% Mizar problem: t1_mesfunc3,mesfunc3,51,17 fof(t1_mesfunc3,conjecture,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(k2_finseq_1(A),k2_finseq_1(B)),k6_supinf_1) & m2_relset_1(C,k2_zfmisc_1(k2_finseq_1(A),k2_finseq_1(B)),k6_supinf_1) ) => ! [D] : ( m2_finseq_1(D,k6_supinf_1) => ! [E] : ( m2_finseq_1(E,k6_supinf_1) => ( ( k5_finsop_1(D) = k2_finseq_1(A) & ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ~ ( r2_hidden(F,k5_finsop_1(D)) & ! [G] : ( m2_finseq_1(G,k6_supinf_1) => ~ ( k5_finsop_1(G) = k2_finseq_1(B) & k2_seq_1(k5_numbers,k6_supinf_1,D,F) = k15_rvsum_1(G) & ! [H] : ( m2_subset_1(H,k1_numbers,k5_numbers) => ( r2_hidden(H,k5_finsop_1(G)) => k2_seq_1(k5_numbers,k6_supinf_1,G,H) = k2_seq_1(k2_zfmisc_1(k2_finseq_1(A),k2_finseq_1(B)),k6_supinf_1,C,k4_tarski(F,H)) ) ) ) ) ) ) & k5_finsop_1(E) = k2_finseq_1(B) & ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ~ ( r2_hidden(F,k5_finsop_1(E)) & ! [G] : ( m2_finseq_1(G,k6_supinf_1) => ~ ( k5_finsop_1(G) = k2_finseq_1(A) & k2_seq_1(k5_numbers,k6_supinf_1,E,F) = k15_rvsum_1(G) & ! [H] : ( m2_subset_1(H,k1_numbers,k5_numbers) => ( r2_hidden(H,k5_finsop_1(G)) => k2_seq_1(k5_numbers,k6_supinf_1,G,H) = k2_seq_1(k2_zfmisc_1(k2_finseq_1(A),k2_finseq_1(B)),k6_supinf_1,C,k4_tarski(H,F)) ) ) ) ) ) ) ) => k15_rvsum_1(D) = k15_rvsum_1(E) ) ) ) ) ) ) ), 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_finseq_1,cc1_membered,cc1_nat_1,cc1_relset_1,cc1_supinf_1,cc1_xreal_0,cc20_membered,cc2_membered,cc2_nat_1,cc2_supinf_1,cc2_xreal_0,cc3_membered,cc3_nat_1,cc3_xreal_0,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,commutativity_k1_nat_1,commutativity_k23_binop_2,commutativity_k2_tarski,commutativity_k2_xcmplx_0,commutativity_k3_rvsum_1,commutativity_k3_xboole_0,commutativity_k4_rvsum_1,commutativity_k5_subset_1,commutativity_k9_binop_2,connectedness_r1_xreal_0,d1_finseq_1,d1_funct_2,d2_finseq_2,d3_finseq_1,d3_funcop_1,d5_tarski,d6_rvsum_1,d8_funct_3,dt_k10_binop_2,dt_k12_finseq_1,dt_k13_funct_3,dt_k15_rvsum_1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_finseqop,dt_k1_funct_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k23_binop_2,dt_k2_finseq_1,dt_k2_finseq_2,dt_k2_funcop_1,dt_k2_partfun1,dt_k2_relat_1,dt_k2_seq_1,dt_k2_tarski,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k34_binop_2,dt_k3_finseq_1,dt_k3_funcop_1,dt_k3_rvsum_1,dt_k3_supinf_1,dt_k3_xboole_0,dt_k4_finseq_1,dt_k4_finseq_2,dt_k4_finseqop,dt_k4_relset_1,dt_k4_rvsum_1,dt_k4_tarski,dt_k5_finseq_1,dt_k5_finsop_1,dt_k5_finsub_1,dt_k5_numbers,dt_k5_ordinal2,dt_k5_relat_1,dt_k5_subset_1,dt_k6_finseq_1,dt_k6_supinf_1,dt_k6_xcmplx_0,dt_k7_finseq_1,dt_k7_relat_1,dt_k7_rvsum_1,dt_k8_finseq_1,dt_k8_rvsum_1,dt_k9_binop_2,dt_k9_finseq_1,dt_m1_finseq_1,dt_m1_finseq_2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_relset_1,dt_m2_subset_1,existence_m1_finseq_1,existence_m1_finseq_2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_finseq_2,existence_m2_relset_1,existence_m2_subset_1,fc10_membered,fc10_xreal_0,fc11_finseq_1,fc11_membered,fc11_xreal_0,fc12_finseq_1,fc12_membered,fc12_xreal_0,fc13_finseq_1,fc13_membered,fc14_finseq_1,fc14_membered,fc15_membered,fc15_xreal_0,fc16_membered,fc16_xreal_0,fc17_finseq_1,fc17_xreal_0,fc18_xreal_0,fc19_xreal_0,fc1_finseq_1,fc1_nat_1,fc1_ordinal2,fc1_subset_1,fc1_supinf_1,fc20_xreal_0,fc27_membered,fc28_membered,fc29_membered,fc2_finseq_1,fc2_membered,fc2_subset_1,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc3_finseq_1,fc3_nat_1,fc3_subset_1,fc3_xreal_0,fc4_finseq_1,fc4_nat_1,fc4_ordinal2,fc4_subset_1,fc5_membered,fc5_xreal_0,fc6_membered,fc7_membered,fc7_xreal_0,fc8_membered,fc8_xreal_0,fc9_membered,fc9_xreal_0,fraenkel_a_1_0_finseq_1,fraenkel_a_1_0_mesfunc3,idempotence_k3_xboole_0,idempotence_k5_subset_1,rc1_finseq_1,rc1_membered,rc1_nat_1,rc1_subset_1,rc1_xreal_0,rc2_finseq_1,rc2_nat_1,rc2_subset_1,rc2_xreal_0,rc3_finseq_1,rc3_nat_1,rc3_supinf_1,rc3_xreal_0,rc4_finseq_1,rc4_xreal_0,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,redefinition_k10_binop_2,redefinition_k12_finseq_1,redefinition_k1_finseqop,redefinition_k1_nat_1,redefinition_k23_binop_2,redefinition_k2_finseq_1,redefinition_k2_partfun1,redefinition_k2_seq_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k4_finseqop,redefinition_k4_relset_1,redefinition_k4_rvsum_1,redefinition_k5_finsop_1,redefinition_k5_numbers,redefinition_k5_subset_1,redefinition_k6_supinf_1,redefinition_k8_finseq_1,redefinition_k8_rvsum_1,redefinition_k9_binop_2,redefinition_k9_finseq_1,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,s1_nat_1__e3_1__mesfunc3,s2_finseq_1__e9_1_2_1__mesfunc3,spc0_boole,spc1_boole,spc1_numerals,t102_rvsum_1,t104_rvsum_1,t106_zfmisc_1,t110_finseq_2,t111_rvsum_1,t118_zfmisc_1,t119_rvsum_1,t119_zfmisc_1,t124_zfmisc_1,t12_relset_1,t14_finseq_2,t17_finseq_1,t17_funcop_1,t1_arithm,t1_numerals,t1_real,t1_subset,t1_xboole_1,t21_finseq_1,t23_finseq_1,t29_nat_1,t2_boole,t2_real,t2_subset,t2_tarski,t32_finseq_1,t38_funct_2,t3_real,t3_subset,t46_relat_1,t47_rvsum_1,t4_arithm,t4_real,t4_subset,t5_real,t5_subset,t61_finseq_3,t64_rvsum_1,t68_funct_1,t6_boole,t6_finseq_1,t6_real,t70_funct_1,t71_funct_3,t7_boole,t7_finseq_1,t7_real,t8_boole,t8_real,t9_finseq_2]), [file(mesfunc3,t1_mesfunc3)]). 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_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ) ), file(finseq_1,cc1_finseq_1), []). fof(cc1_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_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_supinf_1,axiom,( ! [A] : ( m1_subset_1(A,k3_supinf_1) => v3_supinf_1(A) ) ), file(supinf_1,cc1_supinf_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_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_supinf_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & v3_supinf_1(A) ) ) ), file(supinf_1,cc2_supinf_1), []). 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_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_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k1_nat_1(A,B) = k1_nat_1(B,A) ) ), file(nat_1,k1_nat_1), []). fof(commutativity_k23_binop_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k23_binop_2(A,B) = k23_binop_2(B,A) ) ), file(binop_2,k23_binop_2), []). 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_rvsum_1,axiom,( ! [A,B] : ( ( m1_finseq_1(A,k1_numbers) & m1_finseq_1(B,k1_numbers) ) => k3_rvsum_1(A,B) = k3_rvsum_1(B,A) ) ), file(rvsum_1,k3_rvsum_1), []). 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_k4_rvsum_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k4_finseq_2(A,k1_numbers)) & m1_subset_1(C,k4_finseq_2(A,k1_numbers)) ) => k4_rvsum_1(A,B,C) = k4_rvsum_1(A,C,B) ) ), file(rvsum_1,k4_rvsum_1), []). 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(commutativity_k9_binop_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k9_binop_2(A,B) = k9_binop_2(B,A) ) ), file(binop_2,k9_binop_2), []). fof(connectedness_r1_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( r1_xreal_0(A,B) | r1_xreal_0(B,A) ) ) ), file(xreal_0,r1_xreal_0), []). fof(d1_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => k1_finseq_1(A) = a_1_0_finseq_1(A) ) ), file(finseq_1,d1_finseq_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(d2_finseq_2,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : k2_finseq_2(A,B) = k2_funcop_1(k2_finseq_1(A),B) ) ), file(finseq_2,d2_finseq_2), []). fof(d3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( B = k3_finseq_1(A) <=> k2_finseq_1(B) = k1_relat_1(A) ) ) ) ), file(finseq_1,d3_finseq_1), []). fof(d3_funcop_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) ) => k3_funcop_1(A,B,C) = k5_relat_1(k13_funct_3(B,C),A) ) ) ) ), file(funcop_1,d3_funcop_1), []). fof(d5_tarski,axiom,( ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ), file(tarski,d5_tarski), []). fof(d6_rvsum_1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => k7_rvsum_1(A,B) = k1_finseqop(k1_numbers,k1_numbers,k1_numbers,k34_binop_2,A,B) ) ) ), file(rvsum_1,d6_rvsum_1), []). fof(d8_funct_3,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) ) => ( C = k13_funct_3(A,B) <=> ( k1_relat_1(C) = k3_xboole_0(k1_relat_1(A),k1_relat_1(B)) & ! [D] : ( r2_hidden(D,k1_relat_1(C)) => k1_funct_1(C,D) = k4_tarski(k1_funct_1(A,D),k1_funct_1(B,D)) ) ) ) ) ) ) ), file(funct_3,d8_funct_3), []). fof(dt_k10_binop_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k10_binop_2(A,B),k1_numbers) ) ), file(binop_2,k10_binop_2), []). fof(dt_k12_finseq_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m2_finseq_1(k12_finseq_1(A,B),A) ) ), file(finseq_1,k12_finseq_1), []). fof(dt_k13_funct_3,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => ( v1_relat_1(k13_funct_3(A,B)) & v1_funct_1(k13_funct_3(A,B)) ) ) ), file(funct_3,k13_funct_3), []). fof(dt_k15_rvsum_1,axiom,( ! [A] : ( m1_finseq_1(A,k1_numbers) => m1_subset_1(k15_rvsum_1(A),k1_numbers) ) ), file(rvsum_1,k15_rvsum_1), []). fof(dt_k1_card_1,axiom,( ! [A] : v1_card_1(k1_card_1(A)) ), file(card_1,k1_card_1), []). fof(dt_k1_finseq_1,axiom,( $true ), file(finseq_1,k1_finseq_1), []). fof(dt_k1_finseqop,axiom,( ! [A,B,C,D,E,F] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & m1_finseq_1(E,A) & m1_finseq_1(F,B) ) => m2_finseq_1(k1_finseqop(A,B,C,D,E,F),C) ) ), file(finseqop,k1_finseqop), []). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). fof(dt_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => m2_subset_1(k1_nat_1(A,B),k1_numbers,k5_numbers) ) ), file(nat_1,k1_nat_1), []). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), []). fof(dt_k1_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), []). fof(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), []). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), []). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), []). fof(dt_k23_binop_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => m2_subset_1(k23_binop_2(A,B),k1_numbers,k5_numbers) ) ), file(binop_2,k23_binop_2), []). fof(dt_k2_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => m1_subset_1(k2_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ), file(finseq_1,k2_finseq_1), []). fof(dt_k2_finseq_2,axiom,( ! [A,B] : ( v4_ordinal2(A) => ( v1_relat_1(k2_finseq_2(A,B)) & v1_funct_1(k2_finseq_2(A,B)) & v1_finseq_1(k2_finseq_2(A,B)) ) ) ), file(finseq_2,k2_finseq_2), []). fof(dt_k2_funcop_1,axiom,( $true ), file(funcop_1,k2_funcop_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_seq_1,axiom,( ! [A,B,C,D] : ( ( v2_membered(B) & v1_funct_1(C) & m1_relset_1(C,A,B) ) => m1_subset_1(k2_seq_1(A,B,C,D),k1_numbers) ) ), file(seq_1,k2_seq_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_k34_binop_2,axiom, ( v1_funct_1(k34_binop_2) & v1_funct_2(k34_binop_2,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & m2_relset_1(k34_binop_2,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) ), file(binop_2,k34_binop_2), []). fof(dt_k3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers) ) ), file(finseq_1,k3_finseq_1), []). fof(dt_k3_funcop_1,axiom,( $true ), file(funcop_1,k3_funcop_1), []). fof(dt_k3_rvsum_1,axiom,( ! [A,B] : ( ( m1_finseq_1(A,k1_numbers) & m1_finseq_1(B,k1_numbers) ) => m2_finseq_1(k3_rvsum_1(A,B),k1_numbers) ) ), file(rvsum_1,k3_rvsum_1), []). fof(dt_k3_supinf_1,axiom,( $true ), file(supinf_1,k3_supinf_1), []). fof(dt_k3_xboole_0,axiom,( $true ), file(xboole_0,k3_xboole_0), []). fof(dt_k4_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m1_subset_1(k4_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ), file(finseq_1,k4_finseq_1), []). fof(dt_k4_finseq_2,axiom,( ! [A,B] : ( v4_ordinal2(A) => m1_finseq_2(k4_finseq_2(A,B),B) ) ), file(finseq_2,k4_finseq_2), []). fof(dt_k4_finseqop,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k5_numbers) & m1_subset_1(C,A) ) => m2_finseq_2(k4_finseqop(A,B,C),A,k4_finseq_2(B,A)) ) ), file(finseqop,k4_finseqop), []). 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_rvsum_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k4_finseq_2(A,k1_numbers)) & m1_subset_1(C,k4_finseq_2(A,k1_numbers)) ) => m2_finseq_2(k4_rvsum_1(A,B,C),k1_numbers,k4_finseq_2(A,k1_numbers)) ) ), file(rvsum_1,k4_rvsum_1), []). fof(dt_k4_tarski,axiom,( $true ), file(tarski,k4_tarski), []). fof(dt_k5_finseq_1,axiom,( $true ), file(finseq_1,k5_finseq_1), []). fof(dt_k5_finsop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m1_subset_1(k5_finsop_1(A),k5_finsub_1(k5_numbers)) ) ), file(finsop_1,k5_finsop_1), []). fof(dt_k5_finsub_1,axiom,( ! [A] : v4_finsub_1(k5_finsub_1(A)) ), file(finsub_1,k5_finsub_1), []). fof(dt_k5_numbers,axiom,( m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ), file(numbers,k5_numbers), []). fof(dt_k5_ordinal2,axiom,( $true ), file(ordinal2,k5_ordinal2), []). fof(dt_k5_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_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_finseq_1,axiom,( ! [A] : ( v1_xboole_0(k6_finseq_1(A)) & m2_finseq_1(k6_finseq_1(A),A) ) ), file(finseq_1,k6_finseq_1), []). fof(dt_k6_supinf_1,axiom, ( ~ v1_xboole_0(k6_supinf_1) & m1_subset_1(k6_supinf_1,k1_zfmisc_1(k3_supinf_1)) ), file(supinf_1,k6_supinf_1), []). fof(dt_k6_xcmplx_0,axiom,( $true ), file(xcmplx_0,k6_xcmplx_0), []). fof(dt_k7_finseq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( v1_relat_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) ) ) ), file(finseq_1,k7_finseq_1), []). fof(dt_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_rvsum_1,axiom,( ! [A,B] : ( ( m1_finseq_1(A,k1_numbers) & m1_finseq_1(B,k1_numbers) ) => m2_finseq_1(k7_rvsum_1(A,B),k1_numbers) ) ), file(rvsum_1,k7_rvsum_1), []). fof(dt_k8_finseq_1,axiom,( ! [A,B,C] : ( ( m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => m2_finseq_1(k8_finseq_1(A,B,C),A) ) ), file(finseq_1,k8_finseq_1), []). fof(dt_k8_rvsum_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k4_finseq_2(A,k1_numbers)) & m1_subset_1(C,k4_finseq_2(A,k1_numbers)) ) => m2_finseq_2(k8_rvsum_1(A,B,C),k1_numbers,k4_finseq_2(A,k1_numbers)) ) ), file(rvsum_1,k8_rvsum_1), []). fof(dt_k9_binop_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k9_binop_2(A,B),k1_numbers) ) ), file(binop_2,k9_binop_2), []). fof(dt_k9_finseq_1,axiom,( ! [A] : ( v1_relat_1(k9_finseq_1(A)) & v1_funct_1(k9_finseq_1(A)) ) ), file(finseq_1,k9_finseq_1), []). fof(dt_m1_finseq_1,axiom,( ! [A,B] : ( m1_finseq_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) ) ), file(finseq_1,m1_finseq_1), []). fof(dt_m1_finseq_2,axiom,( $true ), file(finseq_2,m1_finseq_2), []). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), []). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), []). fof(dt_m2_finseq_1,axiom,( ! [A,B] : ( m2_finseq_1(B,A) => ( v1_funct_1(B) & v1_finseq_1(B) & m2_relset_1(B,k5_numbers,A) ) ) ), file(finseq_1,m2_finseq_1), []). fof(dt_m2_finseq_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) ) => ! [C] : ( m2_finseq_2(C,A,B) => m2_finseq_1(C,A) ) ) ), file(finseq_2,m2_finseq_2), []). fof(dt_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ), file(relset_1,m2_relset_1), []). fof(dt_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) => m1_subset_1(C,A) ) ) ), file(subset_1,m2_subset_1), []). fof(existence_m1_finseq_1,axiom,( ! [A] : ? [B] : m1_finseq_1(B,A) ), file(finseq_1,m1_finseq_1), []). fof(existence_m1_finseq_2,axiom,( ! [A] : ? [B] : m1_finseq_2(B,A) ), file(finseq_2,m1_finseq_2), []). fof(existence_m1_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), []). fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), []). fof(existence_m2_finseq_1,axiom,( ! [A] : ? [B] : m2_finseq_1(B,A) ), file(finseq_1,m2_finseq_1), []). fof(existence_m2_finseq_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) ) => ? [C] : m2_finseq_2(C,A,B) ) ), file(finseq_2,m2_finseq_2), []). fof(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), []). fof(existence_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ? [C] : m2_subset_1(C,A,B) ) ), file(subset_1,m2_subset_1), []). fof(fc10_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_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v2_xreal_0(k2_xcmplx_0(B,A)) & ~ v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc10_xreal_0), []). fof(fc11_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_finset_1(A) ) => v1_finset_1(k2_relat_1(A)) ) ), file(finseq_1,fc11_finseq_1), []). fof(fc11_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_finseq_1,axiom,( ! [A] : ( ~ v1_xboole_0(k5_finseq_1(A)) & v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) ) ), file(finseq_1,fc12_finseq_1), []). fof(fc12_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_finseq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ~ v1_xboole_0(k7_finseq_1(A,B)) & v1_relat_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finset_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) ) ) ), file(finseq_1,fc13_finseq_1), []). fof(fc13_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(fc14_finseq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ~ v1_xboole_0(k7_finseq_1(B,A)) & v1_relat_1(k7_finseq_1(B,A)) & v1_funct_1(k7_finseq_1(B,A)) & v1_finset_1(k7_finseq_1(B,A)) & v1_finseq_1(k7_finseq_1(B,A)) ) ) ), file(finseq_1,fc14_finseq_1), []). fof(fc14_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(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_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) => v1_finset_1(k1_relat_1(A)) ) ), file(finseq_1,fc17_finseq_1), []). fof(fc17_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v2_xreal_0(k6_xcmplx_0(A,B)) & ~ v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc17_xreal_0), []). fof(fc18_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k6_xcmplx_0(B,A)) & v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & ~ v2_xreal_0(k6_xcmplx_0(B,A)) & v3_xreal_0(k6_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc18_xreal_0), []). fof(fc19_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & ~ v2_xreal_0(k6_xcmplx_0(A,B)) & v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc19_xreal_0), []). fof(fc1_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => v1_finset_1(k1_finseq_1(A)) ) ), file(finseq_1,fc1_finseq_1), []). fof(fc1_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_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ), file(subset_1,fc1_subset_1), []). fof(fc1_supinf_1,axiom,( ~ v1_xboole_0(k3_supinf_1) ), file(supinf_1,fc1_supinf_1), []). 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(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_finseq_1,axiom, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) & v1_funct_1(k1_xboole_0) & v2_funct_1(k1_xboole_0) & v1_finset_1(k1_xboole_0) & v1_finseq_1(k1_xboole_0) ), file(finseq_1,fc2_finseq_1), []). fof(fc2_membered,axiom, ( ~ v1_xboole_0(k1_numbers) & v1_membered(k1_numbers) & v2_membered(k1_numbers) ), file(membered,fc2_membered), []). fof(fc2_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) ), file(subset_1,fc2_subset_1), []). 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(fc3_finseq_1,axiom,( ! [A] : ( v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) ) ), file(finseq_1,fc3_finseq_1), []). fof(fc3_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_subset_1,axiom,( ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ), file(subset_1,fc3_subset_1), []). fof(fc3_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc3_xreal_0), []). fof(fc4_finseq_1,axiom,( ! [A] : ( v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) ) ), file(finseq_1,fc4_finseq_1), []). fof(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_ordinal2,axiom,( ! [A,B] : ( v3_ordinal1(B) => ( v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v1_ordinal2(k2_funcop_1(A,B)) ) ) ), file(ordinal2,fc4_ordinal2), []). 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_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(fc7_membered,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_membered(k1_tarski(A)) ) ), file(membered,fc7_membered), []). 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_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_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_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v2_xreal_0(k2_xcmplx_0(A,B)) & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc9_xreal_0), []). fof(fraenkel_a_1_0_finseq_1,axiom,( ! [A,B] : ( v4_ordinal2(B) => ( r2_hidden(A,a_1_0_finseq_1(B)) <=> ? [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) & A = C & r1_xreal_0(1,C) & r1_xreal_0(C,B) ) ) ) ), file(finseq_1,a_1_0_finseq_1), []). fof(fraenkel_a_1_0_mesfunc3,axiom,( ! [A,B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( r2_hidden(A,a_1_0_mesfunc3(B)) <=> ? [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) & A = C & r1_xreal_0(1,C) & r1_xreal_0(C,B) ) ) ) ), file(mesfunc3,a_1_0_mesfunc3), []). 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(rc1_finseq_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc1_finseq_1), []). fof(rc1_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_subset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) ) ) ), file(subset_1,rc1_subset_1), []). fof(rc1_xreal_0,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(xreal_0,rc1_xreal_0), []). fof(rc2_finseq_1,axiom,( ! [A] : ? [B] : ( m1_relset_1(B,k5_numbers,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc2_finseq_1), []). fof(rc2_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_subset_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) ) ), file(subset_1,rc2_subset_1), []). fof(rc2_xreal_0,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc2_xreal_0), []). fof(rc3_finseq_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc3_finseq_1), []). fof(rc3_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_supinf_1,axiom,( ? [A] : v3_supinf_1(A) ), file(supinf_1,rc3_supinf_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_finseq_1,axiom,( ! [A] : ? [B] : ( m1_finseq_1(B,A) & v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc4_finseq_1), []). fof(rc4_xreal_0,axiom,( ? [A] : ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc4_xreal_0), []). fof(rc6_finseq_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc6_finseq_1), []). fof(rc7_finseq_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc7_finseq_1), []). fof(rc8_finseq_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc8_finseq_1), []). fof(redefinition_k10_binop_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k10_binop_2(A,B) = k6_xcmplx_0(A,B) ) ), file(binop_2,k10_binop_2), []). fof(redefinition_k12_finseq_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => k12_finseq_1(A,B) = k5_finseq_1(B) ) ), file(finseq_1,k12_finseq_1), []). fof(redefinition_k1_finseqop,axiom,( ! [A,B,C,D,E,F] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & m1_finseq_1(E,A) & m1_finseq_1(F,B) ) => k1_finseqop(A,B,C,D,E,F) = k3_funcop_1(D,E,F) ) ), file(finseqop,k1_finseqop), []). fof(redefinition_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k1_nat_1(A,B) = k2_xcmplx_0(A,B) ) ), file(nat_1,k1_nat_1), []). fof(redefinition_k23_binop_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k23_binop_2(A,B) = k2_xcmplx_0(A,B) ) ), file(binop_2,k23_binop_2), []). fof(redefinition_k2_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => k2_finseq_1(A) = k1_finseq_1(A) ) ), file(finseq_1,k2_finseq_1), []). fof(redefinition_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_k2_seq_1,axiom,( ! [A,B,C,D] : ( ( v2_membered(B) & v1_funct_1(C) & m1_relset_1(C,A,B) ) => k2_seq_1(A,B,C,D) = k1_funct_1(C,D) ) ), file(seq_1,k2_seq_1), []). fof(redefinition_k3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k3_finseq_1(A) = k1_card_1(A) ) ), file(finseq_1,k3_finseq_1), []). fof(redefinition_k4_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k4_finseq_1(A) = k1_relat_1(A) ) ), file(finseq_1,k4_finseq_1), []). fof(redefinition_k4_finseqop,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k5_numbers) & m1_subset_1(C,A) ) => k4_finseqop(A,B,C) = k2_finseq_2(B,C) ) ), file(finseqop,k4_finseqop), []). 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_k4_rvsum_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k4_finseq_2(A,k1_numbers)) & m1_subset_1(C,k4_finseq_2(A,k1_numbers)) ) => k4_rvsum_1(A,B,C) = k3_rvsum_1(B,C) ) ), file(rvsum_1,k4_rvsum_1), []). fof(redefinition_k5_finsop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k5_finsop_1(A) = k1_relat_1(A) ) ), file(finsop_1,k5_finsop_1), []). fof(redefinition_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). 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_supinf_1,axiom,( k6_supinf_1 = k1_numbers ), file(supinf_1,k6_supinf_1), []). fof(redefinition_k8_finseq_1,axiom,( ! [A,B,C] : ( ( m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => k8_finseq_1(A,B,C) = k7_finseq_1(B,C) ) ), file(finseq_1,k8_finseq_1), []). fof(redefinition_k8_rvsum_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k4_finseq_2(A,k1_numbers)) & m1_subset_1(C,k4_finseq_2(A,k1_numbers)) ) => k8_rvsum_1(A,B,C) = k7_rvsum_1(B,C) ) ), file(rvsum_1,k8_rvsum_1), []). fof(redefinition_k9_binop_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k9_binop_2(A,B) = k2_xcmplx_0(A,B) ) ), file(binop_2,k9_binop_2), []). fof(redefinition_k9_finseq_1,axiom,( ! [A] : k9_finseq_1(A) = k5_finseq_1(A) ), file(finseq_1,k9_finseq_1), []). fof(redefinition_m2_finseq_1,axiom,( ! [A,B] : ( m2_finseq_1(B,A) <=> m1_finseq_1(B,A) ) ), file(finseq_1,m2_finseq_1), []). fof(redefinition_m2_finseq_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) ) => ! [C] : ( m2_finseq_2(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(finseq_2,m2_finseq_2), []). fof(redefinition_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) <=> m1_relset_1(C,A,B) ) ), file(relset_1,m2_relset_1), []). fof(redefinition_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(subset_1,m2_subset_1), []). fof(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(s1_nat_1__e3_1__mesfunc3,axiom, ( ( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(k2_finseq_1(0),k2_finseq_1(A)),k6_supinf_1) & m2_relset_1(B,k2_zfmisc_1(k2_finseq_1(0),k2_finseq_1(A)),k6_supinf_1) ) => ! [C] : ( m2_finseq_1(C,k6_supinf_1) => ! [D] : ( m2_finseq_1(D,k6_supinf_1) => ( ( k5_finsop_1(C) = k2_finseq_1(0) & ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ~ ( r2_hidden(E,k5_finsop_1(C)) & ! [F] : ( m2_finseq_1(F,k6_supinf_1) => ~ ( k5_finsop_1(F) = k2_finseq_1(A) & k2_seq_1(k5_numbers,k6_supinf_1,C,E) = k15_rvsum_1(F) & ! [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) => ( r2_hidden(G,k5_finsop_1(F)) => k2_seq_1(k5_numbers,k6_supinf_1,F,G) = k2_seq_1(k2_zfmisc_1(k2_finseq_1(0),k2_finseq_1(A)),k6_supinf_1,B,k4_tarski(E,G)) ) ) ) ) ) ) & k5_finsop_1(D) = k2_finseq_1(A) & ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ~ ( r2_hidden(E,k5_finsop_1(D)) & ! [F] : ( m2_finseq_1(F,k6_supinf_1) => ~ ( k5_finsop_1(F) = k2_finseq_1(0) & k2_seq_1(k5_numbers,k6_supinf_1,D,E) = k15_rvsum_1(F) & ! [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) => ( r2_hidden(G,k5_finsop_1(F)) => k2_seq_1(k5_numbers,k6_supinf_1,F,G) = k2_seq_1(k2_zfmisc_1(k2_finseq_1(0),k2_finseq_1(A)),k6_supinf_1,B,k4_tarski(G,E)) ) ) ) ) ) ) ) => k15_rvsum_1(C) = k15_rvsum_1(D) ) ) ) ) ) & ! [H] : ( m2_subset_1(H,k1_numbers,k5_numbers) => ( ! [I] : ( m2_subset_1(I,k1_numbers,k5_numbers) => ! [J] : ( ( v1_funct_1(J) & v1_funct_2(J,k2_zfmisc_1(k2_finseq_1(H),k2_finseq_1(I)),k6_supinf_1) & m2_relset_1(J,k2_zfmisc_1(k2_finseq_1(H),k2_finseq_1(I)),k6_supinf_1) ) => ! [K] : ( m2_finseq_1(K,k6_supinf_1) => ! [L] : ( m2_finseq_1(L,k6_supinf_1) => ( ( k5_finsop_1(K) = k2_finseq_1(H) & ! [M] : ( m2_subset_1(M,k1_numbers,k5_numbers) => ~ ( r2_hidden(M,k5_finsop_1(K)) & ! [N] : ( m2_finseq_1(N,k6_supinf_1) => ~ ( k5_finsop_1(N) = k2_finseq_1(I) & k2_seq_1(k5_numbers,k6_supinf_1,K,M) = k15_rvsum_1(N) & ! [O] : ( m2_subset_1(O,k1_numbers,k5_numbers) => ( r2_hidden(O,k5_finsop_1(N)) => k2_seq_1(k5_numbers,k6_supinf_1,N,O) = k2_seq_1(k2_zfmisc_1(k2_finseq_1(H),k2_finseq_1(I)),k6_supinf_1,J,k4_tarski(M,O)) ) ) ) ) ) ) & k5_finsop_1(L) = k2_finseq_1(I) & ! [M] : ( m2_subset_1(M,k1_numbers,k5_numbers) => ~ ( r2_hidden(M,k5_finsop_1(L)) & ! [N] : ( m2_finseq_1(N,k6_supinf_1) => ~ ( k5_finsop_1(N) = k2_finseq_1(H) & k2_seq_1(k5_numbers,k6_supinf_1,L,M) = k15_rvsum_1(N) & ! [O] : ( m2_subset_1(O,k1_numbers,k5_numbers) => ( r2_hidden(O,k5_finsop_1(N)) => k2_seq_1(k5_numbers,k6_supinf_1,N,O) = k2_seq_1(k2_zfmisc_1(k2_finseq_1(H),k2_finseq_1(I)),k6_supinf_1,J,k4_tarski(O,M)) ) ) ) ) ) ) ) => k15_rvsum_1(K) = k15_rvsum_1(L) ) ) ) ) ) => ! [P] : ( m2_subset_1(P,k1_numbers,k5_numbers) => ! [Q] : ( ( v1_funct_1(Q) & v1_funct_2(Q,k2_zfmisc_1(k2_finseq_1(k1_nat_1(H,1)),k2_finseq_1(P)),k6_supinf_1) & m2_relset_1(Q,k2_zfmisc_1(k2_finseq_1(k1_nat_1(H,1)),k2_finseq_1(P)),k6_supinf_1) ) => ! [R] : ( m2_finseq_1(R,k6_supinf_1) => ! [S] : ( m2_finseq_1(S,k6_supinf_1) => ( ( k5_finsop_1(R) = k2_finseq_1(k1_nat_1(H,1)) & ! [T] : ( m2_subset_1(T,k1_numbers,k5_numbers) => ~ ( r2_hidden(T,k5_finsop_1(R)) & ! [U] : ( m2_finseq_1(U,k6_supinf_1) => ~ ( k5_finsop_1(U) = k2_finseq_1(P) & k2_seq_1(k5_numbers,k6_supinf_1,R,T) = k15_rvsum_1(U) & ! [V] : ( m2_subset_1(V,k1_numbers,k5_numbers) => ( r2_hidden(V,k5_finsop_1(U)) => k2_seq_1(k5_numbers,k6_supinf_1,U,V) = k2_seq_1(k2_zfmisc_1(k2_finseq_1(k1_nat_1(H,1)),k2_finseq_1(P)),k6_supinf_1,Q,k4_tarski(T,V)) ) ) ) ) ) ) & k5_finsop_1(S) = k2_finseq_1(P) & ! [T] : ( m2_subset_1(T,k1_numbers,k5_numbers) => ~ ( r2_hidden(T,k5_finsop_1(S)) & ! [U] : ( m2_finseq_1(U,k6_supinf_1) => ~ ( k5_finsop_1(U) = k2_finseq_1(k1_nat_1(H,1)) & k2_seq_1(k5_numbers,k6_supinf_1,S,T) = k15_rvsum_1(U) & ! [V] : ( m2_subset_1(V,k1_numbers,k5_numbers) => ( r2_hidden(V,k5_finsop_1(U)) => k2_seq_1(k5_numbers,k6_supinf_1,U,V) = k2_seq_1(k2_zfmisc_1(k2_finseq_1(k1_nat_1(H,1)),k2_finseq_1(P)),k6_supinf_1,Q,k4_tarski(V,T)) ) ) ) ) ) ) ) => k15_rvsum_1(R) = k15_rvsum_1(S) ) ) ) ) ) ) ) ) => ! [H] : ( m2_subset_1(H,k1_numbers,k5_numbers) => ! [W] : ( m2_subset_1(W,k1_numbers,k5_numbers) => ! [X] : ( ( v1_funct_1(X) & v1_funct_2(X,k2_zfmisc_1(k2_finseq_1(H),k2_finseq_1(W)),k6_supinf_1) & m2_relset_1(X,k2_zfmisc_1(k2_finseq_1(H),k2_finseq_1(W)),k6_supinf_1) ) => ! [Y] : ( m2_finseq_1(Y,k6_supinf_1) => ! [Z] : ( m2_finseq_1(Z,k6_supinf_1) => ( ( k5_finsop_1(Y) = k2_finseq_1(H) & ! [A1] : ( m2_subset_1(A1,k1_numbers,k5_numbers) => ~ ( r2_hidden(A1,k5_finsop_1(Y)) & ! [B1] : ( m2_finseq_1(B1,k6_supinf_1) => ~ ( k5_finsop_1(B1) = k2_finseq_1(W) & k2_seq_1(k5_numbers,k6_supinf_1,Y,A1) = k15_rvsum_1(B1) & ! [C1] : ( m2_subset_1(C1,k1_numbers,k5_numbers) => ( r2_hidden(C1,k5_finsop_1(B1)) => k2_seq_1(k5_numbers,k6_supinf_1,B1,C1) = k2_seq_1(k2_zfmisc_1(k2_finseq_1(H),k2_finseq_1(W)),k6_supinf_1,X,k4_tarski(A1,C1)) ) ) ) ) ) ) & k5_finsop_1(Z) = k2_finseq_1(W) & ! [A1] : ( m2_subset_1(A1,k1_numbers,k5_numbers) => ~ ( r2_hidden(A1,k5_finsop_1(Z)) & ! [B1] : ( m2_finseq_1(B1,k6_supinf_1) => ~ ( k5_finsop_1(B1) = k2_finseq_1(H) & k2_seq_1(k5_numbers,k6_supinf_1,Z,A1) = k15_rvsum_1(B1) & ! [C1] : ( m2_subset_1(C1,k1_numbers,k5_numbers) => ( r2_hidden(C1,k5_finsop_1(B1)) => k2_seq_1(k5_numbers,k6_supinf_1,B1,C1) = k2_seq_1(k2_zfmisc_1(k2_finseq_1(H),k2_finseq_1(W)),k6_supinf_1,X,k4_tarski(C1,A1)) ) ) ) ) ) ) ) => k15_rvsum_1(Y) = k15_rvsum_1(Z) ) ) ) ) ) ) ), file(mesfunc3,s1_nat_1__e3_1__mesfunc3), []). fof(s2_finseq_1__e9_1_2_1__mesfunc3,axiom,( ! [A,B,C] : ( ( m2_subset_1(A,k1_numbers,k5_numbers) & m2_subset_1(B,k1_numbers,k5_numbers) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(k2_finseq_1(k23_binop_2(A,1)),k2_finseq_1(B)),k6_supinf_1) & m2_relset_1(C,k2_zfmisc_1(k2_finseq_1(k23_binop_2(A,1)),k2_finseq_1(B)),k6_supinf_1) ) => ? [D] : ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) & k3_finseq_1(D) = B & ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ( r2_hidden(E,k2_finseq_1(B)) => k1_funct_1(D,E) = k2_seq_1(k2_zfmisc_1(k2_finseq_1(k23_binop_2(A,1)),k2_finseq_1(B)),k6_supinf_1,C,k4_tarski(k23_binop_2(A,1),E)) ) ) ) ) ), file(mesfunc3,s2_finseq_1__e9_1_2_1__mesfunc3), []). 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(t102_rvsum_1,axiom,( k15_rvsum_1(k6_finseq_1(k1_numbers)) = 0 ), file(rvsum_1,t102_rvsum_1), []). fof(t104_rvsum_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => k15_rvsum_1(k8_finseq_1(k1_numbers,B,k12_finseq_1(k1_numbers,A))) = k9_binop_2(k15_rvsum_1(B),A) ) ) ), file(rvsum_1,t104_rvsum_1), []). fof(t106_zfmisc_1,axiom,( ! [A,B,C,D] : ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D)) <=> ( r2_hidden(A,C) & r2_hidden(B,D) ) ) ), file(zfmisc_1,t106_zfmisc_1), []). fof(t110_finseq_2,axiom,( ! [A,B] : ( m2_finseq_1(B,A) => m1_subset_1(B,k4_finseq_2(k3_finseq_1(B),A)) ) ), file(finseq_2,t110_finseq_2), []). fof(t111_rvsum_1,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => k15_rvsum_1(k4_finseqop(k1_numbers,A,0)) = 0 ) ), file(rvsum_1,t111_rvsum_1), []). fof(t118_zfmisc_1,axiom,( ! [A,B,C] : ( r1_tarski(A,B) => ( r1_tarski(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)) & r1_tarski(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) ) ) ), file(zfmisc_1,t118_zfmisc_1), []). fof(t119_rvsum_1,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_finseq_2(B,k1_numbers,k4_finseq_2(A,k1_numbers)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k4_finseq_2(A,k1_numbers)) => k15_rvsum_1(k4_rvsum_1(A,B,C)) = k9_binop_2(k15_rvsum_1(B),k15_rvsum_1(C)) ) ) ) ), file(rvsum_1,t119_rvsum_1), []). fof(t119_zfmisc_1,axiom,( ! [A,B,C,D] : ( ( r1_tarski(A,B) & r1_tarski(C,D) ) => r1_tarski(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) ) ), file(zfmisc_1,t119_zfmisc_1), []). fof(t124_zfmisc_1,axiom,( ! [A,B,C,D] : ( ( r1_tarski(A,B) & r1_tarski(C,D) ) => k3_xboole_0(k2_zfmisc_1(A,D),k2_zfmisc_1(B,C)) = k2_zfmisc_1(A,C) ) ), file(zfmisc_1,t124_zfmisc_1), []). fof(t12_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => ( r1_tarski(k1_relat_1(C),A) & r1_tarski(k2_relat_1(C),B) ) ) ), file(relset_1,t12_relset_1), []). fof(t14_finseq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( r2_hidden(C,k4_finseq_1(A)) => r2_hidden(k1_funct_1(A,C),B) ) ) => m2_finseq_1(A,B) ) ) ), file(finseq_2,t14_finseq_2), []). fof(t17_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ( k4_finseq_1(A) = k4_finseq_1(B) & ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( r2_hidden(C,k4_finseq_1(A)) => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) ) => A = B ) ) ) ), file(finseq_1,t17_finseq_1), []). fof(t17_funcop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ! [C] : ( r2_hidden(C,k1_relat_1(A)) => k1_funct_1(A,C) = B ) => A = k2_funcop_1(k1_relat_1(A),B) ) ) ), file(funcop_1,t17_funcop_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(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(t21_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( ( r1_xreal_0(A,k3_finseq_1(B)) & C = k7_relat_1(B,k2_finseq_1(A)) ) => ( k3_finseq_1(C) = A & k4_finseq_1(C) = k2_finseq_1(A) ) ) ) ) ) ), file(finseq_1,t21_finseq_1), []). fof(t23_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B,C] : ( m2_finseq_1(C,B) => m2_finseq_1(k7_relat_1(C,k2_finseq_1(A)),B) ) ) ), file(finseq_1,t23_finseq_1), []). fof(t29_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => r1_xreal_0(A,k2_xcmplx_0(A,B)) ) ) ), file(nat_1,t29_nat_1), []). fof(t2_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_tarski,axiom,( ! [A,B] : ( ! [C] : ( r2_hidden(C,A) <=> r2_hidden(C,B) ) => A = B ) ), file(tarski,t2_tarski), []). fof(t32_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( A = k6_finseq_1(B) <=> k3_finseq_1(A) = 0 ) ) ), file(finseq_1,t32_finseq_1), []). fof(t38_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(C,A) => ( ( B = k1_xboole_0 & A != k1_xboole_0 ) | ( v1_funct_1(k2_partfun1(A,B,D,C)) & v1_funct_2(k2_partfun1(A,B,D,C),C,B) & m2_relset_1(k2_partfun1(A,B,D,C),C,B) ) ) ) ) ), file(funct_2,t38_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(t46_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( r1_tarski(k2_relat_1(A),k1_relat_1(B)) => k1_relat_1(k5_relat_1(A,B)) = k1_relat_1(A) ) ) ) ), file(relat_1,t46_relat_1), []). fof(t47_rvsum_1,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( m2_finseq_1(C,k1_numbers) => ( r2_hidden(A,k4_finseq_1(k7_rvsum_1(B,C))) => k2_seq_1(k5_numbers,k1_numbers,k7_rvsum_1(B,C),A) = k10_binop_2(k2_seq_1(k5_numbers,k1_numbers,B,A),k2_seq_1(k5_numbers,k1_numbers,C,A)) ) ) ) ) ), file(rvsum_1,t47_rvsum_1), []). 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_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(t61_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( v4_ordinal2(C) => ( ( k3_finseq_1(A) = k2_xcmplx_0(C,1) & B = k7_relat_1(A,k2_finseq_1(C)) ) => A = k7_finseq_1(B,k9_finseq_1(k1_funct_1(A,k2_xcmplx_0(C,1)))) ) ) ) ) ), file(finseq_3,t61_finseq_3), []). fof(t64_rvsum_1,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_finseq_2(B,k1_numbers,k4_finseq_2(A,k1_numbers)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k4_finseq_2(A,k1_numbers)) => B = k4_rvsum_1(A,k8_rvsum_1(A,B,C),C) ) ) ) ), file(rvsum_1,t64_rvsum_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(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t6_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => r2_hidden(k2_xcmplx_0(A,1),k2_finseq_1(k2_xcmplx_0(A,1))) ) ), file(finseq_1,t6_finseq_1), []). 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(t70_funct_1,axiom,( ! [A,B,C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(B,k1_relat_1(k7_relat_1(C,A))) => k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B) ) ) ), file(funct_1,t70_funct_1), []). fof(t71_funct_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => r1_tarski(k2_relat_1(k13_funct_3(A,B)),k2_zfmisc_1(k2_relat_1(A),k2_relat_1(B))) ) ) ), file(funct_3,t71_funct_3), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t7_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ( r1_xreal_0(A,B) <=> r1_tarski(k2_finseq_1(A),k2_finseq_1(B)) ) ) ) ), file(finseq_1,t7_finseq_1), []). fof(t7_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v2_xreal_0(A) & ~ v3_xreal_0(B) ) ) ) ), file(real,t7_real), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t8_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v3_xreal_0(B) & ~ v2_xreal_0(A) ) ) ) ), file(real,t8_real), []). fof(t9_finseq_2,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( r2_hidden(A,k2_finseq_1(B)) => r2_hidden(A,k2_finseq_1(k1_nat_1(B,C))) ) ) ) ) ), file(finseq_2,t9_finseq_2), []).