B) => ! [C] : ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k7_ami_3(A,B),C),k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) = k11_ami_3(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,C)) & ( A != B => k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k7_ami_3(A,B),C),A) = k5_int_1(k2_ami_3(C,A),k2_ami_3(C,B)) ) & k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k7_ami_3(A,B),C),B) = k6_int_1(k2_ami_3(C,A),k2_ami_3(C,B)) & ! [D] : ( m1_ami_3(D) => ~ ( D != A & D != B & k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k7_ami_3(A,B),C),D) != k2_ami_3(C,D) ) ) ) ) ) ) ), file(ami_3,t12_ami_3), []). fof(t1_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(A,0) = A ) ), file(arithm,t1_arithm), []). fof(t1_boole,axiom,( ! [A] : k2_xboole_0(A,k1_xboole_0) = A ), file(boole,t1_boole), []). fof(t1_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(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(t72_funct_1,axiom,( ! [A,B,C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(B,A) => k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B) ) ) ), file(funct_1,t72_funct_1), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t87_ami_5,axiom,( ! [A] : ( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) & ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3) & m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) ) => ! [B] : ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ! [C] : ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ( ( r1_tarski(A,B) & r1_tarski(A,C) ) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ! [E] : ( m2_subset_1(E,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)) => ( E = k8_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D)) => ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D)) = k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D)) & E = k8_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D)) ) ) ) ) ) ) ) ) ), file(ami_5,t87_ami_5), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []).