% Mizar problem: t21_polyeq_3,polyeq_3,515,50 fof(t21_polyeq_3,conjecture,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,k1_numbers) => ! [D] : ( m1_subset_1(D,k2_numbers) => ( ( k6_polyeq_3(A,0,B,C,D) = 0 & k4_complex1(D) = 0 ) => ( A = 0 | ! [E] : ( m1_subset_1(E,k1_numbers) => ! [F] : ( m1_subset_1(F,k1_numbers) => ~ ( k3_complex1(D) = k3_real_1(E,F) & k3_real_1(k4_real_1(k4_real_1(3,F),E),k6_real_1(B,A)) = 0 & D != k3_real_1(k2_power(3,k3_real_1(k1_real_1(k6_real_1(C,k4_real_1(2,A))),k9_square_1(k3_real_1(k6_real_1(k7_square_1(C),k4_real_1(4,k7_square_1(A))),k3_prepower(k6_real_1(B,k4_real_1(3,A)),3))))),k2_power(3,k5_real_1(k1_real_1(k6_real_1(C,k4_real_1(2,A))),k9_square_1(k3_real_1(k6_real_1(k7_square_1(C),k4_real_1(4,k7_square_1(A))),k3_prepower(k6_real_1(B,k4_real_1(3,A)),3)))))) & D != k3_real_1(k2_power(3,k3_real_1(k1_real_1(k6_real_1(C,k4_real_1(2,A))),k9_square_1(k3_real_1(k6_real_1(k7_square_1(C),k4_real_1(4,k7_square_1(A))),k3_prepower(k6_real_1(B,k4_real_1(3,A)),3))))),k2_power(3,k3_real_1(k1_real_1(k6_real_1(C,k4_real_1(2,A))),k9_square_1(k3_real_1(k6_real_1(k7_square_1(C),k4_real_1(4,k7_square_1(A))),k3_prepower(k6_real_1(B,k4_real_1(3,A)),3)))))) & D != k3_real_1(k2_power(3,k5_real_1(k1_real_1(k6_real_1(C,k4_real_1(2,A))),k9_square_1(k3_real_1(k6_real_1(k7_square_1(C),k4_real_1(4,k7_square_1(A))),k3_prepower(k6_real_1(B,k4_real_1(3,A)),3))))),k2_power(3,k5_real_1(k1_real_1(k6_real_1(C,k4_real_1(2,A))),k9_square_1(k3_real_1(k6_real_1(k7_square_1(C),k4_real_1(4,k7_square_1(A))),k3_prepower(k6_real_1(B,k4_real_1(3,A)),3)))))) ) ) ) ) ) ) ) ) ) ), inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_nat_1,cc1_square_1,cc1_xcmplx_0,cc1_xreal_0,cc20_membered,cc2_membered,cc2_nat_1,cc2_xcmplx_0,cc2_xreal_0,cc3_membered,cc3_nat_1,cc3_xreal_0,cc4_membered,cc4_xreal_0,cc5_membered,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,commutativity_k1_polyeq_3,commutativity_k2_polyeq_3,commutativity_k2_tarski,commutativity_k2_xcmplx_0,commutativity_k3_real_1,commutativity_k3_xcmplx_0,commutativity_k4_real_1,commutativity_k8_complex1,commutativity_k9_complex1,connectedness_r1_xreal_0,d10_complex1,d1_polyeq_3,d1_xcmplx_0,d2_polyeq_3,d3_polyeq_3,d3_square_1,d4_polyeq_1,d7_arytm_0,d8_xcmplx_0,d9_xcmplx_0,dt_k13_arytm_3,dt_k1_complex1,dt_k1_numbers,dt_k1_polyeq_3,dt_k1_power,dt_k1_real_1,dt_k1_xboole_0,dt_k1_xcmplx_0,dt_k1_zfmisc_1,dt_k2_complex1,dt_k2_newton,dt_k2_numbers,dt_k2_polyeq_3,dt_k2_power,dt_k2_real_1,dt_k2_tarski,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_complex1,dt_k3_newton,dt_k3_polyeq_3,dt_k3_prepower,dt_k3_real_1,dt_k3_xcmplx_0,dt_k4_complex1,dt_k4_funct_4,dt_k4_ordinal2,dt_k4_real_1,dt_k4_xcmplx_0,dt_k5_arytm_0,dt_k5_funct_4,dt_k5_numbers,dt_k5_ordinal2,dt_k5_polyeq_3,dt_k5_real_1,dt_k5_square_1,dt_k5_xcmplx_0,dt_k6_arytm_3,dt_k6_polyeq_3,dt_k6_real_1,dt_k6_xcmplx_0,dt_k7_complex1,dt_k7_polyeq_1,dt_k7_square_1,dt_k7_xcmplx_0,dt_k8_complex1,dt_k8_polyeq_1,dt_k8_square_1,dt_k9_complex1,dt_k9_square_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc10_xreal_0,fc11_xreal_0,fc12_membered,fc12_xreal_0,fc13_membered,fc13_xreal_0,fc14_membered,fc14_xreal_0,fc15_membered,fc15_xreal_0,fc16_membered,fc16_xreal_0,fc17_xreal_0,fc18_xreal_0,fc19_xreal_0,fc1_membered,fc1_nat_1,fc1_square_1,fc1_xcmplx_0,fc1_xreal_0,fc20_xreal_0,fc21_xreal_0,fc22_xreal_0,fc23_xreal_0,fc24_xreal_0,fc25_xreal_0,fc26_xreal_0,fc27_xreal_0,fc28_xreal_0,fc29_xreal_0,fc2_membered,fc2_nat_1,fc2_square_1,fc2_xcmplx_0,fc2_xreal_0,fc30_xreal_0,fc3_nat_1,fc3_xcmplx_0,fc3_xreal_0,fc4_nat_1,fc4_xcmplx_0,fc4_xreal_0,fc5_membered,fc5_xcmplx_0,fc5_xreal_0,fc6_membered,fc6_polyeq_1,fc6_xcmplx_0,fc6_xreal_0,fc7_xcmplx_0,fc7_xreal_0,fc8_xcmplx_0,fc8_xreal_0,fc9_xcmplx_0,fc9_xreal_0,involutiveness_k1_real_1,involutiveness_k2_real_1,involutiveness_k4_xcmplx_0,involutiveness_k5_xcmplx_0,rc1_membered,rc1_nat_1,rc1_xcmplx_0,rc1_xreal_0,rc2_nat_1,rc2_xcmplx_0,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,redefinition_k13_arytm_3,redefinition_k1_polyeq_3,redefinition_k1_real_1,redefinition_k2_polyeq_3,redefinition_k2_power,redefinition_k2_real_1,redefinition_k3_complex1,redefinition_k3_newton,redefinition_k3_polyeq_3,redefinition_k3_prepower,redefinition_k3_real_1,redefinition_k4_complex1,redefinition_k4_real_1,redefinition_k5_funct_4,redefinition_k5_numbers,redefinition_k5_real_1,redefinition_k6_real_1,redefinition_k7_complex1,redefinition_k7_square_1,redefinition_k8_complex1,redefinition_k8_polyeq_1,redefinition_k9_complex1,redefinition_k9_square_1,redefinition_m2_relset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,spc0_boole,spc1_boole,spc1_numerals,spc2_boole,spc2_numerals,spc3_boole,spc3_numerals,spc4_boole,spc4_numerals,t104_xcmplx_1,t11_polyeq_3,t16_newton,t19_polyeq_1,t1_arithm,t1_numerals,t1_real,t1_subset,t27_complex1,t28_complex1,t29_complex1,t2_arithm,t2_real,t2_subset,t3_arithm,t3_real,t3_subset,t4_arithm,t4_real,t4_subset,t5_arithm,t5_real,t5_subset,t60_square_1,t69_square_1,t6_arithm,t6_boole,t6_real,t7_boole,t7_real,t89_xcmplx_1,t8_boole,t8_real]), [file(polyeq_3,t21_polyeq_3)]). fof(antisymmetry_r2_hidden,axiom,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), []). fof(cc10_membered,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,A) => v1_xcmplx_0(B) ) ) ), file(membered,cc10_membered), []). fof(cc11_membered,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) ) ) ) ), file(membered,cc11_membered), []). fof(cc12_membered,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_rat_1(B) ) ) ) ), file(membered,cc12_membered), []). fof(cc13_membered,axiom,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc13_membered), []). fof(cc14_membered,axiom,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v4_ordinal2(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc14_membered), []). fof(cc15_membered,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc15_membered), []). fof(cc16_membered,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_membered(B) ) ) ), file(membered,cc16_membered), []). fof(cc17_membered,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) ) ) ) ), file(membered,cc17_membered), []). fof(cc18_membered,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) ) ) ) ), file(membered,cc18_membered), []). fof(cc19_membered,axiom,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) ) ) ) ), file(membered,cc19_membered), []). fof(cc1_membered,axiom,( ! [A] : ( v5_membered(A) => v4_membered(A) ) ), file(membered,cc1_membered), []). 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_square_1,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => v1_xcmplx_0(A) ) ), file(square_1,cc1_square_1), []). fof(cc1_xcmplx_0,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => v1_xcmplx_0(A) ) ), file(xcmplx_0,cc1_xcmplx_0), []). fof(cc1_xreal_0,axiom,( ! [A] : ( v4_ordinal2(A) => v1_xreal_0(A) ) ), file(xreal_0,cc1_xreal_0), []). fof(cc20_membered,axiom,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) ) ) ) ), file(membered,cc20_membered), []). fof(cc2_membered,axiom,( ! [A] : ( v4_membered(A) => v3_membered(A) ) ), file(membered,cc2_membered), []). 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_xcmplx_0,axiom,( ! [A] : ( v4_ordinal2(A) => v1_xcmplx_0(A) ) ), file(xcmplx_0,cc2_xcmplx_0), []). fof(cc2_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xcmplx_0(A) ) ), file(xreal_0,cc2_xreal_0), []). fof(cc3_membered,axiom,( ! [A] : ( v3_membered(A) => v2_membered(A) ) ), file(membered,cc3_membered), []). 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_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xreal_0(A) ) => ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(xreal_0,cc3_xreal_0), []). fof(cc4_membered,axiom,( ! [A] : ( v2_membered(A) => v1_membered(A) ) ), file(membered,cc4_membered), []). fof(cc4_xreal_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A) ) ) ), file(xreal_0,cc4_xreal_0), []). fof(cc5_membered,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_numbers)) => v1_membered(A) ) ), file(membered,cc5_membered), []). fof(cc5_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & v3_xreal_0(A) ) => ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) ) ) ), file(xreal_0,cc5_xreal_0), []). fof(cc6_membered,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v1_membered(A) & v2_membered(A) ) ) ), file(membered,cc6_membered), []). fof(cc6_xreal_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & v3_xreal_0(A) ) ) ), file(xreal_0,cc6_xreal_0), []). fof(cc7_xreal_0,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(xreal_0,cc7_xreal_0), []). fof(cc8_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(xreal_0,cc8_xreal_0), []). fof(cc9_membered,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k5_numbers)) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc9_membered), []). fof(commutativity_k1_polyeq_3,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k2_numbers) ) => k1_polyeq_3(A,B) = k1_polyeq_3(B,A) ) ), file(polyeq_3,k1_polyeq_3), []). fof(commutativity_k2_polyeq_3,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k2_numbers) ) => k2_polyeq_3(A,B) = k2_polyeq_3(B,A) ) ), file(polyeq_3,k2_polyeq_3), []). 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_k3_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k3_real_1(A,B) = k3_real_1(B,A) ) ), file(real_1,k3_real_1), []). fof(commutativity_k3_xcmplx_0,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k3_xcmplx_0(A,B) = k3_xcmplx_0(B,A) ) ), file(xcmplx_0,k3_xcmplx_0), []). fof(commutativity_k4_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k4_real_1(A,B) = k4_real_1(B,A) ) ), file(real_1,k4_real_1), []). fof(commutativity_k8_complex1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) ) => k8_complex1(A,B) = k8_complex1(B,A) ) ), file(complex1,k8_complex1), []). fof(commutativity_k9_complex1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) ) => k9_complex1(A,B) = k9_complex1(B,A) ) ), file(complex1,k9_complex1), []). 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(d10_complex1,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => ! [B] : ( m1_subset_1(B,k2_numbers) => k9_complex1(A,B) = k2_xcmplx_0(k5_real_1(k4_real_1(k3_complex1(A),k3_complex1(B)),k4_real_1(k4_complex1(A),k4_complex1(B))),k3_xcmplx_0(k3_real_1(k4_real_1(k3_complex1(A),k4_complex1(B)),k4_real_1(k3_complex1(B),k4_complex1(A))),k7_complex1)) ) ) ), file(complex1,d10_complex1), []). fof(d1_polyeq_3,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => k3_polyeq_3(A) = k2_polyeq_3(k5_real_1(k7_square_1(k3_complex1(A)),k7_square_1(k4_complex1(A))),k1_polyeq_3(k4_real_1(2,k4_real_1(k3_complex1(A),k4_complex1(A))),k7_complex1)) ) ), file(polyeq_3,d1_polyeq_3), []). fof(d1_xcmplx_0,axiom,( k1_xcmplx_0 = k5_funct_4(k1_numbers,0,1,0,1) ), file(xcmplx_0,d1_xcmplx_0), []). fof(d2_polyeq_3,axiom,( ! [A] : ( v1_xcmplx_0(A) => k5_polyeq_3(A) = k3_xcmplx_0(k5_square_1(A),A) ) ), file(polyeq_3,d2_polyeq_3), []). fof(d3_polyeq_3,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,k1_numbers) => ! [D] : ( m1_subset_1(D,k1_numbers) => ! [E] : ( v1_xcmplx_0(E) => k6_polyeq_3(A,B,C,D,E) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_polyeq_3(A,k5_polyeq_3(E)),k3_xcmplx_0(B,k5_square_1(E))),k3_xcmplx_0(C,E)),D) ) ) ) ) ) ), file(polyeq_3,d3_polyeq_3), []). fof(d3_square_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k5_square_1(A) = k3_xcmplx_0(A,A) ) ), file(square_1,d3_square_1), []). fof(d4_polyeq_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => k7_polyeq_1(A,B,C,D,E) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k2_newton(E,3)),k3_xcmplx_0(B,k5_square_1(E))),k3_xcmplx_0(C,E)),D) ) ) ) ) ) ), file(polyeq_1,d4_polyeq_1), []). fof(d7_arytm_0,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => ( ( B = 0 => k5_arytm_0(A,B) = A ) & ( B != 0 => k5_arytm_0(A,B) = k5_funct_4(k1_numbers,0,k13_arytm_3,A,B) ) ) ) ) ), file(arytm_0,d7_arytm_0), []). fof(d8_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k6_xcmplx_0(A,B) = k2_xcmplx_0(A,k4_xcmplx_0(B)) ) ) ), file(xcmplx_0,d8_xcmplx_0), []). fof(d9_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k7_xcmplx_0(A,B) = k3_xcmplx_0(A,k5_xcmplx_0(B)) ) ) ), file(xcmplx_0,d9_xcmplx_0), []). fof(dt_k13_arytm_3,axiom, ( ~ v1_xboole_0(k13_arytm_3) & v3_ordinal1(k13_arytm_3) & m1_subset_1(k13_arytm_3,k6_arytm_3) ), file(arytm_3,k13_arytm_3), []). fof(dt_k1_complex1,axiom,( $true ), file(complex1,k1_complex1), []). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), []). fof(dt_k1_polyeq_3,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k2_numbers) ) => m1_subset_1(k1_polyeq_3(A,B),k2_numbers) ) ), file(polyeq_3,k1_polyeq_3), []). fof(dt_k1_power,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & v1_xreal_0(B) ) => v1_xreal_0(k1_power(A,B)) ) ), file(power,k1_power), []). fof(dt_k1_real_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => m1_subset_1(k1_real_1(A),k1_numbers) ) ), file(real_1,k1_real_1), []). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), []). fof(dt_k1_xcmplx_0,axiom,( $true ), file(xcmplx_0,k1_xcmplx_0), []). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), []). fof(dt_k2_complex1,axiom,( $true ), file(complex1,k2_complex1), []). fof(dt_k2_newton,axiom,( $true ), file(newton,k2_newton), []). fof(dt_k2_numbers,axiom,( $true ), file(numbers,k2_numbers), []). fof(dt_k2_polyeq_3,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k2_numbers) ) => m1_subset_1(k2_polyeq_3(A,B),k2_numbers) ) ), file(polyeq_3,k2_polyeq_3), []). fof(dt_k2_power,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k2_power(A,B),k1_numbers) ) ), file(power,k2_power), []). fof(dt_k2_real_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => m1_subset_1(k2_real_1(A),k1_numbers) ) ), file(real_1,k2_real_1), []). fof(dt_k2_tarski,axiom,( $true ), file(tarski,k2_tarski), []). 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_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => m1_subset_1(k3_complex1(A),k1_numbers) ) ), file(complex1,k3_complex1), []). fof(dt_k3_newton,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & v4_ordinal2(B) ) => m1_subset_1(k3_newton(A,B),k1_numbers) ) ), file(newton,k3_newton), []). fof(dt_k3_polyeq_3,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => m1_subset_1(k3_polyeq_3(A),k2_numbers) ) ), file(polyeq_3,k3_polyeq_3), []). fof(dt_k3_prepower,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k5_numbers) ) => m1_subset_1(k3_prepower(A,B),k1_numbers) ) ), file(prepower,k3_prepower), []). fof(dt_k3_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k3_real_1(A,B),k1_numbers) ) ), file(real_1,k3_real_1), []). fof(dt_k3_xcmplx_0,axiom,( $true ), file(xcmplx_0,k3_xcmplx_0), []). fof(dt_k4_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => m1_subset_1(k4_complex1(A),k1_numbers) ) ), file(complex1,k4_complex1), []). fof(dt_k4_funct_4,axiom,( $true ), file(funct_4,k4_funct_4), []). fof(dt_k4_ordinal2,axiom, ( v3_ordinal1(k4_ordinal2) & ~ v1_xboole_0(k4_ordinal2) ), file(ordinal2,k4_ordinal2), []). fof(dt_k4_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k4_real_1(A,B),k1_numbers) ) ), file(real_1,k4_real_1), []). fof(dt_k4_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_xcmplx_0(k4_xcmplx_0(A)) ) ), file(xcmplx_0,k4_xcmplx_0), []). fof(dt_k5_arytm_0,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k5_arytm_0(A,B),k2_numbers) ) ), file(arytm_0,k5_arytm_0), []). fof(dt_k5_funct_4,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(A) & m1_subset_1(D,A) & m1_subset_1(E,A) ) => ( v1_funct_1(k5_funct_4(A,B,C,D,E)) & v1_funct_2(k5_funct_4(A,B,C,D,E),k2_tarski(B,C),A) & m2_relset_1(k5_funct_4(A,B,C,D,E),k2_tarski(B,C),A) ) ) ), file(funct_4,k5_funct_4), []). 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_polyeq_3,axiom,( ! [A] : ( v1_xcmplx_0(A) => m1_subset_1(k5_polyeq_3(A),k2_numbers) ) ), file(polyeq_3,k5_polyeq_3), []). fof(dt_k5_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k5_real_1(A,B),k1_numbers) ) ), file(real_1,k5_real_1), []). fof(dt_k5_square_1,axiom,( $true ), file(square_1,k5_square_1), []). fof(dt_k5_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_xcmplx_0(k5_xcmplx_0(A)) ) ), file(xcmplx_0,k5_xcmplx_0), []). fof(dt_k6_arytm_3,axiom,( $true ), file(arytm_3,k6_arytm_3), []). fof(dt_k6_polyeq_3,axiom,( ! [A,B,C,D,E] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) & m1_subset_1(C,k1_numbers) & m1_subset_1(D,k1_numbers) & v1_xcmplx_0(E) ) => m1_subset_1(k6_polyeq_3(A,B,C,D,E),k2_numbers) ) ), file(polyeq_3,k6_polyeq_3), []). fof(dt_k6_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k6_real_1(A,B),k1_numbers) ) ), file(real_1,k6_real_1), []). fof(dt_k6_xcmplx_0,axiom,( $true ), file(xcmplx_0,k6_xcmplx_0), []). fof(dt_k7_complex1,axiom,( m1_subset_1(k7_complex1,k2_numbers) ), file(complex1,k7_complex1), []). fof(dt_k7_polyeq_1,axiom,( $true ), file(polyeq_1,k7_polyeq_1), []). fof(dt_k7_square_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => m1_subset_1(k7_square_1(A),k1_numbers) ) ), file(square_1,k7_square_1), []). fof(dt_k7_xcmplx_0,axiom,( $true ), file(xcmplx_0,k7_xcmplx_0), []). fof(dt_k8_complex1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) ) => m1_subset_1(k8_complex1(A,B),k2_numbers) ) ), file(complex1,k8_complex1), []). fof(dt_k8_polyeq_1,axiom,( ! [A,B,C,D,E] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) & m1_subset_1(C,k1_numbers) & m1_subset_1(D,k1_numbers) & m1_subset_1(E,k1_numbers) ) => m1_subset_1(k8_polyeq_1(A,B,C,D,E),k1_numbers) ) ), file(polyeq_1,k8_polyeq_1), []). fof(dt_k8_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xreal_0(k8_square_1(A)) ) ), file(square_1,k8_square_1), []). fof(dt_k9_complex1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) ) => m1_subset_1(k9_complex1(A,B),k2_numbers) ) ), file(complex1,k9_complex1), []). fof(dt_k9_square_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => m1_subset_1(k9_square_1(A),k1_numbers) ) ), file(square_1,k9_square_1), []). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), []). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), []). fof(dt_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ), file(relset_1,m2_relset_1), []). fof(existence_m1_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), []). fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), []). fof(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), []). fof(fc10_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v2_xreal_0(k2_xcmplx_0(B,A)) & ~ v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc10_xreal_0), []). fof(fc11_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v2_xreal_0(k2_xcmplx_0(A,B)) & v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc11_xreal_0), []). fof(fc12_membered,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => v1_membered(k2_tarski(A,B)) ) ), file(membered,fc12_membered), []). 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_membered,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) ) ) ), file(membered,fc13_membered), []). fof(fc13_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) ) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & ~ v3_xreal_0(k4_xcmplx_0(A)) ) ) ), file(xreal_0,fc13_xreal_0), []). fof(fc14_membered,axiom,( ! [A,B] : ( ( v1_rat_1(A) & v1_rat_1(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) ) ) ), file(membered,fc14_membered), []). fof(fc14_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & ~ v2_xreal_0(k4_xcmplx_0(A)) ) ) ), file(xreal_0,fc14_xreal_0), []). fof(fc15_membered,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) ) ) ), file(membered,fc15_membered), []). 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_membered,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) & v5_membered(k2_tarski(A,B)) ) ) ), file(membered,fc16_membered), []). 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_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_membered,axiom, ( ~ v1_xboole_0(k2_numbers) & v1_membered(k2_numbers) ), file(membered,fc1_membered), []). 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_square_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_xcmplx_0(k5_square_1(A)) ) ), file(square_1,fc1_square_1), []). fof(fc1_xcmplx_0,axiom,( v1_xcmplx_0(k1_xcmplx_0) ), file(xcmplx_0,fc1_xcmplx_0), []). fof(fc1_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) ) ) ), file(xreal_0,fc1_xreal_0), []). 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(fc21_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & ~ v2_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc21_xreal_0), []). fof(fc22_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(B,A)) & v1_xreal_0(k3_xcmplx_0(B,A)) & ~ v2_xreal_0(k3_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc22_xreal_0), []). fof(fc23_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & ~ v3_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc23_xreal_0), []). fof(fc24_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & ~ v3_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc24_xreal_0), []). fof(fc25_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) ) => ( v1_xcmplx_0(k5_xcmplx_0(A)) & v1_xreal_0(k5_xcmplx_0(A)) & ~ v2_xreal_0(k5_xcmplx_0(A)) ) ) ), file(xreal_0,fc25_xreal_0), []). fof(fc26_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xcmplx_0(k5_xcmplx_0(A)) & v1_xreal_0(k5_xcmplx_0(A)) & ~ v3_xreal_0(k5_xcmplx_0(A)) ) ) ), file(xreal_0,fc26_xreal_0), []). fof(fc27_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) & ~ v2_xreal_0(k7_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc27_xreal_0), []). fof(fc28_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k7_xcmplx_0(B,A)) & v1_xreal_0(k7_xcmplx_0(B,A)) & ~ v2_xreal_0(k7_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc28_xreal_0), []). fof(fc29_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) & ~ v3_xreal_0(k7_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc29_xreal_0), []). fof(fc2_membered,axiom, ( ~ v1_xboole_0(k1_numbers) & v1_membered(k1_numbers) & v2_membered(k1_numbers) ), file(membered,fc2_membered), []). fof(fc2_nat_1,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => ( v4_ordinal2(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(nat_1,fc2_nat_1), []). fof(fc2_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_xcmplx_0(k5_square_1(A)) & v1_xreal_0(k5_square_1(A)) ) ) ), file(square_1,fc2_square_1), []). fof(fc2_xcmplx_0,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => v1_xcmplx_0(k2_xcmplx_0(A,B)) ) ), file(xcmplx_0,fc2_xcmplx_0), []). fof(fc2_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_xcmplx_0(k5_xcmplx_0(A)) & v1_xreal_0(k5_xcmplx_0(A)) ) ) ), file(xreal_0,fc2_xreal_0), []). fof(fc30_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) & ~ v3_xreal_0(k7_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc30_xreal_0), []). 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_xcmplx_0,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => v1_xcmplx_0(k3_xcmplx_0(A,B)) ) ), file(xcmplx_0,fc3_xcmplx_0), []). fof(fc3_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc3_xreal_0), []). fof(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_xcmplx_0,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => v1_xcmplx_0(k6_xcmplx_0(A,B)) ) ), file(xcmplx_0,fc4_xcmplx_0), []). fof(fc4_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc4_xreal_0), []). fof(fc5_membered,axiom, ( v1_membered(k5_ordinal2) & v2_membered(k5_ordinal2) & v3_membered(k5_ordinal2) & v4_membered(k5_ordinal2) & v5_membered(k5_ordinal2) ), file(membered,fc5_membered), []). fof(fc5_xcmplx_0,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => v1_xcmplx_0(k7_xcmplx_0(A,B)) ) ), file(xcmplx_0,fc5_xcmplx_0), []). 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_membered,axiom, ( v1_xboole_0(k1_xboole_0) & v1_membered(k1_xboole_0) & v2_membered(k1_xboole_0) & v3_membered(k1_xboole_0) & v4_membered(k1_xboole_0) & v5_membered(k1_xboole_0) ), file(membered,fc6_membered), []). fof(fc6_polyeq_1,axiom,( ! [A,B,C,D,E] : ( ( v1_xreal_0(A) & v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) & v1_xreal_0(E) ) => ( v1_xcmplx_0(k7_polyeq_1(A,B,C,D,E)) & v1_xreal_0(k7_polyeq_1(A,B,C,D,E)) ) ) ), file(polyeq_1,fc6_polyeq_1), []). fof(fc6_xcmplx_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) ) => ( ~ v1_xboole_0(k4_xcmplx_0(A)) & v1_xcmplx_0(k4_xcmplx_0(A)) ) ) ), file(xcmplx_0,fc6_xcmplx_0), []). fof(fc6_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc6_xreal_0), []). fof(fc7_xcmplx_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) ) => ( ~ v1_xboole_0(k5_xcmplx_0(A)) & v1_xcmplx_0(k5_xcmplx_0(A)) ) ) ), file(xcmplx_0,fc7_xcmplx_0), []). 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_xcmplx_0,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & ~ v1_xboole_0(B) & v1_xcmplx_0(B) ) => ( ~ v1_xboole_0(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)) ) ) ), file(xcmplx_0,fc8_xcmplx_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_xcmplx_0,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & ~ v1_xboole_0(B) & v1_xcmplx_0(B) ) => ( ~ v1_xboole_0(k7_xcmplx_0(A,B)) & v1_xcmplx_0(k7_xcmplx_0(A,B)) ) ) ), file(xcmplx_0,fc9_xcmplx_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(involutiveness_k1_real_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => k1_real_1(k1_real_1(A)) = A ) ), file(real_1,k1_real_1), []). fof(involutiveness_k2_real_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => k2_real_1(k2_real_1(A)) = A ) ), file(real_1,k2_real_1), []). fof(involutiveness_k4_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => k4_xcmplx_0(k4_xcmplx_0(A)) = A ) ), file(xcmplx_0,k4_xcmplx_0), []). fof(involutiveness_k5_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => k5_xcmplx_0(k5_xcmplx_0(A)) = A ) ), file(xcmplx_0,k5_xcmplx_0), []). fof(rc1_membered,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ), file(membered,rc1_membered), []). fof(rc1_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_xcmplx_0,axiom,( ? [A] : v1_xcmplx_0(A) ), file(xcmplx_0,rc1_xcmplx_0), []). fof(rc1_xreal_0,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(xreal_0,rc1_xreal_0), []). 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_xcmplx_0,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) ) ), file(xcmplx_0,rc2_xcmplx_0), []). fof(rc2_xreal_0,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc2_xreal_0), []). fof(rc3_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_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_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(redefinition_k13_arytm_3,axiom,( k13_arytm_3 = k4_ordinal2 ), file(arytm_3,k13_arytm_3), []). fof(redefinition_k1_polyeq_3,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k2_numbers) ) => k1_polyeq_3(A,B) = k3_xcmplx_0(A,B) ) ), file(polyeq_3,k1_polyeq_3), []). fof(redefinition_k1_real_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => k1_real_1(A) = k4_xcmplx_0(A) ) ), file(real_1,k1_real_1), []). fof(redefinition_k2_polyeq_3,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k2_numbers) ) => k2_polyeq_3(A,B) = k2_xcmplx_0(A,B) ) ), file(polyeq_3,k2_polyeq_3), []). fof(redefinition_k2_power,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k1_numbers) ) => k2_power(A,B) = k1_power(A,B) ) ), file(power,k2_power), []). fof(redefinition_k2_real_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => k2_real_1(A) = k5_xcmplx_0(A) ) ), file(real_1,k2_real_1), []). fof(redefinition_k3_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_complex1(A) = k1_complex1(A) ) ), file(complex1,k3_complex1), []). fof(redefinition_k3_newton,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & v4_ordinal2(B) ) => k3_newton(A,B) = k2_newton(A,B) ) ), file(newton,k3_newton), []). fof(redefinition_k3_polyeq_3,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => k3_polyeq_3(A) = k5_square_1(A) ) ), file(polyeq_3,k3_polyeq_3), []). fof(redefinition_k3_prepower,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k5_numbers) ) => k3_prepower(A,B) = k2_newton(A,B) ) ), file(prepower,k3_prepower), []). fof(redefinition_k3_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k3_real_1(A,B) = k2_xcmplx_0(A,B) ) ), file(real_1,k3_real_1), []). fof(redefinition_k4_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k4_complex1(A) = k2_complex1(A) ) ), file(complex1,k4_complex1), []). fof(redefinition_k4_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k4_real_1(A,B) = k3_xcmplx_0(A,B) ) ), file(real_1,k4_real_1), []). fof(redefinition_k5_funct_4,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(A) & m1_subset_1(D,A) & m1_subset_1(E,A) ) => k5_funct_4(A,B,C,D,E) = k4_funct_4(B,C,D,E) ) ), file(funct_4,k5_funct_4), []). fof(redefinition_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_k5_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k5_real_1(A,B) = k6_xcmplx_0(A,B) ) ), file(real_1,k5_real_1), []). fof(redefinition_k6_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k6_real_1(A,B) = k7_xcmplx_0(A,B) ) ), file(real_1,k6_real_1), []). fof(redefinition_k7_complex1,axiom,( k7_complex1 = k1_xcmplx_0 ), file(complex1,k7_complex1), []). fof(redefinition_k7_square_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => k7_square_1(A) = k5_square_1(A) ) ), file(square_1,k7_square_1), []). fof(redefinition_k8_complex1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) ) => k8_complex1(A,B) = k2_xcmplx_0(A,B) ) ), file(complex1,k8_complex1), []). fof(redefinition_k8_polyeq_1,axiom,( ! [A,B,C,D,E] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) & m1_subset_1(C,k1_numbers) & m1_subset_1(D,k1_numbers) & m1_subset_1(E,k1_numbers) ) => k8_polyeq_1(A,B,C,D,E) = k7_polyeq_1(A,B,C,D,E) ) ), file(polyeq_1,k8_polyeq_1), []). fof(redefinition_k9_complex1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) ) => k9_complex1(A,B) = k3_xcmplx_0(A,B) ) ), file(complex1,k9_complex1), []). fof(redefinition_k9_square_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => k9_square_1(A) = k8_square_1(A) ) ), file(square_1,k9_square_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(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(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(spc2_boole,axiom,( ~ v1_xboole_0(2) ), file(boole,spc2_boole), []). fof(spc2_numerals,axiom, ( v2_xreal_0(2) & m1_subset_1(2,k5_numbers) ), file(numerals,spc2_numerals), []). fof(spc3_boole,axiom,( ~ v1_xboole_0(3) ), file(boole,spc3_boole), []). fof(spc3_numerals,axiom, ( v2_xreal_0(3) & m1_subset_1(3,k5_numbers) ), file(numerals,spc3_numerals), []). fof(spc4_boole,axiom,( ~ v1_xboole_0(4) ), file(boole,spc4_boole), []). fof(spc4_numerals,axiom, ( v2_xreal_0(4) & m1_subset_1(4,k5_numbers) ), file(numerals,spc4_numerals), []). fof(t104_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k3_xcmplx_0(k7_xcmplx_0(1,A),k7_xcmplx_0(B,C)) = k7_xcmplx_0(B,k3_xcmplx_0(C,A)) ) ) ) ), file(xcmplx_1,t104_xcmplx_1), []). fof(t11_polyeq_3,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => ( k3_complex1(k5_polyeq_3(A)) = k5_real_1(k3_prepower(k3_complex1(A),3),k4_real_1(k4_real_1(3,k3_complex1(A)),k7_square_1(k4_complex1(A)))) & k4_complex1(k5_polyeq_3(A)) = k3_real_1(k1_real_1(k3_prepower(k4_complex1(A),3)),k4_real_1(k4_real_1(3,k7_square_1(k3_complex1(A))),k4_complex1(A))) ) ) ), file(polyeq_3,t11_polyeq_3), []). fof(t16_newton,axiom,( ! [A] : ( v4_ordinal2(A) => ( r1_xreal_0(1,A) => k3_newton(0,A) = 0 ) ) ), file(newton,t16_newton), []). fof(t19_polyeq_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( k7_polyeq_1(1,0,A,B,C) = 0 => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( C = k2_xcmplx_0(D,E) & k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,E),D),A) = 0 & C != k2_xcmplx_0(k1_power(3,k2_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(B,2)),k8_square_1(k2_xcmplx_0(k7_xcmplx_0(k5_square_1(B),4),k2_newton(k7_xcmplx_0(A,3),3))))),k1_power(3,k6_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(B,2)),k8_square_1(k2_xcmplx_0(k7_xcmplx_0(k5_square_1(B),4),k2_newton(k7_xcmplx_0(A,3),3)))))) & C != k2_xcmplx_0(k1_power(3,k2_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(B,2)),k8_square_1(k2_xcmplx_0(k7_xcmplx_0(k5_square_1(B),4),k2_newton(k7_xcmplx_0(A,3),3))))),k1_power(3,k2_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(B,2)),k8_square_1(k2_xcmplx_0(k7_xcmplx_0(k5_square_1(B),4),k2_newton(k7_xcmplx_0(A,3),3)))))) & C != k2_xcmplx_0(k1_power(3,k6_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(B,2)),k8_square_1(k2_xcmplx_0(k7_xcmplx_0(k5_square_1(B),4),k2_newton(k7_xcmplx_0(A,3),3))))),k1_power(3,k6_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(B,2)),k8_square_1(k2_xcmplx_0(k7_xcmplx_0(k5_square_1(B),4),k2_newton(k7_xcmplx_0(A,3),3)))))) ) ) ) ) ) ) ) ), file(polyeq_1,t19_polyeq_1), []). 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(t27_complex1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => k5_arytm_0(A,B) = k2_xcmplx_0(A,k3_xcmplx_0(B,k7_complex1)) ) ) ), file(complex1,t27_complex1), []). fof(t28_complex1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => ( k3_complex1(k2_xcmplx_0(A,k3_xcmplx_0(B,k7_complex1))) = A & k4_complex1(k2_xcmplx_0(A,k3_xcmplx_0(B,k7_complex1))) = B ) ) ) ), file(complex1,t28_complex1), []). fof(t29_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(k3_complex1(A),k3_xcmplx_0(k4_complex1(A),k7_complex1)) = A ) ), file(complex1,t29_complex1), []). fof(t2_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(A,0) = 0 ) ), file(arithm,t2_arithm), []). 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(t3_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(1,A) = A ) ), file(arithm,t3_arithm), []). 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_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k6_xcmplx_0(A,0) = A ) ), file(arithm,t4_arithm), []). 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(t5_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k7_xcmplx_0(0,A) = 0 ) ), file(arithm,t5_arithm), []). 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(t60_square_1,axiom,( k7_square_1(0) = 0 ), file(square_1,t60_square_1), []). fof(t69_square_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k5_square_1(k7_xcmplx_0(A,B)) = k7_xcmplx_0(k5_square_1(A),k5_square_1(B)) ) ) ), file(square_1,t69_square_1), []). fof(t6_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k7_xcmplx_0(A,1) = A ) ), file(arithm,t6_arithm), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). 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_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(t89_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( A != 0 => B = k3_xcmplx_0(B,k7_xcmplx_0(A,A)) ) ) ) ), file(xcmplx_1,t89_xcmplx_1), []). 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), []).