% Mizar ND problem: t29_rfunct_3,rfunct_3,893,72 fof(dh_c1_45__rfunct_3,definition, ( ( ~ v1_xboole_0(c1_45__rfunct_3) => ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,k4_rfunct_3(c1_45__rfunct_3,A)) => ! [C] : ( m1_subset_1(C,c1_45__rfunct_3) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( r1_rfunct_3(c1_45__rfunct_3,A,B,C) => ( D = 0 | r1_rfunct_3(c1_45__rfunct_3,A,k16_finseq_1(k4_rfunct_3(c1_45__rfunct_3,A),B,D),C) ) ) ) ) ) ) ) => ! [E] : ( ~ v1_xboole_0(E) => ! [F] : ( ~ v1_xboole_0(F) => ! [G] : ( m2_finseq_1(G,k4_rfunct_3(E,F)) => ! [H] : ( m1_subset_1(H,E) => ! [I] : ( m2_subset_1(I,k1_numbers,k5_numbers) => ( r1_rfunct_3(E,F,G,H) => ( I = 0 | r1_rfunct_3(E,F,k16_finseq_1(k4_rfunct_3(E,F),G,I),H) ) ) ) ) ) ) ) ), introduced(definition,[new_symbol(c1_45__rfunct_3),file(rfunct_3,c1_45__rfunct_3)]), [interesting(0.8),axiom,file(rfunct_3,c1_45__rfunct_3)]). fof(dh_c2_45__rfunct_3,definition, ( ( ~ v1_xboole_0(c2_45__rfunct_3) => ! [A] : ( m2_finseq_1(A,k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3)) => ! [B] : ( m1_subset_1(B,c1_45__rfunct_3) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( r1_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3,A,B) => ( C = 0 | r1_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3,k16_finseq_1(k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3),A,C),B) ) ) ) ) ) ) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m2_finseq_1(E,k4_rfunct_3(c1_45__rfunct_3,D)) => ! [F] : ( m1_subset_1(F,c1_45__rfunct_3) => ! [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) => ( r1_rfunct_3(c1_45__rfunct_3,D,E,F) => ( G = 0 | r1_rfunct_3(c1_45__rfunct_3,D,k16_finseq_1(k4_rfunct_3(c1_45__rfunct_3,D),E,G),F) ) ) ) ) ) ) ), introduced(definition,[new_symbol(c2_45__rfunct_3),file(rfunct_3,c2_45__rfunct_3)]), [interesting(0.8),axiom,file(rfunct_3,c2_45__rfunct_3)]). fof(dh_c3_45__rfunct_3,definition, ( ( m2_finseq_1(c3_45__rfunct_3,k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3)) => ! [A] : ( m1_subset_1(A,c1_45__rfunct_3) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( r1_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3,c3_45__rfunct_3,A) => ( B = 0 | r1_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3,k16_finseq_1(k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3),c3_45__rfunct_3,B),A) ) ) ) ) ) => ! [C] : ( m2_finseq_1(C,k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3)) => ! [D] : ( m1_subset_1(D,c1_45__rfunct_3) => ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ( r1_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3,C,D) => ( E = 0 | r1_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3,k16_finseq_1(k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3),C,E),D) ) ) ) ) ) ), introduced(definition,[new_symbol(c3_45__rfunct_3),file(rfunct_3,c3_45__rfunct_3)]), [interesting(0.8),axiom,file(rfunct_3,c3_45__rfunct_3)]). fof(dh_c4_45__rfunct_3,definition, ( ( m1_subset_1(c4_45__rfunct_3,c1_45__rfunct_3) => ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ( r1_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3,c3_45__rfunct_3,c4_45__rfunct_3) => ( A = 0 | r1_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3,k16_finseq_1(k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3),c3_45__rfunct_3,A),c4_45__rfunct_3) ) ) ) ) => ! [B] : ( m1_subset_1(B,c1_45__rfunct_3) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( r1_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3,c3_45__rfunct_3,B) => ( C = 0 | r1_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3,k16_finseq_1(k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3),c3_45__rfunct_3,C),B) ) ) ) ) ), introduced(definition,[new_symbol(c4_45__rfunct_3),file(rfunct_3,c4_45__rfunct_3)]), [interesting(0.8),axiom,file(rfunct_3,c4_45__rfunct_3)]). fof(dh_c5_45__rfunct_3,definition, ( ( m2_subset_1(c5_45__rfunct_3,k1_numbers,k5_numbers) => ( r1_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3,c3_45__rfunct_3,c4_45__rfunct_3) => ( c5_45__rfunct_3 = 0 | r1_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3,k16_finseq_1(k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3),c3_45__rfunct_3,c5_45__rfunct_3),c4_45__rfunct_3) ) ) ) => ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ( r1_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3,c3_45__rfunct_3,c4_45__rfunct_3) => ( A = 0 | r1_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3,k16_finseq_1(k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3),c3_45__rfunct_3,A),c4_45__rfunct_3) ) ) ) ), introduced(definition,[new_symbol(c5_45__rfunct_3),file(rfunct_3,c5_45__rfunct_3)]), [interesting(0.8),axiom,file(rfunct_3,c5_45__rfunct_3)]). fof(e1_45__rfunct_3,assumption, ( r1_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3,c3_45__rfunct_3,c4_45__rfunct_3) & c5_45__rfunct_3 != 0 ), introduced(assumption,[file(rfunct_3,e1_45__rfunct_3)]), [interesting(0.8),axiom,file(rfunct_3,e1_45__rfunct_3)]). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), [interesting(0.9),axiom,file(zfmisc_1,k2_zfmisc_1)]). fof(cc1_relset_1,theorem,( ! [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), [interesting(0.9),axiom,file(relset_1,cc1_relset_1)]). fof(cc3_xreal_0,theorem,( ! [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), [interesting(0.9),axiom,file(xreal_0,cc3_xreal_0)]). fof(cc6_xreal_0,theorem,( ! [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), [interesting(0.9),axiom,file(xreal_0,cc6_xreal_0)]). fof(cc8_xreal_0,theorem,( ! [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), [interesting(0.9),axiom,file(xreal_0,cc8_xreal_0)]). fof(fc14_finset_1,theorem,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_zfmisc_1(A,B)) ) ), file(finset_1,fc14_finset_1), [interesting(0.9),axiom,file(finset_1,fc14_finset_1)]). fof(fc1_seq_1,theorem,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) ) => ( v1_xcmplx_0(k1_funct_1(A,B)) & v1_xreal_0(k1_funct_1(A,B)) ) ) ), file(seq_1,fc1_seq_1), [interesting(0.9),axiom,file(seq_1,fc1_seq_1)]). fof(rc1_seq_1,theorem,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) ) ), file(seq_1,rc1_seq_1), [interesting(0.9),axiom,file(seq_1,rc1_seq_1)]). fof(rc2_xreal_0,theorem,( ? [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), [interesting(0.9),axiom,file(xreal_0,rc2_xreal_0)]). fof(rc3_xreal_0,theorem,( ? [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), [interesting(0.9),axiom,file(xreal_0,rc3_xreal_0)]). fof(rc4_xreal_0,theorem,( ? [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), [interesting(0.9),axiom,file(xreal_0,rc4_xreal_0)]). fof(redefinition_m2_relset_1,definition,( ! [A,B,C] : ( m2_relset_1(C,A,B) <=> m1_relset_1(C,A,B) ) ), file(relset_1,m2_relset_1), [interesting(0.9),axiom,file(relset_1,m2_relset_1)]). fof(dt_k1_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), [interesting(0.9),axiom,file(relat_1,k1_relat_1)]). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]). fof(dt_k4_partfun1,axiom,( $true ), file(partfun1,k4_partfun1), [interesting(0.9),axiom,file(partfun1,k4_partfun1)]). fof(dt_k5_ordinal2,axiom,( $true ), file(ordinal2,k5_ordinal2), [interesting(0.9),axiom,file(ordinal2,k5_ordinal2)]). 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), [interesting(0.9),axiom,file(finseq_1,m1_finseq_1)]). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), [interesting(0.9),axiom,file(relset_1,m1_relset_1)]). fof(dt_m1_rfunct_3,axiom,( $true ), file(rfunct_3,m1_rfunct_3), [interesting(0.9),axiom,file(rfunct_3,m1_rfunct_3)]). 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), [interesting(0.9),axiom,file(relset_1,m2_relset_1)]). fof(cc10_membered,theorem,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,A) => v1_xcmplx_0(B) ) ) ), file(membered,cc10_membered), [interesting(0.9),axiom,file(membered,cc10_membered)]). fof(cc11_membered,theorem,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) ) ) ) ), file(membered,cc11_membered), [interesting(0.9),axiom,file(membered,cc11_membered)]). fof(cc12_membered,theorem,( ! [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), [interesting(0.9),axiom,file(membered,cc12_membered)]). fof(cc13_membered,theorem,( ! [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), [interesting(0.9),axiom,file(membered,cc13_membered)]). fof(cc14_membered,theorem,( ! [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), [interesting(0.9),axiom,file(membered,cc14_membered)]). fof(cc16_membered,theorem,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_membered(B) ) ) ), file(membered,cc16_membered), [interesting(0.9),axiom,file(membered,cc16_membered)]). fof(cc17_membered,theorem,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) ) ) ) ), file(membered,cc17_membered), [interesting(0.9),axiom,file(membered,cc17_membered)]). fof(cc18_membered,theorem,( ! [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), [interesting(0.9),axiom,file(membered,cc18_membered)]). fof(cc19_membered,theorem,( ! [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), [interesting(0.9),axiom,file(membered,cc19_membered)]). fof(cc1_finseq_1,theorem,( ! [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), [interesting(0.9),axiom,file(finseq_1,cc1_finseq_1)]). fof(cc1_membered,theorem,( ! [A] : ( v5_membered(A) => v4_membered(A) ) ), file(membered,cc1_membered), [interesting(0.9),axiom,file(membered,cc1_membered)]). fof(cc1_seq_1,theorem,( ! [A,B] : ( v2_membered(B) => ! [C] : ( m1_relset_1(C,A,B) => ( v1_funct_1(C) => ( v1_funct_1(C) & v1_seq_1(C) ) ) ) ) ), file(seq_1,cc1_seq_1), [interesting(0.9),axiom,file(seq_1,cc1_seq_1)]). fof(cc1_xreal_0,theorem,( ! [A] : ( v4_ordinal2(A) => v1_xreal_0(A) ) ), file(xreal_0,cc1_xreal_0), [interesting(0.9),axiom,file(xreal_0,cc1_xreal_0)]). fof(cc20_membered,theorem,( ! [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), [interesting(0.9),axiom,file(membered,cc20_membered)]). fof(cc2_finset_1,theorem,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_finset_1(B) ) ) ), file(finset_1,cc2_finset_1), [interesting(0.9),axiom,file(finset_1,cc2_finset_1)]). fof(cc2_membered,theorem,( ! [A] : ( v4_membered(A) => v3_membered(A) ) ), file(membered,cc2_membered), [interesting(0.9),axiom,file(membered,cc2_membered)]). fof(cc2_xreal_0,theorem,( ! [A] : ( v1_xreal_0(A) => v1_xcmplx_0(A) ) ), file(xreal_0,cc2_xreal_0), [interesting(0.9),axiom,file(xreal_0,cc2_xreal_0)]). fof(cc3_membered,theorem,( ! [A] : ( v3_membered(A) => v2_membered(A) ) ), file(membered,cc3_membered), [interesting(0.9),axiom,file(membered,cc3_membered)]). fof(cc3_nat_1,theorem,( ! [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), [interesting(0.9),axiom,file(nat_1,cc3_nat_1)]). fof(cc4_membered,theorem,( ! [A] : ( v2_membered(A) => v1_membered(A) ) ), file(membered,cc4_membered), [interesting(0.9),axiom,file(membered,cc4_membered)]). fof(cc4_xreal_0,theorem,( ! [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), [interesting(0.9),axiom,file(xreal_0,cc4_xreal_0)]). fof(cc5_xreal_0,theorem,( ! [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), [interesting(0.9),axiom,file(xreal_0,cc5_xreal_0)]). fof(cc6_membered,theorem,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v1_membered(A) & v2_membered(A) ) ) ), file(membered,cc6_membered), [interesting(0.9),axiom,file(membered,cc6_membered)]). fof(cc7_xreal_0,theorem,( ! [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), [interesting(0.9),axiom,file(xreal_0,cc7_xreal_0)]). fof(cc9_membered,theorem,( ! [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), [interesting(0.9),axiom,file(membered,cc9_membered)]). fof(fc17_finseq_1,theorem,( ! [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), [interesting(0.9),axiom,file(finseq_1,fc17_finseq_1)]). fof(fc1_partfun1,theorem,( ! [A,B] : ~ v1_xboole_0(k4_partfun1(A,B)) ), file(partfun1,fc1_partfun1), [interesting(0.9),axiom,file(partfun1,fc1_partfun1)]). fof(fc5_membered,theorem, ( v1_membered(k5_ordinal2) & v2_membered(k5_ordinal2) & v3_membered(k5_ordinal2) & v4_membered(k5_ordinal2) & v5_membered(k5_ordinal2) ), file(membered,fc5_membered), [interesting(0.9),axiom,file(membered,fc5_membered)]). fof(rc1_finseq_1,theorem,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc1_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc1_finseq_1)]). fof(rc1_finset_1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) ) ), file(finset_1,rc1_finset_1), [interesting(0.9),axiom,file(finset_1,rc1_finset_1)]). fof(rc1_membered,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ), file(membered,rc1_membered), [interesting(0.9),axiom,file(membered,rc1_membered)]). fof(rc1_nat_1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(nat_1,rc1_nat_1), [interesting(0.9),axiom,file(nat_1,rc1_nat_1)]). fof(rc1_rfunct_3,theorem,( ! [A,B] : ? [C] : ( m1_rfunct_3(C,A,B) & ~ v1_xboole_0(C) ) ), file(rfunct_3,rc1_rfunct_3), [interesting(0.9),axiom,file(rfunct_3,rc1_rfunct_3)]). fof(rc1_xreal_0,theorem,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(xreal_0,rc1_xreal_0), [interesting(0.9),axiom,file(xreal_0,rc1_xreal_0)]). fof(rc2_finseq_1,theorem,( ! [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), [interesting(0.9),axiom,file(finseq_1,rc2_finseq_1)]). fof(rc2_nat_1,theorem,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(A) & v3_ordinal1(A) ) ), file(nat_1,rc2_nat_1), [interesting(0.9),axiom,file(nat_1,rc2_nat_1)]). fof(rc2_partfun1,theorem,( ! [A,B] : ? [C] : ( m1_relset_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C) ) ), file(partfun1,rc2_partfun1), [interesting(0.9),axiom,file(partfun1,rc2_partfun1)]). fof(rc3_finset_1,theorem,( ! [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), [interesting(0.9),axiom,file(finset_1,rc3_finset_1)]). fof(rc3_nat_1,theorem,( ? [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), [interesting(0.9),axiom,file(nat_1,rc3_nat_1)]). fof(rc4_finset_1,theorem,( ! [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), [interesting(0.9),axiom,file(finset_1,rc4_finset_1)]). fof(rc7_finseq_1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc7_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc7_finseq_1)]). fof(rc8_finseq_1,theorem,( ? [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), [interesting(0.9),axiom,file(finseq_1,rc8_finseq_1)]). fof(antisymmetry_r2_hidden,theorem,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), [interesting(0.9),axiom,file(hidden,r2_hidden)]). fof(redefinition_k4_finseq_1,definition,( ! [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), [interesting(0.9),axiom,file(finseq_1,k4_finseq_1)]). fof(redefinition_k4_relset_1,definition,( ! [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), [interesting(0.9),axiom,file(relset_1,k4_relset_1)]). fof(redefinition_k4_rfunct_3,definition,( ! [A,B] : k4_rfunct_3(A,B) = k4_partfun1(A,B) ), file(rfunct_3,k4_rfunct_3), [interesting(0.9),axiom,file(rfunct_3,k4_rfunct_3)]). fof(redefinition_k5_numbers,definition,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), [interesting(0.9),axiom,file(numbers,k5_numbers)]). fof(redefinition_m2_finseq_1,definition,( ! [A,B] : ( m2_finseq_1(B,A) <=> m1_finseq_1(B,A) ) ), file(finseq_1,m2_finseq_1), [interesting(0.9),axiom,file(finseq_1,m2_finseq_1)]). fof(redefinition_m2_rfunct_3,definition,( ! [A,B,C] : ( ( ~ v1_xboole_0(C) & m1_rfunct_3(C,A,B) ) => ! [D] : ( m2_rfunct_3(D,A,B,C) <=> m1_subset_1(D,C) ) ) ), file(rfunct_3,m2_rfunct_3), [interesting(0.9),axiom,file(rfunct_3,m2_rfunct_3)]). fof(redefinition_m2_subset_1,definition,( ! [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), [interesting(0.9),axiom,file(subset_1,m2_subset_1)]). fof(dt_k16_finseq_1,axiom,( ! [A,B,C] : ( ( m1_finseq_1(B,A) & v4_ordinal2(C) ) => m2_finseq_1(k16_finseq_1(A,B,C),A) ) ), file(finseq_1,k16_finseq_1), [interesting(0.9),axiom,file(finseq_1,k16_finseq_1)]). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), [interesting(0.9),axiom,file(funct_1,k1_funct_1)]). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), [interesting(0.9),axiom,file(numbers,k1_numbers)]). 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), [interesting(0.9),axiom,file(finseq_1,k4_finseq_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), [interesting(0.9),axiom,file(relset_1,k4_relset_1)]). fof(dt_k4_rfunct_3,axiom,( ! [A,B] : m1_rfunct_3(k4_rfunct_3(A,B),A,B) ), file(rfunct_3,k4_rfunct_3), [interesting(0.9),axiom,file(rfunct_3,k4_rfunct_3)]). fof(dt_k5_numbers,axiom,( m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ), file(numbers,k5_numbers), [interesting(0.9),axiom,file(numbers,k5_numbers)]). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), [interesting(0.9),axiom,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), [interesting(0.9),axiom,file(finseq_1,m2_finseq_1)]). fof(dt_m2_rfunct_3,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(C) & m1_rfunct_3(C,A,B) ) => ! [D] : ( m2_rfunct_3(D,A,B,C) => ( v1_funct_1(D) & m2_relset_1(D,A,B) ) ) ) ), file(rfunct_3,m2_rfunct_3), [interesting(0.9),axiom,file(rfunct_3,m2_rfunct_3)]). 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), [interesting(0.9),axiom,file(subset_1,m2_subset_1)]). fof(dt_c1_45__rfunct_3,assumption,( ~ v1_xboole_0(c1_45__rfunct_3) ), introduced(assumption,[file(rfunct_3,c1_45__rfunct_3)]), [interesting(0.8),axiom,file(rfunct_3,c1_45__rfunct_3)]). fof(dt_c2_45__rfunct_3,assumption,( ~ v1_xboole_0(c2_45__rfunct_3) ), introduced(assumption,[file(rfunct_3,c2_45__rfunct_3)]), [interesting(0.8),axiom,file(rfunct_3,c2_45__rfunct_3)]). fof(dt_c3_45__rfunct_3,assumption,( m2_finseq_1(c3_45__rfunct_3,k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3)) ), introduced(assumption,[file(rfunct_3,c3_45__rfunct_3)]), [interesting(0.8),axiom,file(rfunct_3,c3_45__rfunct_3)]). fof(dt_c4_45__rfunct_3,assumption,( m1_subset_1(c4_45__rfunct_3,c1_45__rfunct_3) ), introduced(assumption,[file(rfunct_3,c4_45__rfunct_3)]), [interesting(0.8),axiom,file(rfunct_3,c4_45__rfunct_3)]). fof(dt_c5_45__rfunct_3,assumption,( m2_subset_1(c5_45__rfunct_3,k1_numbers,k5_numbers) ), introduced(assumption,[file(rfunct_3,c5_45__rfunct_3)]), [interesting(0.8),axiom,file(rfunct_3,c5_45__rfunct_3)]). fof(dt_c6_45__rfunct_3,assumption,( m2_rfunct_3(c6_45__rfunct_3,c1_45__rfunct_3,c2_45__rfunct_3,k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3)) ), introduced(assumption,[file(rfunct_3,c6_45__rfunct_3)]), [interesting(0.8),axiom,file(rfunct_3,c6_45__rfunct_3)]). fof(cc15_membered,theorem,( ! [A] : ( v1_xboole_0(A) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc15_membered), [interesting(0.9),axiom,file(membered,cc15_membered)]). fof(cc1_finset_1,theorem,( ! [A] : ( v1_xboole_0(A) => v1_finset_1(A) ) ), file(finset_1,cc1_finset_1), [interesting(0.9),axiom,file(finset_1,cc1_finset_1)]). fof(cc1_nat_1,theorem,( ! [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), [interesting(0.9),axiom,file(nat_1,cc1_nat_1)]). fof(cc2_nat_1,theorem,( ! [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), [interesting(0.9),axiom,file(nat_1,cc2_nat_1)]). fof(fc2_membered,theorem, ( ~ v1_xboole_0(k1_numbers) & v1_membered(k1_numbers) & v2_membered(k1_numbers) ), file(membered,fc2_membered), [interesting(0.9),axiom,file(membered,fc2_membered)]). fof(d9_rfunct_3,definition,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,k4_rfunct_3(A,B)) => ! [D] : ( m1_subset_1(D,A) => ( r1_rfunct_3(A,B,C,D) <=> ! [E] : ( m2_rfunct_3(E,A,B,k4_rfunct_3(A,B)) => ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ( ( r2_hidden(F,k4_finseq_1(C)) & k1_funct_1(C,F) = E ) => r2_hidden(D,k4_relset_1(A,B,E)) ) ) ) ) ) ) ) ) ), file(rfunct_3,d9_rfunct_3), [interesting(0.9),axiom,file(rfunct_3,d9_rfunct_3)]). fof(dh_c6_45__rfunct_3,definition, ( ( m2_rfunct_3(c6_45__rfunct_3,c1_45__rfunct_3,c2_45__rfunct_3,k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3)) => ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ( ( r2_hidden(A,k4_finseq_1(k16_finseq_1(k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3),c3_45__rfunct_3,c5_45__rfunct_3))) & k1_funct_1(k16_finseq_1(k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3),c3_45__rfunct_3,c5_45__rfunct_3),A) = c6_45__rfunct_3 ) => r2_hidden(c4_45__rfunct_3,k4_relset_1(c1_45__rfunct_3,c2_45__rfunct_3,c6_45__rfunct_3)) ) ) ) => ! [B] : ( m2_rfunct_3(B,c1_45__rfunct_3,c2_45__rfunct_3,k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3)) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( ( r2_hidden(C,k4_finseq_1(k16_finseq_1(k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3),c3_45__rfunct_3,c5_45__rfunct_3))) & k1_funct_1(k16_finseq_1(k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3),c3_45__rfunct_3,c5_45__rfunct_3),C) = B ) => r2_hidden(c4_45__rfunct_3,k4_relset_1(c1_45__rfunct_3,c2_45__rfunct_3,B)) ) ) ) ), introduced(definition,[new_symbol(c6_45__rfunct_3),file(rfunct_3,c6_45__rfunct_3)]), [interesting(0.8),axiom,file(rfunct_3,c6_45__rfunct_3)]). fof(dh_c7_45__rfunct_3,definition, ( ( m2_subset_1(c7_45__rfunct_3,k1_numbers,k5_numbers) => ( ( r2_hidden(c7_45__rfunct_3,k4_finseq_1(k16_finseq_1(k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3),c3_45__rfunct_3,c5_45__rfunct_3))) & k1_funct_1(k16_finseq_1(k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3),c3_45__rfunct_3,c5_45__rfunct_3),c7_45__rfunct_3) = c6_45__rfunct_3 ) => r2_hidden(c4_45__rfunct_3,k4_relset_1(c1_45__rfunct_3,c2_45__rfunct_3,c6_45__rfunct_3)) ) ) => ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ( ( r2_hidden(A,k4_finseq_1(k16_finseq_1(k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3),c3_45__rfunct_3,c5_45__rfunct_3))) & k1_funct_1(k16_finseq_1(k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3),c3_45__rfunct_3,c5_45__rfunct_3),A) = c6_45__rfunct_3 ) => r2_hidden(c4_45__rfunct_3,k4_relset_1(c1_45__rfunct_3,c2_45__rfunct_3,c6_45__rfunct_3)) ) ) ), introduced(definition,[new_symbol(c7_45__rfunct_3),file(rfunct_3,c7_45__rfunct_3)]), [interesting(0.8),axiom,file(rfunct_3,c7_45__rfunct_3)]). fof(dt_c7_45__rfunct_3,assumption,( m2_subset_1(c7_45__rfunct_3,k1_numbers,k5_numbers) ), introduced(assumption,[file(rfunct_3,c7_45__rfunct_3)]), [interesting(0.8),axiom,file(rfunct_3,c7_45__rfunct_3)]). fof(e2_45__rfunct_3,assumption, ( r2_hidden(c7_45__rfunct_3,k4_finseq_1(k16_finseq_1(k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3),c3_45__rfunct_3,c5_45__rfunct_3))) & k1_funct_1(k16_finseq_1(k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3),c3_45__rfunct_3,c5_45__rfunct_3),c7_45__rfunct_3) = c6_45__rfunct_3 ), introduced(assumption,[file(rfunct_3,e2_45__rfunct_3)]), [interesting(0.8),axiom,file(rfunct_3,e2_45__rfunct_3)]). fof(rc1_partfun1,theorem,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_xboole_0(A) ) ), file(partfun1,rc1_partfun1), [interesting(0.9),axiom,file(partfun1,rc1_partfun1)]). fof(rc2_finset_1,theorem,( ! [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), [interesting(0.9),axiom,file(finset_1,rc2_finset_1)]). fof(rc3_finseq_1,theorem,( ? [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), [interesting(0.9),axiom,file(finseq_1,rc3_finseq_1)]). fof(rc4_finseq_1,theorem,( ! [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), [interesting(0.9),axiom,file(finseq_1,rc4_finseq_1)]). fof(rc6_finseq_1,theorem,( ? [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), [interesting(0.9),axiom,file(finseq_1,rc6_finseq_1)]). fof(reflexivity_r1_tarski,theorem,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), [interesting(0.9),axiom,file(tarski,r1_tarski)]). fof(existence_m1_finseq_1,axiom,( ! [A] : ? [B] : m1_finseq_1(B,A) ), file(finseq_1,m1_finseq_1), [interesting(0.9),axiom,file(finseq_1,m1_finseq_1)]). fof(existence_m1_rfunct_3,axiom,( ! [A,B] : ? [C] : m1_rfunct_3(C,A,B) ), file(rfunct_3,m1_rfunct_3), [interesting(0.9),axiom,file(rfunct_3,m1_rfunct_3)]). fof(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), [interesting(0.9),axiom,file(relset_1,m2_relset_1)]). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]). fof(fc2_finseq_1,theorem, ( 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), [interesting(0.9),axiom,file(finseq_1,fc2_finseq_1)]). fof(fc6_membered,theorem, ( 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), [interesting(0.9),axiom,file(membered,fc6_membered)]). fof(t1_real,theorem,( ! [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), [interesting(0.9),axiom,file(real,t1_real)]). fof(t2_real,theorem,( ! [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), [interesting(0.9),axiom,file(real,t2_real)]). fof(t3_real,theorem,( ! [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), [interesting(0.9),axiom,file(real,t3_real)]). fof(t4_real,theorem,( ! [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), [interesting(0.9),axiom,file(real,t4_real)]). fof(t5_real,theorem,( ! [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), [interesting(0.9),axiom,file(real,t5_real)]). fof(t6_real,theorem,( ! [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), [interesting(0.9),axiom,file(real,t6_real)]). fof(t7_real,theorem,( ! [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), [interesting(0.9),axiom,file(real,t7_real)]). fof(t8_real,theorem,( ! [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), [interesting(0.9),axiom,file(real,t8_real)]). fof(existence_m1_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), [interesting(0.9),axiom,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), [interesting(0.9),axiom,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), [interesting(0.9),axiom,file(finseq_1,m2_finseq_1)]). fof(existence_m2_rfunct_3,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(C) & m1_rfunct_3(C,A,B) ) => ? [D] : m2_rfunct_3(D,A,B,C) ) ), file(rfunct_3,m2_rfunct_3), [interesting(0.9),axiom,file(rfunct_3,m2_rfunct_3)]). 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), [interesting(0.9),axiom,file(subset_1,m2_subset_1)]). fof(dt_k1_card_1,axiom,( ! [A] : v1_card_1(k1_card_1(A)) ), file(card_1,k1_card_1), [interesting(0.9),axiom,file(card_1,k1_card_1)]). fof(t2_subset,theorem,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), [interesting(0.9),axiom,file(subset,t2_subset)]). fof(t3_subset,theorem,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), [interesting(0.9),axiom,file(subset,t3_subset)]). fof(t4_subset,theorem,( ! [A,B,C] : ( ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) ) => m1_subset_1(A,C) ) ), file(subset,t4_subset), [interesting(0.9),axiom,file(subset,t4_subset)]). fof(t5_subset,theorem,( ! [A,B,C] : ~ ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C) ) ), file(subset,t5_subset), [interesting(0.9),axiom,file(subset,t5_subset)]). fof(t6_boole,theorem,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), [interesting(0.9),axiom,file(boole,t6_boole)]). fof(t8_boole,theorem,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), [interesting(0.9),axiom,file(boole,t8_boole)]). fof(reflexivity_r1_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => r1_xreal_0(A,A) ) ), file(xreal_0,r1_xreal_0), [interesting(0.9),axiom,file(xreal_0,r1_xreal_0)]). fof(connectedness_r1_xreal_0,theorem,( ! [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), [interesting(0.9),axiom,file(xreal_0,r1_xreal_0)]). fof(redefinition_k3_finseq_1,definition,( ! [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), [interesting(0.9),axiom,file(finseq_1,k3_finseq_1)]). fof(dt_k3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers) ) ), file(finseq_1,k3_finseq_1), [interesting(0.9),axiom,file(finseq_1,k3_finseq_1)]). fof(t1_subset,theorem,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), [interesting(0.9),axiom,file(subset,t1_subset)]). fof(t7_boole,theorem,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), [interesting(0.9),axiom,file(boole,t7_boole)]). fof(e1_45_1_1_1__rfunct_3,assumption,( r1_xreal_0(k3_finseq_1(c3_45__rfunct_3),c5_45__rfunct_3) ), introduced(assumption,[file(rfunct_3,e1_45_1_1_1__rfunct_3)]), [interesting(0.35),axiom,file(rfunct_3,e1_45_1_1_1__rfunct_3)]). fof(fc15_finseq_1,theorem,( ! [A,B] : ( m1_finseq_1(B,A) => ( v1_xboole_0(k16_finseq_1(A,B,0)) & v1_relat_1(k16_finseq_1(A,B,0)) & v1_funct_1(k16_finseq_1(A,B,0)) & v2_funct_1(k16_finseq_1(A,B,0)) & v1_finset_1(k16_finseq_1(A,B,0)) & v1_finseq_1(k16_finseq_1(A,B,0)) ) ) ), file(finseq_1,fc15_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc15_finseq_1)]). fof(spc0_boole,theorem,( v1_xboole_0(0) ), file(boole,spc0_boole), [interesting(0.9),axiom,file(boole,spc0_boole)]). fof(t1_numerals,theorem,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), [interesting(0.9),axiom,file(numerals,t1_numerals)]). fof(spc0_numerals,theorem, ( v2_xreal_0(0) & m2_subset_1(0,k1_numbers,k5_numbers) & m1_subset_1(0,k5_numbers) & m1_subset_1(0,k1_numbers) ), file(numerals,spc0_numerals), [interesting(0.9),axiom,file(numerals,spc0_numerals)]). fof(l10_rfunct_3,plain,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,B) => ( r1_xreal_0(k3_finseq_1(C),A) => k16_finseq_1(B,C,A) = C ) ) ) ) ), file(rfunct_3,l10_rfunct_3), [interesting(0.9),axiom,file(rfunct_3,l10_rfunct_3)]). fof(e2_45_1_1_1__rfunct_3,plain,( k16_finseq_1(k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3),c3_45__rfunct_3,c5_45__rfunct_3) = c3_45__rfunct_3 ), inference(mizar_by,[status(thm),assumptions([dt_c1_45__rfunct_3,dt_c2_45__rfunct_3,dt_c3_45__rfunct_3,dt_c5_45__rfunct_3,e1_45_1_1_1__rfunct_3])],[rc1_seq_1,reflexivity_r1_tarski,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,cc1_seq_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc14_finset_1,rc1_nat_1,rc1_partfun1,rc1_xreal_0,rc2_finseq_1,rc2_finset_1,rc2_nat_1,rc2_partfun1,rc2_xreal_0,rc3_finseq_1,rc3_nat_1,rc3_xreal_0,rc4_finseq_1,rc4_xreal_0,rc6_finseq_1,t1_real,t2_real,t3_real,t4_real,t5_real,t6_real,t7_real,t8_real,antisymmetry_r2_hidden,existence_m1_finseq_1,existence_m1_rfunct_3,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_card_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k4_partfun1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_rfunct_3,dt_m1_subset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finseq_1,cc1_membered,cc1_nat_1,cc1_xreal_0,cc20_membered,cc2_finset_1,cc2_membered,cc2_nat_1,cc2_xreal_0,cc3_membered,cc3_nat_1,cc4_membered,cc6_membered,cc7_xreal_0,cc9_membered,fc1_partfun1,fc2_finseq_1,fc5_membered,fc6_membered,rc1_finseq_1,rc1_finset_1,rc1_membered,rc1_rfunct_3,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m2_finseq_1,existence_m2_subset_1,redefinition_k3_finseq_1,redefinition_k4_rfunct_3,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_subset_1,dt_k16_finseq_1,dt_k1_numbers,dt_k3_finseq_1,dt_k4_rfunct_3,dt_k5_numbers,dt_m2_finseq_1,dt_m2_subset_1,dt_c1_45__rfunct_3,dt_c2_45__rfunct_3,dt_c3_45__rfunct_3,dt_c5_45__rfunct_3,cc15_membered,cc1_finset_1,fc2_membered,t6_boole,t7_boole,t8_boole,e1_45_1_1_1__rfunct_3,l10_rfunct_3]), [interesting(0.35),file(rfunct_3,e2_45_1_1_1__rfunct_3),[file(rfunct_3,e2_45_1_1_1__rfunct_3)]]). fof(e3_45_1_1_1__rfunct_3,plain,( r2_hidden(c4_45__rfunct_3,k4_relset_1(c1_45__rfunct_3,c2_45__rfunct_3,c6_45__rfunct_3)) ), inference(mizar_by,[status(thm),assumptions([dt_c4_45__rfunct_3,dt_c6_45__rfunct_3,dt_c7_45__rfunct_3,dt_c1_45__rfunct_3,dt_c2_45__rfunct_3,dt_c3_45__rfunct_3,dt_c5_45__rfunct_3,e1_45_1_1_1__rfunct_3,e1_45__rfunct_3,e2_45__rfunct_3])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,cc1_relset_1,fc14_finset_1,fc1_seq_1,rc1_partfun1,rc1_seq_1,rc2_finset_1,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_rfunct_3,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k4_partfun1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_rfunct_3,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finseq_1,cc1_membered,cc1_seq_1,cc1_xreal_0,cc20_membered,cc2_finset_1,cc2_membered,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,fc15_finseq_1,fc17_finseq_1,fc1_partfun1,fc2_finseq_1,fc5_membered,fc6_membered,rc1_finseq_1,rc1_finset_1,rc1_membered,rc1_nat_1,rc1_rfunct_3,rc1_xreal_0,rc2_finseq_1,rc2_nat_1,rc2_partfun1,rc2_xreal_0,rc3_finset_1,rc3_nat_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc7_finseq_1,rc8_finseq_1,t3_subset,t4_subset,t5_subset,antisymmetry_r2_hidden,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_rfunct_3,existence_m2_subset_1,redefinition_k4_finseq_1,redefinition_k4_relset_1,redefinition_k4_rfunct_3,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_rfunct_3,redefinition_m2_subset_1,dt_k16_finseq_1,dt_k1_funct_1,dt_k1_numbers,dt_k4_finseq_1,dt_k4_relset_1,dt_k4_rfunct_3,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_rfunct_3,dt_m2_subset_1,dt_c1_45__rfunct_3,dt_c2_45__rfunct_3,dt_c3_45__rfunct_3,dt_c4_45__rfunct_3,dt_c5_45__rfunct_3,dt_c6_45__rfunct_3,dt_c7_45__rfunct_3,cc15_membered,cc1_finset_1,cc1_nat_1,cc2_nat_1,fc2_membered,spc0_boole,t1_numerals,t1_subset,t2_subset,t6_boole,t7_boole,t8_boole,spc0_numerals,spc0_boole,e2_45_1_1_1__rfunct_3,e1_45__rfunct_3,e2_45__rfunct_3,d9_rfunct_3]), [interesting(0.35),file(rfunct_3,e3_45_1_1_1__rfunct_3),[file(rfunct_3,e3_45_1_1_1__rfunct_3)]]). fof(i2_45_1_1_1__rfunct_3,theorem,( $true ), introduced(tautology,[file(rfunct_3,i2_45_1_1_1__rfunct_3)]), [interesting(0.35),trivial,file(rfunct_3,i2_45_1_1_1__rfunct_3)]). fof(i1_45_1_1_1__rfunct_3,plain,( r2_hidden(c4_45__rfunct_3,k4_relset_1(c1_45__rfunct_3,c2_45__rfunct_3,c6_45__rfunct_3)) ), inference(conclusion,[status(thm),assumptions([dt_c4_45__rfunct_3,dt_c6_45__rfunct_3,dt_c7_45__rfunct_3,dt_c1_45__rfunct_3,dt_c2_45__rfunct_3,dt_c3_45__rfunct_3,dt_c5_45__rfunct_3,e1_45_1_1_1__rfunct_3,e1_45__rfunct_3,e2_45__rfunct_3])],[e3_45_1_1_1__rfunct_3,i2_45_1_1_1__rfunct_3]), [interesting(0.35),file(rfunct_3,i1_45_1_1_1__rfunct_3),[file(rfunct_3,i1_45_1_1_1__rfunct_3)]]). fof(i1_45_1_1__rfunct_3,plain, ( r1_xreal_0(k3_finseq_1(c3_45__rfunct_3),c5_45__rfunct_3) => ( r1_xreal_0(k3_finseq_1(c3_45__rfunct_3),c5_45__rfunct_3) & r2_hidden(c4_45__rfunct_3,k4_relset_1(c1_45__rfunct_3,c2_45__rfunct_3,c6_45__rfunct_3)) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c4_45__rfunct_3,dt_c6_45__rfunct_3,dt_c7_45__rfunct_3,dt_c1_45__rfunct_3,dt_c2_45__rfunct_3,dt_c3_45__rfunct_3,dt_c5_45__rfunct_3,e1_45__rfunct_3,e2_45__rfunct_3]),discharge_asm(discharge,[e1_45_1_1_1__rfunct_3])],[e1_45_1_1_1__rfunct_3,i1_45_1_1_1__rfunct_3]), [interesting(0.5),file(rfunct_3,i1_45_1_1__rfunct_3),[file(rfunct_3,i1_45_1_1__rfunct_3)]]). fof(e1_45_1_1_2__rfunct_3,assumption,( ~ r1_xreal_0(k3_finseq_1(c3_45__rfunct_3),c5_45__rfunct_3) ), introduced(assumption,[file(rfunct_3,e1_45_1_1_2__rfunct_3)]), [interesting(0.35),axiom,file(rfunct_3,e1_45_1_1_2__rfunct_3)]). fof(dt_k1_finseq_1,axiom,( $true ), file(finseq_1,k1_finseq_1), [interesting(0.9),axiom,file(finseq_1,k1_finseq_1)]). fof(fc1_finseq_1,theorem,( ! [A] : ( v4_ordinal2(A) => v1_finset_1(k1_finseq_1(A)) ) ), file(finseq_1,fc1_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc1_finseq_1)]). fof(redefinition_k2_finseq_1,definition,( ! [A] : ( v4_ordinal2(A) => k2_finseq_1(A) = k1_finseq_1(A) ) ), file(finseq_1,k2_finseq_1), [interesting(0.9),axiom,file(finseq_1,k2_finseq_1)]). 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), [interesting(0.9),axiom,file(finseq_1,k2_finseq_1)]). fof(fc10_xreal_0,theorem,( ! [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), [interesting(0.9),axiom,file(xreal_0,fc10_xreal_0)]). fof(fc11_xreal_0,theorem,( ! [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), [interesting(0.9),axiom,file(xreal_0,fc11_xreal_0)]). fof(fc12_xreal_0,theorem,( ! [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), [interesting(0.9),axiom,file(xreal_0,fc12_xreal_0)]). fof(fc3_nat_1,theorem,( ! [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), [interesting(0.9),axiom,file(nat_1,fc3_nat_1)]). fof(fc3_xreal_0,theorem,( ! [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), [interesting(0.9),axiom,file(xreal_0,fc3_xreal_0)]). fof(fc4_nat_1,theorem,( ! [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), [interesting(0.9),axiom,file(nat_1,fc4_nat_1)]). fof(fc7_xreal_0,theorem,( ! [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), [interesting(0.9),axiom,file(xreal_0,fc7_xreal_0)]). fof(fc8_xreal_0,theorem,( ! [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), [interesting(0.9),axiom,file(xreal_0,fc8_xreal_0)]). fof(fc9_xreal_0,theorem,( ! [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), [interesting(0.9),axiom,file(xreal_0,fc9_xreal_0)]). fof(spc6_arithm,theorem,( ! [A,B,C] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) ) => k2_xcmplx_0(k2_xcmplx_0(A,B),C) = k2_xcmplx_0(A,k2_xcmplx_0(B,C)) ) ), file(arithm,spc6_arithm), [interesting(0.9),axiom,file(arithm,spc6_arithm)]). fof(t1_arithm,theorem,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(A,0) = A ) ), file(arithm,t1_arithm), [interesting(0.9),axiom,file(arithm,t1_arithm)]). fof(commutativity_k1_nat_1,theorem,( ! [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), [interesting(0.9),axiom,file(nat_1,k1_nat_1)]). fof(commutativity_k2_xcmplx_0,theorem,( ! [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), [interesting(0.9),axiom,file(xcmplx_0,k2_xcmplx_0)]). fof(redefinition_k1_nat_1,definition,( ! [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), [interesting(0.9),axiom,file(nat_1,k1_nat_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), [interesting(0.9),axiom,file(nat_1,k1_nat_1)]). fof(dt_k2_xcmplx_0,axiom,( $true ), file(xcmplx_0,k2_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k2_xcmplx_0)]). fof(fc1_nat_1,theorem,( ! [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), [interesting(0.9),axiom,file(nat_1,fc1_nat_1)]). fof(rqLessOrEqual__r1_xreal_0__r1_r0,theorem,( ~ r1_xreal_0(1,0) ), file(arithm,rqLessOrEqual__r1_xreal_0__r1_r0), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_r0)]). fof(rqRealAdd__k2_xcmplx_0__r0_r0_r0,theorem,( k2_xcmplx_0(0,0) = 0 ), file(arithm,rqRealAdd__k2_xcmplx_0__r0_r0_r0), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_r0_r0)]). fof(spc1_numerals,theorem, ( v2_xreal_0(1) & m2_subset_1(1,k1_numbers,k5_numbers) & m1_subset_1(1,k5_numbers) & m1_subset_1(1,k1_numbers) ), file(numerals,spc1_numerals), [interesting(0.9),axiom,file(numerals,spc1_numerals)]). fof(spc1_boole,theorem,( ~ v1_xboole_0(1) ), file(boole,spc1_boole), [interesting(0.9),axiom,file(boole,spc1_boole)]). fof(rqLessOrEqual__r1_xreal_0__r0_r0,theorem,( r1_xreal_0(0,0) ), file(arithm,rqLessOrEqual__r1_xreal_0__r0_r0), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_r0)]). fof(rqLessOrEqual__r1_xreal_0__r0_r1,theorem,( r1_xreal_0(0,1) ), file(arithm,rqLessOrEqual__r1_xreal_0__r0_r1), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_r1)]). fof(rqLessOrEqual__r1_xreal_0__r1_r1,theorem,( r1_xreal_0(1,1) ), file(arithm,rqLessOrEqual__r1_xreal_0__r1_r1), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_r1)]). fof(e3_45_1_1_2__rfunct_3,plain,( ~ r1_xreal_0(c5_45__rfunct_3,0) ), inference(mizar_by,[status(thm),assumptions([dt_c1_45__rfunct_3,dt_c2_45__rfunct_3,dt_c3_45__rfunct_3,dt_c4_45__rfunct_3,dt_c5_45__rfunct_3,e1_45__rfunct_3])],[rc1_seq_1,reflexivity_r1_tarski,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_finseq_1,cc1_relset_1,cc1_seq_1,fc14_finset_1,rc1_finseq_1,rc1_partfun1,rc2_finseq_1,rc2_finset_1,rc2_partfun1,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,existence_m1_finseq_1,existence_m1_rfunct_3,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k4_partfun1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_rfunct_3,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc1_partfun1,fc2_finseq_1,fc5_membered,fc6_membered,rc1_finset_1,rc1_membered,rc1_nat_1,rc1_rfunct_3,rc1_xreal_0,rc2_nat_1,rc2_xreal_0,rc3_finset_1,rc3_nat_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_subset_1,redefinition_k4_rfunct_3,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_subset_1,dt_k1_numbers,dt_k4_rfunct_3,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_subset_1,cc15_membered,cc1_finset_1,cc1_nat_1,cc2_nat_1,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc2_membered,t1_numerals,t1_real,t2_subset,t4_real,t6_boole,t7_boole,t8_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,dt_c1_45__rfunct_3,dt_c2_45__rfunct_3,dt_c3_45__rfunct_3,dt_c4_45__rfunct_3,dt_c5_45__rfunct_3,rqLessOrEqual__r1_xreal_0__r0_r0,spc0_numerals,spc0_boole,e1_45__rfunct_3]), [interesting(0.35),file(rfunct_3,e3_45_1_1_2__rfunct_3),[file(rfunct_3,e3_45_1_1_2__rfunct_3)]]). fof(t38_nat_1,theorem,( ! [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), [interesting(0.9),axiom,file(nat_1,t38_nat_1)]). fof(rqRealAdd__k2_xcmplx_0__r0_r1_r1,theorem,( k2_xcmplx_0(0,1) = 1 ), file(arithm,rqRealAdd__k2_xcmplx_0__r0_r1_r1), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_r1_r1)]). fof(rqRealAdd__k2_xcmplx_0__r1_r0_r1,theorem,( k2_xcmplx_0(1,0) = 1 ), file(arithm,rqRealAdd__k2_xcmplx_0__r1_r0_r1), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_r0_r1)]). fof(e4_45_1_1_2__rfunct_3,plain,( r1_xreal_0(k1_nat_1(0,1),c5_45__rfunct_3) ), inference(mizar_by,[status(thm),assumptions([dt_c1_45__rfunct_3,dt_c2_45__rfunct_3,dt_c3_45__rfunct_3,dt_c4_45__rfunct_3,dt_c5_45__rfunct_3,e1_45__rfunct_3])],[reflexivity_r1_tarski,cc1_finseq_1,rc1_finseq_1,rc1_partfun1,rc2_finset_1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc2_finseq_1,fc5_membered,fc6_membered,rc1_finset_1,rc1_membered,rc2_nat_1,rc3_finset_1,rc3_nat_1,rc4_finset_1,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc1_finset_1,cc1_nat_1,cc2_nat_1,cc2_xreal_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc2_membered,fc3_nat_1,fc3_xreal_0,fc4_nat_1,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,rc1_nat_1,rc1_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,spc6_arithm,t1_arithm,t1_numerals,t1_real,t2_real,t2_subset,t3_real,t4_real,t5_real,t6_boole,t6_real,t7_boole,t7_real,t8_boole,t8_real,commutativity_k1_nat_1,commutativity_k2_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k1_nat_1,dt_k1_nat_1,dt_k2_xcmplx_0,dt_c5_45__rfunct_3,cc1_xreal_0,cc3_nat_1,fc1_nat_1,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r1_r1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e3_45_1_1_2__rfunct_3,t38_nat_1,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqLessOrEqual__r1_xreal_0__r1_r0]), [interesting(0.35),file(rfunct_3,e4_45_1_1_2__rfunct_3),[file(rfunct_3,e4_45_1_1_2__rfunct_3)]]). fof(t27_finseq_3,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v4_ordinal2(B) => ( r2_hidden(B,k4_finseq_1(A)) <=> ( r1_xreal_0(1,B) & r1_xreal_0(B,k3_finseq_1(A)) ) ) ) ) ), file(finseq_3,t27_finseq_3), [interesting(0.9),axiom,file(finseq_3,t27_finseq_3)]). fof(e5_45_1_1_2__rfunct_3,plain,( r2_hidden(c5_45__rfunct_3,k4_finseq_1(c3_45__rfunct_3)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_45__rfunct_3,dt_c2_45__rfunct_3,dt_c3_45__rfunct_3,dt_c4_45__rfunct_3,dt_c5_45__rfunct_3,e1_45__rfunct_3,e1_45_1_1_2__rfunct_3])],[rc1_seq_1,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,cc1_seq_1,fc14_finset_1,rc1_partfun1,rc2_finseq_1,rc2_finset_1,rc2_partfun1,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m1_rfunct_3,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k4_partfun1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_rfunct_3,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc1_partfun1,fc2_finseq_1,fc5_membered,fc6_membered,rc1_membered,rc1_rfunct_3,rc2_nat_1,rc3_nat_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_subset_1,redefinition_k4_rfunct_3,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k4_rfunct_3,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_subset_1,dt_c1_45__rfunct_3,dt_c2_45__rfunct_3,cc15_membered,cc1_finset_1,cc1_nat_1,cc2_finset_1,cc2_nat_1,cc2_xreal_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc17_finseq_1,fc2_membered,fc3_nat_1,fc3_xreal_0,fc4_nat_1,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,rc1_finset_1,rc1_nat_1,rc1_xreal_0,rc2_xreal_0,rc3_finset_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc7_finseq_1,rc8_finseq_1,spc6_arithm,t1_arithm,t1_numerals,t1_real,t2_real,t2_subset,t3_real,t3_subset,t4_real,t4_subset,t5_real,t5_subset,t6_boole,t6_real,t7_real,t8_boole,t8_real,commutativity_k1_nat_1,commutativity_k2_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,redefinition_k1_nat_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,dt_k1_nat_1,dt_k2_xcmplx_0,dt_k3_finseq_1,dt_k4_finseq_1,dt_c3_45__rfunct_3,dt_c5_45__rfunct_3,cc1_finseq_1,cc1_xreal_0,cc3_nat_1,fc1_nat_1,rc1_finseq_1,rqLessOrEqual__r1_xreal_0__r1_r0,rqRealAdd__k2_xcmplx_0__r0_r0_r0,t1_subset,t7_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e4_45_1_1_2__rfunct_3,e1_45_1_1_2__rfunct_3,t27_finseq_3,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r0_r0]), [interesting(0.35),file(rfunct_3,e5_45_1_1_2__rfunct_3),[file(rfunct_3,e5_45_1_1_2__rfunct_3)]]). fof(t80_finseq_1,theorem,( ! [A,B] : ( m2_finseq_1(B,A) => ! [C] : ( v4_ordinal2(C) => ( r1_xreal_0(C,k3_finseq_1(B)) => k3_finseq_1(k16_finseq_1(A,B,C)) = C ) ) ) ), file(finseq_1,t80_finseq_1), [interesting(0.9),axiom,file(finseq_1,t80_finseq_1)]). fof(d3_finseq_1,definition,( ! [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), [interesting(0.9),axiom,file(finseq_1,d3_finseq_1)]). fof(e2_45_1_1_2__rfunct_3,plain, ( k4_finseq_1(c3_45__rfunct_3) = k2_finseq_1(k3_finseq_1(c3_45__rfunct_3)) & k4_finseq_1(k16_finseq_1(k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3),c3_45__rfunct_3,c5_45__rfunct_3)) = k2_finseq_1(k3_finseq_1(k16_finseq_1(k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3),c3_45__rfunct_3,c5_45__rfunct_3))) & k3_finseq_1(k16_finseq_1(k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3),c3_45__rfunct_3,c5_45__rfunct_3)) = c5_45__rfunct_3 ), inference(mizar_by,[status(thm),assumptions([dt_c1_45__rfunct_3,dt_c2_45__rfunct_3,dt_c3_45__rfunct_3,dt_c5_45__rfunct_3,e1_45_1_1_2__rfunct_3])],[rc1_partfun1,rc1_seq_1,rc2_finset_1,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_relset_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_relset_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc1_seq_1,cc20_membered,cc2_membered,cc3_membered,cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,fc14_finset_1,fc2_finseq_1,fc6_membered,rc1_membered,rc2_finseq_1,rc2_nat_1,rc2_partfun1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,t1_real,t1_subset,t4_real,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_finseq_1,existence_m1_rfunct_3,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_zfmisc_1,dt_k4_partfun1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_rfunct_3,dt_m1_subset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_nat_1,cc2_finset_1,cc2_nat_1,cc2_xreal_0,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc7_xreal_0,cc9_membered,fc17_finseq_1,fc1_finseq_1,fc1_partfun1,fc5_membered,rc1_finset_1,rc1_nat_1,rc1_rfunct_3,rc1_xreal_0,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t2_real,t2_subset,t3_real,t3_subset,t6_boole,t7_boole,t8_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m2_finseq_1,existence_m2_subset_1,redefinition_k2_finseq_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k4_rfunct_3,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_subset_1,dt_k16_finseq_1,dt_k1_numbers,dt_k1_relat_1,dt_k2_finseq_1,dt_k3_finseq_1,dt_k4_finseq_1,dt_k4_rfunct_3,dt_k5_numbers,dt_m2_finseq_1,dt_m2_subset_1,dt_c1_45__rfunct_3,dt_c2_45__rfunct_3,dt_c3_45__rfunct_3,dt_c5_45__rfunct_3,cc1_finseq_1,cc1_xreal_0,cc3_nat_1,fc2_membered,rc1_finseq_1,e1_45_1_1_2__rfunct_3,t80_finseq_1,d3_finseq_1]), [interesting(0.35),file(rfunct_3,e2_45_1_1_2__rfunct_3),[file(rfunct_3,e2_45_1_1_2__rfunct_3)]]). fof(t19_rfinseq,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( ( r2_hidden(C,k4_finseq_1(B)) & r2_hidden(D,k2_finseq_1(C)) ) => ( k1_funct_1(k16_finseq_1(A,B,C),D) = k1_funct_1(B,D) & r2_hidden(D,k4_finseq_1(B)) ) ) ) ) ) ) ), file(rfinseq,t19_rfinseq), [interesting(0.9),axiom,file(rfinseq,t19_rfinseq)]). fof(e6_45_1_1_2__rfunct_3,plain, ( c6_45__rfunct_3 = k1_funct_1(c3_45__rfunct_3,c7_45__rfunct_3) & r2_hidden(c7_45__rfunct_3,k4_finseq_1(c3_45__rfunct_3)) ), inference(mizar_by,[status(thm),assumptions([dt_c6_45__rfunct_3,dt_c7_45__rfunct_3,dt_c4_45__rfunct_3,e1_45__rfunct_3,e2_45__rfunct_3,dt_c1_45__rfunct_3,dt_c2_45__rfunct_3,dt_c3_45__rfunct_3,dt_c5_45__rfunct_3,e1_45_1_1_2__rfunct_3])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_seq_1,rc1_seq_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,reflexivity_r1_tarski,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,cc1_seq_1,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc14_finset_1,rc1_nat_1,rc1_partfun1,rc1_xreal_0,rc2_finseq_1,rc2_finset_1,rc2_nat_1,rc2_partfun1,rc3_finseq_1,rc3_nat_1,rc4_finseq_1,rc6_finseq_1,existence_m1_finseq_1,existence_m1_rfunct_3,existence_m1_subset_1,existence_m2_relset_1,existence_m2_rfunct_3,redefinition_m2_relset_1,redefinition_m2_rfunct_3,dt_k1_card_1,dt_k1_finseq_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k4_partfun1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_rfunct_3,dt_m1_subset_1,dt_m2_relset_1,dt_m2_rfunct_3,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finseq_1,cc1_membered,cc1_nat_1,cc1_xreal_0,cc20_membered,cc2_finset_1,cc2_membered,cc2_nat_1,cc3_membered,cc3_nat_1,cc4_membered,cc6_membered,cc9_membered,fc17_finseq_1,fc1_finseq_1,fc1_partfun1,fc2_finseq_1,fc5_membered,fc6_membered,rc1_finseq_1,rc1_finset_1,rc1_membered,rc1_rfunct_3,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t3_subset,t4_subset,t5_subset,antisymmetry_r2_hidden,existence_m2_finseq_1,existence_m2_subset_1,redefinition_k2_finseq_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k4_rfunct_3,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_subset_1,dt_k16_finseq_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_finseq_1,dt_k3_finseq_1,dt_k4_finseq_1,dt_k4_rfunct_3,dt_k5_numbers,dt_m2_finseq_1,dt_m2_subset_1,dt_c1_45__rfunct_3,dt_c2_45__rfunct_3,dt_c3_45__rfunct_3,dt_c5_45__rfunct_3,dt_c6_45__rfunct_3,dt_c7_45__rfunct_3,cc15_membered,cc1_finset_1,fc2_membered,t1_subset,t6_boole,t7_boole,t8_boole,e5_45_1_1_2__rfunct_3,e2_45__rfunct_3,e2_45_1_1_2__rfunct_3,t19_rfinseq]), [interesting(0.35),file(rfunct_3,e6_45_1_1_2__rfunct_3),[file(rfunct_3,e6_45_1_1_2__rfunct_3)]]). fof(e7_45_1_1_2__rfunct_3,plain,( r2_hidden(c4_45__rfunct_3,k4_relset_1(c1_45__rfunct_3,c2_45__rfunct_3,c6_45__rfunct_3)) ), inference(mizar_by,[status(thm),assumptions([dt_c6_45__rfunct_3,dt_c7_45__rfunct_3,dt_c4_45__rfunct_3,e2_45__rfunct_3,dt_c1_45__rfunct_3,dt_c2_45__rfunct_3,dt_c3_45__rfunct_3,dt_c5_45__rfunct_3,e1_45_1_1_2__rfunct_3,e1_45__rfunct_3])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,cc1_relset_1,fc14_finset_1,fc1_seq_1,rc1_partfun1,rc1_seq_1,rc2_finset_1,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_rfunct_3,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k4_partfun1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_rfunct_3,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finseq_1,cc1_membered,cc1_seq_1,cc1_xreal_0,cc20_membered,cc2_finset_1,cc2_membered,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,fc17_finseq_1,fc1_partfun1,fc2_finseq_1,fc5_membered,fc6_membered,rc1_finseq_1,rc1_finset_1,rc1_membered,rc1_nat_1,rc1_rfunct_3,rc1_xreal_0,rc2_finseq_1,rc2_nat_1,rc2_partfun1,rc2_xreal_0,rc3_finset_1,rc3_nat_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc7_finseq_1,rc8_finseq_1,t3_subset,t4_subset,t5_subset,antisymmetry_r2_hidden,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_rfunct_3,existence_m2_subset_1,redefinition_k4_finseq_1,redefinition_k4_relset_1,redefinition_k4_rfunct_3,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_rfunct_3,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k4_finseq_1,dt_k4_relset_1,dt_k4_rfunct_3,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_rfunct_3,dt_m2_subset_1,dt_c1_45__rfunct_3,dt_c2_45__rfunct_3,dt_c3_45__rfunct_3,dt_c4_45__rfunct_3,dt_c5_45__rfunct_3,dt_c6_45__rfunct_3,dt_c7_45__rfunct_3,cc15_membered,cc1_finset_1,cc1_nat_1,cc2_nat_1,fc2_membered,spc0_boole,t1_numerals,t1_subset,t2_subset,t6_boole,t7_boole,t8_boole,spc0_numerals,spc0_boole,e6_45_1_1_2__rfunct_3,e1_45__rfunct_3,d9_rfunct_3]), [interesting(0.35),file(rfunct_3,e7_45_1_1_2__rfunct_3),[file(rfunct_3,e7_45_1_1_2__rfunct_3)]]). fof(i2_45_1_1_2__rfunct_3,theorem,( $true ), introduced(tautology,[file(rfunct_3,i2_45_1_1_2__rfunct_3)]), [interesting(0.35),trivial,file(rfunct_3,i2_45_1_1_2__rfunct_3)]). fof(i1_45_1_1_2__rfunct_3,plain,( r2_hidden(c4_45__rfunct_3,k4_relset_1(c1_45__rfunct_3,c2_45__rfunct_3,c6_45__rfunct_3)) ), inference(conclusion,[status(thm),assumptions([dt_c6_45__rfunct_3,dt_c7_45__rfunct_3,dt_c4_45__rfunct_3,e2_45__rfunct_3,dt_c1_45__rfunct_3,dt_c2_45__rfunct_3,dt_c3_45__rfunct_3,dt_c5_45__rfunct_3,e1_45_1_1_2__rfunct_3,e1_45__rfunct_3])],[e7_45_1_1_2__rfunct_3,i2_45_1_1_2__rfunct_3]), [interesting(0.35),file(rfunct_3,i1_45_1_1_2__rfunct_3),[file(rfunct_3,i1_45_1_1_2__rfunct_3)]]). fof(i2_45_1_1__rfunct_3,plain, ( ~ r1_xreal_0(k3_finseq_1(c3_45__rfunct_3),c5_45__rfunct_3) => ( ~ r1_xreal_0(k3_finseq_1(c3_45__rfunct_3),c5_45__rfunct_3) & r2_hidden(c4_45__rfunct_3,k4_relset_1(c1_45__rfunct_3,c2_45__rfunct_3,c6_45__rfunct_3)) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c6_45__rfunct_3,dt_c7_45__rfunct_3,dt_c4_45__rfunct_3,e2_45__rfunct_3,dt_c1_45__rfunct_3,dt_c2_45__rfunct_3,dt_c3_45__rfunct_3,dt_c5_45__rfunct_3,e1_45__rfunct_3]),discharge_asm(discharge,[e1_45_1_1_2__rfunct_3])],[e1_45_1_1_2__rfunct_3,i1_45_1_1_2__rfunct_3]), [interesting(0.5),file(rfunct_3,i2_45_1_1__rfunct_3),[file(rfunct_3,i2_45_1_1__rfunct_3)]]). fof(e1_45_1_1__rfunct_3,plain,( ~ ( ~ r1_xreal_0(k3_finseq_1(c3_45__rfunct_3),c5_45__rfunct_3) & r1_xreal_0(k3_finseq_1(c3_45__rfunct_3),c5_45__rfunct_3) ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_45__rfunct_3,dt_c2_45__rfunct_3,dt_c3_45__rfunct_3,dt_c5_45__rfunct_3])],[rc1_partfun1,rc1_seq_1,rc2_finset_1,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_relset_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_relset_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc1_seq_1,cc1_xreal_0,cc20_membered,cc2_membered,cc3_membered,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc14_finset_1,fc2_finseq_1,fc6_membered,rc1_membered,rc1_nat_1,rc2_finseq_1,rc2_nat_1,rc2_partfun1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,t1_real,t1_subset,t2_real,t3_real,t4_real,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_finseq_1,existence_m1_rfunct_3,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k4_partfun1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_rfunct_3,dt_m1_subset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_nat_1,cc2_finset_1,cc2_nat_1,cc4_membered,cc6_membered,cc7_xreal_0,cc9_membered,fc1_partfun1,fc5_membered,rc1_finset_1,rc1_rfunct_3,rc1_xreal_0,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,existence_m2_finseq_1,existence_m2_subset_1,redefinition_k4_rfunct_3,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_numbers,dt_k4_rfunct_3,dt_k5_numbers,dt_m2_finseq_1,dt_m2_subset_1,dt_c1_45__rfunct_3,dt_c2_45__rfunct_3,cc1_finseq_1,cc2_xreal_0,fc2_membered,rc1_finseq_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k3_finseq_1,dt_k3_finseq_1,dt_c3_45__rfunct_3,dt_c5_45__rfunct_3]), [interesting(0.5),file(rfunct_3,e1_45_1_1__rfunct_3),[file(rfunct_3,e1_45_1_1__rfunct_3)]]). fof(e3_45__rfunct_3,plain, ( ( r1_xreal_0(k3_finseq_1(c3_45__rfunct_3),c5_45__rfunct_3) & r2_hidden(c4_45__rfunct_3,k4_relset_1(c1_45__rfunct_3,c2_45__rfunct_3,c6_45__rfunct_3)) ) | ( ~ r1_xreal_0(k3_finseq_1(c3_45__rfunct_3),c5_45__rfunct_3) & r2_hidden(c4_45__rfunct_3,k4_relset_1(c1_45__rfunct_3,c2_45__rfunct_3,c6_45__rfunct_3)) ) ), inference(percases,[status(thm),assumptions([dt_c6_45__rfunct_3,dt_c7_45__rfunct_3,dt_c4_45__rfunct_3,e2_45__rfunct_3,e1_45__rfunct_3,dt_c1_45__rfunct_3,dt_c2_45__rfunct_3,dt_c3_45__rfunct_3,dt_c5_45__rfunct_3])],[i1_45_1_1__rfunct_3,i2_45_1_1__rfunct_3,e1_45_1_1__rfunct_3]), [interesting(0.8),file(rfunct_3,e3_45__rfunct_3),[file(rfunct_3,e3_45__rfunct_3)]]). fof(e4_45__rfunct_3,plain,( r2_hidden(c4_45__rfunct_3,k4_relset_1(c1_45__rfunct_3,c2_45__rfunct_3,c6_45__rfunct_3)) ), inference(mizar_by,[status(thm),assumptions([dt_c6_45__rfunct_3,dt_c7_45__rfunct_3,dt_c4_45__rfunct_3,e2_45__rfunct_3,e1_45__rfunct_3,dt_c1_45__rfunct_3,dt_c2_45__rfunct_3,dt_c3_45__rfunct_3,dt_c5_45__rfunct_3])],[dt_k2_zfmisc_1,cc1_relset_1,fc14_finset_1,rc1_partfun1,rc1_seq_1,rc2_finset_1,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m1_rfunct_3,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k4_partfun1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_rfunct_3,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_seq_1,cc1_xreal_0,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc3_nat_1,cc3_xreal_0,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc17_finseq_1,fc1_partfun1,fc2_finseq_1,fc5_membered,fc6_membered,rc1_finset_1,rc1_membered,rc1_nat_1,rc1_rfunct_3,rc1_xreal_0,rc2_finseq_1,rc2_nat_1,rc2_xreal_0,rc3_finset_1,rc3_nat_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc7_finseq_1,rc8_finseq_1,t1_real,t2_real,t3_real,t4_real,t5_real,t6_real,t7_real,t8_real,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_rfunct_3,existence_m2_subset_1,redefinition_k4_rfunct_3,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_rfunct_3,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k4_rfunct_3,dt_k5_numbers,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_rfunct_3,dt_m2_subset_1,cc15_membered,cc1_finseq_1,cc1_finset_1,cc1_nat_1,cc2_nat_1,cc2_xreal_0,cc6_membered,cc7_xreal_0,cc9_membered,fc2_membered,rc1_finseq_1,rc2_partfun1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,redefinition_k3_finseq_1,redefinition_k4_relset_1,dt_k3_finseq_1,dt_k4_relset_1,dt_c1_45__rfunct_3,dt_c2_45__rfunct_3,dt_c3_45__rfunct_3,dt_c4_45__rfunct_3,dt_c5_45__rfunct_3,dt_c6_45__rfunct_3,t1_subset,t7_boole,e3_45__rfunct_3]), [interesting(0.8),file(rfunct_3,e4_45__rfunct_3),[file(rfunct_3,e4_45__rfunct_3)]]). fof(i9_45__rfunct_3,theorem,( $true ), introduced(tautology,[file(rfunct_3,i9_45__rfunct_3)]), [interesting(0.8),trivial,file(rfunct_3,i9_45__rfunct_3)]). fof(i8_45__rfunct_3,plain,( r2_hidden(c4_45__rfunct_3,k4_relset_1(c1_45__rfunct_3,c2_45__rfunct_3,c6_45__rfunct_3)) ), inference(conclusion,[status(thm),assumptions([dt_c6_45__rfunct_3,dt_c7_45__rfunct_3,dt_c4_45__rfunct_3,e2_45__rfunct_3,e1_45__rfunct_3,dt_c1_45__rfunct_3,dt_c2_45__rfunct_3,dt_c3_45__rfunct_3,dt_c5_45__rfunct_3])],[e4_45__rfunct_3,i9_45__rfunct_3]), [interesting(0.8),file(rfunct_3,i8_45__rfunct_3),[file(rfunct_3,i8_45__rfunct_3)]]). fof(i8_45_tmp__rfunct_3,plain, ( ( r2_hidden(c7_45__rfunct_3,k4_finseq_1(k16_finseq_1(k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3),c3_45__rfunct_3,c5_45__rfunct_3))) & k1_funct_1(k16_finseq_1(k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3),c3_45__rfunct_3,c5_45__rfunct_3),c7_45__rfunct_3) = c6_45__rfunct_3 ) => r2_hidden(c4_45__rfunct_3,k4_relset_1(c1_45__rfunct_3,c2_45__rfunct_3,c6_45__rfunct_3)) ), inference(discharge_asm,[status(thm),assumptions([dt_c6_45__rfunct_3,dt_c7_45__rfunct_3,dt_c4_45__rfunct_3,e1_45__rfunct_3,dt_c1_45__rfunct_3,dt_c2_45__rfunct_3,dt_c3_45__rfunct_3,dt_c5_45__rfunct_3]),discharge_asm(discharge,[e2_45__rfunct_3])],[e2_45__rfunct_3,i8_45__rfunct_3]), [interesting(0.8),i7_45__rfunct_3]). fof(i7_45__rfunct_3,plain, ( ( r2_hidden(c7_45__rfunct_3,k4_finseq_1(k16_finseq_1(k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3),c3_45__rfunct_3,c5_45__rfunct_3))) & k1_funct_1(k16_finseq_1(k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3),c3_45__rfunct_3,c5_45__rfunct_3),c7_45__rfunct_3) = c6_45__rfunct_3 ) => r2_hidden(c4_45__rfunct_3,k4_relset_1(c1_45__rfunct_3,c2_45__rfunct_3,c6_45__rfunct_3)) ), inference(mizar_def_expansion,[status(thm),assumptions([dt_c6_45__rfunct_3,dt_c7_45__rfunct_3,dt_c4_45__rfunct_3,e1_45__rfunct_3,dt_c1_45__rfunct_3,dt_c2_45__rfunct_3,dt_c3_45__rfunct_3,dt_c5_45__rfunct_3])],[i8_45_tmp__rfunct_3,dt_k2_zfmisc_1,cc1_relset_1,cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,fc14_finset_1,fc1_seq_1,rc1_seq_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,redefinition_m2_relset_1,dt_k5_ordinal2,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_seq_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_xreal_0,cc3_membered,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc17_finseq_1,fc5_membered,rc1_finset_1,rc1_membered,rc1_nat_1,rc1_xreal_0,rc2_finseq_1,rc2_nat_1,rc3_finset_1,rc3_nat_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_rfunct_3,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k4_partfun1,dt_k5_numbers,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_rfunct_3,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_rfunct_3,dt_m2_subset_1,cc15_membered,cc1_finseq_1,cc1_finset_1,cc1_nat_1,cc1_xreal_0,cc2_nat_1,cc3_nat_1,cc6_membered,cc9_membered,fc1_partfun1,fc2_membered,rc1_finseq_1,rc1_rfunct_3,rc2_partfun1,antisymmetry_r2_hidden,redefinition_k4_finseq_1,redefinition_k4_relset_1,redefinition_k4_rfunct_3,dt_k16_finseq_1,dt_k1_funct_1,dt_k4_finseq_1,dt_k4_relset_1,dt_k4_rfunct_3,dt_c1_45__rfunct_3,dt_c2_45__rfunct_3,dt_c3_45__rfunct_3,dt_c4_45__rfunct_3,dt_c5_45__rfunct_3,dt_c6_45__rfunct_3,dt_c7_45__rfunct_3]), [interesting(0.8),file(rfunct_3,i7_45__rfunct_3),[file(rfunct_3,i7_45__rfunct_3)]]). fof(i7_45_tmp__rfunct_3,plain, ( m2_subset_1(c7_45__rfunct_3,k1_numbers,k5_numbers) => ( ( r2_hidden(c7_45__rfunct_3,k4_finseq_1(k16_finseq_1(k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3),c3_45__rfunct_3,c5_45__rfunct_3))) & k1_funct_1(k16_finseq_1(k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3),c3_45__rfunct_3,c5_45__rfunct_3),c7_45__rfunct_3) = c6_45__rfunct_3 ) => r2_hidden(c4_45__rfunct_3,k4_relset_1(c1_45__rfunct_3,c2_45__rfunct_3,c6_45__rfunct_3)) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c6_45__rfunct_3,dt_c4_45__rfunct_3,e1_45__rfunct_3,dt_c1_45__rfunct_3,dt_c2_45__rfunct_3,dt_c3_45__rfunct_3,dt_c5_45__rfunct_3]),discharge_asm(discharge,[dt_c7_45__rfunct_3])],[dt_c7_45__rfunct_3,i7_45__rfunct_3]), [interesting(0.8),i6_45__rfunct_3]). fof(i6_45__rfunct_3,plain,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ( ( r2_hidden(A,k4_finseq_1(k16_finseq_1(k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3),c3_45__rfunct_3,c5_45__rfunct_3))) & k1_funct_1(k16_finseq_1(k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3),c3_45__rfunct_3,c5_45__rfunct_3),A) = c6_45__rfunct_3 ) => r2_hidden(c4_45__rfunct_3,k4_relset_1(c1_45__rfunct_3,c2_45__rfunct_3,c6_45__rfunct_3)) ) ) ), inference(let,[status(thm),assumptions([dt_c6_45__rfunct_3,dt_c4_45__rfunct_3,e1_45__rfunct_3,dt_c1_45__rfunct_3,dt_c2_45__rfunct_3,dt_c3_45__rfunct_3,dt_c5_45__rfunct_3])],[i7_45_tmp__rfunct_3,dh_c7_45__rfunct_3]), [interesting(0.8),file(rfunct_3,i6_45__rfunct_3),[file(rfunct_3,i6_45__rfunct_3)]]). fof(i6_45_tmp__rfunct_3,plain, ( m2_rfunct_3(c6_45__rfunct_3,c1_45__rfunct_3,c2_45__rfunct_3,k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3)) => ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ( ( r2_hidden(A,k4_finseq_1(k16_finseq_1(k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3),c3_45__rfunct_3,c5_45__rfunct_3))) & k1_funct_1(k16_finseq_1(k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3),c3_45__rfunct_3,c5_45__rfunct_3),A) = c6_45__rfunct_3 ) => r2_hidden(c4_45__rfunct_3,k4_relset_1(c1_45__rfunct_3,c2_45__rfunct_3,c6_45__rfunct_3)) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c4_45__rfunct_3,e1_45__rfunct_3,dt_c1_45__rfunct_3,dt_c2_45__rfunct_3,dt_c3_45__rfunct_3,dt_c5_45__rfunct_3]),discharge_asm(discharge,[dt_c6_45__rfunct_3])],[dt_c6_45__rfunct_3,i6_45__rfunct_3]), [interesting(0.8),i5_45__rfunct_3]). fof(i5_45__rfunct_3,plain,( r1_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3,k16_finseq_1(k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3),c3_45__rfunct_3,c5_45__rfunct_3),c4_45__rfunct_3) ), inference(let,[status(thm),assumptions([dt_c4_45__rfunct_3,e1_45__rfunct_3,dt_c1_45__rfunct_3,dt_c2_45__rfunct_3,dt_c3_45__rfunct_3,dt_c5_45__rfunct_3])],[i6_45_tmp__rfunct_3,dt_k2_zfmisc_1,cc1_relset_1,cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,fc14_finset_1,fc1_seq_1,rc1_seq_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k4_partfun1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_rfunct_3,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finseq_1,cc1_membered,cc1_seq_1,cc1_xreal_0,cc20_membered,cc2_finset_1,cc2_membered,cc2_xreal_0,cc3_membered,cc3_nat_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc7_xreal_0,cc9_membered,fc17_finseq_1,fc1_partfun1,fc5_membered,rc1_finseq_1,rc1_finset_1,rc1_membered,rc1_nat_1,rc1_rfunct_3,rc1_xreal_0,rc2_finseq_1,rc2_nat_1,rc2_partfun1,rc3_finset_1,rc3_nat_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,redefinition_k4_finseq_1,redefinition_k4_relset_1,redefinition_k4_rfunct_3,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_rfunct_3,redefinition_m2_subset_1,dt_k16_finseq_1,dt_k1_funct_1,dt_k1_numbers,dt_k4_finseq_1,dt_k4_relset_1,dt_k4_rfunct_3,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_rfunct_3,dt_m2_subset_1,dt_c1_45__rfunct_3,dt_c2_45__rfunct_3,dt_c3_45__rfunct_3,dt_c4_45__rfunct_3,dt_c5_45__rfunct_3,cc15_membered,cc1_finset_1,cc1_nat_1,cc2_nat_1,fc2_membered,d9_rfunct_3,dh_c6_45__rfunct_3]), [interesting(0.8),file(rfunct_3,i5_45__rfunct_3),[file(rfunct_3,i5_45__rfunct_3)]]). fof(i4_45__rfunct_3,plain, ( r1_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3,c3_45__rfunct_3,c4_45__rfunct_3) => ( c5_45__rfunct_3 = 0 | r1_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3,k16_finseq_1(k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3),c3_45__rfunct_3,c5_45__rfunct_3),c4_45__rfunct_3) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c4_45__rfunct_3,dt_c1_45__rfunct_3,dt_c2_45__rfunct_3,dt_c3_45__rfunct_3,dt_c5_45__rfunct_3]),discharge_asm(discharge,[e1_45__rfunct_3])],[e1_45__rfunct_3,i5_45__rfunct_3]), [interesting(0.8),file(rfunct_3,i4_45__rfunct_3),[file(rfunct_3,i4_45__rfunct_3)]]). fof(i4_45_tmp__rfunct_3,plain, ( m2_subset_1(c5_45__rfunct_3,k1_numbers,k5_numbers) => ( r1_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3,c3_45__rfunct_3,c4_45__rfunct_3) => ( c5_45__rfunct_3 = 0 | r1_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3,k16_finseq_1(k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3),c3_45__rfunct_3,c5_45__rfunct_3),c4_45__rfunct_3) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c4_45__rfunct_3,dt_c1_45__rfunct_3,dt_c2_45__rfunct_3,dt_c3_45__rfunct_3]),discharge_asm(discharge,[dt_c5_45__rfunct_3])],[dt_c5_45__rfunct_3,i4_45__rfunct_3]), [interesting(0.8),i3_45__rfunct_3]). fof(i3_45__rfunct_3,plain,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ( r1_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3,c3_45__rfunct_3,c4_45__rfunct_3) => ( A = 0 | r1_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3,k16_finseq_1(k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3),c3_45__rfunct_3,A),c4_45__rfunct_3) ) ) ) ), inference(let,[status(thm),assumptions([dt_c4_45__rfunct_3,dt_c1_45__rfunct_3,dt_c2_45__rfunct_3,dt_c3_45__rfunct_3])],[i4_45_tmp__rfunct_3,dh_c5_45__rfunct_3]), [interesting(0.8),file(rfunct_3,i3_45__rfunct_3),[file(rfunct_3,i3_45__rfunct_3)]]). fof(i3_45_tmp__rfunct_3,plain, ( m1_subset_1(c4_45__rfunct_3,c1_45__rfunct_3) => ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ( r1_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3,c3_45__rfunct_3,c4_45__rfunct_3) => ( A = 0 | r1_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3,k16_finseq_1(k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3),c3_45__rfunct_3,A),c4_45__rfunct_3) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_45__rfunct_3,dt_c2_45__rfunct_3,dt_c3_45__rfunct_3]),discharge_asm(discharge,[dt_c4_45__rfunct_3])],[dt_c4_45__rfunct_3,i3_45__rfunct_3]), [interesting(0.8),i2_45__rfunct_3]). fof(i2_45__rfunct_3,plain,( ! [A] : ( m1_subset_1(A,c1_45__rfunct_3) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( r1_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3,c3_45__rfunct_3,A) => ( B = 0 | r1_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3,k16_finseq_1(k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3),c3_45__rfunct_3,B),A) ) ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_45__rfunct_3,dt_c2_45__rfunct_3,dt_c3_45__rfunct_3])],[i3_45_tmp__rfunct_3,dh_c4_45__rfunct_3]), [interesting(0.8),file(rfunct_3,i2_45__rfunct_3),[file(rfunct_3,i2_45__rfunct_3)]]). fof(i2_45_tmp__rfunct_3,plain, ( m2_finseq_1(c3_45__rfunct_3,k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3)) => ! [A] : ( m1_subset_1(A,c1_45__rfunct_3) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( r1_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3,c3_45__rfunct_3,A) => ( B = 0 | r1_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3,k16_finseq_1(k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3),c3_45__rfunct_3,B),A) ) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_45__rfunct_3,dt_c2_45__rfunct_3]),discharge_asm(discharge,[dt_c3_45__rfunct_3])],[dt_c3_45__rfunct_3,i2_45__rfunct_3]), [interesting(0.8),i1_45__rfunct_3]). fof(i1_45__rfunct_3,plain,( ! [A] : ( m2_finseq_1(A,k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3)) => ! [B] : ( m1_subset_1(B,c1_45__rfunct_3) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( r1_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3,A,B) => ( C = 0 | r1_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3,k16_finseq_1(k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3),A,C),B) ) ) ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_45__rfunct_3,dt_c2_45__rfunct_3])],[i2_45_tmp__rfunct_3,dh_c3_45__rfunct_3]), [interesting(0.8),file(rfunct_3,i1_45__rfunct_3),[file(rfunct_3,i1_45__rfunct_3)]]). fof(i1_45_tmp__rfunct_3,plain, ( ( ~ v1_xboole_0(c1_45__rfunct_3) & ~ v1_xboole_0(c2_45__rfunct_3) ) => ! [A] : ( m2_finseq_1(A,k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3)) => ! [B] : ( m1_subset_1(B,c1_45__rfunct_3) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( r1_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3,A,B) => ( C = 0 | r1_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3,k16_finseq_1(k4_rfunct_3(c1_45__rfunct_3,c2_45__rfunct_3),A,C),B) ) ) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_45__rfunct_3,dt_c2_45__rfunct_3])],[dt_c1_45__rfunct_3,dt_c2_45__rfunct_3,i1_45__rfunct_3]), [interesting(1),t29_rfunct_3]). fof(t29_rfunct_3,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,k4_rfunct_3(A,B)) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ( r1_rfunct_3(A,B,C,D) => ( E = 0 | r1_rfunct_3(A,B,k16_finseq_1(k4_rfunct_3(A,B),C,E),D) ) ) ) ) ) ) ) ), inference(let,[status(thm),assumptions([])],[i1_45_tmp__rfunct_3,dh_c1_45__rfunct_3,dh_c2_45__rfunct_3]), [interesting(1),file(rfunct_3,t29_rfunct_3),[file(rfunct_3,t29_rfunct_3)]]).