% Mizar problem: t73_stirl2_1,stirl2_1,3783,44 fof(t73_stirl2_1,conjecture,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k5_numbers)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k5_numbers)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) ) => ~ ( v1_finset_1(k5_relset_1(A,B,C)) & ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k5_relset_1(A,B,C),k5_relset_1(A,B,C)) & v3_funct_2(E,k5_relset_1(A,B,C),k5_relset_1(A,B,C)) & m2_relset_1(E,k5_relset_1(A,B,C),k5_relset_1(A,B,C)) ) => ~ ( C = k1_partfun1(A,B,k5_relset_1(A,B,C),k5_relset_1(A,B,C),D,E) & k5_relset_1(A,B,C) = k5_relset_1(A,B,D) & v2_stirl2_1(D,A,B) ) ) ) ) ) ) ) ), 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_afinsq_1,cc1_finset_1,cc1_funct_1,cc1_funct_2,cc1_membered,cc1_nat_1,cc1_relat_1,cc1_relset_1,cc1_stirl2_1,cc1_xreal_0,cc20_membered,cc2_finset_1,cc2_funct_1,cc2_funct_2,cc2_int_1,cc2_membered,cc2_nat_1,cc2_xreal_0,cc3_funct_2,cc3_int_1,cc3_membered,cc3_nat_1,cc3_xreal_0,cc4_int_1,cc4_membered,cc4_xreal_0,cc5_funct_2,cc5_xreal_0,cc6_funct_2,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,commutativity_k2_xboole_0,commutativity_k2_xcmplx_0,commutativity_k3_xboole_0,commutativity_k5_subset_1,connectedness_r1_xreal_0,d10_xboole_0,d13_funct_1,d1_funct_2,d1_henmodel,d1_tarski,d2_xboole_0,d3_funct_2,d3_tarski,d4_funct_2,d4_xboole_0,d5_funct_1,d5_real_1,d5_stirl2_1,dt_k10_relat_1,dt_k13_cqc_sim1,dt_k1_card_1,dt_k1_fraenkel,dt_k1_funct_1,dt_k1_funct_2,dt_k1_henmodel,dt_k1_numbers,dt_k1_partfun1,dt_k1_relat_1,dt_k1_stirl2_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_afinsq_1,dt_k2_funct_1,dt_k2_partfun1,dt_k2_relat_1,dt_k2_xboole_0,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_funct_2,dt_k3_xboole_0,dt_k4_card_1,dt_k4_relset_1,dt_k4_xboole_0,dt_k5_numbers,dt_k5_ordinal2,dt_k5_relat_1,dt_k5_relset_1,dt_k5_stirl2_1,dt_k5_subset_1,dt_k6_funct_2,dt_k6_partfun1,dt_k6_relat_1,dt_k6_subset_1,dt_k7_funct_2,dt_k7_relat_1,dt_k7_relset_1,dt_m1_fraenkel,dt_m1_relset_1,dt_m1_subset_1,dt_m2_fraenkel,dt_m2_relset_1,dt_m2_subset_1,existence_m1_fraenkel,existence_m1_relset_1,existence_m1_subset_1,existence_m2_fraenkel,existence_m2_relset_1,existence_m2_subset_1,fc10_finset_1,fc10_membered,fc10_relat_1,fc10_xreal_0,fc11_finset_1,fc11_membered,fc11_xreal_0,fc12_finset_1,fc12_relat_1,fc12_xreal_0,fc13_relat_1,fc14_finset_1,fc1_afinsq_1,fc1_finset_1,fc1_funct_1,fc1_funct_2,fc1_int_1,fc1_nat_1,fc1_ordinal2,fc1_relat_1,fc1_stirl2_1,fc1_subset_1,fc1_xboole_0,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc27_membered,fc28_membered,fc29_membered,fc2_afinsq_1,fc2_funct_1,fc2_funct_2,fc2_membered,fc2_relat_1,fc2_subset_1,fc2_xboole_0,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc37_membered,fc38_membered,fc39_membered,fc3_nat_1,fc3_relat_1,fc3_xboole_0,fc3_xreal_0,fc40_membered,fc41_membered,fc4_funct_1,fc4_nat_1,fc4_relat_1,fc4_subset_1,fc5_membered,fc5_relat_1,fc6_int_1,fc6_membered,fc6_relat_1,fc7_membered,fc7_relat_1,fc7_xreal_0,fc8_membered,fc8_relat_1,fc8_xreal_0,fc9_finset_1,fc9_membered,fc9_relat_1,fc9_xreal_0,idempotence_k2_xboole_0,idempotence_k3_xboole_0,idempotence_k5_subset_1,l35_stirl2_1,l77_stirl2_1,l81_stirl2_1,rc1_afinsq_1,rc1_finset_1,rc1_funct_1,rc1_funct_2,rc1_int_1,rc1_membered,rc1_nat_1,rc1_relat_1,rc1_subset_1,rc1_xboole_0,rc1_xreal_0,rc2_finset_1,rc2_funct_1,rc2_funct_2,rc2_int_1,rc2_nat_1,rc2_relat_1,rc2_subset_1,rc2_xboole_0,rc2_xreal_0,rc3_afinsq_1,rc3_finset_1,rc3_funct_1,rc3_nat_1,rc3_relat_1,rc3_xreal_0,rc4_afinsq_1,rc4_finset_1,rc4_funct_1,rc4_xreal_0,redefinition_k13_cqc_sim1,redefinition_k1_fraenkel,redefinition_k1_partfun1,redefinition_k1_stirl2_1,redefinition_k2_afinsq_1,redefinition_k2_partfun1,redefinition_k3_funct_2,redefinition_k4_card_1,redefinition_k4_relset_1,redefinition_k5_numbers,redefinition_k5_relset_1,redefinition_k5_stirl2_1,redefinition_k5_subset_1,redefinition_k6_funct_2,redefinition_k6_partfun1,redefinition_k6_subset_1,redefinition_k7_funct_2,redefinition_k7_relset_1,redefinition_m2_fraenkel,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,s2_stirl2_1__e22_97_2_1_1_2_1_1_2__stirl2_1,s9_stirl2_1__e3_97__stirl2_1,spc0_boole,spc1_boole,spc1_numerals,t10_xreal_1,t13_finset_1,t167_relat_1,t19_funct_2,t1_arithm,t1_boole,t1_euler_1,t1_numerals,t1_real,t1_subset,t1_xboole_1,t20_funct_1,t20_funct_2,t22_funct_1,t23_funct_2,t28_xboole_1,t2_boole,t2_real,t2_subset,t2_xreal_1,t31_funct_2,t36_xboole_1,t38_nat_1,t3_boole,t3_funct_2,t3_real,t3_subset,t3_xboole_1,t46_funct_1,t4_boole,t4_real,t4_subset,t51_xboole_1,t52_funct_1,t55_funct_1,t55_relat_1,t56_funct_1,t57_funct_1,t5_real,t5_subset,t60_relat_1,t61_funct_1,t62_relat_1,t64_relat_1,t64_stirl2_1,t64_zfmisc_1,t65_relat_1,t66_zfmisc_1,t67_stirl2_1,t68_funct_1,t68_stirl2_1,t69_stirl2_1,t6_boole,t6_real,t71_relat_1,t71_stirl2_1,t7_boole,t7_real,t8_boole,t8_funct_2,t8_real,t8_stirl2_1,t99_relat_1]), [file(stirl2_1,t73_stirl2_1)]). 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_afinsq_1,axiom,( ! [A] : ( v4_ordinal2(A) => v1_finset_1(A) ) ), file(afinsq_1,cc1_afinsq_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_funct_2,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_partfun1(C,A,B) ) => ( v1_funct_1(C) & v1_funct_2(C,A,B) ) ) ) ), file(funct_2,cc1_funct_2), []). fof(cc1_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_relat_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_relat_1(A) ) ), file(relat_1,cc1_relat_1), []). fof(cc1_relset_1,axiom,( ! [A,B,C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => v1_relat_1(C) ) ), file(relset_1,cc1_relset_1), []). fof(cc1_stirl2_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ! [B] : ( m1_subset_1(B,A) => ( v4_ordinal2(B) & v1_xcmplx_0(B) & v1_finset_1(B) & v1_xreal_0(B) & ~ v3_xreal_0(B) & v1_int_1(B) ) ) ) ), file(stirl2_1,cc1_stirl2_1), []). 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_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_funct_2,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & v3_funct_2(C,A,B) ) => ( v1_funct_1(C) & v2_funct_1(C) & v1_funct_2(C,A,B) & v2_funct_2(C,A,B) ) ) ) ), file(funct_2,cc2_funct_2), []). fof(cc2_int_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_int_1(A) ) ) ), file(int_1,cc2_int_1), []). fof(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_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xcmplx_0(A) ) ), file(xreal_0,cc2_xreal_0), []). fof(cc3_funct_2,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v2_funct_1(C) & v1_funct_2(C,A,B) & v2_funct_2(C,A,B) ) => ( v1_funct_1(C) & v1_funct_2(C,A,B) & v3_funct_2(C,A,B) ) ) ) ), file(funct_2,cc3_funct_2), []). fof(cc3_int_1,axiom,( ! [A] : ( v4_ordinal2(A) => v1_int_1(A) ) ), file(int_1,cc3_int_1), []). 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_int_1,axiom,( ! [A] : ( v1_int_1(A) => ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(int_1,cc4_int_1), []). 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_funct_2,axiom,( ! [A,B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_funct_2(C,A,B) ) => ( v1_funct_1(C) & v1_partfun1(C,A,B) & v1_funct_2(C,A,B) ) ) ) ) ), file(funct_2,cc5_funct_2), []). fof(cc5_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & v3_xreal_0(A) ) => ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) ) ) ), file(xreal_0,cc5_xreal_0), []). fof(cc6_funct_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ! [C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_funct_2(C,A,B) ) => ( v1_funct_1(C) & ~ v1_xboole_0(C) & v1_partfun1(C,A,B) & v1_funct_2(C,A,B) ) ) ) ) ), file(funct_2,cc6_funct_2), []). fof(cc6_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_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ), file(xboole_0,k2_xboole_0), []). fof(commutativity_k2_xcmplx_0,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ), file(xcmplx_0,k2_xcmplx_0), []). fof(commutativity_k3_xboole_0,axiom,( ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ), file(xboole_0,k3_xboole_0), []). fof(commutativity_k5_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k5_subset_1(A,B,C) = k5_subset_1(A,C,B) ) ), file(subset_1,k5_subset_1), []). 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_xboole_0,axiom,( ! [A,B] : ( A = B <=> ( r1_tarski(A,B) & r1_tarski(B,A) ) ) ), file(xboole_0,d10_xboole_0), []). fof(d13_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B,C] : ( C = k10_relat_1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,k1_relat_1(A)) & r2_hidden(k1_funct_1(A,D),B) ) ) ) ) ), file(funct_1,d13_funct_1), []). fof(d1_funct_2,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => ( ( ( B = k1_xboole_0 => A = k1_xboole_0 ) => ( v1_funct_2(C,A,B) <=> A = k4_relset_1(A,B,C) ) ) & ( B = k1_xboole_0 => ( A = k1_xboole_0 | ( v1_funct_2(C,A,B) <=> C = k1_xboole_0 ) ) ) ) ) ), file(funct_2,d1_funct_2), []). fof(d1_henmodel,axiom,( ! [A,B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k5_numbers)) ) => ( B = k1_henmodel(A) <=> ( r2_hidden(B,A) & ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( r2_hidden(C,A) => r1_xreal_0(B,C) ) ) ) ) ) & ( ~ ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k5_numbers)) ) => ( B = k1_henmodel(A) <=> B = 0 ) ) ) ) ), file(henmodel,d1_henmodel), []). fof(d1_tarski,axiom,( ! [A,B] : ( B = k1_tarski(A) <=> ! [C] : ( r2_hidden(C,B) <=> C = A ) ) ), file(tarski,d1_tarski), []). fof(d2_xboole_0,axiom,( ! [A,B,C] : ( C = k2_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) | r2_hidden(D,B) ) ) ) ), file(xboole_0,d2_xboole_0), []). fof(d3_funct_2,axiom,( ! [A,B,C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) ) => ( v2_funct_2(C,A,B) <=> k2_relat_1(C) = B ) ) ), file(funct_2,d3_funct_2), []). fof(d3_tarski,axiom,( ! [A,B] : ( r1_tarski(A,B) <=> ! [C] : ( r2_hidden(C,A) => r2_hidden(C,B) ) ) ), file(tarski,d3_tarski), []). fof(d4_funct_2,axiom,( ! [A,B,C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) ) => ( v3_funct_2(C,A,B) <=> ( v2_funct_1(C) & v2_funct_2(C,A,B) ) ) ) ), file(funct_2,d4_funct_2), []). fof(d4_xboole_0,axiom,( ! [A,B,C] : ( C = k4_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) & ~ r2_hidden(D,B) ) ) ) ), file(xboole_0,d4_xboole_0), []). 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_real_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) <=> ~ ( r1_xreal_0(B,A) & B != A ) ) ) ) ), file(real_1,d5_real_1), []). fof(d5_stirl2_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k5_numbers)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k5_numbers)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) ) => ( v2_stirl2_1(C,A,B) <=> ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ~ ( r2_hidden(D,k5_relset_1(A,B,C)) & r2_hidden(E,k5_relset_1(A,B,C)) & ~ r1_xreal_0(E,D) & r1_xreal_0(k1_henmodel(k3_funct_2(A,B,C,k1_stirl2_1(E))),k1_henmodel(k3_funct_2(A,B,C,k1_stirl2_1(D)))) ) ) ) ) ) ) ) ), file(stirl2_1,d5_stirl2_1), []). fof(dt_k10_relat_1,axiom,( $true ), file(relat_1,k10_relat_1), []). fof(dt_k13_cqc_sim1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m2_fraenkel(k13_cqc_sim1(A),A,A,k1_fraenkel(A,A)) ) ), file(cqc_sim1,k13_cqc_sim1), []). fof(dt_k1_card_1,axiom,( ! [A] : v1_card_1(k1_card_1(A)) ), file(card_1,k1_card_1), []). fof(dt_k1_fraenkel,axiom,( ! [A,B] : ( ~ v1_xboole_0(B) => m1_fraenkel(k1_fraenkel(A,B),A,B) ) ), file(fraenkel,k1_fraenkel), []). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). fof(dt_k1_funct_2,axiom,( $true ), file(funct_2,k1_funct_2), []). fof(dt_k1_henmodel,axiom,( ! [A] : m2_subset_1(k1_henmodel(A),k1_numbers,k5_numbers) ), file(henmodel,k1_henmodel), []). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), []). fof(dt_k1_partfun1,axiom,( ! [A,B,C,D,E,F] : ( ( v1_funct_1(E) & m1_relset_1(E,A,B) & v1_funct_1(F) & m1_relset_1(F,C,D) ) => ( v1_funct_1(k1_partfun1(A,B,C,D,E,F)) & m2_relset_1(k1_partfun1(A,B,C,D,E,F),A,D) ) ) ), file(partfun1,k1_partfun1), []). fof(dt_k1_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), []). fof(dt_k1_stirl2_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => m1_subset_1(k1_stirl2_1(A),k1_zfmisc_1(k5_numbers)) ) ), file(stirl2_1,k1_stirl2_1), []). fof(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), []). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), []). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), []). fof(dt_k2_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_finset_1(A) ) => m1_subset_1(k2_afinsq_1(A),k1_zfmisc_1(k5_numbers)) ) ), file(afinsq_1,k2_afinsq_1), []). fof(dt_k2_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k2_funct_1(A)) & v1_funct_1(k2_funct_1(A)) ) ) ), file(funct_1,k2_funct_1), []). fof(dt_k2_partfun1,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & m1_relset_1(C,A,B) ) => ( v1_funct_1(k2_partfun1(A,B,C,D)) & m2_relset_1(k2_partfun1(A,B,C,D),A,B) ) ) ), file(partfun1,k2_partfun1), []). fof(dt_k2_relat_1,axiom,( $true ), file(relat_1,k2_relat_1), []). fof(dt_k2_xboole_0,axiom,( $true ), file(xboole_0,k2_xboole_0), []). fof(dt_k2_xcmplx_0,axiom,( $true ), file(xcmplx_0,k2_xcmplx_0), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). fof(dt_k3_funct_2,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & m1_relset_1(C,A,B) ) => m1_subset_1(k3_funct_2(A,B,C,D),k1_zfmisc_1(A)) ) ), file(funct_2,k3_funct_2), []). fof(dt_k3_xboole_0,axiom,( $true ), file(xboole_0,k3_xboole_0), []). 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_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(relset_1,k4_relset_1), []). fof(dt_k4_xboole_0,axiom,( $true ), file(xboole_0,k4_xboole_0), []). 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_relat_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => v1_relat_1(k5_relat_1(A,B)) ) ), file(relat_1,k5_relat_1), []). fof(dt_k5_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => m1_subset_1(k5_relset_1(A,B,C),k1_zfmisc_1(B)) ) ), file(relset_1,k5_relset_1), []). fof(dt_k5_stirl2_1,axiom,( ! [A,B,C,D] : ( ( m1_subset_1(B,k5_numbers) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) ) => m1_subset_1(k5_stirl2_1(A,B,C,D),B) ) ), file(stirl2_1,k5_stirl2_1), []). fof(dt_k5_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => m1_subset_1(k5_subset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(subset_1,k5_subset_1), []). fof(dt_k6_funct_2,axiom,( ! [A,B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,A) & v3_funct_2(B,A,A) & m1_relset_1(B,A,A) ) => ( v1_funct_1(k6_funct_2(A,B)) & v1_funct_2(k6_funct_2(A,B),A,A) & v3_funct_2(k6_funct_2(A,B),A,A) & m2_relset_1(k6_funct_2(A,B),A,A) ) ) ), file(funct_2,k6_funct_2), []). fof(dt_k6_partfun1,axiom,( ! [A] : ( v1_partfun1(k6_partfun1(A),A,A) & m2_relset_1(k6_partfun1(A),A,A) ) ), file(partfun1,k6_partfun1), []). fof(dt_k6_relat_1,axiom,( ! [A] : v1_relat_1(k6_relat_1(A)) ), file(relat_1,k6_relat_1), []). fof(dt_k6_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => m1_subset_1(k6_subset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(subset_1,k6_subset_1), []). fof(dt_k7_funct_2,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(D,A,B) & m1_relset_1(D,A,B) & v1_funct_1(E) & v1_funct_2(E,B,C) & m1_relset_1(E,B,C) ) => ( v1_funct_1(k7_funct_2(A,B,C,D,E)) & v1_funct_2(k7_funct_2(A,B,C,D,E),A,C) & m2_relset_1(k7_funct_2(A,B,C,D,E),A,C) ) ) ), file(funct_2,k7_funct_2), []). fof(dt_k7_relat_1,axiom,( ! [A,B] : ( v1_relat_1(A) => v1_relat_1(k7_relat_1(A,B)) ) ), file(relat_1,k7_relat_1), []). fof(dt_k7_relset_1,axiom,( ! [A,B,C,D,E,F] : ( ( m1_relset_1(E,A,B) & m1_relset_1(F,C,D) ) => m2_relset_1(k7_relset_1(A,B,C,D,E,F),A,D) ) ), file(relset_1,k7_relset_1), []). fof(dt_m1_fraenkel,axiom,( ! [A,B,C] : ( m1_fraenkel(C,A,B) => ( ~ v1_xboole_0(C) & v1_fraenkel(C) ) ) ), file(fraenkel,m1_fraenkel), []). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), []). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), []). fof(dt_m2_fraenkel,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(B) & m1_fraenkel(C,A,B) ) => ! [D] : ( m2_fraenkel(D,A,B,C) => ( v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) ) ) ) ), file(fraenkel,m2_fraenkel), []). 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_fraenkel,axiom,( ! [A,B] : ? [C] : m1_fraenkel(C,A,B) ), file(fraenkel,m1_fraenkel), []). fof(existence_m1_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), []). fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), []). fof(existence_m2_fraenkel,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(B) & m1_fraenkel(C,A,B) ) => ? [D] : m2_fraenkel(D,A,B,C) ) ), file(fraenkel,m2_fraenkel), []). 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_finset_1,axiom,( ! [A,B] : ( v1_finset_1(B) => v1_finset_1(k3_xboole_0(A,B)) ) ), file(finset_1,fc10_finset_1), []). fof(fc10_membered,axiom,( ! [A] : ( v1_int_1(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) ) ) ), file(membered,fc10_membered), []). fof(fc10_relat_1,axiom,( ! [A,B] : ( ( v1_xboole_0(A) & v1_relat_1(B) ) => ( v1_xboole_0(k5_relat_1(B,A)) & v1_relat_1(k5_relat_1(B,A)) ) ) ), file(relat_1,fc10_relat_1), []). fof(fc10_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v2_xreal_0(k2_xcmplx_0(B,A)) & ~ v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc10_xreal_0), []). fof(fc11_finset_1,axiom,( ! [A,B] : ( v1_finset_1(A) => v1_finset_1(k3_xboole_0(A,B)) ) ), file(finset_1,fc11_finset_1), []). fof(fc11_membered,axiom,( ! [A] : ( v4_ordinal2(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) & v5_membered(k1_tarski(A)) ) ) ), file(membered,fc11_membered), []). 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_finset_1,axiom,( ! [A,B] : ( v1_finset_1(A) => v1_finset_1(k4_xboole_0(A,B)) ) ), file(finset_1,fc12_finset_1), []). fof(fc12_relat_1,axiom, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) ), file(relat_1,fc12_relat_1), []). fof(fc12_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & ~ v2_xreal_0(k2_xcmplx_0(B,A)) & v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc12_xreal_0), []). fof(fc13_relat_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v3_relat_1(A) ) => ( v1_relat_1(k7_relat_1(A,B)) & v3_relat_1(k7_relat_1(A,B)) ) ) ), file(relat_1,fc13_relat_1), []). fof(fc14_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(fc1_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_finset_1(A) ) => ( v1_ordinal1(k1_relat_1(A)) & v2_ordinal1(k1_relat_1(A)) & v3_ordinal1(k1_relat_1(A)) & v4_ordinal2(k1_relat_1(A)) & v1_xcmplx_0(k1_relat_1(A)) & v1_xreal_0(k1_relat_1(A)) ) ) ), file(afinsq_1,fc1_afinsq_1), []). 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_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => ( v1_relat_1(k5_relat_1(A,B)) & v1_funct_1(k5_relat_1(A,B)) ) ) ), file(funct_1,fc1_funct_1), []). fof(fc1_funct_2,axiom,( ! [A,B] : ( ~ v1_xboole_0(B) => ~ v1_xboole_0(k1_funct_2(A,B)) ) ), file(funct_2,fc1_funct_2), []). fof(fc1_int_1,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_int_1(k2_xcmplx_0(A,B)) ) ) ), file(int_1,fc1_int_1), []). fof(fc1_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_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_relat_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => v1_relat_1(k3_xboole_0(A,B)) ) ), file(relat_1,fc1_relat_1), []). fof(fc1_stirl2_1,axiom,( ! [A,B,C,D] : ( ( m1_subset_1(B,k1_zfmisc_1(k5_numbers)) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) ) => ( v4_ordinal2(k1_funct_1(C,D)) & v1_xcmplx_0(k1_funct_1(C,D)) & v1_finset_1(k1_funct_1(C,D)) & v1_xreal_0(k1_funct_1(C,D)) & ~ v3_xreal_0(k1_funct_1(C,D)) & v1_int_1(k1_funct_1(C,D)) ) ) ), file(stirl2_1,fc1_stirl2_1), []). fof(fc1_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ), file(subset_1,fc1_subset_1), []). fof(fc1_xboole_0,axiom,( v1_xboole_0(k1_xboole_0) ), file(xboole_0,fc1_xboole_0), []). fof(fc22_membered,axiom,( ! [A,B] : ( ( v1_membered(A) & v1_membered(B) ) => v1_membered(k2_xboole_0(A,B)) ) ), file(membered,fc22_membered), []). fof(fc23_membered,axiom,( ! [A,B] : ( ( v2_membered(A) & v2_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc23_membered), []). fof(fc24_membered,axiom,( ! [A,B] : ( ( v3_membered(A) & v3_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc24_membered), []). fof(fc25_membered,axiom,( ! [A,B] : ( ( v4_membered(A) & v4_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc25_membered), []). fof(fc26_membered,axiom,( ! [A,B] : ( ( v5_membered(A) & v5_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) & v5_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc26_membered), []). fof(fc27_membered,axiom,( ! [A,B] : ( v1_membered(A) => v1_membered(k3_xboole_0(A,B)) ) ), file(membered,fc27_membered), []). fof(fc28_membered,axiom,( ! [A,B] : ( v1_membered(A) => v1_membered(k3_xboole_0(B,A)) ) ), file(membered,fc28_membered), []). fof(fc29_membered,axiom,( ! [A,B] : ( v2_membered(A) => ( v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) ) ) ), file(membered,fc29_membered), []). fof(fc2_afinsq_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_ordinal1(k1_xboole_0) & v2_ordinal1(k1_xboole_0) & v3_ordinal1(k1_xboole_0) & v5_ordinal1(k1_xboole_0) & v4_ordinal2(k1_xboole_0) & v1_xcmplx_0(k1_xboole_0) & v1_finset_1(k1_xboole_0) & v1_finseq_1(k1_xboole_0) & v1_funcop_1(k1_xboole_0) & v1_funct_7(k1_xboole_0) & v1_xreal_0(k1_xboole_0) & ~ v2_xreal_0(k1_xboole_0) & ~ v3_xreal_0(k1_xboole_0) ), file(afinsq_1,fc2_afinsq_1), []). fof(fc2_funct_1,axiom,( ! [A] : ( v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) ) ), file(funct_1,fc2_funct_1), []). fof(fc2_funct_2,axiom,( ! [A] : ~ v1_xboole_0(k1_funct_2(A,A)) ), file(funct_2,fc2_funct_2), []). fof(fc2_membered,axiom, ( ~ v1_xboole_0(k1_numbers) & v1_membered(k1_numbers) & v2_membered(k1_numbers) ), file(membered,fc2_membered), []). fof(fc2_relat_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => v1_relat_1(k2_xboole_0(A,B)) ) ), file(relat_1,fc2_relat_1), []). fof(fc2_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) ), file(subset_1,fc2_subset_1), []). fof(fc2_xboole_0,axiom,( ! [A,B] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k2_xboole_0(A,B)) ) ), file(xboole_0,fc2_xboole_0), []). fof(fc30_membered,axiom,( ! [A,B] : ( v2_membered(A) => ( v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) ) ) ), file(membered,fc30_membered), []). fof(fc31_membered,axiom,( ! [A,B] : ( v3_membered(A) => ( v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) ) ) ), file(membered,fc31_membered), []). fof(fc32_membered,axiom,( ! [A,B] : ( v3_membered(A) => ( v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) ) ) ), file(membered,fc32_membered), []). fof(fc33_membered,axiom,( ! [A,B] : ( v4_membered(A) => ( v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) ) ) ), file(membered,fc33_membered), []). fof(fc34_membered,axiom,( ! [A,B] : ( v4_membered(A) => ( v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) & v4_membered(k3_xboole_0(B,A)) ) ) ), file(membered,fc34_membered), []). fof(fc35_membered,axiom,( ! [A,B] : ( v5_membered(A) => ( v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) & v5_membered(k3_xboole_0(A,B)) ) ) ), file(membered,fc35_membered), []). fof(fc36_membered,axiom,( ! [A,B] : ( v5_membered(A) => ( v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) & v4_membered(k3_xboole_0(B,A)) & v5_membered(k3_xboole_0(B,A)) ) ) ), file(membered,fc36_membered), []). fof(fc37_membered,axiom,( ! [A,B] : ( v1_membered(A) => v1_membered(k4_xboole_0(A,B)) ) ), file(membered,fc37_membered), []). fof(fc38_membered,axiom,( ! [A,B] : ( v2_membered(A) => ( v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) ) ) ), file(membered,fc38_membered), []). fof(fc39_membered,axiom,( ! [A,B] : ( v3_membered(A) => ( v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) ) ) ), file(membered,fc39_membered), []). 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_relat_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => v1_relat_1(k4_xboole_0(A,B)) ) ), file(relat_1,fc3_relat_1), []). fof(fc3_xboole_0,axiom,( ! [A,B] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k2_xboole_0(B,A)) ) ), file(xboole_0,fc3_xboole_0), []). fof(fc3_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc3_xreal_0), []). fof(fc40_membered,axiom,( ! [A,B] : ( v4_membered(A) => ( v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) & v4_membered(k4_xboole_0(A,B)) ) ) ), file(membered,fc40_membered), []). fof(fc41_membered,axiom,( ! [A,B] : ( v5_membered(A) => ( v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) & v4_membered(k4_xboole_0(A,B)) & v5_membered(k4_xboole_0(A,B)) ) ) ), file(membered,fc41_membered), []). fof(fc4_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)) ) ) ), file(funct_1,fc4_funct_1), []). fof(fc4_nat_1,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & ~ v1_xboole_0(B) & v4_ordinal2(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v4_ordinal2(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(nat_1,fc4_nat_1), []). fof(fc4_relat_1,axiom, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) ), file(relat_1,fc4_relat_1), []). fof(fc4_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ), file(subset_1,fc4_subset_1), []). fof(fc5_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_relat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) ) => ~ v1_xboole_0(k1_relat_1(A)) ) ), file(relat_1,fc5_relat_1), []). fof(fc6_int_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & v1_int_1(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v1_int_1(k2_xcmplx_0(B,A)) ) ) ), file(int_1,fc6_int_1), []). fof(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_relat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) ) => ~ v1_xboole_0(k2_relat_1(A)) ) ), file(relat_1,fc6_relat_1), []). fof(fc7_membered,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_membered(k1_tarski(A)) ) ), file(membered,fc7_membered), []). fof(fc7_relat_1,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_xboole_0(k1_relat_1(A)) & v1_relat_1(k1_relat_1(A)) ) ) ), file(relat_1,fc7_relat_1), []). fof(fc7_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc7_xreal_0), []). fof(fc8_membered,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) ) ) ), file(membered,fc8_membered), []). fof(fc8_relat_1,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_xboole_0(k2_relat_1(A)) & v1_relat_1(k2_relat_1(A)) ) ) ), file(relat_1,fc8_relat_1), []). fof(fc8_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v2_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc8_xreal_0), []). fof(fc9_finset_1,axiom,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_xboole_0(A,B)) ) ), file(finset_1,fc9_finset_1), []). fof(fc9_membered,axiom,( ! [A] : ( v1_rat_1(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) ) ) ), file(membered,fc9_membered), []). fof(fc9_relat_1,axiom,( ! [A,B] : ( ( v1_xboole_0(A) & v1_relat_1(B) ) => ( v1_xboole_0(k5_relat_1(A,B)) & v1_relat_1(k5_relat_1(A,B)) ) ) ), file(relat_1,fc9_relat_1), []). fof(fc9_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v2_xreal_0(k2_xcmplx_0(A,B)) & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc9_xreal_0), []). fof(idempotence_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,A) = A ), file(xboole_0,k2_xboole_0), []). fof(idempotence_k3_xboole_0,axiom,( ! [A,B] : k3_xboole_0(A,A) = A ), file(xboole_0,k3_xboole_0), []). fof(idempotence_k5_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k5_subset_1(A,B,B) = B ) ), file(subset_1,k5_subset_1), []). fof(l35_stirl2_1,axiom,( ! [A] : ( k1_card_1(A) = 0 <=> v1_xboole_0(A) ) ), file(stirl2_1,l35_stirl2_1), []). fof(l77_stirl2_1,axiom,( ! [A,B] : ( r2_hidden(B,A) => k2_xboole_0(k4_xboole_0(A,k1_tarski(B)),k1_tarski(B)) = A ) ), file(stirl2_1,l77_stirl2_1), []). fof(l81_stirl2_1,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k5_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k4_card_1(B)) & m2_relset_1(C,B,k4_card_1(B)) ) => ~ ( r2_hidden(A,B) & v3_funct_2(C,B,k4_card_1(B)) & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ~ ( r2_hidden(D,k4_relset_1(B,k4_card_1(B),C)) & r2_hidden(E,k4_relset_1(B,k4_card_1(B),C)) & ~ r1_xreal_0(E,D) & r1_xreal_0(k5_stirl2_1(B,k4_card_1(B),C,E),k5_stirl2_1(B,k4_card_1(B),C,D)) ) ) ) & ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,B,B) & v3_funct_2(D,B,B) & m2_relset_1(D,B,B) ) => ? [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) & r2_hidden(E,B) & ~ ( ( ~ r1_xreal_0(A,E) => k1_funct_1(D,E) = k1_funct_1(k2_funct_1(C),k2_xcmplx_0(k5_stirl2_1(B,k4_card_1(B),C,E),1)) ) & ( E = A => k1_funct_1(D,E) = k1_funct_1(k2_funct_1(C),0) ) & ( ~ r1_xreal_0(E,A) => k1_funct_1(D,E) = E ) ) ) ) ) ) ) ) ), file(stirl2_1,l81_stirl2_1), []). fof(rc1_afinsq_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_finset_1(A) ) ), file(afinsq_1,rc1_afinsq_1), []). fof(rc1_finset_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) ) ), file(finset_1,rc1_finset_1), []). fof(rc1_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc1_funct_1), []). fof(rc1_funct_2,axiom,( ! [A,B] : ? [C] : ( m1_relset_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C) & v1_funct_2(C,A,B) ) ), file(funct_2,rc1_funct_2), []). fof(rc1_int_1,axiom,( ? [A] : ( m1_subset_1(A,k1_numbers) & v1_xcmplx_0(A) & v1_xreal_0(A) & v1_int_1(A) ) ), file(int_1,rc1_int_1), []). fof(rc1_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_relat_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) ) ), file(relat_1,rc1_relat_1), []). fof(rc1_subset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) ) ) ), file(subset_1,rc1_subset_1), []). fof(rc1_xboole_0,axiom,( ? [A] : v1_xboole_0(A) ), file(xboole_0,rc1_xboole_0), []). fof(rc1_xreal_0,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(xreal_0,rc1_xreal_0), []). fof(rc2_finset_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_ordinal1(B) & v2_ordinal1(B) & v3_ordinal1(B) & v4_ordinal2(B) & v1_finset_1(B) ) ), file(finset_1,rc2_finset_1), []). fof(rc2_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) ), file(funct_1,rc2_funct_1), []). fof(rc2_funct_2,axiom,( ! [A] : ? [B] : ( m1_relset_1(B,A,A) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_funct_2(B,A,A) & v2_funct_2(B,A,A) & v3_funct_2(B,A,A) ) ), file(funct_2,rc2_funct_2), []). fof(rc2_int_1,axiom,( ? [A] : v1_int_1(A) ), file(int_1,rc2_int_1), []). fof(rc2_nat_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(A) & v3_ordinal1(A) ) ), file(nat_1,rc2_nat_1), []). fof(rc2_relat_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) ) ), file(relat_1,rc2_relat_1), []). fof(rc2_subset_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) ) ), file(subset_1,rc2_subset_1), []). fof(rc2_xboole_0,axiom,( ? [A] : ~ v1_xboole_0(A) ), file(xboole_0,rc2_xboole_0), []). fof(rc2_xreal_0,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc2_xreal_0), []). fof(rc3_afinsq_1,axiom,( ! [A] : ? [B] : ( m1_relset_1(B,k5_numbers,A) & v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) ), file(afinsq_1,rc3_afinsq_1), []). fof(rc3_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc3_finset_1), []). fof(rc3_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ), file(funct_1,rc3_funct_1), []). fof(rc3_nat_1,axiom,( ? [A] : ( m1_subset_1(A,k5_numbers) & ~ v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(nat_1,rc3_nat_1), []). fof(rc3_relat_1,axiom,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) ) ), file(relat_1,rc3_relat_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_afinsq_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v5_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_finset_1(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(afinsq_1,rc4_afinsq_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_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_cqc_sim1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k13_cqc_sim1(A) = k6_relat_1(A) ) ), file(cqc_sim1,k13_cqc_sim1), []). fof(redefinition_k1_fraenkel,axiom,( ! [A,B] : ( ~ v1_xboole_0(B) => k1_fraenkel(A,B) = k1_funct_2(A,B) ) ), file(fraenkel,k1_fraenkel), []). fof(redefinition_k1_partfun1,axiom,( ! [A,B,C,D,E,F] : ( ( v1_funct_1(E) & m1_relset_1(E,A,B) & v1_funct_1(F) & m1_relset_1(F,C,D) ) => k1_partfun1(A,B,C,D,E,F) = k5_relat_1(E,F) ) ), file(partfun1,k1_partfun1), []). fof(redefinition_k1_stirl2_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => k1_stirl2_1(A) = k1_tarski(A) ) ), file(stirl2_1,k1_stirl2_1), []). fof(redefinition_k2_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_finset_1(A) ) => k2_afinsq_1(A) = k1_relat_1(A) ) ), file(afinsq_1,k2_afinsq_1), []). fof(redefinition_k2_partfun1,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & m1_relset_1(C,A,B) ) => k2_partfun1(A,B,C,D) = k7_relat_1(C,D) ) ), file(partfun1,k2_partfun1), []). fof(redefinition_k3_funct_2,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & m1_relset_1(C,A,B) ) => k3_funct_2(A,B,C,D) = k10_relat_1(C,D) ) ), file(funct_2,k3_funct_2), []). 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_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => k4_relset_1(A,B,C) = k1_relat_1(C) ) ), file(relset_1,k4_relset_1), []). fof(redefinition_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_k5_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => k5_relset_1(A,B,C) = k2_relat_1(C) ) ), file(relset_1,k5_relset_1), []). fof(redefinition_k5_stirl2_1,axiom,( ! [A,B,C,D] : ( ( m1_subset_1(B,k5_numbers) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) ) => k5_stirl2_1(A,B,C,D) = k1_funct_1(C,D) ) ), file(stirl2_1,k5_stirl2_1), []). fof(redefinition_k5_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k5_subset_1(A,B,C) = k3_xboole_0(B,C) ) ), file(subset_1,k5_subset_1), []). fof(redefinition_k6_funct_2,axiom,( ! [A,B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,A) & v3_funct_2(B,A,A) & m1_relset_1(B,A,A) ) => k6_funct_2(A,B) = k2_funct_1(B) ) ), file(funct_2,k6_funct_2), []). fof(redefinition_k6_partfun1,axiom,( ! [A] : k6_partfun1(A) = k6_relat_1(A) ), file(partfun1,k6_partfun1), []). fof(redefinition_k6_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k6_subset_1(A,B,C) = k4_xboole_0(B,C) ) ), file(subset_1,k6_subset_1), []). fof(redefinition_k7_funct_2,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(D,A,B) & m1_relset_1(D,A,B) & v1_funct_1(E) & v1_funct_2(E,B,C) & m1_relset_1(E,B,C) ) => k7_funct_2(A,B,C,D,E) = k5_relat_1(D,E) ) ), file(funct_2,k7_funct_2), []). fof(redefinition_k7_relset_1,axiom,( ! [A,B,C,D,E,F] : ( ( m1_relset_1(E,A,B) & m1_relset_1(F,C,D) ) => k7_relset_1(A,B,C,D,E,F) = k5_relat_1(E,F) ) ), file(relset_1,k7_relset_1), []). fof(redefinition_m2_fraenkel,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(B) & m1_fraenkel(C,A,B) ) => ! [D] : ( m2_fraenkel(D,A,B,C) <=> m1_subset_1(D,C) ) ) ), file(fraenkel,m2_fraenkel), []). fof(redefinition_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) <=> m1_relset_1(C,A,B) ) ), file(relset_1,m2_relset_1), []). fof(redefinition_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(subset_1,m2_subset_1), []). fof(reflexivity_r1_tarski,axiom,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), []). fof(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(s2_stirl2_1__e22_97_2_1_1_2_1_1_2__stirl2_1,axiom,( ! [A,B,C,D,E,F,G,H] : ( ( m1_subset_1(A,k1_zfmisc_1(k5_numbers)) & m1_subset_1(B,k1_zfmisc_1(k5_numbers)) & v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(k5_numbers)) & ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(k5_numbers)) & ~ v1_xboole_0(F) & v1_finset_1(F) & m1_subset_1(F,k1_zfmisc_1(k5_numbers)) & m1_subset_1(G,k1_zfmisc_1(k5_numbers)) & v1_funct_1(H) & v1_funct_2(H,G,F) & m2_relset_1(H,G,F) ) => ( ( ! [I] : ( r2_hidden(I,k4_xboole_0(A,G)) => r2_hidden(k1_funct_1(C,k1_henmodel(E)),D) ) & r1_tarski(G,A) & r1_tarski(F,D) & ( v1_xboole_0(F) => v1_xboole_0(G) ) ) => ? [I] : ( v1_funct_1(I) & v1_funct_2(I,A,D) & m2_relset_1(I,A,D) & k2_partfun1(A,D,I,G) = H & ! [J] : ( r2_hidden(J,k4_xboole_0(A,G)) => k1_funct_1(I,J) = k1_funct_1(C,k1_henmodel(E)) ) ) ) ) ), file(stirl2_1,s2_stirl2_1__e22_97_2_1_1_2_1_1_2__stirl2_1), []). fof(s9_stirl2_1__e3_97__stirl2_1,axiom, ( ( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k5_numbers)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k5_numbers)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) ) => ~ ( C = k1_xboole_0 & v1_finset_1(k5_relset_1(A,B,C)) & ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k5_relset_1(A,B,C),k5_relset_1(A,B,C)) & v3_funct_2(D,k5_relset_1(A,B,C),k5_relset_1(A,B,C)) & m2_relset_1(D,k5_relset_1(A,B,C),k5_relset_1(A,B,C)) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) ) => ~ ( C = k1_partfun1(A,B,k5_relset_1(A,B,C),k5_relset_1(A,B,C),E,D) & k5_relset_1(A,B,C) = k5_relset_1(A,B,E) & ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ! [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) => ~ ( r2_hidden(F,k5_relset_1(A,B,E)) & r2_hidden(G,k5_relset_1(A,B,E)) & ~ r1_xreal_0(G,F) & r1_xreal_0(k1_henmodel(k3_funct_2(A,B,E,k1_stirl2_1(G))),k1_henmodel(k3_funct_2(A,B,E,k1_stirl2_1(F)))) ) ) ) ) ) ) ) ) ) ) & ! [H] : ( ( v1_relat_1(H) & v1_funct_1(H) ) => ( ! [I] : ( ( r2_hidden(I,k2_relat_1(H)) & I = k1_funct_1(H,k1_henmodel(k1_relat_1(H))) ) => ! [J] : ( m1_subset_1(J,k1_zfmisc_1(k5_numbers)) => ! [K] : ( m1_subset_1(K,k1_zfmisc_1(k5_numbers)) => ! [L] : ( ( v1_funct_1(L) & v1_funct_2(L,J,K) & m2_relset_1(L,J,K) ) => ~ ( L = k7_relat_1(H,k4_xboole_0(k1_relat_1(H),k10_relat_1(H,k1_tarski(I)))) & v1_finset_1(k5_relset_1(J,K,L)) & ! [M] : ( ( v1_funct_1(M) & v1_funct_2(M,k5_relset_1(J,K,L),k5_relset_1(J,K,L)) & v3_funct_2(M,k5_relset_1(J,K,L),k5_relset_1(J,K,L)) & m2_relset_1(M,k5_relset_1(J,K,L),k5_relset_1(J,K,L)) ) => ! [N] : ( ( v1_funct_1(N) & v1_funct_2(N,J,K) & m2_relset_1(N,J,K) ) => ~ ( L = k1_partfun1(J,K,k5_relset_1(J,K,L),k5_relset_1(J,K,L),N,M) & k5_relset_1(J,K,L) = k5_relset_1(J,K,N) & ! [O] : ( m2_subset_1(O,k1_numbers,k5_numbers) => ! [P] : ( m2_subset_1(P,k1_numbers,k5_numbers) => ~ ( r2_hidden(O,k5_relset_1(J,K,N)) & r2_hidden(P,k5_relset_1(J,K,N)) & ~ r1_xreal_0(P,O) & r1_xreal_0(k1_henmodel(k3_funct_2(J,K,N,k1_stirl2_1(P))),k1_henmodel(k3_funct_2(J,K,N,k1_stirl2_1(O)))) ) ) ) ) ) ) ) ) ) ) ) => ! [Q] : ( m1_subset_1(Q,k1_zfmisc_1(k5_numbers)) => ! [R] : ( m1_subset_1(R,k1_zfmisc_1(k5_numbers)) => ! [S] : ( ( v1_funct_1(S) & v1_funct_2(S,Q,R) & m2_relset_1(S,Q,R) ) => ~ ( S = H & v1_finset_1(k5_relset_1(Q,R,S)) & ! [T] : ( ( v1_funct_1(T) & v1_funct_2(T,k5_relset_1(Q,R,S),k5_relset_1(Q,R,S)) & v3_funct_2(T,k5_relset_1(Q,R,S),k5_relset_1(Q,R,S)) & m2_relset_1(T,k5_relset_1(Q,R,S),k5_relset_1(Q,R,S)) ) => ! [U] : ( ( v1_funct_1(U) & v1_funct_2(U,Q,R) & m2_relset_1(U,Q,R) ) => ~ ( S = k1_partfun1(Q,R,k5_relset_1(Q,R,S),k5_relset_1(Q,R,S),U,T) & k5_relset_1(Q,R,S) = k5_relset_1(Q,R,U) & ! [V] : ( m2_subset_1(V,k1_numbers,k5_numbers) => ! [W] : ( m2_subset_1(W,k1_numbers,k5_numbers) => ~ ( r2_hidden(V,k5_relset_1(Q,R,U)) & r2_hidden(W,k5_relset_1(Q,R,U)) & ~ r1_xreal_0(W,V) & r1_xreal_0(k1_henmodel(k3_funct_2(Q,R,U,k1_stirl2_1(W))),k1_henmodel(k3_funct_2(Q,R,U,k1_stirl2_1(V)))) ) ) ) ) ) ) ) ) ) ) ) ) ) => ! [H] : ( ( v1_relat_1(H) & v1_funct_1(H) ) => ( v1_finset_1(k2_relat_1(H)) => ! [X] : ( m1_subset_1(X,k1_zfmisc_1(k5_numbers)) => ! [Y] : ( m1_subset_1(Y,k1_zfmisc_1(k5_numbers)) => ! [Z] : ( ( v1_funct_1(Z) & v1_funct_2(Z,X,Y) & m2_relset_1(Z,X,Y) ) => ~ ( Z = H & v1_finset_1(k5_relset_1(X,Y,Z)) & ! [A1] : ( ( v1_funct_1(A1) & v1_funct_2(A1,k5_relset_1(X,Y,Z),k5_relset_1(X,Y,Z)) & v3_funct_2(A1,k5_relset_1(X,Y,Z),k5_relset_1(X,Y,Z)) & m2_relset_1(A1,k5_relset_1(X,Y,Z),k5_relset_1(X,Y,Z)) ) => ! [B1] : ( ( v1_funct_1(B1) & v1_funct_2(B1,X,Y) & m2_relset_1(B1,X,Y) ) => ~ ( Z = k1_partfun1(X,Y,k5_relset_1(X,Y,Z),k5_relset_1(X,Y,Z),B1,A1) & k5_relset_1(X,Y,Z) = k5_relset_1(X,Y,B1) & ! [C1] : ( m2_subset_1(C1,k1_numbers,k5_numbers) => ! [D1] : ( m2_subset_1(D1,k1_numbers,k5_numbers) => ~ ( r2_hidden(C1,k5_relset_1(X,Y,B1)) & r2_hidden(D1,k5_relset_1(X,Y,B1)) & ~ r1_xreal_0(D1,C1) & r1_xreal_0(k1_henmodel(k3_funct_2(X,Y,B1,k1_stirl2_1(D1))),k1_henmodel(k3_funct_2(X,Y,B1,k1_stirl2_1(C1)))) ) ) ) ) ) ) ) ) ) ) ) ) ), file(stirl2_1,s9_stirl2_1__e3_97__stirl2_1), []). 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(t10_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xreal_0(B,A) & r1_xreal_0(C,D) & r1_xreal_0(k2_xcmplx_0(B,D),k2_xcmplx_0(A,C)) ) ) ) ) ) ), file(xreal_1,t10_xreal_1), []). fof(t13_finset_1,axiom,( ! [A,B] : ( ( r1_tarski(A,B) & v1_finset_1(B) ) => v1_finset_1(A) ) ), file(finset_1,t13_finset_1), []). fof(t167_relat_1,axiom,( ! [A,B] : ( v1_relat_1(B) => r1_tarski(k10_relat_1(B,A),k1_relat_1(B)) ) ), file(relat_1,t167_relat_1), []). fof(t19_funct_2,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,B,C) & m2_relset_1(E,B,C) ) => ( ~ ( B = k1_xboole_0 & C != k1_xboole_0 & A != k1_xboole_0 ) => ( v1_funct_1(k1_partfun1(A,B,B,C,D,E)) & v1_funct_2(k1_partfun1(A,B,B,C,D,E),A,C) & m2_relset_1(k1_partfun1(A,B,B,C,D,E),A,C) ) ) ) ) ), file(funct_2,t19_funct_2), []). fof(t1_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(A,0) = A ) ), file(arithm,t1_arithm), []). fof(t1_boole,axiom,( ! [A] : k2_xboole_0(A,k1_xboole_0) = A ), file(boole,t1_boole), []). fof(t1_euler_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ( r2_hidden(A,B) <=> ~ r1_xreal_0(B,A) ) ) ) ), file(euler_1,t1_euler_1), []). 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_xboole_1,axiom,( ! [A,B,C] : ( ( r1_tarski(A,B) & r1_tarski(B,C) ) => r1_tarski(A,C) ) ), file(xboole_1,t1_xboole_1), []). fof(t20_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( ! [D] : ( r2_hidden(D,k1_relat_1(C)) <=> ( r2_hidden(D,k1_relat_1(A)) & r2_hidden(k1_funct_1(A,D),k1_relat_1(B)) ) ) & ! [D] : ( r2_hidden(D,k1_relat_1(C)) => k1_funct_1(C,D) = k1_funct_1(B,k1_funct_1(A,D)) ) ) => C = k5_relat_1(A,B) ) ) ) ) ), file(funct_1,t20_funct_1), []). fof(t20_funct_2,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,B,C) & m2_relset_1(E,B,C) ) => ( ( k2_relat_1(D) = B & k2_relat_1(E) = C ) => ( B = k1_xboole_0 | C = k1_xboole_0 | k2_relat_1(k1_partfun1(A,B,B,C,D,E)) = C ) ) ) ) ), file(funct_2,t20_funct_2), []). fof(t22_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(A,k1_relat_1(k5_relat_1(C,B))) => k1_funct_1(k5_relat_1(C,B),A) = k1_funct_1(B,k1_funct_1(C,A)) ) ) ) ), file(funct_1,t22_funct_1), []). fof(t23_funct_2,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => ( k7_relset_1(A,A,A,B,k6_partfun1(A),C) = C & k7_relset_1(A,B,B,B,C,k6_partfun1(B)) = C ) ) ), file(funct_2,t23_funct_2), []). fof(t28_xboole_1,axiom,( ! [A,B] : ( r1_tarski(A,B) => k3_xboole_0(A,B) = A ) ), file(xboole_1,t28_xboole_1), []). fof(t2_boole,axiom,( ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ), file(boole,t2_boole), []). 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_funct_2,axiom,( ! [A,B,C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) ) => ( ( v2_funct_1(C) & k2_relat_1(C) = B ) => ( v1_funct_1(k2_funct_1(C)) & v1_funct_2(k2_funct_1(C),B,A) & m2_relset_1(k2_funct_1(C),B,A) ) ) ) ), file(funct_2,t31_funct_2), []). fof(t36_xboole_1,axiom,( ! [A,B] : r1_tarski(k4_xboole_0(A,B),A) ), file(xboole_1,t36_xboole_1), []). fof(t38_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ( ~ r1_xreal_0(k2_xcmplx_0(B,1),A) <=> r1_xreal_0(A,B) ) ) ) ), file(nat_1,t38_nat_1), []). fof(t3_boole,axiom,( ! [A] : k4_xboole_0(A,k1_xboole_0) = A ), file(boole,t3_boole), []). fof(t3_funct_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_funct_1(A) & v1_funct_2(A,k1_relat_1(A),k2_relat_1(A)) & m2_relset_1(A,k1_relat_1(A),k2_relat_1(A)) ) ) ), file(funct_2,t3_funct_2), []). 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(t3_xboole_1,axiom,( ! [A] : ( r1_tarski(A,k1_xboole_0) => A = k1_xboole_0 ) ), file(xboole_1,t3_xboole_1), []). fof(t46_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( v2_funct_1(A) & v2_funct_1(B) ) => v2_funct_1(k5_relat_1(A,B)) ) ) ) ), file(funct_1,t46_funct_1), []). fof(t4_boole,axiom,( ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ), file(boole,t4_boole), []). 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(t51_xboole_1,axiom,( ! [A,B] : k2_xboole_0(k3_xboole_0(A,B),k4_xboole_0(A,B)) = A ), file(xboole_1,t51_xboole_1), []). fof(t52_funct_1,axiom,( ! [A] : v2_funct_1(k6_relat_1(A)) ), file(funct_1,t52_funct_1), []). fof(t55_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v2_funct_1(A) => ( k2_relat_1(A) = k1_relat_1(k2_funct_1(A)) & k1_relat_1(A) = k2_relat_1(k2_funct_1(A)) ) ) ) ), file(funct_1,t55_funct_1), []). fof(t55_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ! [C] : ( v1_relat_1(C) => k5_relat_1(k5_relat_1(A,B),C) = k5_relat_1(A,k5_relat_1(B,C)) ) ) ) ), file(relat_1,t55_relat_1), []). fof(t56_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( v2_funct_1(B) & r2_hidden(A,k1_relat_1(B)) ) => ( A = k1_funct_1(k2_funct_1(B),k1_funct_1(B,A)) & A = k1_funct_1(k5_relat_1(B,k2_funct_1(B)),A) ) ) ) ), file(funct_1,t56_funct_1), []). fof(t57_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( v2_funct_1(B) & r2_hidden(A,k2_relat_1(B)) ) => ( A = k1_funct_1(B,k1_funct_1(k2_funct_1(B),A)) & A = k1_funct_1(k5_relat_1(k2_funct_1(B),B),A) ) ) ) ), file(funct_1,t57_funct_1), []). 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_relat_1,axiom, ( k1_relat_1(k1_xboole_0) = k1_xboole_0 & k2_relat_1(k1_xboole_0) = k1_xboole_0 ), file(relat_1,t60_relat_1), []). fof(t61_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v2_funct_1(A) => ( k5_relat_1(A,k2_funct_1(A)) = k6_relat_1(k1_relat_1(A)) & k5_relat_1(k2_funct_1(A),A) = k6_relat_1(k2_relat_1(A)) ) ) ) ), file(funct_1,t61_funct_1), []). fof(t62_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ( k5_relat_1(k1_xboole_0,A) = k1_xboole_0 & k5_relat_1(A,k1_xboole_0) = k1_xboole_0 ) ) ), file(relat_1,t62_relat_1), []). 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(t64_stirl2_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( k2_relat_1(k7_relat_1(A,k4_xboole_0(k1_relat_1(A),k10_relat_1(A,k1_tarski(B))))) = k4_xboole_0(k2_relat_1(A),k1_tarski(B)) & ! [C] : ( C != B => k10_relat_1(k7_relat_1(A,k4_xboole_0(k1_relat_1(A),k10_relat_1(A,k1_tarski(B)))),k1_tarski(C)) = k10_relat_1(A,k1_tarski(C)) ) ) ) ), file(stirl2_1,t64_stirl2_1), []). fof(t64_zfmisc_1,axiom,( ! [A,B,C] : ( r2_hidden(A,k4_xboole_0(B,k1_tarski(C))) <=> ( r2_hidden(A,B) & A != C ) ) ), file(zfmisc_1,t64_zfmisc_1), []). fof(t65_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ( k1_relat_1(A) = k1_xboole_0 <=> k2_relat_1(A) = k1_xboole_0 ) ) ), file(relat_1,t65_relat_1), []). fof(t66_zfmisc_1,axiom,( ! [A,B] : ~ ( k4_xboole_0(A,k1_tarski(B)) = k1_xboole_0 & A != k1_xboole_0 & A != k1_tarski(B) ) ), file(zfmisc_1,t66_zfmisc_1), []). fof(t67_stirl2_1,axiom,( ! [A,B,C,D] : ~ ( ( v1_xboole_0(B) => v1_xboole_0(A) ) & ~ r2_hidden(C,A) & ? [E] : ( v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k2_xboole_0(A,k1_tarski(C)),k2_xboole_0(B,k1_tarski(D))) & m2_relset_1(F,k2_xboole_0(A,k1_tarski(C)),k2_xboole_0(B,k1_tarski(D))) ) => ~ ( k2_partfun1(k2_xboole_0(A,k1_tarski(C)),k2_xboole_0(B,k1_tarski(D)),F,A) = E & k1_funct_1(F,C) = D ) ) ) ) ), file(stirl2_1,t67_stirl2_1), []). fof(t68_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( B = k7_relat_1(C,A) <=> ( k1_relat_1(B) = k3_xboole_0(k1_relat_1(C),A) & ! [D] : ( r2_hidden(D,k1_relat_1(B)) => k1_funct_1(B,D) = k1_funct_1(C,D) ) ) ) ) ) ), file(funct_1,t68_funct_1), []). fof(t68_stirl2_1,axiom,( ! [A,B,C,D] : ( ( v1_xboole_0(B) => v1_xboole_0(A) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k2_xboole_0(A,k1_tarski(C)),k2_xboole_0(B,k1_tarski(D))) & m2_relset_1(F,k2_xboole_0(A,k1_tarski(C)),k2_xboole_0(B,k1_tarski(D))) ) => ( ( k2_partfun1(k2_xboole_0(A,k1_tarski(C)),k2_xboole_0(B,k1_tarski(D)),F,A) = E & k1_funct_1(F,C) = D ) => ( ( v2_funct_2(E,A,B) => v2_funct_2(F,k2_xboole_0(A,k1_tarski(C)),k2_xboole_0(B,k1_tarski(D))) ) & ( v2_funct_1(E) => ( r2_hidden(D,B) | v2_funct_1(F) ) ) ) ) ) ) ) ), file(stirl2_1,t68_stirl2_1), []). fof(t69_stirl2_1,axiom,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k5_numbers)) ) => ? [B] : ( v1_funct_1(B) & v1_funct_2(B,A,k4_card_1(A)) & m2_relset_1(B,A,k4_card_1(A)) & v3_funct_2(B,A,k4_card_1(A)) & ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ~ ( r2_hidden(C,k4_relset_1(A,k4_card_1(A),B)) & r2_hidden(D,k4_relset_1(A,k4_card_1(A),B)) & ~ r1_xreal_0(D,C) & r1_xreal_0(k5_stirl2_1(A,k4_card_1(A),B,D),k5_stirl2_1(A,k4_card_1(A),B,C)) ) ) ) ) ) ), file(stirl2_1,t69_stirl2_1), []). 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(t71_relat_1,axiom,( ! [A] : ( k1_relat_1(k6_relat_1(A)) = A & k2_relat_1(k6_relat_1(A)) = A ) ), file(relat_1,t71_relat_1), []). fof(t71_stirl2_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ~ ( r2_hidden(C,k2_relat_1(k5_relat_1(A,B))) & v2_funct_1(B) & ! [D] : ~ ( r2_hidden(D,k1_relat_1(B)) & r2_hidden(D,k2_relat_1(A)) & k10_relat_1(B,k1_tarski(C)) = k1_tarski(D) & k10_relat_1(A,k1_tarski(D)) = k10_relat_1(k5_relat_1(A,B),k1_tarski(C)) ) ) ) ) ), file(stirl2_1,t71_stirl2_1), []). 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(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t8_funct_2,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) ) => ( r1_tarski(k2_relat_1(D),C) => ( ( B = k1_xboole_0 & A != k1_xboole_0 ) | ( v1_funct_1(D) & v1_funct_2(D,A,C) & m2_relset_1(D,A,C) ) ) ) ) ), file(funct_2,t8_funct_2), []). 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_stirl2_1,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => m1_subset_1(A,k1_zfmisc_1(k5_numbers)) ) ), file(stirl2_1,t8_stirl2_1), []). fof(t99_relat_1,axiom,( ! [A,B] : ( v1_relat_1(B) => r1_tarski(k2_relat_1(k7_relat_1(B,A)),k2_relat_1(B)) ) ), file(relat_1,t99_relat_1), []).