% Mizar problem: t12_polynom6,polynom6,1121,36 fof(t12_polynom6,conjecture,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( m1_polynom1(C,A,k14_polynom1(A)) => ! [D] : ( m1_polynom1(D,B,k14_polynom1(B)) => ! [E] : ( m2_finseq_1(E,k3_finseq_2(k14_polynom1(k14_ordinal2(A,B)))) => ( ( k4_finseq_1(E) = k4_finseq_1(k20_polynom1(A,C)) & ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ~ ( r2_hidden(F,k4_finseq_1(k20_polynom1(A,C))) & ! [G] : ( m1_polynom1(G,A,k14_polynom1(A)) => ! [H] : ( m2_finseq_1(H,k14_polynom1(k14_ordinal2(A,B))) => ~ ( H = k1_matrlin(k14_polynom1(k14_ordinal2(A,B)),k5_numbers,k3_finseq_2(k14_polynom1(k14_ordinal2(A,B))),E,F) & k4_finseq_4(k5_numbers,k13_polynom1(A),k20_polynom1(A,C),F) = G & k3_finseq_1(H) = k3_finseq_1(k20_polynom1(B,D)) & ! [I] : ( m2_subset_1(I,k1_numbers,k5_numbers) => ~ ( r2_hidden(I,k4_finseq_1(H)) & ! [J] : ( m1_polynom1(J,B,k14_polynom1(B)) => ~ ( k4_finseq_4(k5_numbers,k13_polynom1(B),k20_polynom1(B,D),I) = J & k4_finseq_4(k5_numbers,k14_polynom1(k14_ordinal2(A,B)),H,I) = k1_polynom6(A,B,G,J) ) ) ) ) ) ) ) ) ) ) => k20_polynom1(k14_ordinal2(A,B),k1_polynom6(A,B,C,D)) = k15_dtconstr(k14_polynom1(k14_ordinal2(A,B)),E) ) ) ) ) ) ) ), inference(mizar_bg_added,[status(thm)],[antisymmetry_r1_polynom1,antisymmetry_r2_hidden,cc1_arytm_3,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_gobrd13,cc1_polynom1,cc1_relset_1,cc1_xreal_0,cc2_arytm_3,cc2_finset_1,cc2_funct_1,cc2_gobrd13,cc2_xreal_0,cc3_arytm_3,cc3_polynom1,cc3_xreal_0,cc4_xreal_0,cc5_polynom1,cc5_xreal_0,cc6_polynom1,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,commutativity_k1_nat_1,commutativity_k2_tarski,commutativity_k2_xcmplx_0,commutativity_k9_binop_2,connectedness_r1_xreal_0,d12_polynom1,d14_polynom1,d16_polynom1,d18_polynom1,d2_triang_1,d3_finseq_1,d4_finseq_1,d4_finseq_4,d5_funct_1,d5_tarski,d8_funct_1,dt_k12_finseq_1,dt_k13_binarith,dt_k13_finseq_1,dt_k13_polynom1,dt_k14_ordinal2,dt_k14_polynom1,dt_k15_dtconstr,dt_k15_rvsum_1,dt_k16_finseq_1,dt_k17_polynom1,dt_k1_card_1,dt_k1_card_3,dt_k1_finseq_1,dt_k1_funct_1,dt_k1_matrlin,dt_k1_nat_1,dt_k1_numbers,dt_k1_polynom3,dt_k1_polynom6,dt_k1_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k20_polynom1,dt_k2_finseq_1,dt_k2_finseq_3,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_finseq_2,dt_k3_lang1,dt_k3_matrlin,dt_k3_relat_1,dt_k4_card_1,dt_k4_finseq_1,dt_k4_finseq_2,dt_k4_finseq_4,dt_k4_tarski,dt_k4_wsierp_1,dt_k5_binarith,dt_k5_finseq_1,dt_k5_numbers,dt_k5_ordinal2,dt_k5_polynom1,dt_k6_xcmplx_0,dt_k7_finseq_1,dt_k8_finseq_1,dt_k9_binop_2,dt_k9_finseq_1,dt_k9_wsierp_1,dt_m1_finseq_1,dt_m1_finseq_2,dt_m1_matrix_1,dt_m1_pboole,dt_m1_polynom1,dt_m1_relset_1,dt_m1_subset_1,dt_m1_trees_4,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_relset_1,dt_m2_subset_1,existence_m1_finseq_1,existence_m1_finseq_2,existence_m1_matrix_1,existence_m1_pboole,existence_m1_polynom1,existence_m1_relset_1,existence_m1_subset_1,existence_m1_trees_4,existence_m2_finseq_1,existence_m2_finseq_2,existence_m2_relset_1,existence_m2_subset_1,fc10_xreal_0,fc11_finseq_1,fc11_polynom1,fc11_xreal_0,fc12_finseq_1,fc12_polynom1,fc12_xreal_0,fc13_finseq_1,fc13_polynom1,fc14_finseq_1,fc14_finset_1,fc14_polynom1,fc15_finseq_1,fc15_xreal_0,fc16_finseq_1,fc16_xreal_0,fc17_finseq_1,fc17_xreal_0,fc18_xreal_0,fc19_xreal_0,fc1_finseq_1,fc1_finseq_2,fc1_finset_1,fc1_ordinal2,fc1_polynom6,fc20_polynom1,fc20_xreal_0,fc25_polynom1,fc26_polynom1,fc29_polynom1,fc2_finseq_1,fc2_finset_1,fc2_polynom1,fc2_polynom6,fc3_arytm_3,fc3_finseq_1,fc3_polynom1,fc3_xreal_0,fc4_finseq_1,fc5_polynom1,fc5_xreal_0,fc6_polynom1,fc7_funcop_1,fc7_polynom1,fc7_xreal_0,fc8_xreal_0,fc9_finseq_1,fc9_polynom1,fc9_xreal_0,rc10_polynom1,rc11_polynom1,rc13_polynom1,rc1_arytm_3,rc1_finseq_1,rc1_finseq_2,rc1_finset_1,rc1_funcop_1,rc1_funct_1,rc1_xreal_0,rc2_finseq_1,rc2_finset_1,rc2_funct_1,rc2_polynom1,rc2_xreal_0,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc3_polynom1,rc3_xreal_0,rc4_finseq_1,rc4_finset_1,rc4_funct_1,rc4_polynom1,rc4_xreal_0,rc6_finseq_1,rc7_finseq_1,rc7_polynom1,rc8_finseq_1,rc8_polynom1,rc9_polynom1,redefinition_k12_finseq_1,redefinition_k13_binarith,redefinition_k14_polynom1,redefinition_k1_matrlin,redefinition_k1_nat_1,redefinition_k1_polynom3,redefinition_k2_finseq_1,redefinition_k3_finseq_1,redefinition_k3_finseq_2,redefinition_k3_lang1,redefinition_k3_matrlin,redefinition_k4_card_1,redefinition_k4_finseq_1,redefinition_k4_wsierp_1,redefinition_k5_numbers,redefinition_k5_polynom1,redefinition_k8_finseq_1,redefinition_k9_binop_2,redefinition_k9_finseq_1,redefinition_k9_wsierp_1,redefinition_m1_polynom1,redefinition_m1_trees_4,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_relset_1,redefinition_m2_subset_1,redefinition_r6_pboole,reflexivity_r1_tarski,reflexivity_r1_xreal_0,reflexivity_r2_polynom1,reflexivity_r3_polynom1,reflexivity_r6_pboole,spc0_boole,spc1_boole,spc1_numerals,symmetry_r6_pboole,t100_orders_1,t104_rvsum_1,t10_polynom6,t11_polynom6,t12_funct_1,t12_jordan3,t12_polynom1,t133_orders_1,t134_orders_1,t13_dtconstr,t13_polynom1,t14_scmfsa_7,t16_polynom3,t18_polynom3,t19_polynom3,t1_numerals,t1_real,t1_subset,t1_xreal_1,t21_xreal_1,t25_finseq_1,t27_finseq_3,t29_nat_1,t2_real,t2_subset,t2_xreal_1,t31_finseq_3,t31_xreal_1,t32_polynom1,t33_polynom1,t3_real,t3_subset,t48_finseq_1,t4_polyalg1,t4_real,t4_subset,t50_binarith,t53_binarith,t5_real,t5_subset,t64_relat_1,t6_boole,t6_finseq_5,t6_polynom6,t6_real,t7_boole,t7_polynom6,t7_real,t8_boole,t8_real,t8_xreal_1,t9_polynom6]), [file(polynom6,t12_polynom6)]). fof(antisymmetry_r1_polynom1,axiom,( ! [A,B,C] : ( ( v3_ordinal1(A) & v7_seqm_3(B) & v1_polynom1(B) & m1_pboole(B,A) & v7_seqm_3(C) & v1_polynom1(C) & m1_pboole(C,A) ) => ( r1_polynom1(A,B,C) => ~ r1_polynom1(A,C,B) ) ) ), file(polynom1,r1_polynom1), []). 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_finset_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_finset_1(A) ) ), file(finset_1,cc1_finset_1), []). fof(cc1_funct_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_funct_1(A) ) ), file(funct_1,cc1_funct_1), []). fof(cc1_gobrd13,axiom,( ! [A,B] : ( m1_finseq_1(B,k3_finseq_2(A)) => v1_matrlin(B) ) ), file(gobrd13,cc1_gobrd13), []). fof(cc1_polynom1,axiom,( ! [A] : ( m1_finseq_1(A,k5_numbers) => v1_card_3(A) ) ), file(polynom1,cc1_polynom1), []). 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_arytm_3,axiom,( ! [A] : ( ( v1_xboole_0(A) & v3_ordinal1(A) ) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ) ), file(arytm_3,cc2_arytm_3), []). fof(cc2_finset_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_finset_1(B) ) ) ), file(finset_1,cc2_finset_1), []). fof(cc2_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ) ), file(funct_1,cc2_funct_1), []). fof(cc2_gobrd13,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_matrlin(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) ) ), file(gobrd13,cc2_gobrd13), []). fof(cc2_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xcmplx_0(A) ) ), file(xreal_0,cc2_xreal_0), []). fof(cc3_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_ordinal2) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ) ), file(arytm_3,cc3_arytm_3), []). fof(cc3_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_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_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_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_binop_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k9_binop_2(A,B) = k9_binop_2(B,A) ) ), file(binop_2,k9_binop_2), []). 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_polynom1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( v7_seqm_3(B) & v1_polynom1(B) & m1_pboole(B,A) ) => ! [C] : ( ( v7_seqm_3(C) & v1_polynom1(C) & m1_pboole(C,A) ) => ( r2_polynom1(A,B,C) <=> ( r1_polynom1(A,B,C) | r6_pboole(A,B,C) ) ) ) ) ) ), file(polynom1,d12_polynom1), []). 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(d16_polynom1,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 = k17_polynom1(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) <=> r2_polynom1(A,C,D) ) ) ) ) ) ) ), file(polynom1,d16_polynom1), []). fof(d18_polynom1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( v7_seqm_3(B) & v1_polynom1(B) & m1_pboole(B,A) ) => ! [C] : ( m1_trees_4(C,k13_polynom1(A),k14_polynom1(A)) => ( C = k20_polynom1(A,B) <=> ? [D] : ( ~ v1_xboole_0(D) & v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(k14_polynom1(A))) & C = k2_triang_1(k14_polynom1(A),D,k17_polynom1(A)) & ! [E] : ( ( v7_seqm_3(E) & v1_polynom1(E) & m1_pboole(E,A) ) => ( r2_hidden(E,D) <=> r3_polynom1(A,E,B) ) ) ) ) ) ) ) ), file(polynom1,d18_polynom1), []). 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(d3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( B = k3_finseq_1(A) <=> k2_finseq_1(B) = k1_relat_1(A) ) ) ) ), file(finseq_1,d3_finseq_1), []). fof(d4_finseq_1,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( m1_finseq_1(B,A) <=> r1_tarski(k2_relat_1(B),A) ) ) ), file(finseq_1,d4_finseq_1), []). fof(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_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( B = k2_relat_1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( r2_hidden(D,k1_relat_1(A)) & C = k1_funct_1(A,D) ) ) ) ) ), file(funct_1,d5_funct_1), []). fof(d5_tarski,axiom,( ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ), file(tarski,d5_tarski), []). fof(d8_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v2_funct_1(A) <=> ! [B,C] : ( ( r2_hidden(B,k1_relat_1(A)) & r2_hidden(C,k1_relat_1(A)) & k1_funct_1(A,B) = k1_funct_1(A,C) ) => B = C ) ) ) ), file(funct_1,d8_funct_1), []). fof(dt_k12_finseq_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m2_finseq_1(k12_finseq_1(A,B),A) ) ), file(finseq_1,k12_finseq_1), []). fof(dt_k13_binarith,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m2_finseq_2(k13_binarith(A,B),A,k4_finseq_2(1,A)) ) ), file(binarith,k13_binarith), []). fof(dt_k13_finseq_1,axiom,( $true ), file(finseq_1,k13_finseq_1), []). fof(dt_k13_polynom1,axiom,( $true ), file(polynom1,k13_polynom1), []). fof(dt_k14_ordinal2,axiom,( ! [A,B] : ( ( v3_ordinal1(A) & v3_ordinal1(B) ) => v3_ordinal1(k14_ordinal2(A,B)) ) ), file(ordinal2,k14_ordinal2), []). fof(dt_k14_polynom1,axiom,( ! [A] : m1_subset_1(k14_polynom1(A),k1_zfmisc_1(k13_polynom1(A))) ), file(polynom1,k14_polynom1), []). fof(dt_k15_dtconstr,axiom,( ! [A,B] : ( m1_finseq_1(B,k3_finseq_2(A)) => m2_finseq_2(k15_dtconstr(A,B),A,k3_finseq_2(A)) ) ), file(dtconstr,k15_dtconstr), []). fof(dt_k15_rvsum_1,axiom,( ! [A] : ( m1_finseq_1(A,k1_numbers) => m1_subset_1(k15_rvsum_1(A),k1_numbers) ) ), file(rvsum_1,k15_rvsum_1), []). fof(dt_k16_finseq_1,axiom,( ! [A,B,C] : ( ( m1_finseq_1(B,A) & v4_ordinal2(C) ) => m2_finseq_1(k16_finseq_1(A,B,C),A) ) ), file(finseq_1,k16_finseq_1), []). fof(dt_k17_polynom1,axiom,( ! [A] : ( v3_ordinal1(A) => ( v1_partfun1(k17_polynom1(A),k14_polynom1(A),k14_polynom1(A)) & v1_relat_2(k17_polynom1(A)) & v4_relat_2(k17_polynom1(A)) & v8_relat_2(k17_polynom1(A)) & m2_relset_1(k17_polynom1(A),k14_polynom1(A),k14_polynom1(A)) ) ) ), file(polynom1,k17_polynom1), []). fof(dt_k1_card_1,axiom,( ! [A] : v1_card_1(k1_card_1(A)) ), file(card_1,k1_card_1), []). fof(dt_k1_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k1_card_3(A)) & v1_funct_1(k1_card_3(A)) & v1_card_3(k1_card_3(A)) ) ) ), file(card_3,k1_card_3), []). fof(dt_k1_finseq_1,axiom,( $true ), file(finseq_1,k1_finseq_1), []). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). fof(dt_k1_matrlin,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(C) & m1_finseq_2(C,A) & v1_funct_1(D) & m1_relset_1(D,B,C) ) => m2_finseq_2(k1_matrlin(A,B,C,D,E),A,C) ) ), file(matrlin,k1_matrlin), []). 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_polynom3,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k5_numbers) & m1_finseq_1(C,A) ) => m2_finseq_1(k1_polynom3(A,B,C),A) ) ), file(polynom3,k1_polynom3), []). fof(dt_k1_polynom6,axiom,( ! [A,B,C,D] : ( ( v3_ordinal1(A) & v3_ordinal1(B) & m1_subset_1(C,k14_polynom1(A)) & m1_subset_1(D,k14_polynom1(B)) ) => m1_polynom1(k1_polynom6(A,B,C,D),k14_ordinal2(A,B),k14_polynom1(k14_ordinal2(A,B))) ) ), file(polynom6,k1_polynom6), []). 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_k20_polynom1,axiom,( ! [A,B] : ( ( v3_ordinal1(A) & v7_seqm_3(B) & v1_polynom1(B) & m1_pboole(B,A) ) => m1_trees_4(k20_polynom1(A,B),k13_polynom1(A),k14_polynom1(A)) ) ), file(polynom1,k20_polynom1), []). fof(dt_k2_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => m1_subset_1(k2_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ), file(finseq_1,k2_finseq_1), []). fof(dt_k2_finseq_3,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( v1_relat_1(k2_finseq_3(A,B)) & v1_funct_1(k2_finseq_3(A,B)) & v1_finseq_1(k2_finseq_3(A,B)) ) ) ), file(finseq_3,k2_finseq_3), []). 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_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(k3_finseq_2(A)) & m1_finseq_2(k3_finseq_2(A),A) ) ), file(finseq_2,k3_finseq_2), []). fof(dt_k3_lang1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m2_finseq_2(k3_lang1(A,B),A,k3_finseq_2(A)) ) ), file(lang1,k3_lang1), []). fof(dt_k3_matrlin,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,A) ) => m1_matrix_1(k3_matrlin(A,B),A,1,k3_finseq_1(B)) ) ), file(matrlin,k3_matrlin), []). fof(dt_k3_relat_1,axiom,( $true ), file(relat_1,k3_relat_1), []). fof(dt_k4_card_1,axiom,( ! [A] : ( v1_finset_1(A) => m2_subset_1(k4_card_1(A),k1_numbers,k5_numbers) ) ), file(card_1,k4_card_1), []). fof(dt_k4_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m1_subset_1(k4_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ), file(finseq_1,k4_finseq_1), []). fof(dt_k4_finseq_2,axiom,( ! [A,B] : ( v4_ordinal2(A) => m1_finseq_2(k4_finseq_2(A,B),B) ) ), file(finseq_2,k4_finseq_2), []). 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_k4_wsierp_1,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) & m1_finseq_1(C,B) & m1_finseq_1(D,B) ) => m1_trees_4(k4_wsierp_1(A,B,C,D),A,B) ) ), file(wsierp_1,k4_wsierp_1), []). fof(dt_k5_binarith,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => m2_subset_1(k5_binarith(A,B),k1_numbers,k5_numbers) ) ), file(binarith,k5_binarith), []). fof(dt_k5_finseq_1,axiom,( $true ), file(finseq_1,k5_finseq_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_k5_polynom1,axiom,( ! [A,B] : ( m1_finseq_1(B,k3_finseq_2(A)) => ( v1_card_3(k5_polynom1(A,B)) & m1_trees_4(k5_polynom1(A,B),k1_numbers,k5_numbers) ) ) ), file(polynom1,k5_polynom1), []). fof(dt_k6_xcmplx_0,axiom,( $true ), file(xcmplx_0,k6_xcmplx_0), []). fof(dt_k7_finseq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( v1_relat_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) ) ) ), file(finseq_1,k7_finseq_1), []). fof(dt_k8_finseq_1,axiom,( ! [A,B,C] : ( ( m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => m2_finseq_1(k8_finseq_1(A,B,C),A) ) ), file(finseq_1,k8_finseq_1), []). fof(dt_k9_binop_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k9_binop_2(A,B),k1_numbers) ) ), file(binop_2,k9_binop_2), []). fof(dt_k9_finseq_1,axiom,( ! [A] : ( v1_relat_1(k9_finseq_1(A)) & v1_funct_1(k9_finseq_1(A)) ) ), file(finseq_1,k9_finseq_1), []). fof(dt_k9_wsierp_1,axiom,( ! [A] : ( m1_finseq_1(A,k5_numbers) => m2_subset_1(k9_wsierp_1(A),k1_numbers,k5_numbers) ) ), file(wsierp_1,k9_wsierp_1), []). fof(dt_m1_finseq_1,axiom,( ! [A,B] : ( m1_finseq_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) ) ), file(finseq_1,m1_finseq_1), []). fof(dt_m1_finseq_2,axiom,( $true ), file(finseq_2,m1_finseq_2), []). fof(dt_m1_matrix_1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k5_numbers) & m1_subset_1(C,k5_numbers) ) => ! [D] : ( m1_matrix_1(D,A,B,C) => ( v1_matrix_1(D) & m2_finseq_1(D,k3_finseq_2(A)) ) ) ) ), file(matrix_1,m1_matrix_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_m1_trees_4,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m1_trees_4(C,A,B) => m2_finseq_1(C,A) ) ) ), file(trees_4,m1_trees_4), []). 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_finseq_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) ) => ! [C] : ( m2_finseq_2(C,A,B) => m2_finseq_1(C,A) ) ) ), file(finseq_2,m2_finseq_2), []). 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(existence_m1_finseq_1,axiom,( ! [A] : ? [B] : m1_finseq_1(B,A) ), file(finseq_1,m1_finseq_1), []). fof(existence_m1_finseq_2,axiom,( ! [A] : ? [B] : m1_finseq_2(B,A) ), file(finseq_2,m1_finseq_2), []). fof(existence_m1_matrix_1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k5_numbers) & m1_subset_1(C,k5_numbers) ) => ? [D] : m1_matrix_1(D,A,B,C) ) ), file(matrix_1,m1_matrix_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_m1_trees_4,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ? [C] : m1_trees_4(C,A,B) ) ), file(trees_4,m1_trees_4), []). fof(existence_m2_finseq_1,axiom,( ! [A] : ? [B] : m2_finseq_1(B,A) ), file(finseq_1,m2_finseq_1), []). fof(existence_m2_finseq_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) ) => ? [C] : m2_finseq_2(C,A,B) ) ), file(finseq_2,m2_finseq_2), []). 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_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_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_polynom1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & ~ v1_xboole_0(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) & v1_funcop_1(k5_finseq_1(A)) & v1_matrlin(k5_finseq_1(A)) ) ) ), file(polynom1,fc11_polynom1), []). 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_finseq_1,axiom,( ! [A] : ( ~ v1_xboole_0(k5_finseq_1(A)) & v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) ) ), file(finseq_1,fc12_finseq_1), []). fof(fc12_polynom1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_matrlin(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_matrlin(B) ) => ( v1_relat_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finset_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) & v1_funcop_1(k7_finseq_1(A,B)) & v1_matrlin(k7_finseq_1(A,B)) ) ) ), file(polynom1,fc12_polynom1), []). fof(fc12_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & ~ v2_xreal_0(k2_xcmplx_0(B,A)) & v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc12_xreal_0), []). fof(fc13_finseq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ~ v1_xboole_0(k7_finseq_1(A,B)) & v1_relat_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finset_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) ) ) ), file(finseq_1,fc13_finseq_1), []). fof(fc13_polynom1,axiom,( ! [A,B] : ( ( v1_xboole_0(B) & m1_finseq_1(B,k3_finseq_2(A)) ) => ( v1_relat_1(k15_dtconstr(A,B)) & v1_funct_1(k15_dtconstr(A,B)) & v2_funct_1(k15_dtconstr(A,B)) & v1_xboole_0(k15_dtconstr(A,B)) & v1_finset_1(k15_dtconstr(A,B)) & v1_finseq_1(k15_dtconstr(A,B)) & v1_membered(k15_dtconstr(A,B)) & v2_membered(k15_dtconstr(A,B)) & v3_membered(k15_dtconstr(A,B)) & v4_membered(k15_dtconstr(A,B)) & v5_membered(k15_dtconstr(A,B)) ) ) ), file(polynom1,fc13_polynom1), []). fof(fc14_finseq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ~ v1_xboole_0(k7_finseq_1(B,A)) & v1_relat_1(k7_finseq_1(B,A)) & v1_funct_1(k7_finseq_1(B,A)) & v1_finset_1(k7_finseq_1(B,A)) & v1_finseq_1(k7_finseq_1(B,A)) ) ) ), file(finseq_1,fc14_finseq_1), []). fof(fc14_finset_1,axiom,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_zfmisc_1(A,B)) ) ), file(finset_1,fc14_finset_1), []). fof(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_finseq_1,axiom,( ! [A,B] : ( m1_finseq_1(B,A) => ( v1_xboole_0(k16_finseq_1(A,B,0)) & v1_relat_1(k16_finseq_1(A,B,0)) & v1_funct_1(k16_finseq_1(A,B,0)) & v2_funct_1(k16_finseq_1(A,B,0)) & v1_finset_1(k16_finseq_1(A,B,0)) & v1_finseq_1(k16_finseq_1(A,B,0)) ) ) ), file(finseq_1,fc15_finseq_1), []). fof(fc15_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & ~ v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc15_xreal_0), []). 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(fc16_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & ~ v2_xreal_0(k6_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc16_xreal_0), []). 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_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v2_xreal_0(k6_xcmplx_0(A,B)) & ~ v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc17_xreal_0), []). fof(fc18_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k6_xcmplx_0(B,A)) & v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & ~ v2_xreal_0(k6_xcmplx_0(B,A)) & v3_xreal_0(k6_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc18_xreal_0), []). fof(fc19_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & ~ v2_xreal_0(k6_xcmplx_0(A,B)) & v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc19_xreal_0), []). fof(fc1_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => v1_finset_1(k1_finseq_1(A)) ) ), file(finseq_1,fc1_finseq_1), []). fof(fc1_finseq_2,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k4_finseq_2(A,B)) ) ), file(finseq_2,fc1_finseq_2), []). 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_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_polynom6,axiom,( ! [A,B] : ( ( v3_ordinal1(A) & v3_ordinal1(B) & ~ v1_xboole_0(B) ) => ( v3_ordinal1(k14_ordinal2(A,B)) & ~ v1_xboole_0(k14_ordinal2(A,B)) ) ) ), file(polynom6,fc1_polynom6), []). 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(fc20_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k6_xcmplx_0(B,A)) & v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & v2_xreal_0(k6_xcmplx_0(B,A)) & ~ v3_xreal_0(k6_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc20_xreal_0), []). fof(fc25_polynom1,axiom,( ! [A] : ~ v1_xboole_0(k13_polynom1(A)) ), file(polynom1,fc25_polynom1), []). fof(fc26_polynom1,axiom,( ! [A] : ( v3_ordinal1(A) => ( v1_relat_1(k17_polynom1(A)) & v1_partfun1(k17_polynom1(A),k14_polynom1(A),k14_polynom1(A)) & v3_orders_1(k17_polynom1(A)) & v1_relat_2(k17_polynom1(A)) & v4_relat_2(k17_polynom1(A)) & v8_relat_2(k17_polynom1(A)) ) ) ), file(polynom1,fc26_polynom1), []). fof(fc29_polynom1,axiom,( ! [A,B] : ( ( v3_ordinal1(A) & v7_seqm_3(B) & v1_polynom1(B) & m1_pboole(B,A) ) => ( v1_relat_1(k20_polynom1(A,B)) & v1_funct_1(k20_polynom1(A,B)) & v2_funct_1(k20_polynom1(A,B)) & ~ v1_xboole_0(k20_polynom1(A,B)) & v1_finset_1(k20_polynom1(A,B)) & v1_finseq_1(k20_polynom1(A,B)) & v1_polynom1(k20_polynom1(A,B)) ) ) ), file(polynom1,fc29_polynom1), []). 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_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_polynom6,axiom,( ! [A,B] : ( ( v3_ordinal1(A) & v3_ordinal1(B) & ~ v1_xboole_0(B) ) => ( v3_ordinal1(k14_ordinal2(B,A)) & ~ v1_xboole_0(k14_ordinal2(B,A)) ) ) ), file(polynom6,fc2_polynom6), []). fof(fc3_arytm_3,axiom,( ! [A,B] : ( ( v3_ordinal1(A) & v4_ordinal2(A) & v3_ordinal1(B) & v4_ordinal2(B) ) => ( v1_ordinal1(k14_ordinal2(A,B)) & v2_ordinal1(k14_ordinal2(A,B)) & v3_ordinal1(k14_ordinal2(A,B)) & v4_ordinal2(k14_ordinal2(A,B)) ) ) ), file(arytm_3,fc3_arytm_3), []). fof(fc3_finseq_1,axiom,( ! [A] : ( v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) ) ), file(finseq_1,fc3_finseq_1), []). fof(fc3_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_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_finseq_1,axiom,( ! [A] : ( v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) ) ), file(finseq_1,fc4_finseq_1), []). fof(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_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc5_xreal_0), []). fof(fc6_polynom1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(k1_card_3(A)) & v1_funct_1(k1_card_3(A)) & v1_finset_1(k1_card_3(A)) & v1_finseq_1(k1_card_3(A)) & v1_card_3(k1_card_3(A)) ) ) ), file(polynom1,fc6_polynom1), []). fof(fc7_funcop_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => ( v1_relat_1(k1_funct_1(A,B)) & v1_funct_1(k1_funct_1(A,B)) ) ) ), file(funcop_1,fc7_funcop_1), []). fof(fc7_polynom1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_card_3(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_card_3(B) ) => ( v1_relat_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finset_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) & v1_card_3(k7_finseq_1(A,B)) ) ) ), file(polynom1,fc7_polynom1), []). fof(fc7_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc7_xreal_0), []). fof(fc8_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v2_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc8_xreal_0), []). fof(fc9_finseq_1,axiom,( ! [A] : ~ v1_xboole_0(k13_finseq_1(A)) ), file(finseq_1,fc9_finseq_1), []). fof(fc9_polynom1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_xboole_0(A) ) => ( v1_relat_1(k1_card_3(A)) & v1_funct_1(k1_card_3(A)) & v2_funct_1(k1_card_3(A)) & v1_xboole_0(k1_card_3(A)) & v1_finset_1(k1_card_3(A)) & v1_membered(k1_card_3(A)) & v2_membered(k1_card_3(A)) & v3_membered(k1_card_3(A)) & v4_membered(k1_card_3(A)) & v5_membered(k1_card_3(A)) & v1_card_3(k1_card_3(A)) ) ) ), file(polynom1,fc9_polynom1), []). 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(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(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_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_finseq_2,axiom,( ! [A] : ? [B] : ( m1_finseq_2(B,A) & ~ v1_xboole_0(B) ) ), file(finseq_2,rc1_finseq_2), []). fof(rc1_finset_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) ) ), file(finset_1,rc1_finset_1), []). fof(rc1_funcop_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) ), file(funcop_1,rc1_funcop_1), []). fof(rc1_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc1_funct_1), []). fof(rc1_xreal_0,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(xreal_0,rc1_xreal_0), []). fof(rc2_finseq_1,axiom,( ! [A] : ? [B] : ( m1_relset_1(B,k5_numbers,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc2_finseq_1), []). fof(rc2_finset_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_ordinal1(B) & v2_ordinal1(B) & v3_ordinal1(B) & v4_ordinal2(B) & v1_finset_1(B) ) ), file(finset_1,rc2_finset_1), []). fof(rc2_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) ), file(funct_1,rc2_funct_1), []). fof(rc2_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_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_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_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(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_k12_finseq_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => k12_finseq_1(A,B) = k5_finseq_1(B) ) ), file(finseq_1,k12_finseq_1), []). fof(redefinition_k13_binarith,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => k13_binarith(A,B) = k5_finseq_1(B) ) ), file(binarith,k13_binarith), []). fof(redefinition_k14_polynom1,axiom,( ! [A] : k14_polynom1(A) = k13_polynom1(A) ), file(polynom1,k14_polynom1), []). fof(redefinition_k1_matrlin,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(C) & m1_finseq_2(C,A) & v1_funct_1(D) & m1_relset_1(D,B,C) ) => k1_matrlin(A,B,C,D,E) = k4_finseq_4(B,C,D,E) ) ), file(matrlin,k1_matrlin), []). 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_polynom3,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k5_numbers) & m1_finseq_1(C,A) ) => k1_polynom3(A,B,C) = k2_finseq_3(B,C) ) ), file(polynom3,k1_polynom3), []). fof(redefinition_k2_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => k2_finseq_1(A) = k1_finseq_1(A) ) ), file(finseq_1,k2_finseq_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_k3_finseq_2,axiom,( ! [A] : k3_finseq_2(A) = k13_finseq_1(A) ), file(finseq_2,k3_finseq_2), []). fof(redefinition_k3_lang1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => k3_lang1(A,B) = k5_finseq_1(B) ) ), file(lang1,k3_lang1), []). fof(redefinition_k3_matrlin,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,A) ) => k3_matrlin(A,B) = k5_finseq_1(B) ) ), file(matrlin,k3_matrlin), []). fof(redefinition_k4_card_1,axiom,( ! [A] : ( v1_finset_1(A) => k4_card_1(A) = k1_card_1(A) ) ), file(card_1,k4_card_1), []). fof(redefinition_k4_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k4_finseq_1(A) = k1_relat_1(A) ) ), file(finseq_1,k4_finseq_1), []). fof(redefinition_k4_wsierp_1,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) & m1_finseq_1(C,B) & m1_finseq_1(D,B) ) => k4_wsierp_1(A,B,C,D) = k7_finseq_1(C,D) ) ), file(wsierp_1,k4_wsierp_1), []). fof(redefinition_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_k5_polynom1,axiom,( ! [A,B] : ( m1_finseq_1(B,k3_finseq_2(A)) => k5_polynom1(A,B) = k1_card_3(B) ) ), file(polynom1,k5_polynom1), []). fof(redefinition_k8_finseq_1,axiom,( ! [A,B,C] : ( ( m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => k8_finseq_1(A,B,C) = k7_finseq_1(B,C) ) ), file(finseq_1,k8_finseq_1), []). fof(redefinition_k9_binop_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k9_binop_2(A,B) = k2_xcmplx_0(A,B) ) ), file(binop_2,k9_binop_2), []). fof(redefinition_k9_finseq_1,axiom,( ! [A] : k9_finseq_1(A) = k5_finseq_1(A) ), file(finseq_1,k9_finseq_1), []). fof(redefinition_k9_wsierp_1,axiom,( ! [A] : ( m1_finseq_1(A,k5_numbers) => k9_wsierp_1(A) = k15_rvsum_1(A) ) ), file(wsierp_1,k9_wsierp_1), []). 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_m1_trees_4,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m1_trees_4(C,A,B) <=> m1_finseq_1(C,B) ) ) ), file(trees_4,m1_trees_4), []). 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_finseq_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) ) => ! [C] : ( m2_finseq_2(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(finseq_2,m2_finseq_2), []). fof(redefinition_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) <=> m1_relset_1(C,A,B) ) ), file(relset_1,m2_relset_1), []). fof(redefinition_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(subset_1,m2_subset_1), []). fof(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_r2_polynom1,axiom,( ! [A,B,C] : ( ( v3_ordinal1(A) & v7_seqm_3(B) & v1_polynom1(B) & m1_pboole(B,A) & v7_seqm_3(C) & v1_polynom1(C) & m1_pboole(C,A) ) => r2_polynom1(A,B,B) ) ), file(polynom1,r2_polynom1), []). fof(reflexivity_r3_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) ) => r3_polynom1(A,B,B) ) ), file(polynom1,r3_polynom1), []). 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(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(t100_orders_1,axiom,( ! [A,B] : ( ( v1_relat_2(B) & v4_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) ) => k3_relat_1(B) = A ) ), file(orders_1,t100_orders_1), []). fof(t104_rvsum_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => k15_rvsum_1(k8_finseq_1(k1_numbers,B,k12_finseq_1(k1_numbers,A))) = k9_binop_2(k15_rvsum_1(B),A) ) ) ), file(rvsum_1,t104_rvsum_1), []). fof(t10_polynom6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( ( v7_seqm_3(C) & v1_polynom1(C) & m1_pboole(C,k14_ordinal2(A,B)) ) => ! [D] : ( m1_polynom1(D,A,k14_polynom1(A)) => ! [E] : ( m1_polynom1(E,B,k14_polynom1(B)) => ~ ( r3_polynom1(k14_ordinal2(A,B),C,k1_polynom6(A,B,D,E)) & ! [F] : ( m1_polynom1(F,A,k14_polynom1(A)) => ! [G] : ( m1_polynom1(G,B,k14_polynom1(B)) => ~ ( r3_polynom1(A,F,D) & r3_polynom1(B,G,E) & r6_pboole(k14_ordinal2(A,B),C,k1_polynom6(A,B,F,G)) ) ) ) ) ) ) ) ) ) ), file(polynom6,t10_polynom6), []). fof(t11_polynom6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( m1_polynom1(C,A,k14_polynom1(A)) => ! [D] : ( m1_polynom1(D,A,k14_polynom1(A)) => ! [E] : ( m1_polynom1(E,B,k14_polynom1(B)) => ! [F] : ( m1_polynom1(F,B,k14_polynom1(B)) => ( r1_polynom1(k14_ordinal2(A,B),k1_polynom6(A,B,C,E),k1_polynom6(A,B,D,F)) <=> ( r1_polynom1(A,C,D) | ( r6_pboole(A,C,D) & r1_polynom1(B,E,F) ) ) ) ) ) ) ) ) ) ), file(polynom6,t11_polynom6), []). 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(t12_jordan3,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ( ~ ( r1_xreal_0(B,A) & ~ r1_xreal_0(k2_xcmplx_0(A,1),B) ) => r1_xreal_0(A,k5_binarith(B,1)) ) ) ) ), file(jordan3,t12_jordan3), []). fof(t12_polynom1,axiom,( ! [A] : k1_card_3(k9_finseq_1(A)) = k9_finseq_1(k1_card_1(A)) ), file(polynom1,t12_polynom1), []). 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(t13_dtconstr,axiom,( ! [A,B] : ( m2_finseq_2(B,A,k3_finseq_2(A)) => k15_dtconstr(A,k3_lang1(k3_finseq_2(A),B)) = B ) ), file(dtconstr,t13_dtconstr), []). fof(t13_polynom1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => k1_card_3(k7_finseq_1(A,B)) = k7_finseq_1(k1_card_3(A),k1_card_3(B)) ) ) ), file(polynom1,t13_polynom1), []). fof(t14_scmfsa_7,axiom,( ! [A,B] : ( m2_finseq_1(B,k13_finseq_1(A)) => ! [C] : ( m2_finseq_1(C,k13_finseq_1(A)) => k15_dtconstr(A,k8_finseq_1(k13_finseq_1(A),B,C)) = k8_finseq_1(A,k15_dtconstr(A,B),k15_dtconstr(A,C)) ) ) ), file(scmfsa_7,t14_scmfsa_7), []). fof(t16_polynom3,axiom,( ! [A,B] : ( m2_finseq_1(B,k3_finseq_2(A)) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => k5_polynom1(A,k16_finseq_1(k3_finseq_2(A),B,C)) = k16_finseq_1(k5_numbers,k5_polynom1(A,B),C) ) ) ), file(polynom3,t16_polynom3), []). fof(t18_polynom3,axiom,( ! [A] : ( m1_trees_4(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( r1_xreal_0(B,C) => r1_xreal_0(k9_wsierp_1(k16_finseq_1(k5_numbers,A,B)),k9_wsierp_1(k16_finseq_1(k5_numbers,A,C))) ) ) ) ) ), file(polynom3,t18_polynom3), []). fof(t19_polynom3,axiom,( ! [A,B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( ~ r1_xreal_0(k3_finseq_1(B),C) => k16_finseq_1(A,B,k1_nat_1(C,1)) = k7_finseq_1(k16_finseq_1(A,B,C),k9_finseq_1(k1_funct_1(B,k1_nat_1(C,1)))) ) ) ) ), file(polynom3,t19_polynom3), []). fof(t1_numerals,axiom,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), []). fof(t1_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & v2_xreal_0(A) ) => v2_xreal_0(B) ) ) ) ), file(real,t1_real), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t1_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & r1_xreal_0(B,A) ) => A = B ) ) ) ), file(xreal_1,t1_xreal_1), []). fof(t21_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xreal_0(k2_xcmplx_0(A,B),C) <=> r1_xreal_0(A,k6_xcmplx_0(C,B)) ) ) ) ) ), file(xreal_1,t21_xreal_1), []). fof(t25_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( k3_finseq_1(A) = 0 <=> A = k1_xboole_0 ) ) ), file(finseq_1,t25_finseq_1), []). 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_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xreal_0(A,B) & r1_xreal_0(B,C) ) => r1_xreal_0(A,C) ) ) ) ) ), file(xreal_1,t2_xreal_1), []). fof(t31_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( k3_finseq_1(A) = k3_finseq_1(B) <=> k4_finseq_1(A) = k4_finseq_1(B) ) ) ) ), file(finseq_3,t31_finseq_3), []). fof(t31_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,0) & r1_xreal_0(k2_xcmplx_0(B,A),B) ) ) ) ), file(xreal_1,t31_xreal_1), []). fof(t32_polynom1,axiom,( ! [A,B] : ( m2_finseq_1(B,k3_finseq_2(A)) => ! [C] : ~ ( r2_hidden(C,k4_finseq_1(k15_dtconstr(A,B))) & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ~ ( r2_hidden(D,k4_finseq_1(B)) & r2_hidden(E,k4_finseq_1(k1_funct_1(B,D))) & C = k1_nat_1(k9_wsierp_1(k5_polynom1(A,k16_finseq_1(k3_finseq_2(A),B,k5_binarith(D,1)))),E) & k1_funct_1(k1_funct_1(B,D),E) = k1_funct_1(k15_dtconstr(A,B),C) ) ) ) ) ) ), file(polynom1,t32_polynom1), []). fof(t33_polynom1,axiom,( ! [A,B] : ( m2_finseq_1(B,k3_finseq_2(A)) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( ( r2_hidden(C,k4_finseq_1(B)) & r2_hidden(D,k4_finseq_1(k1_funct_1(B,C))) ) => ( r2_hidden(k1_nat_1(k9_wsierp_1(k5_polynom1(A,k16_finseq_1(k3_finseq_2(A),B,k5_binarith(C,1)))),D),k4_finseq_1(k15_dtconstr(A,B))) & k1_funct_1(k1_funct_1(B,C),D) = k1_funct_1(k15_dtconstr(A,B),k1_nat_1(k9_wsierp_1(k5_polynom1(A,k16_finseq_1(k3_finseq_2(A),B,k5_binarith(C,1)))),D)) ) ) ) ) ) ), file(polynom1,t33_polynom1), []). 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(t48_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( k7_finseq_1(A,B) = k1_xboole_0 => ( A = k1_xboole_0 & B = k1_xboole_0 ) ) ) ) ), file(finseq_1,t48_finseq_1), []). fof(t4_polyalg1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,A) ) => B = k7_finseq_1(k9_finseq_1(k1_funct_1(B,1)),k1_polynom3(A,1,B)) ) ) ), file(polyalg1,t4_polyalg1), []). fof(t4_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xreal_0(A,B) & ~ v2_xreal_0(B) & v2_xreal_0(A) ) ) ) ), file(real,t4_real), []). fof(t4_subset,axiom,( ! [A,B,C] : ( ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) ) => m1_subset_1(A,C) ) ), file(subset,t4_subset), []). fof(t50_binarith,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ( r1_xreal_0(A,B) => k5_binarith(B,A) = k6_xcmplx_0(B,A) ) ) ) ), file(binarith,t50_binarith), []). fof(t53_binarith,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ( r1_xreal_0(B,A) => k2_xcmplx_0(k5_binarith(A,B),B) = A ) ) ) ), file(binarith,t53_binarith), []). 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(t64_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ( ( k1_relat_1(A) = k1_xboole_0 | k2_relat_1(A) = k1_xboole_0 ) => A = k1_xboole_0 ) ) ), file(relat_1,t64_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_polynom6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( m1_polynom1(C,k14_ordinal2(A,B),k14_polynom1(k14_ordinal2(A,B))) => ? [D] : ( m1_polynom1(D,A,k14_polynom1(A)) & ? [E] : ( m1_polynom1(E,B,k14_polynom1(B)) & r6_pboole(k14_ordinal2(A,B),C,k1_polynom6(A,B,D,E)) ) ) ) ) ) ), file(polynom6,t6_polynom6), []). 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(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t7_polynom6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( m1_polynom1(C,A,k14_polynom1(A)) => ! [D] : ( m1_polynom1(D,A,k14_polynom1(A)) => ! [E] : ( m1_polynom1(E,B,k14_polynom1(B)) => ! [F] : ( m1_polynom1(F,B,k14_polynom1(B)) => ( r6_pboole(k14_ordinal2(A,B),k1_polynom6(A,B,C,E),k1_polynom6(A,B,D,F)) => ( r6_pboole(A,C,D) & r6_pboole(B,E,F) ) ) ) ) ) ) ) ) ), file(polynom6,t7_polynom6), []). fof(t7_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v2_xreal_0(A) & ~ v3_xreal_0(B) ) ) ) ), file(real,t7_real), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t8_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_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xreal_0(A,B) <=> r1_xreal_0(k2_xcmplx_0(A,C),k2_xcmplx_0(B,C)) ) ) ) ) ), file(xreal_1,t8_xreal_1), []). fof(t9_polynom6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( m1_polynom1(C,A,k14_polynom1(A)) => ! [D] : ( m1_polynom1(D,A,k14_polynom1(A)) => ! [E] : ( m1_polynom1(E,B,k14_polynom1(B)) => ! [F] : ( m1_polynom1(F,B,k14_polynom1(B)) => ( ( r3_polynom1(A,C,D) & r3_polynom1(B,E,F) ) => r3_polynom1(k14_ordinal2(A,B),k1_polynom6(A,B,C,E),k1_polynom6(A,B,D,F)) ) ) ) ) ) ) ) ), file(polynom6,t9_polynom6), []).