% Mizar problem: t26_bagorder,bagorder,1538,56 fof(t26_bagorder,conjecture,( ! [A] : ( v3_ordinal1(A) => v2_wellord1(k4_bagorder(A)) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v1_orders_2,antisymmetry_r2_hidden,cc1_card_1,cc1_card_5,cc1_finseq_1,cc1_finset_1,cc1_finsub_1,cc1_funct_1,cc1_funct_2,cc1_nat_1,cc1_ordinal1,cc1_polynom1,cc1_relat_1,cc1_relset_1,cc1_xreal_0,cc2_card_1,cc2_card_5,cc2_finset_1,cc2_finsub_1,cc2_funct_1,cc2_funct_2,cc2_nat_1,cc2_ordinal1,cc2_xreal_0,cc3_card_1,cc3_funct_2,cc3_nat_1,cc3_ordinal1,cc3_polynom1,cc3_xreal_0,cc4_funct_2,cc4_polynom1,cc4_xreal_0,cc5_funct_2,cc5_polynom1,cc5_xreal_0,cc6_funct_2,cc6_polynom1,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,commutativity_k1_nat_1,commutativity_k2_tarski,commutativity_k2_xcmplx_0,commutativity_k9_polynom1,connectedness_r1_xreal_0,d12_relat_2,d14_dickson,d14_polynom1,d15_dickson,d16_relat_2,d1_wellord2,d2_triang_1,d2_wellfnd1,d3_bagorder,d3_pboole,d4_finseq_4,d5_real_1,d5_tarski,d5_wellord1,d7_bagorder,d7_polynom1,d7_wellfnd1,d8_bagorder,d9_relat_2,dt_g1_orders_2,dt_k10_dickson,dt_k11_dickson,dt_k11_polynom1,dt_k13_polynom1,dt_k14_polynom1,dt_k16_polynom1,dt_k1_card_1,dt_k1_domain_1,dt_k1_funct_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_polynom2,dt_k1_relat_1,dt_k1_tarski,dt_k1_wellord2,dt_k1_xboole_0,dt_k1_yellow_1,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_tarski,dt_k2_triang_1,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_finseq_1,dt_k3_relat_1,dt_k4_bagorder,dt_k4_finseq_1,dt_k4_finseq_4,dt_k4_tarski,dt_k5_numbers,dt_k5_ordinal2,dt_k7_relat_1,dt_k8_funct_2,dt_k8_polynom1,dt_k9_polynom1,dt_l1_orders_2,dt_l1_struct_0,dt_m1_finseq_1,dt_m1_pboole,dt_m1_polynom1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_orders_2,dt_u1_struct_0,existence_l1_orders_2,existence_l1_struct_0,existence_m1_finseq_1,existence_m1_pboole,existence_m1_polynom1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_relset_1,existence_m2_subset_1,fc10_dickson,fc10_xreal_0,fc11_dickson,fc11_finseq_1,fc11_xreal_0,fc12_dickson,fc12_relat_1,fc12_xreal_0,fc13_dickson,fc13_relat_1,fc14_dickson,fc14_finset_1,fc14_polynom1,fc15_dickson,fc17_finseq_1,fc17_polynom1,fc18_polynom1,fc1_bagorder,fc1_finset_1,fc1_finsub_1,fc1_nat_1,fc1_numbers,fc1_orders_2,fc1_ordinal2,fc1_struct_0,fc1_subset_1,fc20_polynom1,fc21_polynom1,fc23_polynom1,fc25_polynom1,fc2_bagorder,fc2_card_1,fc2_finseq_1,fc2_finset_1,fc2_orders_2,fc2_ordinal1,fc2_polynom1,fc2_subset_1,fc3_nat_1,fc3_orders_2,fc3_polynom1,fc3_subset_1,fc3_xreal_0,fc4_funct_1,fc4_nat_1,fc4_relat_1,fc4_subset_1,fc5_polynom1,fc5_relat_1,fc6_relat_1,fc7_bagorder,fc7_relat_1,fc7_xreal_0,fc8_polynom1,fc8_relat_1,fc8_xreal_0,fc9_xreal_0,fraenkel_a_0_2_dickson,free_g1_orders_2,rc10_polynom1,rc11_polynom1,rc12_polynom1,rc12_waybel_0,rc13_polynom1,rc1_bagorder,rc1_card_1,rc1_card_5,rc1_finseq_1,rc1_finset_1,rc1_funct_1,rc1_funct_2,rc1_nat_1,rc1_orders_2,rc1_ordinal1,rc1_polynom1,rc1_relat_1,rc1_subset_1,rc1_xreal_0,rc2_card_1,rc2_card_5,rc2_finseq_1,rc2_finset_1,rc2_funct_1,rc2_funct_2,rc2_nat_1,rc2_orders_2,rc2_ordinal1,rc2_polynom1,rc2_relat_1,rc2_subset_1,rc2_xreal_0,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc3_nat_1,rc3_ordinal1,rc3_polynom1,rc3_relat_1,rc3_struct_0,rc3_xreal_0,rc4_finseq_1,rc4_finset_1,rc4_funct_1,rc4_polynom1,rc4_xreal_0,rc5_struct_0,rc6_finseq_1,rc7_finseq_1,rc7_polynom1,rc8_finseq_1,rc8_polynom1,rc9_polynom1,redefinition_k14_polynom1,redefinition_k1_domain_1,redefinition_k1_nat_1,redefinition_k1_polynom2,redefinition_k1_yellow_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_k8_funct_2,redefinition_k8_polynom1,redefinition_m1_polynom1,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,redefinition_r6_pboole,reflexivity_r1_tarski,reflexivity_r1_xreal_0,reflexivity_r6_pboole,s1_nat_1__e3_42_1_1_3__bagorder,s2_ordinal1__e2_42__bagorder,s3_funct_2__e18_42_1_1__bagorder,s3_funct_2__e29_42_1_1__bagorder,spc0_boole,spc1_boole,spc1_numerals,symmetry_r6_pboole,t107_orders_1,t11_bagorder,t11_finseq_2,t12_funct_1,t133_orders_1,t134_orders_1,t15_wellfnd1,t19_ordinal1,t1_arithm,t1_numerals,t1_real,t1_subset,t20_bagorder,t21_bagorder,t23_ordinal1,t24_ordinal1,t27_finseq_3,t29_nat_1,t2_real,t2_subset,t2_tarski,t3_real,t3_subset,t4_real,t4_subset,t56_polynom1,t5_real,t5_subset,t5_wellord1,t60_relat_1,t6_boole,t6_finseq_5,t6_real,t72_funct_1,t7_boole,t7_ordinal1,t7_real,t7_wellord2,t8_boole,t8_real,t8_wellord1,t92_orders_1,t97_orders_1,t9_funct_1,t9_partit_2]), [file(bagorder,t26_bagorder)]). fof(abstractness_v1_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_orders_2(A) => A = g1_orders_2(u1_struct_0(A),u1_orders_2(A)) ) ) ), file(orders_2,v1_orders_2), []). fof(antisymmetry_r2_hidden,axiom,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), []). fof(cc1_card_1,axiom,( ! [A] : ( v1_card_1(A) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) ) ) ), file(card_1,cc1_card_1), []). fof(cc1_card_5,axiom,( ! [A] : ( ~ v1_finset_1(A) => ~ v1_xboole_0(A) ) ), file(card_5,cc1_card_5), []). 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_finsub_1,axiom,( ! [A] : ( v4_finsub_1(A) => ( v1_finsub_1(A) & v3_finsub_1(A) ) ) ), file(finsub_1,cc1_finsub_1), []). fof(cc1_funct_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_funct_1(A) ) ), file(funct_1,cc1_funct_1), []). fof(cc1_funct_2,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_partfun1(C,A,B) ) => ( v1_funct_1(C) & v1_funct_2(C,A,B) ) ) ) ), file(funct_2,cc1_funct_2), []). 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_ordinal1,axiom,( ! [A] : ( v3_ordinal1(A) => ( v1_ordinal1(A) & v2_ordinal1(A) ) ) ), file(ordinal1,cc1_ordinal1), []). fof(cc1_polynom1,axiom,( ! [A] : ( m1_finseq_1(A,k5_numbers) => v1_card_3(A) ) ), file(polynom1,cc1_polynom1), []). fof(cc1_relat_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_relat_1(A) ) ), file(relat_1,cc1_relat_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_xreal_0,axiom,( ! [A] : ( v4_ordinal2(A) => v1_xreal_0(A) ) ), file(xreal_0,cc1_xreal_0), []). fof(cc2_card_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_card_1(A) ) ) ), file(card_1,cc2_card_1), []). fof(cc2_card_5,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) ) => ! [B] : ( m1_subset_1(B,A) => ( v1_ordinal1(B) & v2_ordinal1(B) & v3_ordinal1(B) ) ) ) ), file(card_5,cc2_card_5), []). 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_finsub_1,axiom,( ! [A] : ( ( v1_finsub_1(A) & v3_finsub_1(A) ) => v4_finsub_1(A) ) ), file(finsub_1,cc2_finsub_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_funct_2,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & v3_funct_2(C,A,B) ) => ( v1_funct_1(C) & v2_funct_1(C) & v1_funct_2(C,A,B) & v2_funct_2(C,A,B) ) ) ) ), file(funct_2,cc2_funct_2), []). 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_ordinal1,axiom,( ! [A] : ( ( v1_ordinal1(A) & v2_ordinal1(A) ) => v3_ordinal1(A) ) ), file(ordinal1,cc2_ordinal1), []). fof(cc2_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xcmplx_0(A) ) ), file(xreal_0,cc2_xreal_0), []). fof(cc3_card_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_finset_1(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_card_1(A) ) ) ), file(card_1,cc3_card_1), []). fof(cc3_funct_2,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v2_funct_1(C) & v1_funct_2(C,A,B) & v2_funct_2(C,A,B) ) => ( v1_funct_1(C) & v1_funct_2(C,A,B) & v3_funct_2(C,A,B) ) ) ) ), file(funct_2,cc3_funct_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_ordinal1,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) ) ) ), file(ordinal1,cc3_ordinal1), []). fof(cc3_polynom1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v7_seqm_3(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) ) ) ), file(polynom1,cc3_polynom1), []). 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_funct_2,axiom,( ! [A,B] : ( m1_relset_1(B,A,A) => ( ( v1_funct_1(B) & v1_partfun1(B,A,A) & v1_relat_2(B) & v1_funct_2(B,A,A) ) => ( v1_funct_1(B) & v2_funct_1(B) & v1_funct_2(B,A,A) & v2_funct_2(B,A,A) & v3_funct_2(B,A,A) ) ) ) ), file(funct_2,cc4_funct_2), []). fof(cc4_polynom1,axiom,( ! [A,B] : ( m1_relset_1(B,A,k5_numbers) => ( ( v1_funct_1(B) & v1_funct_2(B,A,k5_numbers) ) => ( v1_funct_1(B) & v1_funct_2(B,A,k5_numbers) & v7_seqm_3(B) ) ) ) ), file(polynom1,cc4_polynom1), []). 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_funct_2,axiom,( ! [A,B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_funct_2(C,A,B) ) => ( v1_funct_1(C) & v1_partfun1(C,A,B) & v1_funct_2(C,A,B) ) ) ) ) ), file(funct_2,cc5_funct_2), []). fof(cc5_polynom1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_polynom1(A) ) ) ), file(polynom1,cc5_polynom1), []). 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_funct_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ! [C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_funct_2(C,A,B) ) => ( v1_funct_1(C) & ~ v1_xboole_0(C) & v1_partfun1(C,A,B) & v1_funct_2(C,A,B) ) ) ) ) ), file(funct_2,cc6_funct_2), []). fof(cc6_polynom1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_pboole(B,A) => v1_polynom1(B) ) ) ), file(polynom1,cc6_polynom1), []). fof(cc6_xreal_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & v3_xreal_0(A) ) ) ), file(xreal_0,cc6_xreal_0), []). fof(cc7_xreal_0,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(xreal_0,cc7_xreal_0), []). fof(cc8_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(xreal_0,cc8_xreal_0), []). fof(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_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_k9_polynom1,axiom,( ! [A,B,C] : ( ( v1_seq_1(B) & m1_pboole(B,A) & v1_seq_1(C) & m1_pboole(C,A) ) => k9_polynom1(A,B,C) = k9_polynom1(A,C,B) ) ), file(polynom1,k9_polynom1), []). fof(connectedness_r1_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( r1_xreal_0(A,B) | r1_xreal_0(B,A) ) ) ), file(xreal_0,r1_xreal_0), []). fof(d12_relat_2,axiom,( ! [A] : ( v1_relat_1(A) => ( v4_relat_2(A) <=> r4_relat_2(A,k3_relat_1(A)) ) ) ), file(relat_2,d12_relat_2), []). fof(d14_dickson,axiom,( k10_dickson = a_0_2_dickson ), file(dickson,d14_dickson), []). fof(d14_polynom1,axiom,( ! [A,B] : ( B = k13_polynom1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ( v7_seqm_3(C) & v1_polynom1(C) & m1_pboole(C,A) ) ) ) ), file(polynom1,d14_polynom1), []). fof(d15_dickson,axiom,( k11_dickson = g1_orders_2(k5_numbers,k10_dickson) ), file(dickson,d15_dickson), []). fof(d16_relat_2,axiom,( ! [A] : ( v1_relat_1(A) => ( v8_relat_2(A) <=> r8_relat_2(A,k3_relat_1(A)) ) ) ), file(relat_2,d16_relat_2), []). fof(d1_wellord2,axiom,( ! [A,B] : ( v1_relat_1(B) => ( B = k1_wellord2(A) <=> ( k3_relat_1(B) = A & ! [C,D] : ( ( r2_hidden(C,A) & r2_hidden(D,A) ) => ( r2_hidden(k4_tarski(C,D),B) <=> r1_tarski(C,D) ) ) ) ) ) ), file(wellord2,d1_wellord2), []). fof(d2_triang_1,axiom,( ! [A,B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( ( v1_relat_2(C) & v4_relat_2(C) & v8_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) ) => ( r3_orders_1(C,B) => ! [D] : ( m2_finseq_1(D,A) => ( D = k2_triang_1(A,B,C) <=> ( k2_relat_1(D) = B & ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ( ( r2_hidden(E,k4_finseq_1(D)) & r2_hidden(F,k4_finseq_1(D)) ) => ( r1_xreal_0(F,E) | ( k4_finseq_4(k5_numbers,A,D,E) != k4_finseq_4(k5_numbers,A,D,F) & r2_hidden(k4_tarski(k4_finseq_4(k5_numbers,A,D,E),k4_finseq_4(k5_numbers,A,D,F)),C) ) ) ) ) ) ) ) ) ) ) ) ), file(triang_1,d2_triang_1), []). fof(d2_wellfnd1,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_wellfnd1(A) <=> r1_wellord1(u1_orders_2(A),u1_struct_0(A)) ) ) ), file(wellfnd1,d2_wellfnd1), []). fof(d3_bagorder,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & m2_relset_1(B,k5_numbers,u1_struct_0(A)) ) => ( v1_bagorder(B,A) <=> ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => r2_hidden(k1_domain_1(u1_struct_0(A),u1_struct_0(A),k8_funct_2(k5_numbers,u1_struct_0(A),B,k1_nat_1(C,1)),k8_funct_2(k5_numbers,u1_struct_0(A),B,C)),u1_orders_2(A)) ) ) ) ) ), file(bagorder,d3_bagorder), []). fof(d3_pboole,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( m1_pboole(B,A) <=> k1_relat_1(B) = A ) ) ), file(pboole,d3_pboole), []). fof(d4_finseq_4,axiom,( ! [A,B,C] : ( ( v1_funct_1(C) & m2_relset_1(C,A,B) ) => ! [D] : ( r2_hidden(D,k1_relat_1(C)) => k4_finseq_4(A,B,C,D) = k1_funct_1(C,D) ) ) ), file(finseq_4,d4_finseq_4), []). fof(d5_real_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) <=> ~ ( r1_xreal_0(B,A) & B != A ) ) ) ) ), file(real_1,d5_real_1), []). fof(d5_tarski,axiom,( ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ), file(tarski,d5_tarski), []). fof(d5_wellord1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r2_wellord1(A,B) <=> ( r1_relat_2(A,B) & r8_relat_2(A,B) & r4_relat_2(A,B) & r6_relat_2(A,B) & r1_wellord1(A,B) ) ) ) ), file(wellord1,d5_wellord1), []). fof(d7_bagorder,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A)) & v1_relat_2(B) & v4_relat_2(B) & v8_relat_2(B) & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) ) => ( v2_bagorder(B,A) <=> ( r7_relat_2(B,k14_polynom1(A)) & ! [C] : ( ( v7_seqm_3(C) & v1_polynom1(C) & m1_pboole(C,A) ) => r2_hidden(k4_tarski(k16_polynom1(A),C),B) ) & ! [C] : ( ( v7_seqm_3(C) & v1_polynom1(C) & m1_pboole(C,A) ) => ! [D] : ( ( v7_seqm_3(D) & v1_polynom1(D) & m1_pboole(D,A) ) => ! [E] : ( ( v7_seqm_3(E) & v1_polynom1(E) & m1_pboole(E,A) ) => ( r2_hidden(k4_tarski(C,D),B) => r2_hidden(k4_tarski(k9_polynom1(A,C,E),k9_polynom1(A,D,E)),B) ) ) ) ) ) ) ) ) ), file(bagorder,d7_bagorder), []). fof(d7_polynom1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( B = k11_polynom1(A) <=> ! [C] : ( r2_hidden(C,B) <=> k1_funct_1(A,C) != 0 ) ) ) ), file(polynom1,d7_polynom1), []). fof(d7_wellfnd1,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & m2_relset_1(B,k5_numbers,u1_struct_0(A)) ) => ( v3_wellfnd1(B,A) <=> ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( k8_funct_2(k5_numbers,u1_struct_0(A),B,k1_nat_1(C,1)) != k8_funct_2(k5_numbers,u1_struct_0(A),B,C) & r2_hidden(k4_tarski(k8_funct_2(k5_numbers,u1_struct_0(A),B,k1_nat_1(C,1)),k8_funct_2(k5_numbers,u1_struct_0(A),B,C)),u1_orders_2(A)) ) ) ) ) ) ), file(wellfnd1,d7_wellfnd1), []). fof(d8_bagorder,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A)) & v1_relat_2(B) & v4_relat_2(B) & v8_relat_2(B) & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) ) => ( B = k4_bagorder(A) <=> ! [C] : ( ( v7_seqm_3(C) & v1_polynom1(C) & m1_pboole(C,A) ) => ! [D] : ( ( v7_seqm_3(D) & v1_polynom1(D) & m1_pboole(D,A) ) => ( r2_hidden(k4_tarski(C,D),B) <=> ~ ( ~ r6_pboole(A,C,D) & ! [E] : ( v3_ordinal1(E) => ~ ( r2_hidden(E,A) & ~ r1_xreal_0(k8_polynom1(D,E),k8_polynom1(C,E)) & ! [F] : ( v3_ordinal1(F) => ( ( r2_hidden(E,F) & r2_hidden(F,A) ) => k8_polynom1(C,F) = k8_polynom1(D,F) ) ) ) ) ) ) ) ) ) ) ) ), file(bagorder,d8_bagorder), []). fof(d9_relat_2,axiom,( ! [A] : ( v1_relat_1(A) => ( v1_relat_2(A) <=> r1_relat_2(A,k3_relat_1(A)) ) ) ), file(relat_2,d9_relat_2), []). fof(dt_g1_orders_2,axiom,( ! [A,B] : ( m1_relset_1(B,A,A) => ( v1_orders_2(g1_orders_2(A,B)) & l1_orders_2(g1_orders_2(A,B)) ) ) ), file(orders_2,g1_orders_2), []). fof(dt_k10_dickson,axiom,( m2_relset_1(k10_dickson,k5_numbers,k5_numbers) ), file(dickson,k10_dickson), []). fof(dt_k11_dickson,axiom, ( ~ v3_struct_0(k11_dickson) & l1_orders_2(k11_dickson) ), file(dickson,k11_dickson), []). fof(dt_k11_polynom1,axiom,( $true ), file(polynom1,k11_polynom1), []). fof(dt_k13_polynom1,axiom,( $true ), file(polynom1,k13_polynom1), []). fof(dt_k14_polynom1,axiom,( ! [A] : m1_subset_1(k14_polynom1(A),k1_zfmisc_1(k13_polynom1(A))) ), file(polynom1,k14_polynom1), []). fof(dt_k16_polynom1,axiom,( ! [A] : m1_polynom1(k16_polynom1(A),A,k14_polynom1(A)) ), file(polynom1,k16_polynom1), []). fof(dt_k1_card_1,axiom,( ! [A] : v1_card_1(k1_card_1(A)) ), file(card_1,k1_card_1), []). fof(dt_k1_domain_1,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(C,A) & m1_subset_1(D,B) ) => m1_subset_1(k1_domain_1(A,B,C,D),k2_zfmisc_1(A,B)) ) ), file(domain_1,k1_domain_1), []). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_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_polynom2,axiom,( ! [A,B] : ( ( v7_seqm_3(B) & v1_polynom1(B) & m1_pboole(B,A) ) => ( v1_finset_1(k1_polynom2(A,B)) & m1_subset_1(k1_polynom2(A,B),k1_zfmisc_1(A)) ) ) ), file(polynom2,k1_polynom2), []). 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_wellord2,axiom,( ! [A] : v1_relat_1(k1_wellord2(A)) ), file(wellord2,k1_wellord2), []). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), []). fof(dt_k1_yellow_1,axiom,( ! [A] : ( v1_relat_2(k1_yellow_1(A)) & v4_relat_2(k1_yellow_1(A)) & v8_relat_2(k1_yellow_1(A)) & v1_partfun1(k1_yellow_1(A),A,A) & m2_relset_1(k1_yellow_1(A),A,A) ) ), file(yellow_1,k1_yellow_1), []). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), []). fof(dt_k2_relat_1,axiom,( $true ), file(relat_1,k2_relat_1), []). fof(dt_k2_tarski,axiom,( $true ), file(tarski,k2_tarski), []). fof(dt_k2_triang_1,axiom,( ! [A,B,C] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(A)) & v1_relat_2(C) & v4_relat_2(C) & v8_relat_2(C) & v1_partfun1(C,A,A) & m1_relset_1(C,A,A) ) => m2_finseq_1(k2_triang_1(A,B,C),A) ) ), file(triang_1,k2_triang_1), []). fof(dt_k2_xcmplx_0,axiom,( $true ), file(xcmplx_0,k2_xcmplx_0), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). fof(dt_k3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers) ) ), file(finseq_1,k3_finseq_1), []). fof(dt_k3_relat_1,axiom,( $true ), file(relat_1,k3_relat_1), []). fof(dt_k4_bagorder,axiom,( ! [A] : ( v3_ordinal1(A) => ( v1_partfun1(k4_bagorder(A),k14_polynom1(A),k14_polynom1(A)) & v1_relat_2(k4_bagorder(A)) & v4_relat_2(k4_bagorder(A)) & v8_relat_2(k4_bagorder(A)) & m2_relset_1(k4_bagorder(A),k14_polynom1(A),k14_polynom1(A)) ) ) ), file(bagorder,k4_bagorder), []). fof(dt_k4_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m1_subset_1(k4_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ), file(finseq_1,k4_finseq_1), []). fof(dt_k4_finseq_4,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & m1_relset_1(C,A,B) ) => m1_subset_1(k4_finseq_4(A,B,C,D),B) ) ), file(finseq_4,k4_finseq_4), []). fof(dt_k4_tarski,axiom,( $true ), file(tarski,k4_tarski), []). 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_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_funct_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,A) ) => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ), file(funct_2,k8_funct_2), []). fof(dt_k8_polynom1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v7_seqm_3(A) ) => m2_subset_1(k8_polynom1(A,B),k1_numbers,k5_numbers) ) ), file(polynom1,k8_polynom1), []). fof(dt_k9_polynom1,axiom,( ! [A,B,C] : ( ( v1_seq_1(B) & m1_pboole(B,A) & v1_seq_1(C) & m1_pboole(C,A) ) => m1_pboole(k9_polynom1(A,B,C),A) ) ), file(polynom1,k9_polynom1), []). fof(dt_l1_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => l1_struct_0(A) ) ), file(orders_2,l1_orders_2), []). fof(dt_l1_struct_0,axiom,( $true ), file(struct_0,l1_struct_0), []). fof(dt_m1_finseq_1,axiom,( ! [A,B] : ( m1_finseq_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) ) ), file(finseq_1,m1_finseq_1), []). fof(dt_m1_pboole,axiom,( ! [A,B] : ( m1_pboole(B,A) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ), file(pboole,m1_pboole), []). fof(dt_m1_polynom1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k14_polynom1(A))) ) => ! [C] : ( m1_polynom1(C,A,B) => ( v7_seqm_3(C) & v1_polynom1(C) & m1_pboole(C,A) ) ) ) ), file(polynom1,m1_polynom1), []). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), []). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), []). fof(dt_m2_finseq_1,axiom,( ! [A,B] : ( m2_finseq_1(B,A) => ( v1_funct_1(B) & v1_finseq_1(B) & m2_relset_1(B,k5_numbers,A) ) ) ), file(finseq_1,m2_finseq_1), []). fof(dt_m2_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_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => m2_relset_1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)) ) ), file(orders_2,u1_orders_2), []). fof(dt_u1_struct_0,axiom,( $true ), file(struct_0,u1_struct_0), []). fof(existence_l1_orders_2,axiom,( ? [A] : l1_orders_2(A) ), file(orders_2,l1_orders_2), []). fof(existence_l1_struct_0,axiom,( ? [A] : l1_struct_0(A) ), file(struct_0,l1_struct_0), []). fof(existence_m1_finseq_1,axiom,( ! [A] : ? [B] : m1_finseq_1(B,A) ), file(finseq_1,m1_finseq_1), []). fof(existence_m1_pboole,axiom,( ! [A] : ? [B] : m1_pboole(B,A) ), file(pboole,m1_pboole), []). fof(existence_m1_polynom1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k14_polynom1(A))) ) => ? [C] : m1_polynom1(C,A,B) ) ), file(polynom1,m1_polynom1), []). fof(existence_m1_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), []). fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), []). fof(existence_m2_finseq_1,axiom,( ! [A] : ? [B] : m2_finseq_1(B,A) ), file(finseq_1,m2_finseq_1), []). fof(existence_m2_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_dickson,axiom, ( ~ v3_struct_0(k11_dickson) & v16_waybel_0(k11_dickson) ), file(dickson,fc10_dickson), []). 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_dickson,axiom, ( ~ v3_struct_0(k11_dickson) & v4_dickson(k11_dickson) ), file(dickson,fc11_dickson), []). fof(fc11_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_finset_1(A) ) => v1_finset_1(k2_relat_1(A)) ) ), file(finseq_1,fc11_finseq_1), []). fof(fc11_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_dickson,axiom, ( ~ v3_struct_0(k11_dickson) & v3_dickson(k11_dickson) ), file(dickson,fc12_dickson), []). fof(fc12_relat_1,axiom, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) ), file(relat_1,fc12_relat_1), []). fof(fc12_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & ~ v2_xreal_0(k2_xcmplx_0(B,A)) & v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc12_xreal_0), []). fof(fc13_dickson,axiom, ( ~ v3_struct_0(k11_dickson) & v4_orders_2(k11_dickson) ), file(dickson,fc13_dickson), []). fof(fc13_relat_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v3_relat_1(A) ) => ( v1_relat_1(k7_relat_1(A,B)) & v3_relat_1(k7_relat_1(A,B)) ) ) ), file(relat_1,fc13_relat_1), []). fof(fc14_dickson,axiom, ( ~ v3_struct_0(k11_dickson) & v3_orders_2(k11_dickson) ), file(dickson,fc14_dickson), []). 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(fc14_polynom1,axiom, ( 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_xboole_0(k1_xboole_0) & v1_finset_1(k1_xboole_0) & v1_finseq_1(k1_xboole_0) & v1_funcop_1(k1_xboole_0) & v1_membered(k1_xboole_0) & v2_membered(k1_xboole_0) & v3_membered(k1_xboole_0) & v4_membered(k1_xboole_0) & v5_membered(k1_xboole_0) & v1_seq_1(k1_xboole_0) & v1_matrlin(k1_xboole_0) & v7_seqm_3(k1_xboole_0) ), file(polynom1,fc14_polynom1), []). fof(fc15_dickson,axiom, ( ~ v3_struct_0(k11_dickson) & v1_wellfnd1(k11_dickson) ), file(dickson,fc15_dickson), []). 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(fc17_polynom1,axiom,( ! [A,B,C] : ( ( v1_seq_1(B) & m1_pboole(B,A) & v1_seq_1(C) & m1_pboole(C,A) ) => ( v1_relat_1(k9_polynom1(A,B,C)) & v1_funct_1(k9_polynom1(A,B,C)) & v1_seq_1(k9_polynom1(A,B,C)) ) ) ), file(polynom1,fc17_polynom1), []). fof(fc18_polynom1,axiom,( ! [A,B,C] : ( ( v7_seqm_3(B) & m1_pboole(B,A) & v7_seqm_3(C) & m1_pboole(C,A) ) => ( v1_relat_1(k9_polynom1(A,B,C)) & v1_funct_1(k9_polynom1(A,B,C)) & v1_seq_1(k9_polynom1(A,B,C)) & v7_seqm_3(k9_polynom1(A,B,C)) ) ) ), file(polynom1,fc18_polynom1), []). fof(fc1_bagorder,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v7_seqm_3(A) ) => ( v1_relat_1(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)) & v1_seq_1(k7_relat_1(A,B)) & v7_seqm_3(k7_relat_1(A,B)) ) ) ), file(bagorder,fc1_bagorder), []). 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_finsub_1,axiom,( ! [A] : ( ~ v1_xboole_0(k1_zfmisc_1(A)) & v1_finsub_1(k1_zfmisc_1(A)) & v3_finsub_1(k1_zfmisc_1(A)) & v4_finsub_1(k1_zfmisc_1(A)) ) ), file(finsub_1,fc1_finsub_1), []). 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_numbers,axiom,( ~ v1_xboole_0(k1_numbers) ), file(numbers,fc1_numbers), []). fof(fc1_orders_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_relset_1(B,A,A) ) => ( ~ v3_struct_0(g1_orders_2(A,B)) & v1_orders_2(g1_orders_2(A,B)) ) ) ), file(orders_2,fc1_orders_2), []). 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_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ), file(subset_1,fc1_subset_1), []). fof(fc20_polynom1,axiom, ( 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_xboole_0(k1_xboole_0) & v1_finset_1(k1_xboole_0) & v1_finseq_1(k1_xboole_0) & v1_funcop_1(k1_xboole_0) & v1_membered(k1_xboole_0) & v2_membered(k1_xboole_0) & v3_membered(k1_xboole_0) & v4_membered(k1_xboole_0) & v5_membered(k1_xboole_0) & v1_seq_1(k1_xboole_0) & v1_matrlin(k1_xboole_0) & v7_seqm_3(k1_xboole_0) & v1_polynom1(k1_xboole_0) ), file(polynom1,fc20_polynom1), []). fof(fc21_polynom1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_polynom1(A) ) => v1_finset_1(k11_polynom1(A)) ) ), file(polynom1,fc21_polynom1), []). fof(fc23_polynom1,axiom,( ! [A,B,C] : ( ( v7_seqm_3(B) & v1_polynom1(B) & m1_pboole(B,A) & v7_seqm_3(C) & v1_polynom1(C) & m1_pboole(C,A) ) => ( v1_relat_1(k9_polynom1(A,B,C)) & v1_funct_1(k9_polynom1(A,B,C)) & v1_seq_1(k9_polynom1(A,B,C)) & v7_seqm_3(k9_polynom1(A,B,C)) & v1_polynom1(k9_polynom1(A,B,C)) ) ) ), file(polynom1,fc23_polynom1), []). fof(fc25_polynom1,axiom,( ! [A] : ~ v1_xboole_0(k13_polynom1(A)) ), file(polynom1,fc25_polynom1), []). fof(fc2_bagorder,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_polynom1(A) ) => ( v1_relat_1(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)) & v1_polynom1(k7_relat_1(A,B)) ) ) ), file(bagorder,fc2_bagorder), []). fof(fc2_card_1,axiom,( ! [A] : ( v1_finset_1(A) => ( v1_ordinal1(k1_card_1(A)) & v2_ordinal1(k1_card_1(A)) & v3_ordinal1(k1_card_1(A)) & v1_finset_1(k1_card_1(A)) & v1_card_1(k1_card_1(A)) ) ) ), file(card_1,fc2_card_1), []). fof(fc2_finseq_1,axiom, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) & v1_funct_1(k1_xboole_0) & v2_funct_1(k1_xboole_0) & v1_finset_1(k1_xboole_0) & v1_finseq_1(k1_xboole_0) ), file(finseq_1,fc2_finseq_1), []). fof(fc2_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_orders_2,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ( v1_relat_1(u1_orders_2(A)) & v1_relat_2(u1_orders_2(A)) & v4_relat_2(u1_orders_2(A)) & v8_relat_2(u1_orders_2(A)) & v1_partfun1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)) ) ) ), file(orders_2,fc2_orders_2), []). fof(fc2_ordinal1,axiom, ( 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_xboole_0(k1_xboole_0) & v1_ordinal1(k1_xboole_0) & v2_ordinal1(k1_xboole_0) & v3_ordinal1(k1_xboole_0) ), file(ordinal1,fc2_ordinal1), []). fof(fc2_polynom1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(A)) & v1_partfun1(C,A,A) & v3_orders_1(C) & v1_relat_2(C) & v4_relat_2(C) & v8_relat_2(C) & m1_relset_1(C,A,A) ) => ( v1_relat_1(k2_triang_1(A,B,C)) & v1_funct_1(k2_triang_1(A,B,C)) & v2_funct_1(k2_triang_1(A,B,C)) & ~ v1_xboole_0(k2_triang_1(A,B,C)) & v1_finset_1(k2_triang_1(A,B,C)) & v1_finseq_1(k2_triang_1(A,B,C)) ) ) ), file(polynom1,fc2_polynom1), []). fof(fc2_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) ), file(subset_1,fc2_subset_1), []). 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_orders_2,axiom,( ! [A,B] : ( ( v1_relat_2(B) & v4_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) ) => ( v1_orders_2(g1_orders_2(A,B)) & v2_orders_2(g1_orders_2(A,B)) & v3_orders_2(g1_orders_2(A,B)) & v4_orders_2(g1_orders_2(A,B)) ) ) ), file(orders_2,fc3_orders_2), []). fof(fc3_polynom1,axiom, ( 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_xboole_0(k1_xboole_0) & v1_finset_1(k1_xboole_0) & v1_finseq_1(k1_xboole_0) & v1_funcop_1(k1_xboole_0) & v1_membered(k1_xboole_0) & v2_membered(k1_xboole_0) & v3_membered(k1_xboole_0) & v4_membered(k1_xboole_0) & v5_membered(k1_xboole_0) & v1_matrlin(k1_xboole_0) ), file(polynom1,fc3_polynom1), []). fof(fc3_subset_1,axiom,( ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ), file(subset_1,fc3_subset_1), []). fof(fc3_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc3_xreal_0), []). fof(fc4_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)) ) ) ), file(funct_1,fc4_funct_1), []). fof(fc4_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_relat_1,axiom, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) ), file(relat_1,fc4_relat_1), []). fof(fc4_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ), file(subset_1,fc4_subset_1), []). fof(fc5_polynom1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_matrlin(A) ) => ( v1_relat_1(k1_funct_1(A,B)) & v1_funct_1(k1_funct_1(A,B)) & v1_finset_1(k1_funct_1(A,B)) & v1_finseq_1(k1_funct_1(A,B)) ) ) ), file(polynom1,fc5_polynom1), []). fof(fc5_relat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) ) => ~ v1_xboole_0(k1_relat_1(A)) ) ), file(relat_1,fc5_relat_1), []). fof(fc6_relat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) ) => ~ v1_xboole_0(k2_relat_1(A)) ) ), file(relat_1,fc6_relat_1), []). fof(fc7_bagorder,axiom,( ! [A] : ( v3_ordinal1(A) => ( v1_relat_1(k4_bagorder(A)) & v1_partfun1(k4_bagorder(A),k14_polynom1(A),k14_polynom1(A)) & v1_relat_2(k4_bagorder(A)) & v4_relat_2(k4_bagorder(A)) & v8_relat_2(k4_bagorder(A)) & v2_bagorder(k4_bagorder(A),A) ) ) ), file(bagorder,fc7_bagorder), []). fof(fc7_relat_1,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_xboole_0(k1_relat_1(A)) & v1_relat_1(k1_relat_1(A)) ) ) ), file(relat_1,fc7_relat_1), []). fof(fc7_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc7_xreal_0), []). fof(fc8_polynom1,axiom,( ! [A,B] : ( ( m1_finseq_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => ( v1_relat_1(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)) & v1_card_3(k7_relat_1(A,B)) ) ) ), file(polynom1,fc8_polynom1), []). fof(fc8_relat_1,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_xboole_0(k2_relat_1(A)) & v1_relat_1(k2_relat_1(A)) ) ) ), file(relat_1,fc8_relat_1), []). fof(fc8_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v2_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc8_xreal_0), []). fof(fc9_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v2_xreal_0(k2_xcmplx_0(A,B)) & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc9_xreal_0), []). fof(fraenkel_a_0_2_dickson,axiom,( ! [A] : ( r2_hidden(A,a_0_2_dickson) <=> ? [B,C] : ( m2_subset_1(B,k1_numbers,k5_numbers) & m2_subset_1(C,k1_numbers,k5_numbers) & A = k1_domain_1(k5_numbers,k5_numbers,B,C) & r1_xreal_0(B,C) ) ) ), file(dickson,a_0_2_dickson), []). fof(free_g1_orders_2,axiom,( ! [A,B] : ( m1_relset_1(B,A,A) => ! [C,D] : ( g1_orders_2(A,B) = g1_orders_2(C,D) => ( A = C & B = D ) ) ) ), file(orders_2,g1_orders_2), []). fof(rc10_polynom1,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_seq_1(B) ) ), file(polynom1,rc10_polynom1), []). fof(rc11_polynom1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_seq_1(A) & v7_seqm_3(A) & v1_polynom1(A) ) ), file(polynom1,rc11_polynom1), []). fof(rc12_polynom1,axiom,( ! [A] : ? [B] : ( m1_relset_1(B,A,k5_numbers) & v1_relat_1(B) & v1_funct_1(B) & v1_funct_2(B,A,k5_numbers) & v1_seq_1(B) & v7_seqm_3(B) & v1_polynom1(B) ) ), file(polynom1,rc12_polynom1), []). fof(rc12_waybel_0,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v16_waybel_0(A) ) ), file(waybel_0,rc12_waybel_0), []). fof(rc13_polynom1,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_seq_1(B) & v7_seqm_3(B) & v1_polynom1(B) ) ), file(polynom1,rc13_polynom1), []). fof(rc1_bagorder,axiom,( ! [A] : ( v3_ordinal1(A) => ? [B] : ( m1_relset_1(B,k14_polynom1(A),k14_polynom1(A)) & v1_relat_1(B) & v1_partfun1(B,k14_polynom1(A),k14_polynom1(A)) & v1_relat_2(B) & v4_relat_2(B) & v8_relat_2(B) & v2_bagorder(B,A) ) ) ), file(bagorder,rc1_bagorder), []). fof(rc1_card_1,axiom,( ? [A] : v1_card_1(A) ), file(card_1,rc1_card_1), []). fof(rc1_card_5,axiom,( ? [A] : ~ v1_finset_1(A) ), file(card_5,rc1_card_5), []). 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_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc1_funct_1), []). fof(rc1_funct_2,axiom,( ! [A,B] : ? [C] : ( m1_relset_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C) & v1_funct_2(C,A,B) ) ), file(funct_2,rc1_funct_2), []). 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_orders_2,axiom,( ? [A] : ( l1_orders_2(A) & v1_orders_2(A) ) ), file(orders_2,rc1_orders_2), []). fof(rc1_ordinal1,axiom,( ? [A] : ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) ) ), file(ordinal1,rc1_ordinal1), []). fof(rc1_polynom1,axiom,( ! [A] : ? [B] : ( m1_relset_1(B,A,A) & v1_relat_1(B) & v1_partfun1(B,A,A) & v3_orders_1(B) & v2_wellord1(B) & v1_relat_2(B) & v4_relat_2(B) & v8_relat_2(B) ) ), file(polynom1,rc1_polynom1), []). fof(rc1_relat_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) ) ), file(relat_1,rc1_relat_1), []). fof(rc1_subset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) ) ) ), file(subset_1,rc1_subset_1), []). fof(rc1_xreal_0,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(xreal_0,rc1_xreal_0), []). fof(rc2_card_1,axiom,( ? [A] : ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v1_finset_1(A) & v1_card_1(A) ) ), file(card_1,rc2_card_1), []). fof(rc2_card_5,axiom,( ? [A] : ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & ~ v1_finset_1(A) & v1_card_1(A) ) ), file(card_5,rc2_card_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_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_funct_2,axiom,( ! [A] : ? [B] : ( m1_relset_1(B,A,A) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_funct_2(B,A,A) & v2_funct_2(B,A,A) & v3_funct_2(B,A,A) ) ), file(funct_2,rc2_funct_2), []). 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_orders_2,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v1_orders_2(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) ) ), file(orders_2,rc2_orders_2), []). fof(rc2_ordinal1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) ) ), file(ordinal1,rc2_ordinal1), []). fof(rc2_polynom1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_funcop_1(A) & v1_matrlin(A) ) ), file(polynom1,rc2_polynom1), []). fof(rc2_relat_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) ) ), file(relat_1,rc2_relat_1), []). fof(rc2_subset_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) ) ), file(subset_1,rc2_subset_1), []). fof(rc2_xreal_0,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc2_xreal_0), []). fof(rc3_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_ordinal1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) ) ), file(ordinal1,rc3_ordinal1), []). fof(rc3_polynom1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_card_3(A) ) ), file(polynom1,rc3_polynom1), []). fof(rc3_relat_1,axiom,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) ) ), file(relat_1,rc3_relat_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_finseq_1,axiom,( ! [A] : ? [B] : ( m1_finseq_1(B,A) & v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc4_finseq_1), []). fof(rc4_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc4_finset_1), []). fof(rc4_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc4_funct_1), []). fof(rc4_polynom1,axiom,( ? [A] : ( m1_finseq_1(A,k5_numbers) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_card_3(A) ) ), file(polynom1,rc4_polynom1), []). 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_struct_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) ) ) ), file(struct_0,rc5_struct_0), []). fof(rc6_finseq_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc6_finseq_1), []). fof(rc7_finseq_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc7_finseq_1), []). fof(rc7_polynom1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) & v7_seqm_3(A) ) ), file(polynom1,rc7_polynom1), []). 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(rc8_polynom1,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_seq_1(B) & v7_seqm_3(B) ) ), file(polynom1,rc8_polynom1), []). fof(rc9_polynom1,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_seq_1(B) ) ), file(polynom1,rc9_polynom1), []). fof(redefinition_k14_polynom1,axiom,( ! [A] : k14_polynom1(A) = k13_polynom1(A) ), file(polynom1,k14_polynom1), []). fof(redefinition_k1_domain_1,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(C,A) & m1_subset_1(D,B) ) => k1_domain_1(A,B,C,D) = k4_tarski(C,D) ) ), file(domain_1,k1_domain_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_polynom2,axiom,( ! [A,B] : ( ( v7_seqm_3(B) & v1_polynom1(B) & m1_pboole(B,A) ) => k1_polynom2(A,B) = k11_polynom1(B) ) ), file(polynom2,k1_polynom2), []). fof(redefinition_k1_yellow_1,axiom,( ! [A] : k1_yellow_1(A) = k1_wellord2(A) ), file(yellow_1,k1_yellow_1), []). fof(redefinition_k3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k3_finseq_1(A) = k1_card_1(A) ) ), file(finseq_1,k3_finseq_1), []). fof(redefinition_k4_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k4_finseq_1(A) = k1_relat_1(A) ) ), file(finseq_1,k4_finseq_1), []). fof(redefinition_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_k8_funct_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,A) ) => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ), file(funct_2,k8_funct_2), []). fof(redefinition_k8_polynom1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v7_seqm_3(A) ) => k8_polynom1(A,B) = k1_funct_1(A,B) ) ), file(polynom1,k8_polynom1), []). fof(redefinition_m1_polynom1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k14_polynom1(A))) ) => ! [C] : ( m1_polynom1(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(polynom1,m1_polynom1), []). fof(redefinition_m2_finseq_1,axiom,( ! [A,B] : ( m2_finseq_1(B,A) <=> m1_finseq_1(B,A) ) ), file(finseq_1,m2_finseq_1), []). fof(redefinition_m2_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_r6_pboole,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => ( r6_pboole(A,B,C) <=> B = C ) ) ), file(pboole,r6_pboole), []). fof(reflexivity_r1_tarski,axiom,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), []). fof(reflexivity_r1_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => r1_xreal_0(A,A) ) ), file(xreal_0,r1_xreal_0), []). fof(reflexivity_r6_pboole,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => r6_pboole(A,B,B) ) ), file(pboole,r6_pboole), []). fof(s1_nat_1__e3_42_1_1_3__bagorder,axiom,( ! [A,B,C] : ( ( v3_ordinal1(A) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(g1_orders_2(k14_polynom1(A),k4_bagorder(A)))) & m2_relset_1(B,k5_numbers,u1_struct_0(g1_orders_2(k14_polynom1(A),k4_bagorder(A)))) & v3_ordinal1(C) ) => ( ( ! [D] : ( v3_ordinal1(D) => ! [E] : ( ( v7_seqm_3(E) & v1_polynom1(E) & m1_pboole(E,A) ) => ( ( r2_hidden(C,D) & r2_hidden(D,A) & k8_funct_2(k5_numbers,u1_struct_0(g1_orders_2(k14_polynom1(A),k4_bagorder(A))),B,0) = E ) => k8_polynom1(E,D) = 0 ) ) ) & ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ( ! [G] : ( v3_ordinal1(G) => ! [H] : ( ( v7_seqm_3(H) & v1_polynom1(H) & m1_pboole(H,A) ) => ( ( r2_hidden(C,G) & r2_hidden(G,A) & k8_funct_2(k5_numbers,u1_struct_0(g1_orders_2(k14_polynom1(A),k4_bagorder(A))),B,F) = H ) => k8_polynom1(H,G) = 0 ) ) ) => ! [I] : ( v3_ordinal1(I) => ! [J] : ( ( v7_seqm_3(J) & v1_polynom1(J) & m1_pboole(J,A) ) => ( ( r2_hidden(C,I) & r2_hidden(I,A) & k8_funct_2(k5_numbers,u1_struct_0(g1_orders_2(k14_polynom1(A),k4_bagorder(A))),B,k1_nat_1(F,1)) = J ) => k8_polynom1(J,I) = 0 ) ) ) ) ) ) => ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ! [K] : ( v3_ordinal1(K) => ! [L] : ( ( v7_seqm_3(L) & v1_polynom1(L) & m1_pboole(L,A) ) => ( ( r2_hidden(C,K) & r2_hidden(K,A) & k8_funct_2(k5_numbers,u1_struct_0(g1_orders_2(k14_polynom1(A),k4_bagorder(A))),B,F) = L ) => k8_polynom1(L,K) = 0 ) ) ) ) ) ) ), file(bagorder,s1_nat_1__e3_42_1_1_3__bagorder), []). fof(s2_ordinal1__e2_42__bagorder,axiom, ( ! [A] : ( v3_ordinal1(A) => ( ! [B] : ( v3_ordinal1(B) => ( r2_hidden(B,A) => v2_wellord1(k4_bagorder(B)) ) ) => v2_wellord1(k4_bagorder(A)) ) ) => ! [A] : ( v3_ordinal1(A) => v2_wellord1(k4_bagorder(A)) ) ), file(bagorder,s2_ordinal1__e2_42__bagorder), []). fof(s3_funct_2__e18_42_1_1__bagorder,axiom,( ! [A,B,C] : ( ( v3_ordinal1(A) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(g1_orders_2(k14_polynom1(A),k4_bagorder(A)))) & m2_relset_1(B,k5_numbers,u1_struct_0(g1_orders_2(k14_polynom1(A),k4_bagorder(A)))) & v3_ordinal1(C) ) => ( ! [D] : ( m1_subset_1(D,k5_numbers) => ? [E] : ( m1_subset_1(E,k5_numbers) & ? [F] : ( v7_seqm_3(F) & v1_polynom1(F) & m1_pboole(F,A) & k1_funct_1(B,D) = F & E = k8_polynom1(F,C) ) ) ) => ? [D] : ( v1_funct_1(D) & v1_funct_2(D,k5_numbers,k5_numbers) & m2_relset_1(D,k5_numbers,k5_numbers) & ! [E] : ( m1_subset_1(E,k5_numbers) => ? [G] : ( v7_seqm_3(G) & v1_polynom1(G) & m1_pboole(G,A) & k1_funct_1(B,E) = G & k8_funct_2(k5_numbers,k5_numbers,D,E) = k8_polynom1(G,C) ) ) ) ) ) ), file(bagorder,s3_funct_2__e18_42_1_1__bagorder), []). fof(s3_funct_2__e29_42_1_1__bagorder,axiom,( ! [A,B,C,D] : ( ( v3_ordinal1(A) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(g1_orders_2(k14_polynom1(A),k4_bagorder(A)))) & m2_relset_1(B,k5_numbers,u1_struct_0(g1_orders_2(k14_polynom1(A),k4_bagorder(A)))) & v3_ordinal1(C) & m2_subset_1(D,k1_numbers,k5_numbers) ) => ( ! [E] : ( m1_subset_1(E,k5_numbers) => ? [F] : ( m1_subset_1(F,k14_polynom1(C)) & ? [G] : ( v7_seqm_3(G) & v1_polynom1(G) & m1_pboole(G,A) & G = k8_funct_2(k5_numbers,u1_struct_0(g1_orders_2(k14_polynom1(A),k4_bagorder(A))),B,k1_nat_1(D,E)) & F = k7_relat_1(G,C) ) ) ) => ? [E] : ( v1_funct_1(E) & v1_funct_2(E,k5_numbers,k14_polynom1(C)) & m2_relset_1(E,k5_numbers,k14_polynom1(C)) & ! [F] : ( m1_subset_1(F,k5_numbers) => ? [H] : ( v7_seqm_3(H) & v1_polynom1(H) & m1_pboole(H,A) & H = k8_funct_2(k5_numbers,u1_struct_0(g1_orders_2(k14_polynom1(A),k4_bagorder(A))),B,k1_nat_1(D,F)) & k8_funct_2(k5_numbers,k14_polynom1(C),E,F) = k7_relat_1(H,C) ) ) ) ) ) ), file(bagorder,s3_funct_2__e29_42_1_1__bagorder), []). 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_r6_pboole,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => ( r6_pboole(A,B,C) => r6_pboole(A,C,B) ) ) ), file(pboole,r6_pboole), []). fof(t107_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ( v2_wellord1(A) => ( v1_orders_1(A) & v2_orders_1(A) & v3_orders_1(A) ) ) ) ), file(orders_1,t107_orders_1), []). fof(t11_bagorder,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & m2_relset_1(B,k5_numbers,u1_struct_0(A)) ) => ~ ( v1_wellfnd1(A) & v1_bagorder(B,A) & ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ? [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) & r1_xreal_0(C,D) & k8_funct_2(k5_numbers,u1_struct_0(A),B,C) != k8_funct_2(k5_numbers,u1_struct_0(A),B,D) ) ) ) ) ) ), file(bagorder,t11_bagorder), []). fof(t11_finseq_2,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ~ ( r2_hidden(A,k2_relat_1(B)) & ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ~ ( r2_hidden(C,k4_finseq_1(B)) & k1_funct_1(B,C) = A ) ) ) ) ), file(finseq_2,t11_finseq_2), []). fof(t12_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r2_hidden(A,k1_relat_1(B)) => r2_hidden(k1_funct_1(B,A),k2_relat_1(B)) ) ) ), file(funct_1,t12_funct_1), []). fof(t133_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ( v3_orders_1(A) => r3_orders_1(A,k3_relat_1(A)) ) ) ), file(orders_1,t133_orders_1), []). fof(t134_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B,C] : ( ( r3_orders_1(A,B) & r1_tarski(C,B) ) => r3_orders_1(A,C) ) ) ), file(orders_1,t134_orders_1), []). fof(t15_wellfnd1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ( v1_wellfnd1(A) <=> ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & m2_relset_1(B,k5_numbers,u1_struct_0(A)) ) => ~ v3_wellfnd1(B,A) ) ) ) ), file(wellfnd1,t15_wellfnd1), []). fof(t19_ordinal1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v1_ordinal1(C) => ( ( r2_hidden(C,A) & r2_hidden(A,B) ) => r2_hidden(C,B) ) ) ) ) ), file(ordinal1,t19_ordinal1), []). fof(t1_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(A,0) = A ) ), file(arithm,t1_arithm), []). fof(t1_numerals,axiom,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), []). fof(t1_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & v2_xreal_0(A) ) => v2_xreal_0(B) ) ) ) ), file(real,t1_real), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t20_bagorder,axiom,( ! [A,B] : ( ( v7_seqm_3(B) & v1_polynom1(B) & m1_pboole(B,A) ) => ( k1_polynom2(A,B) = k1_xboole_0 => r6_pboole(A,B,k16_polynom1(A)) ) ) ), file(bagorder,t20_bagorder), []). fof(t21_bagorder,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( ( v7_seqm_3(C) & v1_polynom1(C) & m1_pboole(C,A) ) => ( r2_hidden(B,A) => ( v7_seqm_3(k7_relat_1(C,B)) & v1_polynom1(k7_relat_1(C,B)) & m1_pboole(k7_relat_1(C,B),B) ) ) ) ) ) ), file(bagorder,t21_bagorder), []). fof(t23_ordinal1,axiom,( ! [A,B] : ( v3_ordinal1(B) => ( r2_hidden(A,B) => v3_ordinal1(A) ) ) ), file(ordinal1,t23_ordinal1), []). fof(t24_ordinal1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ~ ( ~ r2_hidden(A,B) & A != B & ~ r2_hidden(B,A) ) ) ) ), file(ordinal1,t24_ordinal1), []). fof(t27_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v4_ordinal2(B) => ( r2_hidden(B,k4_finseq_1(A)) <=> ( r1_xreal_0(1,B) & r1_xreal_0(B,k3_finseq_1(A)) ) ) ) ) ), file(finseq_3,t27_finseq_3), []). fof(t29_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => r1_xreal_0(A,k2_xcmplx_0(A,B)) ) ) ), file(nat_1,t29_nat_1), []). fof(t2_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & v3_xreal_0(B) ) => v3_xreal_0(A) ) ) ) ), file(real,t2_real), []). fof(t2_subset,axiom,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), []). fof(t2_tarski,axiom,( ! [A,B] : ( ! [C] : ( r2_hidden(C,A) <=> r2_hidden(C,B) ) => A = B ) ), file(tarski,t2_tarski), []). fof(t3_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xreal_0(A,B) & ~ v3_xreal_0(A) & v3_xreal_0(B) ) ) ) ), file(real,t3_real), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t4_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xreal_0(A,B) & ~ v2_xreal_0(B) & v2_xreal_0(A) ) ) ) ), file(real,t4_real), []). fof(t4_subset,axiom,( ! [A,B,C] : ( ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) ) => m1_subset_1(A,C) ) ), file(subset,t4_subset), []). fof(t56_polynom1,axiom,( ! [A,B] : k8_polynom1(k16_polynom1(A),B) = 0 ), file(polynom1,t56_polynom1), []). fof(t5_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) => ( v1_xboole_0(B) | v3_xreal_0(A) | v2_xreal_0(B) ) ) ) ) ), file(real,t5_real), []). fof(t5_subset,axiom,( ! [A,B,C] : ~ ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C) ) ), file(subset,t5_subset), []). fof(t5_wellord1,axiom,( ! [A] : ( v1_relat_1(A) => ( v1_wellord1(A) <=> r1_wellord1(A,k3_relat_1(A)) ) ) ), file(wellord1,t5_wellord1), []). fof(t60_relat_1,axiom, ( k1_relat_1(k1_xboole_0) = k1_xboole_0 & k2_relat_1(k1_xboole_0) = k1_xboole_0 ), file(relat_1,t60_relat_1), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t6_finseq_5,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( r2_hidden(1,k4_finseq_1(A)) & r2_hidden(k3_finseq_1(A),k4_finseq_1(A)) ) ) ), file(finseq_5,t6_finseq_5), []). fof(t6_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) => ( v1_xboole_0(A) | v2_xreal_0(B) | v3_xreal_0(A) ) ) ) ) ), file(real,t6_real), []). fof(t72_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(t7_ordinal1,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & r1_tarski(B,A) ) ), file(ordinal1,t7_ordinal1), []). fof(t7_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v2_xreal_0(A) & ~ v3_xreal_0(B) ) ) ) ), file(real,t7_real), []). fof(t7_wellord2,axiom,( ! [A] : ( v3_ordinal1(A) => v2_wellord1(k1_wellord2(A)) ) ), file(wellord2,t7_wellord2), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t8_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v3_xreal_0(B) & ~ v2_xreal_0(A) ) ) ) ), file(real,t8_real), []). fof(t8_wellord1,axiom,( ! [A] : ( v1_relat_1(A) => ( r2_wellord1(A,k3_relat_1(A)) <=> v2_wellord1(A) ) ) ), file(wellord1,t8_wellord1), []). fof(t92_orders_1,axiom,( ! [A,B] : ( v1_relat_1(B) => ( r7_relat_2(B,A) <=> ( r1_relat_2(B,A) & r6_relat_2(B,A) ) ) ) ), file(orders_1,t92_orders_1), []). fof(t97_orders_1,axiom,( ! [A,B] : ( ( v1_partfun1(B,A,A) & m2_relset_1(B,A,A) ) => k3_relat_1(B) = A ) ), file(orders_1,t97_orders_1), []). fof(t9_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( 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) ) ) => A = B ) ) ) ), file(funct_1,t9_funct_1), []). fof(t9_partit_2,axiom,( ! [A,B] : ( m2_relset_1(B,A,A) => ( r1_relat_2(B,A) => A = k3_relat_1(B) ) ) ), file(partit_2,t9_partit_2), []).