% Mizar ND problem: t79_rfunct_3,rfunct_3,2932,33 fof(dh_c1_103__rfunct_3,definition, ( ( ~ v1_xboole_0(c1_103__rfunct_3) => ! [A] : ( ( v1_funct_1(A) & m2_relset_1(A,c1_103__rfunct_3,k1_numbers) ) => ! [B,C] : ( ( v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,A,k2_xboole_0(B,C)))) & r1_xboole_0(B,C) ) => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,A,k2_xboole_0(B,C)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,A,B),k22_rfunct_3(c1_103__rfunct_3,A,C))) ) ) ) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( v1_funct_1(E) & m2_relset_1(E,D,k1_numbers) ) => ! [F,G] : ( ( v1_finset_1(k4_relset_1(D,k1_numbers,k2_partfun1(D,k1_numbers,E,k2_xboole_0(F,G)))) & r1_xboole_0(F,G) ) => r1_rfinseq(k22_rfunct_3(D,E,k2_xboole_0(F,G)),k8_finseq_1(k1_numbers,k22_rfunct_3(D,E,F),k22_rfunct_3(D,E,G))) ) ) ) ), introduced(definition,[new_symbol(c1_103__rfunct_3),file(rfunct_3,c1_103__rfunct_3)]), [interesting(0.8),axiom,file(rfunct_3,c1_103__rfunct_3)]). fof(dh_c2_103__rfunct_3,definition, ( ( ( v1_funct_1(c2_103__rfunct_3) & m2_relset_1(c2_103__rfunct_3,c1_103__rfunct_3,k1_numbers) ) => ! [A,B] : ( ( v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(A,B)))) & r1_xboole_0(A,B) ) => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(A,B)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,A),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,B))) ) ) => ! [C] : ( ( v1_funct_1(C) & m2_relset_1(C,c1_103__rfunct_3,k1_numbers) ) => ! [D,E] : ( ( v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,C,k2_xboole_0(D,E)))) & r1_xboole_0(D,E) ) => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,C,k2_xboole_0(D,E)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,C,D),k22_rfunct_3(c1_103__rfunct_3,C,E))) ) ) ), introduced(definition,[new_symbol(c2_103__rfunct_3),file(rfunct_3,c2_103__rfunct_3)]), [interesting(0.8),axiom,file(rfunct_3,c2_103__rfunct_3)]). fof(dh_c3_103__rfunct_3,definition, ( ! [A] : ( ( v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,A)))) & r1_xboole_0(c3_103__rfunct_3,A) ) => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,A)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,A))) ) => ! [B,C] : ( ( v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(B,C)))) & r1_xboole_0(B,C) ) => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(B,C)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,B),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,C))) ) ), introduced(definition,[new_symbol(c3_103__rfunct_3),file(rfunct_3,c3_103__rfunct_3)]), [interesting(0.8),axiom,file(rfunct_3,c3_103__rfunct_3)]). fof(dh_c4_103__rfunct_3,definition, ( ( ( v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c4_103__rfunct_3)))) & r1_xboole_0(c3_103__rfunct_3,c4_103__rfunct_3) ) => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c4_103__rfunct_3)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c4_103__rfunct_3))) ) => ! [A] : ( ( v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,A)))) & r1_xboole_0(c3_103__rfunct_3,A) ) => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,A)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,A))) ) ), introduced(definition,[new_symbol(c4_103__rfunct_3),file(rfunct_3,c4_103__rfunct_3)]), [interesting(0.8),axiom,file(rfunct_3,c4_103__rfunct_3)]). fof(e1_103__rfunct_3,assumption,( v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c4_103__rfunct_3)))) ), introduced(assumption,[file(rfunct_3,e1_103__rfunct_3)]), [interesting(0.8),axiom,file(rfunct_3,e1_103__rfunct_3)]). 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(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(dt_k5_ordinal2,axiom,( $true ), file(ordinal2,k5_ordinal2), [interesting(0.9),axiom,file(ordinal2,k5_ordinal2)]). 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(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_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_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(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(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_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_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_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(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(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(redefinition_k5_numbers,definition,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), [interesting(0.9),axiom,file(numbers,k5_numbers)]). 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_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), [interesting(0.9),axiom,file(zfmisc_1,k2_zfmisc_1)]). 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(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_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(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(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_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(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(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(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(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_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(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(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(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_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_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), [interesting(0.9),axiom,file(finseq_1,k7_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), [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_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_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(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_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_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_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(cc2_membered,theorem,( ! [A] : ( v4_membered(A) => v3_membered(A) ) ), file(membered,cc2_membered), [interesting(0.9),axiom,file(membered,cc2_membered)]). fof(cc3_membered,theorem,( ! [A] : ( v3_membered(A) => v2_membered(A) ) ), file(membered,cc3_membered), [interesting(0.9),axiom,file(membered,cc3_membered)]). fof(cc4_membered,theorem,( ! [A] : ( v2_membered(A) => v1_membered(A) ) ), file(membered,cc4_membered), [interesting(0.9),axiom,file(membered,cc4_membered)]). fof(fc10_finset_1,theorem,( ! [A,B] : ( v1_finset_1(B) => v1_finset_1(k3_xboole_0(A,B)) ) ), file(finset_1,fc10_finset_1), [interesting(0.9),axiom,file(finset_1,fc10_finset_1)]). fof(fc11_finset_1,theorem,( ! [A,B] : ( v1_finset_1(A) => v1_finset_1(k3_xboole_0(A,B)) ) ), file(finset_1,fc11_finset_1), [interesting(0.9),axiom,file(finset_1,fc11_finset_1)]). fof(fc13_finseq_1,theorem,( ! [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), [interesting(0.9),axiom,file(finseq_1,fc13_finseq_1)]). fof(fc14_finseq_1,theorem,( ! [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), [interesting(0.9),axiom,file(finseq_1,fc14_finseq_1)]). fof(fc22_membered,theorem,( ! [A,B] : ( ( v1_membered(A) & v1_membered(B) ) => v1_membered(k2_xboole_0(A,B)) ) ), file(membered,fc22_membered), [interesting(0.9),axiom,file(membered,fc22_membered)]). fof(fc23_membered,theorem,( ! [A,B] : ( ( v2_membered(A) & v2_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc23_membered), [interesting(0.9),axiom,file(membered,fc23_membered)]). fof(fc24_membered,theorem,( ! [A,B] : ( ( v3_membered(A) & v3_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc24_membered), [interesting(0.9),axiom,file(membered,fc24_membered)]). fof(fc25_membered,theorem,( ! [A,B] : ( ( v4_membered(A) & v4_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc25_membered), [interesting(0.9),axiom,file(membered,fc25_membered)]). fof(fc26_membered,theorem,( ! [A,B] : ( ( v5_membered(A) & v5_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) & v5_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc26_membered), [interesting(0.9),axiom,file(membered,fc26_membered)]). fof(fc27_membered,theorem,( ! [A,B] : ( v1_membered(A) => v1_membered(k3_xboole_0(A,B)) ) ), file(membered,fc27_membered), [interesting(0.9),axiom,file(membered,fc27_membered)]). fof(fc28_membered,theorem,( ! [A,B] : ( v1_membered(A) => v1_membered(k3_xboole_0(B,A)) ) ), file(membered,fc28_membered), [interesting(0.9),axiom,file(membered,fc28_membered)]). fof(fc29_membered,theorem,( ! [A,B] : ( v2_membered(A) => ( v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) ) ) ), file(membered,fc29_membered), [interesting(0.9),axiom,file(membered,fc29_membered)]). fof(fc30_membered,theorem,( ! [A,B] : ( v2_membered(A) => ( v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) ) ) ), file(membered,fc30_membered), [interesting(0.9),axiom,file(membered,fc30_membered)]). fof(fc31_membered,theorem,( ! [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), [interesting(0.9),axiom,file(membered,fc31_membered)]). fof(fc32_membered,theorem,( ! [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), [interesting(0.9),axiom,file(membered,fc32_membered)]). fof(fc33_membered,theorem,( ! [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), [interesting(0.9),axiom,file(membered,fc33_membered)]). fof(fc34_membered,theorem,( ! [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), [interesting(0.9),axiom,file(membered,fc34_membered)]). fof(fc35_membered,theorem,( ! [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), [interesting(0.9),axiom,file(membered,fc35_membered)]). fof(fc36_membered,theorem,( ! [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), [interesting(0.9),axiom,file(membered,fc36_membered)]). fof(fc9_finset_1,theorem,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_xboole_0(A,B)) ) ), file(finset_1,fc9_finset_1), [interesting(0.9),axiom,file(finset_1,fc9_finset_1)]). 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_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(rc1_rfinseq,theorem,( ? [A] : ( m1_finseq_1(A,k1_numbers) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_rfinseq(A) ) ), file(rfinseq,rc1_rfinseq), [interesting(0.9),axiom,file(rfinseq,rc1_rfinseq)]). 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(rc2_rfunct_3,theorem,( ! [A,B] : ? [C] : ( m1_relset_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C) & v1_finset_1(C) ) ), file(rfunct_3,rc2_rfunct_3), [interesting(0.9),axiom,file(rfunct_3,rc2_rfunct_3)]). 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(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(commutativity_k2_xboole_0,theorem,( ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ), file(xboole_0,k2_xboole_0), [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]). fof(idempotence_k2_xboole_0,theorem,( ! [A,B] : k2_xboole_0(A,A) = A ), file(xboole_0,k2_xboole_0), [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]). fof(commutativity_k3_xboole_0,theorem,( ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ), file(xboole_0,k3_xboole_0), [interesting(0.9),axiom,file(xboole_0,k3_xboole_0)]). fof(idempotence_k3_xboole_0,theorem,( ! [A,B] : k3_xboole_0(A,A) = A ), file(xboole_0,k3_xboole_0), [interesting(0.9),axiom,file(xboole_0,k3_xboole_0)]). fof(symmetry_r1_rfinseq,theorem,( ! [A,B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => ( r1_rfinseq(A,B) => r1_rfinseq(B,A) ) ) ), file(rfinseq,r1_rfinseq), [interesting(0.9),axiom,file(rfinseq,r1_rfinseq)]). fof(reflexivity_r1_rfinseq,theorem,( ! [A,B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => r1_rfinseq(A,A) ) ), file(rfinseq,r1_rfinseq), [interesting(0.9),axiom,file(rfinseq,r1_rfinseq)]). fof(symmetry_r1_xboole_0,theorem,( ! [A,B] : ( r1_xboole_0(A,B) => r1_xboole_0(B,A) ) ), file(xboole_0,r1_xboole_0), [interesting(0.9),axiom,file(xboole_0,r1_xboole_0)]). fof(redefinition_k8_finseq_1,definition,( ! [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), [interesting(0.9),axiom,file(finseq_1,k8_finseq_1)]). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), [interesting(0.9),axiom,file(numbers,k1_numbers)]). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]). fof(dt_k22_rfunct_3,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & m1_relset_1(B,A,k1_numbers) ) => ( v1_rfinseq(k22_rfunct_3(A,B,C)) & m2_finseq_1(k22_rfunct_3(A,B,C),k1_numbers) ) ) ), file(rfunct_3,k22_rfunct_3), [interesting(0.9),axiom,file(rfunct_3,k22_rfunct_3)]). fof(dt_k2_xboole_0,axiom,( $true ), file(xboole_0,k2_xboole_0), [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]). fof(dt_k3_xboole_0,axiom,( $true ), file(xboole_0,k3_xboole_0), [interesting(0.9),axiom,file(xboole_0,k3_xboole_0)]). 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), [interesting(0.9),axiom,file(finseq_1,k8_finseq_1)]). fof(dt_c1_103__rfunct_3,assumption,( ~ v1_xboole_0(c1_103__rfunct_3) ), introduced(assumption,[file(rfunct_3,c1_103__rfunct_3)]), [interesting(0.8),axiom,file(rfunct_3,c1_103__rfunct_3)]). fof(dt_c2_103__rfunct_3,assumption, ( v1_funct_1(c2_103__rfunct_3) & m2_relset_1(c2_103__rfunct_3,c1_103__rfunct_3,k1_numbers) ), introduced(assumption,[file(rfunct_3,c2_103__rfunct_3)]), [interesting(0.8),axiom,file(rfunct_3,c2_103__rfunct_3)]). fof(dt_c3_103__rfunct_3,assumption,( $true ), introduced(assumption,[file(rfunct_3,c3_103__rfunct_3)]), [interesting(0.8),axiom,file(rfunct_3,c3_103__rfunct_3)]). fof(dt_c4_103__rfunct_3,assumption,( $true ), introduced(assumption,[file(rfunct_3,c4_103__rfunct_3)]), [interesting(0.8),axiom,file(rfunct_3,c4_103__rfunct_3)]). 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(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(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(e9_103__rfunct_3,assumption,( k3_xboole_0(c3_103__rfunct_3,c4_103__rfunct_3) = k1_xboole_0 ), introduced(assumption,[file(rfunct_3,e9_103__rfunct_3)]), [interesting(0.8),axiom,file(rfunct_3,e9_103__rfunct_3)]). fof(d7_xboole_0,definition,( ! [A,B] : ( r1_xboole_0(A,B) <=> k3_xboole_0(A,B) = k1_xboole_0 ) ), file(xboole_0,d7_xboole_0), [interesting(0.9),axiom,file(xboole_0,d7_xboole_0)]). fof(reflexivity_r1_tarski,theorem,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), [interesting(0.9),axiom,file(tarski,r1_tarski)]). 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(fc2_seq_1,theorem,( ! [A,B] : ( ( v1_relat_1(A) & v1_seq_1(A) ) => ( v1_relat_1(k7_relat_1(A,B)) & v1_seq_1(k7_relat_1(A,B)) ) ) ), file(seq_1,fc2_seq_1), [interesting(0.9),axiom,file(seq_1,fc2_seq_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(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(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_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_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_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(dt_k1_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), [interesting(0.9),axiom,file(relat_1,k1_relat_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), [interesting(0.9),axiom,file(relat_1,k7_relat_1)]). 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_rfinseq,theorem,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(B) ) => ( v1_relat_1(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)) & v1_finset_1(k7_relat_1(A,B)) ) ) ), file(rfinseq,fc1_rfinseq), [interesting(0.9),axiom,file(rfinseq,fc1_rfinseq)]). 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(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(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(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(redefinition_k2_partfun1,definition,( ! [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), [interesting(0.9),axiom,file(partfun1,k2_partfun1)]). fof(redefinition_k4_card_1,definition,( ! [A] : ( v1_finset_1(A) => k4_card_1(A) = k1_card_1(A) ) ), file(card_1,k4_card_1), [interesting(0.9),axiom,file(card_1,k4_card_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_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_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), [interesting(0.9),axiom,file(partfun1,k2_partfun1)]). fof(dt_k4_card_1,axiom,( ! [A] : ( v1_finset_1(A) => m2_subset_1(k4_card_1(A),k1_numbers,k5_numbers) ) ), file(card_1,k4_card_1), [interesting(0.9),axiom,file(card_1,k4_card_1)]). fof(dt_k4_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(relset_1,k4_relset_1), [interesting(0.9),axiom,file(relset_1,k4_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), [interesting(0.9),axiom,file(subset_1,m2_subset_1)]). 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(de_c5_103__rfunct_3,definition,( c5_103__rfunct_3 = k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c4_103__rfunct_3)) ), introduced(definition,[new_symbol(c5_103__rfunct_3),file(rfunct_3,c5_103__rfunct_3)]), [interesting(0.8),axiom,file(rfunct_3,c5_103__rfunct_3)]). fof(t1_boole,theorem,( ! [A] : k2_xboole_0(A,k1_xboole_0) = A ), file(boole,t1_boole), [interesting(0.9),axiom,file(boole,t1_boole)]). fof(fc11_finseq_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_finset_1(A) ) => v1_finset_1(k2_relat_1(A)) ) ), file(finseq_1,fc11_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc11_finseq_1)]). fof(dt_k2_relat_1,axiom,( $true ), file(relat_1,k2_relat_1), [interesting(0.9),axiom,file(relat_1,k2_relat_1)]). fof(t7_xboole_1,theorem,( ! [A,B] : r1_tarski(A,k2_xboole_0(A,B)) ), file(xboole_1,t7_xboole_1), [interesting(0.9),axiom,file(xboole_1,t7_xboole_1)]). fof(e2_103__rfunct_3,plain,( r1_tarski(c4_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c4_103__rfunct_3)) ), inference(mizar_by,[status(thm),assumptions([dt_c3_103__rfunct_3,dt_c4_103__rfunct_3])],[existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,dt_k2_xboole_0,dt_c3_103__rfunct_3,dt_c4_103__rfunct_3,t3_subset,t7_xboole_1]), [interesting(0.8),file(rfunct_3,e2_103__rfunct_3),[file(rfunct_3,e2_103__rfunct_3)]]). fof(t104_relat_1,theorem,( ! [A,B,C] : ( v1_relat_1(C) => ( r1_tarski(A,B) => r1_tarski(k7_relat_1(C,A),k7_relat_1(C,B)) ) ) ), file(relat_1,t104_relat_1), [interesting(0.9),axiom,file(relat_1,t104_relat_1)]). fof(e3_103__rfunct_3,plain,( r1_tarski(k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c4_103__rfunct_3),k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c4_103__rfunct_3))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c3_103__rfunct_3,dt_c4_103__rfunct_3])],[cc1_finseq_1,cc1_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_partfun1,rc2_xreal_0,rc3_finseq_1,rc3_xreal_0,rc4_xreal_0,rc6_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc14_finset_1,fc1_rfinseq,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc2_seq_1,fc6_membered,fc9_finset_1,rc1_finset_1,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_rfunct_3,rc3_finset_1,rc4_finset_1,rc7_finseq_1,t1_boole,t1_subset,t4_subset,t5_subset,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_seq_1,cc4_membered,cc6_membered,fc22_membered,fc23_membered,rc2_partfun1,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,redefinition_k2_partfun1,dt_k1_numbers,dt_k2_partfun1,dt_k2_xboole_0,dt_k7_relat_1,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c3_103__rfunct_3,dt_c4_103__rfunct_3,fc2_membered,t3_subset,e2_103__rfunct_3,t104_relat_1]), [interesting(0.8),file(rfunct_3,e3_103__rfunct_3),[file(rfunct_3,e3_103__rfunct_3)]]). fof(t25_relat_1,theorem,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( r1_tarski(A,B) => ( r1_tarski(k1_relat_1(A),k1_relat_1(B)) & r1_tarski(k2_relat_1(A),k2_relat_1(B)) ) ) ) ) ), file(relat_1,t25_relat_1), [interesting(0.9),axiom,file(relat_1,t25_relat_1)]). fof(e4_103__rfunct_3,plain,( r1_tarski(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c4_103__rfunct_3)),k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c4_103__rfunct_3)))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c3_103__rfunct_3,dt_c4_103__rfunct_3])],[cc1_finseq_1,cc1_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_partfun1,rc2_xreal_0,rc3_finseq_1,rc3_xreal_0,rc4_xreal_0,rc6_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc11_finseq_1,fc14_finset_1,fc17_finseq_1,fc1_rfinseq,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc2_seq_1,fc6_membered,fc9_finset_1,rc1_finset_1,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_rfunct_3,rc3_finset_1,rc4_finset_1,rc7_finseq_1,t1_boole,t1_subset,t4_subset,t5_subset,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k7_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_seq_1,cc4_membered,cc6_membered,fc22_membered,fc23_membered,rc2_partfun1,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,redefinition_k2_partfun1,redefinition_k4_relset_1,dt_k1_numbers,dt_k1_relat_1,dt_k2_partfun1,dt_k2_relat_1,dt_k2_xboole_0,dt_k4_relset_1,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c3_103__rfunct_3,dt_c4_103__rfunct_3,fc2_membered,t3_subset,e3_103__rfunct_3,t25_relat_1]), [interesting(0.8),file(rfunct_3,e4_103__rfunct_3),[file(rfunct_3,e4_103__rfunct_3)]]). fof(t13_finset_1,theorem,( ! [A,B] : ( ( r1_tarski(A,B) & v1_finset_1(B) ) => v1_finset_1(A) ) ), file(finset_1,t13_finset_1), [interesting(0.9),axiom,file(finset_1,t13_finset_1)]). fof(e5_103__rfunct_3,plain,( v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c4_103__rfunct_3))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c3_103__rfunct_3,dt_c4_103__rfunct_3,e1_103__rfunct_3])],[cc1_finseq_1,cc1_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_partfun1,rc2_xreal_0,rc3_finseq_1,rc3_xreal_0,rc4_xreal_0,rc6_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc14_finset_1,fc17_finseq_1,fc1_rfinseq,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc2_seq_1,fc6_membered,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_partfun1,rc2_rfunct_3,rc7_finseq_1,t1_boole,t1_subset,t4_subset,t5_subset,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k7_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_seq_1,cc2_finset_1,cc4_membered,cc6_membered,fc22_membered,fc23_membered,rc1_finset_1,rc3_finset_1,rc4_finset_1,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,redefinition_k2_partfun1,redefinition_k4_relset_1,dt_k1_numbers,dt_k2_partfun1,dt_k2_xboole_0,dt_k4_relset_1,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c3_103__rfunct_3,dt_c4_103__rfunct_3,fc2_membered,fc9_finset_1,t3_subset,e4_103__rfunct_3,e1_103__rfunct_3,t13_finset_1]), [interesting(0.8),file(rfunct_3,e5_103__rfunct_3),[file(rfunct_3,e5_103__rfunct_3)]]). fof(dt_c5_103__rfunct_3,plain,( v1_finset_1(c5_103__rfunct_3) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c3_103__rfunct_3,dt_c4_103__rfunct_3,e1_103__rfunct_3])],[cc1_finseq_1,cc1_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_partfun1,rc2_xreal_0,rc3_finseq_1,rc3_xreal_0,rc4_xreal_0,rc6_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc14_finset_1,fc17_finseq_1,fc1_rfinseq,fc2_finseq_1,fc2_seq_1,fc6_membered,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_partfun1,rc2_rfunct_3,rc7_finseq_1,t1_subset,t4_subset,t5_subset,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k7_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_seq_1,cc2_finset_1,cc4_membered,cc6_membered,rc1_finset_1,rc3_finset_1,rc4_finset_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,redefinition_k2_partfun1,redefinition_k4_relset_1,dt_k1_numbers,dt_k2_partfun1,dt_k4_relset_1,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c4_103__rfunct_3,fc2_membered,de_c5_103__rfunct_3,e5_103__rfunct_3]), [interesting(0.8),file(rfunct_3,c5_103__rfunct_3),[file(rfunct_3,c5_103__rfunct_3)]]). fof(t2_boole,theorem,( ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ), file(boole,t2_boole), [interesting(0.9),axiom,file(boole,t2_boole)]). fof(e10_103__rfunct_3,plain,( k4_card_1(c5_103__rfunct_3) = k4_card_1(c5_103__rfunct_3) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c3_103__rfunct_3,dt_c4_103__rfunct_3,e1_103__rfunct_3])],[cc1_finseq_1,cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_finseq_1,rc1_partfun1,rc2_finseq_1,rc2_finset_1,rc2_xreal_0,rc3_finseq_1,rc3_xreal_0,rc4_xreal_0,rc6_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc1_xreal_0,cc20_membered,cc2_membered,cc2_xreal_0,cc3_membered,cc3_nat_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc14_finset_1,fc17_finseq_1,fc1_rfinseq,fc2_finseq_1,fc2_seq_1,fc6_membered,rc1_membered,rc1_nat_1,rc1_seq_1,rc1_xreal_0,rc2_nat_1,rc2_partfun1,rc2_rfunct_3,rc3_nat_1,rc7_finseq_1,t1_subset,t4_subset,t5_subset,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_k7_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_nat_1,cc1_seq_1,cc2_finset_1,cc2_nat_1,cc4_membered,cc6_membered,cc9_membered,fc5_membered,rc1_finset_1,rc3_finset_1,rc4_finset_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,existence_m2_subset_1,redefinition_k2_partfun1,redefinition_k4_relset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_numbers,dt_k2_partfun1,dt_k4_relset_1,dt_k5_numbers,dt_m2_subset_1,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c4_103__rfunct_3,fc2_membered,redefinition_k4_card_1,dt_k4_card_1,dt_c5_103__rfunct_3,de_c5_103__rfunct_3]), [interesting(0.8),file(rfunct_3,e10_103__rfunct_3),[file(rfunct_3,e10_103__rfunct_3)]]). 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(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(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(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(dt_k2_xcmplx_0,axiom,( $true ), file(xcmplx_0,k2_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k2_xcmplx_0)]). 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(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(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(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(spc0_boole,theorem,( v1_xboole_0(0) ), file(boole,spc0_boole), [interesting(0.9),axiom,file(boole,spc0_boole)]). fof(spc1_boole,theorem,( ~ v1_xboole_0(1) ), file(boole,spc1_boole), [interesting(0.9),axiom,file(boole,spc1_boole)]). fof(s1_nat_1__e8_103__rfunct_3,theorem,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & m2_relset_1(B,A,k1_numbers) ) => ( ( ! [D,E] : ( v1_finset_1(E) => ( ( E = k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,D)) & v1_finset_1(k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,k2_xboole_0(C,D)))) & k3_xboole_0(C,D) = k1_xboole_0 & 0 = k4_card_1(E) ) => r1_rfinseq(k22_rfunct_3(A,B,k2_xboole_0(C,D)),k8_finseq_1(k1_numbers,k22_rfunct_3(A,B,C),k22_rfunct_3(A,B,D))) ) ) & ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ( ! [G,H] : ( v1_finset_1(H) => ( ( H = k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,G)) & v1_finset_1(k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,k2_xboole_0(C,G)))) & k3_xboole_0(C,G) = k1_xboole_0 & F = k4_card_1(H) ) => r1_rfinseq(k22_rfunct_3(A,B,k2_xboole_0(C,G)),k8_finseq_1(k1_numbers,k22_rfunct_3(A,B,C),k22_rfunct_3(A,B,G))) ) ) => ! [I,J] : ( v1_finset_1(J) => ( ( J = k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,I)) & v1_finset_1(k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,k2_xboole_0(C,I)))) & k3_xboole_0(C,I) = k1_xboole_0 & k1_nat_1(F,1) = k4_card_1(J) ) => r1_rfinseq(k22_rfunct_3(A,B,k2_xboole_0(C,I)),k8_finseq_1(k1_numbers,k22_rfunct_3(A,B,C),k22_rfunct_3(A,B,I))) ) ) ) ) ) => ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ! [K,L] : ( v1_finset_1(L) => ( ( L = k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,K)) & v1_finset_1(k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,k2_xboole_0(C,K)))) & k3_xboole_0(C,K) = k1_xboole_0 & F = k4_card_1(L) ) => r1_rfinseq(k22_rfunct_3(A,B,k2_xboole_0(C,K)),k8_finseq_1(k1_numbers,k22_rfunct_3(A,B,C),k22_rfunct_3(A,B,K))) ) ) ) ) ) ), file(rfunct_3,s1_nat_1__e8_103__rfunct_3), [interesting(0.9),axiom,file(rfunct_3,s1_nat_1__e8_103__rfunct_3)]). fof(dh_c1_103_1__rfunct_3,definition, ( ! [A] : ( v1_finset_1(A) => ( ( A = k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c1_103_1__rfunct_3)) & v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c1_103_1__rfunct_3)))) & k3_xboole_0(c3_103__rfunct_3,c1_103_1__rfunct_3) = k1_xboole_0 & 0 = k4_card_1(A) ) => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c1_103_1__rfunct_3)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c1_103_1__rfunct_3))) ) ) => ! [B,C] : ( v1_finset_1(C) => ( ( C = k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,B)) & v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,B)))) & k3_xboole_0(c3_103__rfunct_3,B) = k1_xboole_0 & 0 = k4_card_1(C) ) => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,B)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,B))) ) ) ), introduced(definition,[new_symbol(c1_103_1__rfunct_3),file(rfunct_3,c1_103_1__rfunct_3)]), [interesting(0.65),axiom,file(rfunct_3,c1_103_1__rfunct_3)]). fof(dh_c2_103_1__rfunct_3,definition, ( ( v1_finset_1(c2_103_1__rfunct_3) => ( ( c2_103_1__rfunct_3 = k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c1_103_1__rfunct_3)) & v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c1_103_1__rfunct_3)))) & k3_xboole_0(c3_103__rfunct_3,c1_103_1__rfunct_3) = k1_xboole_0 & 0 = k4_card_1(c2_103_1__rfunct_3) ) => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c1_103_1__rfunct_3)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c1_103_1__rfunct_3))) ) ) => ! [A] : ( v1_finset_1(A) => ( ( A = k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c1_103_1__rfunct_3)) & v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c1_103_1__rfunct_3)))) & k3_xboole_0(c3_103__rfunct_3,c1_103_1__rfunct_3) = k1_xboole_0 & 0 = k4_card_1(A) ) => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c1_103_1__rfunct_3)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c1_103_1__rfunct_3))) ) ) ), introduced(definition,[new_symbol(c2_103_1__rfunct_3),file(rfunct_3,c2_103_1__rfunct_3)]), [interesting(0.65),axiom,file(rfunct_3,c2_103_1__rfunct_3)]). fof(e1_103_1__rfunct_3,assumption, ( c2_103_1__rfunct_3 = k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c1_103_1__rfunct_3)) & v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c1_103_1__rfunct_3)))) & k3_xboole_0(c3_103__rfunct_3,c1_103_1__rfunct_3) = k1_xboole_0 & 0 = k4_card_1(c2_103_1__rfunct_3) ), introduced(assumption,[file(rfunct_3,e1_103_1__rfunct_3)]), [interesting(0.65),axiom,file(rfunct_3,e1_103_1__rfunct_3)]). fof(dt_c1_103_1__rfunct_3,assumption,( $true ), introduced(assumption,[file(rfunct_3,c1_103_1__rfunct_3)]), [interesting(0.65),axiom,file(rfunct_3,c1_103_1__rfunct_3)]). fof(t1_numerals,theorem,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), [interesting(0.9),axiom,file(numerals,t1_numerals)]). fof(commutativity_k4_subset_1,theorem,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k4_subset_1(A,B,C) = k4_subset_1(A,C,B) ) ), file(subset_1,k4_subset_1), [interesting(0.9),axiom,file(subset_1,k4_subset_1)]). fof(idempotence_k4_subset_1,theorem,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k4_subset_1(A,B,B) = B ) ), file(subset_1,k4_subset_1), [interesting(0.9),axiom,file(subset_1,k4_subset_1)]). fof(redefinition_k4_subset_1,definition,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k4_subset_1(A,B,C) = k2_xboole_0(B,C) ) ), file(subset_1,k4_subset_1), [interesting(0.9),axiom,file(subset_1,k4_subset_1)]). fof(dt_k4_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(k4_subset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(subset_1,k4_subset_1), [interesting(0.9),axiom,file(subset_1,k4_subset_1)]). fof(dt_c2_103_1__rfunct_3,assumption,( v1_finset_1(c2_103_1__rfunct_3) ), introduced(assumption,[file(rfunct_3,c2_103_1__rfunct_3)]), [interesting(0.65),axiom,file(rfunct_3,c2_103_1__rfunct_3)]). fof(t59_card_2,theorem,( ! [A] : ( k1_card_1(A) = 0 => A = k1_xboole_0 ) ), file(card_2,t59_card_2), [interesting(0.9),axiom,file(card_2,t59_card_2)]). fof(e5_103_1__rfunct_3,plain,( k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c1_103_1__rfunct_3)) = k1_xboole_0 ), inference(mizar_by,[status(thm),assumptions([dt_c1_103__rfunct_3,dt_c1_103_1__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_1__rfunct_3,dt_c3_103__rfunct_3,e1_103_1__rfunct_3])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k2_zfmisc_1,dt_k5_ordinal2,cc1_relset_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc14_finset_1,fc2_seq_1,fc5_membered,rc1_nat_1,rc1_seq_1,rc1_xreal_0,rc2_finset_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,t1_subset,t4_subset,t5_subset,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k5_numbers,dt_k7_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finseq_1,cc1_finset_1,cc1_membered,cc1_nat_1,cc1_seq_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_nat_1,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc17_finseq_1,fc1_rfinseq,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,rc1_finseq_1,rc1_finset_1,rc1_membered,rc1_partfun1,rc2_finseq_1,rc2_partfun1,rc2_rfunct_3,rc3_finseq_1,rc3_finset_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t1_numerals,t2_subset,t3_subset,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k3_xboole_0,idempotence_k3_xboole_0,redefinition_k2_partfun1,redefinition_k4_card_1,redefinition_k4_relset_1,dt_k1_card_1,dt_k1_numbers,dt_k1_xboole_0,dt_k2_partfun1,dt_k2_xboole_0,dt_k3_xboole_0,dt_k4_card_1,dt_k4_relset_1,dt_c1_103__rfunct_3,dt_c1_103_1__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_1__rfunct_3,dt_c3_103__rfunct_3,fc10_finset_1,fc11_finset_1,fc2_finseq_1,fc2_membered,fc6_membered,fc9_finset_1,t1_boole,t2_boole,t6_boole,spc0_numerals,spc0_boole,e1_103_1__rfunct_3,t59_card_2]), [interesting(0.65),file(rfunct_3,e5_103_1__rfunct_3),[file(rfunct_3,e5_103_1__rfunct_3)]]). 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(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), [interesting(0.9),axiom,file(funct_1,k1_funct_1)]). fof(t68_funct_1,theorem,( ! [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), [interesting(0.9),axiom,file(funct_1,t68_funct_1)]). fof(e1_103_1_1__rfunct_3,plain,( k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c1_103_1__rfunct_3))) = k3_xboole_0(k4_relset_1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3),k2_xboole_0(c3_103__rfunct_3,c1_103_1__rfunct_3)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103__rfunct_3,dt_c1_103_1__rfunct_3,dt_c2_103__rfunct_3,dt_c3_103__rfunct_3])],[cc1_finseq_1,cc1_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_partfun1,rc2_xreal_0,rc3_finseq_1,rc3_xreal_0,rc4_xreal_0,rc6_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc10_finset_1,fc11_finset_1,fc14_finset_1,fc17_finseq_1,fc1_rfinseq,fc1_seq_1,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc2_seq_1,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc6_membered,fc9_finset_1,rc1_finset_1,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_rfunct_3,rc3_finset_1,rc4_finset_1,rc7_finseq_1,t1_boole,t2_boole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_seq_1,cc4_membered,cc6_membered,fc22_membered,fc23_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,rc2_partfun1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,redefinition_k2_partfun1,redefinition_k4_relset_1,dt_k1_funct_1,dt_k1_numbers,dt_k1_relat_1,dt_k2_partfun1,dt_k2_xboole_0,dt_k3_xboole_0,dt_k4_relset_1,dt_k7_relat_1,dt_c1_103__rfunct_3,dt_c1_103_1__rfunct_3,dt_c2_103__rfunct_3,dt_c3_103__rfunct_3,fc2_membered,t1_subset,t7_boole,t68_funct_1]), [interesting(0.5),file(rfunct_3,e1_103_1_1__rfunct_3),[file(rfunct_3,e1_103_1_1__rfunct_3)]]). fof(t23_xboole_1,theorem,( ! [A,B,C] : k3_xboole_0(A,k2_xboole_0(B,C)) = k2_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C)) ), file(xboole_1,t23_xboole_1), [interesting(0.9),axiom,file(xboole_1,t23_xboole_1)]). fof(e2_103_1_1__rfunct_3,plain,( k3_xboole_0(k4_relset_1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3),k2_xboole_0(c3_103__rfunct_3,c1_103_1__rfunct_3)) = k2_xboole_0(k3_xboole_0(k4_relset_1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3),c3_103__rfunct_3),k3_xboole_0(k4_relset_1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3),c1_103_1__rfunct_3)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103__rfunct_3,dt_c1_103_1__rfunct_3,dt_c2_103__rfunct_3,dt_c3_103__rfunct_3])],[cc1_finseq_1,cc1_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_partfun1,rc2_xreal_0,rc3_finseq_1,rc3_xreal_0,rc4_xreal_0,rc6_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc10_finset_1,fc11_finset_1,fc14_finset_1,fc17_finseq_1,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc6_membered,fc9_finset_1,rc1_finset_1,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_partfun1,rc2_rfunct_3,rc3_finset_1,rc4_finset_1,rc7_finseq_1,t1_boole,t1_subset,t2_boole,t4_subset,t5_subset,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_seq_1,cc4_membered,cc6_membered,fc22_membered,fc23_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k3_xboole_0,idempotence_k3_xboole_0,redefinition_k4_relset_1,dt_k1_numbers,dt_k2_xboole_0,dt_k3_xboole_0,dt_k4_relset_1,dt_c1_103__rfunct_3,dt_c1_103_1__rfunct_3,dt_c2_103__rfunct_3,dt_c3_103__rfunct_3,fc2_membered,t23_xboole_1]), [interesting(0.5),file(rfunct_3,e2_103_1_1__rfunct_3),[file(rfunct_3,e2_103_1_1__rfunct_3)]]). fof(e3_103_1_1__rfunct_3,plain,( k2_xboole_0(k3_xboole_0(k4_relset_1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3),c3_103__rfunct_3),k3_xboole_0(k4_relset_1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3),c1_103_1__rfunct_3)) = k2_xboole_0(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c3_103__rfunct_3)),k3_xboole_0(k4_relset_1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3),c1_103_1__rfunct_3)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103__rfunct_3,dt_c1_103_1__rfunct_3,dt_c2_103__rfunct_3,dt_c3_103__rfunct_3])],[cc1_finseq_1,cc1_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_partfun1,rc2_xreal_0,rc3_finseq_1,rc3_xreal_0,rc4_xreal_0,rc6_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc10_finset_1,fc11_finset_1,fc14_finset_1,fc17_finseq_1,fc1_rfinseq,fc1_seq_1,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc2_seq_1,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc6_membered,fc9_finset_1,rc1_finset_1,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_rfunct_3,rc3_finset_1,rc4_finset_1,rc7_finseq_1,t1_boole,t2_boole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_seq_1,cc4_membered,cc6_membered,fc22_membered,fc23_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,rc2_partfun1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,redefinition_k2_partfun1,redefinition_k4_relset_1,dt_k1_funct_1,dt_k1_numbers,dt_k1_relat_1,dt_k2_partfun1,dt_k2_xboole_0,dt_k3_xboole_0,dt_k4_relset_1,dt_k7_relat_1,dt_c1_103__rfunct_3,dt_c1_103_1__rfunct_3,dt_c2_103__rfunct_3,dt_c3_103__rfunct_3,fc2_membered,t1_subset,t7_boole,t68_funct_1]), [interesting(0.5),file(rfunct_3,e3_103_1_1__rfunct_3),[file(rfunct_3,e3_103_1_1__rfunct_3)]]). fof(e4_103_1_1__rfunct_3,plain,( k2_xboole_0(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c3_103__rfunct_3)),k3_xboole_0(k4_relset_1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3),c1_103_1__rfunct_3)) = k4_subset_1(c1_103__rfunct_3,k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c3_103__rfunct_3)),k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c1_103_1__rfunct_3))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103__rfunct_3,dt_c1_103_1__rfunct_3,dt_c2_103__rfunct_3,dt_c3_103__rfunct_3])],[cc1_finseq_1,cc1_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_partfun1,rc2_xreal_0,rc3_finseq_1,rc3_xreal_0,rc4_xreal_0,rc6_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc10_finset_1,fc11_finset_1,fc14_finset_1,fc17_finseq_1,fc1_rfinseq,fc1_seq_1,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc2_seq_1,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc6_membered,fc9_finset_1,rc1_finset_1,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_rfunct_3,rc3_finset_1,rc4_finset_1,rc7_finseq_1,t1_boole,t2_boole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_seq_1,cc4_membered,cc6_membered,fc22_membered,fc23_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,rc2_partfun1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k3_xboole_0,idempotence_k3_xboole_0,commutativity_k4_subset_1,idempotence_k4_subset_1,antisymmetry_r2_hidden,redefinition_k2_partfun1,redefinition_k4_relset_1,redefinition_k4_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k1_relat_1,dt_k2_partfun1,dt_k2_xboole_0,dt_k3_xboole_0,dt_k4_relset_1,dt_k4_subset_1,dt_k7_relat_1,dt_c1_103__rfunct_3,dt_c1_103_1__rfunct_3,dt_c2_103__rfunct_3,dt_c3_103__rfunct_3,fc2_membered,t1_subset,t7_boole,t68_funct_1]), [interesting(0.5),file(rfunct_3,e4_103_1_1__rfunct_3),[file(rfunct_3,e4_103_1_1__rfunct_3)]]). fof(e2_103_1__rfunct_3,plain,( k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c1_103_1__rfunct_3))) = k4_subset_1(c1_103__rfunct_3,k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c3_103__rfunct_3)),k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c1_103_1__rfunct_3))) ), inference(iterative_eq,[status(thm),assumptions([dt_c1_103__rfunct_3,dt_c1_103_1__rfunct_3,dt_c2_103__rfunct_3,dt_c3_103__rfunct_3])],[cc1_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_nat_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc10_finset_1,fc11_finset_1,fc14_finset_1,fc17_finseq_1,fc1_rfinseq,fc24_membered,fc25_membered,fc26_membered,fc2_seq_1,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc9_finset_1,rc1_finset_1,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_partfun1,rc2_rfunct_3,rc3_finset_1,rc4_finset_1,rc7_finseq_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k7_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_seq_1,cc4_membered,cc6_membered,fc22_membered,fc23_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k3_xboole_0,idempotence_k3_xboole_0,commutativity_k4_subset_1,idempotence_k4_subset_1,redefinition_k2_partfun1,redefinition_k4_relset_1,redefinition_k4_subset_1,dt_k1_numbers,dt_k2_partfun1,dt_k2_xboole_0,dt_k3_xboole_0,dt_k4_relset_1,dt_k4_subset_1,dt_c1_103__rfunct_3,dt_c1_103_1__rfunct_3,dt_c2_103__rfunct_3,dt_c3_103__rfunct_3,fc2_membered,e1_103_1_1__rfunct_3,e2_103_1_1__rfunct_3,e3_103_1_1__rfunct_3,e4_103_1_1__rfunct_3]), [interesting(0.65),file(rfunct_3,e2_103_1__rfunct_3),[file(rfunct_3,e2_103_1__rfunct_3)]]). fof(t66_rfunct_3,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m2_relset_1(B,A,k1_numbers) ) => ! [C] : ( v1_finset_1(k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,C))) => k22_rfunct_3(A,B,k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,C))) = k22_rfunct_3(A,B,C) ) ) ) ), file(rfunct_3,t66_rfunct_3), [interesting(0.9),axiom,file(rfunct_3,t66_rfunct_3)]). fof(e1_103_1_2__rfunct_3,plain,( k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c1_103_1__rfunct_3)) = k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c3_103__rfunct_3))) ), inference(mizar_by,[status(thm),assumptions([dt_c2_103_1__rfunct_3,e1_103_1__rfunct_3,dt_c1_103__rfunct_3,dt_c1_103_1__rfunct_3,dt_c2_103__rfunct_3,dt_c3_103__rfunct_3])],[reflexivity_r1_tarski,existence_m1_finseq_1,dt_k5_ordinal2,dt_m1_finseq_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc2_seq_1,fc5_membered,rc1_nat_1,rc1_rfinseq,rc1_seq_1,rc1_xreal_0,rc2_finset_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_finseq_1,rc4_xreal_0,antisymmetry_r2_hidden,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_numbers,dt_k7_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_subset_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_relset_1,cc1_seq_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_nat_1,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc14_finset_1,fc17_finseq_1,fc1_rfinseq,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,rc1_finseq_1,rc1_membered,rc1_partfun1,rc2_finseq_1,rc2_partfun1,rc2_rfunct_3,rc3_finseq_1,rc3_finset_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t1_numerals,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k3_xboole_0,idempotence_k3_xboole_0,commutativity_k4_subset_1,idempotence_k4_subset_1,existence_m2_relset_1,redefinition_k2_partfun1,redefinition_k4_card_1,redefinition_k4_relset_1,redefinition_k4_subset_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k22_rfunct_3,dt_k2_partfun1,dt_k2_xboole_0,dt_k3_xboole_0,dt_k4_card_1,dt_k4_relset_1,dt_k4_subset_1,dt_m2_relset_1,dt_c1_103__rfunct_3,dt_c1_103_1__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_1__rfunct_3,dt_c3_103__rfunct_3,cc15_membered,cc1_finset_1,fc10_finset_1,fc11_finset_1,fc2_finseq_1,fc2_membered,fc6_membered,fc9_finset_1,rc1_finset_1,spc0_boole,t1_boole,t2_boole,t6_boole,t7_boole,t8_boole,spc0_numerals,spc0_boole,e5_103_1__rfunct_3,e1_103_1__rfunct_3,e2_103_1__rfunct_3,t66_rfunct_3]), [interesting(0.5),file(rfunct_3,e1_103_1_2__rfunct_3),[file(rfunct_3,e1_103_1_2__rfunct_3)]]). fof(e3_103_1__rfunct_3,plain, ( r1_tarski(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c3_103__rfunct_3)),k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c1_103_1__rfunct_3)))) & r1_tarski(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c1_103_1__rfunct_3)),k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c1_103_1__rfunct_3)))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103__rfunct_3,dt_c1_103_1__rfunct_3,dt_c2_103__rfunct_3,dt_c3_103__rfunct_3])],[cc1_finseq_1,cc1_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_partfun1,rc2_xreal_0,rc3_finseq_1,rc3_xreal_0,rc4_xreal_0,rc6_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc14_finset_1,fc17_finseq_1,fc1_rfinseq,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc2_seq_1,fc6_membered,fc9_finset_1,rc1_finset_1,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_partfun1,rc2_rfunct_3,rc3_finset_1,rc4_finset_1,rc7_finseq_1,t1_boole,t1_subset,t4_subset,t5_subset,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k7_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_seq_1,cc4_membered,cc6_membered,fc22_membered,fc23_membered,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k4_subset_1,idempotence_k4_subset_1,reflexivity_r1_tarski,redefinition_k2_partfun1,redefinition_k4_relset_1,redefinition_k4_subset_1,dt_k1_numbers,dt_k2_partfun1,dt_k2_xboole_0,dt_k4_relset_1,dt_k4_subset_1,dt_c1_103__rfunct_3,dt_c1_103_1__rfunct_3,dt_c2_103__rfunct_3,dt_c3_103__rfunct_3,fc2_membered,t3_subset,e2_103_1__rfunct_3,t7_xboole_1]), [interesting(0.65),file(rfunct_3,e3_103_1__rfunct_3),[file(rfunct_3,e3_103_1__rfunct_3)]]). fof(e4_103_1__rfunct_3,plain, ( v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c3_103__rfunct_3))) & v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c1_103_1__rfunct_3))) ), inference(mizar_by,[status(thm),assumptions([dt_c2_103_1__rfunct_3,dt_c1_103__rfunct_3,dt_c1_103_1__rfunct_3,dt_c2_103__rfunct_3,dt_c3_103__rfunct_3,e1_103_1__rfunct_3])],[antisymmetry_r2_hidden,dt_k2_zfmisc_1,dt_k5_ordinal2,cc1_relset_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc14_finset_1,fc2_seq_1,fc5_membered,rc1_nat_1,rc1_seq_1,rc1_xreal_0,rc2_finset_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,t1_subset,t4_subset,t5_subset,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k5_numbers,dt_k7_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finseq_1,cc1_finset_1,cc1_membered,cc1_nat_1,cc1_seq_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_nat_1,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc17_finseq_1,fc1_rfinseq,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,rc1_finseq_1,rc1_finset_1,rc1_membered,rc1_partfun1,rc2_finseq_1,rc2_partfun1,rc2_rfunct_3,rc3_finseq_1,rc3_finset_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t1_numerals,t2_subset,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k3_xboole_0,idempotence_k3_xboole_0,reflexivity_r1_tarski,redefinition_k2_partfun1,redefinition_k4_card_1,redefinition_k4_relset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k2_partfun1,dt_k2_xboole_0,dt_k3_xboole_0,dt_k4_card_1,dt_k4_relset_1,dt_c1_103__rfunct_3,dt_c1_103_1__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_1__rfunct_3,dt_c3_103__rfunct_3,fc10_finset_1,fc11_finset_1,fc2_finseq_1,fc2_membered,fc6_membered,fc9_finset_1,t1_boole,t2_boole,t3_subset,t6_boole,spc0_numerals,spc0_boole,e3_103_1__rfunct_3,e1_103_1__rfunct_3,t13_finset_1]), [interesting(0.65),file(rfunct_3,e4_103_1__rfunct_3),[file(rfunct_3,e4_103_1__rfunct_3)]]). fof(e2_103_1_2__rfunct_3,plain,( k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c3_103__rfunct_3))) = k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3) ), inference(mizar_by,[status(thm),assumptions([dt_c2_103_1__rfunct_3,dt_c1_103__rfunct_3,dt_c1_103_1__rfunct_3,dt_c2_103__rfunct_3,dt_c3_103__rfunct_3,e1_103_1__rfunct_3])],[dt_k5_ordinal2,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc5_membered,rc2_finset_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,reflexivity_r1_tarski,existence_m1_finseq_1,redefinition_k5_numbers,dt_k5_numbers,dt_m1_finseq_1,cc1_finseq_1,cc1_nat_1,cc1_xreal_0,cc2_nat_1,cc2_xreal_0,cc3_nat_1,cc7_xreal_0,cc9_membered,fc17_finseq_1,fc1_rfinseq,fc2_seq_1,rc1_finseq_1,rc1_nat_1,rc1_partfun1,rc1_rfinseq,rc1_seq_1,rc1_xreal_0,rc2_finseq_1,rc2_partfun1,rc2_rfunct_3,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k7_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc1_seq_1,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,cc6_membered,fc14_finset_1,fc2_finseq_1,fc6_membered,rc1_membered,rc3_finset_1,rc4_finset_1,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,existence_m2_relset_1,redefinition_k2_partfun1,redefinition_k4_relset_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k22_rfunct_3,dt_k2_partfun1,dt_k4_relset_1,dt_m2_relset_1,dt_c1_103__rfunct_3,dt_c1_103_1__rfunct_3,dt_c2_103__rfunct_3,dt_c3_103__rfunct_3,cc15_membered,cc1_finset_1,fc2_membered,rc1_finset_1,t6_boole,t7_boole,t8_boole,e4_103_1__rfunct_3,t66_rfunct_3]), [interesting(0.5),file(rfunct_3,e2_103_1_2__rfunct_3),[file(rfunct_3,e2_103_1_2__rfunct_3)]]). 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), [interesting(0.9),axiom,file(finseq_1,k6_finseq_1)]). fof(t47_finseq_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( k7_finseq_1(A,k1_xboole_0) = A & k7_finseq_1(k1_xboole_0,A) = A ) ) ), file(finseq_1,t47_finseq_1), [interesting(0.9),axiom,file(finseq_1,t47_finseq_1)]). fof(e3_103_1_2__rfunct_3,plain,( k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3) = k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k6_finseq_1(k1_numbers)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c3_103__rfunct_3])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,reflexivity_r1_tarski,dt_k5_ordinal2,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc5_membered,rc1_nat_1,rc1_xreal_0,rc2_finset_1,rc2_nat_1,rc3_nat_1,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k5_numbers,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_nat_1,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_nat_1,cc6_membered,cc9_membered,fc14_finset_1,rc1_seq_1,rc2_finseq_1,rc3_finset_1,rc4_finset_1,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,existence_m1_finseq_1,existence_m1_relset_1,existence_m2_finseq_1,existence_m2_relset_1,redefinition_m2_finseq_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m2_finseq_1,dt_m2_relset_1,cc15_membered,cc1_finset_1,cc1_membered,cc1_seq_1,cc2_membered,cc3_membered,cc4_membered,fc13_finseq_1,fc14_finseq_1,rc1_finset_1,rc1_membered,rc1_partfun1,rc1_rfinseq,rc2_partfun1,rc2_rfunct_3,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t7_boole,t8_boole,redefinition_k8_finseq_1,dt_k1_numbers,dt_k1_xboole_0,dt_k22_rfunct_3,dt_k6_finseq_1,dt_k7_finseq_1,dt_k8_finseq_1,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c3_103__rfunct_3,cc1_finseq_1,fc2_finseq_1,fc2_membered,fc6_membered,rc1_finseq_1,t6_boole,t47_finseq_1]), [interesting(0.5),file(rfunct_3,e3_103_1_2__rfunct_3),[file(rfunct_3,e3_103_1_2__rfunct_3)]]). fof(t71_rfunct_3,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m2_relset_1(B,A,k1_numbers) ) => k22_rfunct_3(A,B,k1_xboole_0) = k6_finseq_1(k1_numbers) ) ) ), file(rfunct_3,t71_rfunct_3), [interesting(0.9),axiom,file(rfunct_3,t71_rfunct_3)]). fof(e4_103_1_2__rfunct_3,plain,( k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k6_finseq_1(k1_numbers)) = k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c1_103_1__rfunct_3)))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103__rfunct_3,dt_c1_103_1__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_1__rfunct_3,dt_c3_103__rfunct_3,e1_103_1__rfunct_3])],[dt_k5_ordinal2,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc5_membered,rc2_finset_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,reflexivity_r1_tarski,redefinition_k5_numbers,dt_k5_numbers,cc1_nat_1,cc1_xreal_0,cc2_nat_1,cc2_xreal_0,cc3_nat_1,cc7_xreal_0,cc9_membered,fc2_seq_1,rc1_nat_1,rc1_seq_1,rc1_xreal_0,rc2_finseq_1,antisymmetry_r2_hidden,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k7_finseq_1,dt_k7_relat_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_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_relset_1,cc1_seq_1,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,cc6_membered,fc13_finseq_1,fc14_finseq_1,fc14_finset_1,fc17_finseq_1,fc1_rfinseq,rc1_finseq_1,rc1_finset_1,rc1_membered,rc1_partfun1,rc1_rfinseq,rc2_partfun1,rc2_rfunct_3,rc3_finseq_1,rc3_finset_1,rc4_finseq_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,existence_m2_relset_1,redefinition_k2_partfun1,redefinition_k4_relset_1,redefinition_k8_finseq_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k22_rfunct_3,dt_k2_partfun1,dt_k4_relset_1,dt_k6_finseq_1,dt_k8_finseq_1,dt_m2_relset_1,dt_c1_103__rfunct_3,dt_c1_103_1__rfunct_3,dt_c2_103__rfunct_3,dt_c3_103__rfunct_3,cc15_membered,cc1_finset_1,fc2_finseq_1,fc2_membered,fc6_membered,t6_boole,t7_boole,t8_boole,e5_103_1__rfunct_3,t71_rfunct_3]), [interesting(0.5),file(rfunct_3,e4_103_1_2__rfunct_3),[file(rfunct_3,e4_103_1_2__rfunct_3)]]). fof(e5_103_1_2__rfunct_3,plain,( k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c1_103_1__rfunct_3)))) = k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c1_103_1__rfunct_3)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103__rfunct_3,dt_c1_103_1__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_1__rfunct_3,dt_c3_103__rfunct_3,e1_103_1__rfunct_3])],[reflexivity_r1_tarski,dt_k5_ordinal2,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc2_seq_1,fc5_membered,rc1_nat_1,rc1_seq_1,rc1_xreal_0,rc2_finset_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,antisymmetry_r2_hidden,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_numbers,dt_k7_finseq_1,dt_k7_relat_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_subset_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_relset_1,cc1_seq_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_nat_1,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc13_finseq_1,fc14_finseq_1,fc14_finset_1,fc17_finseq_1,fc1_rfinseq,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,rc1_finseq_1,rc1_membered,rc1_partfun1,rc1_rfinseq,rc2_finseq_1,rc2_partfun1,rc2_rfunct_3,rc3_finseq_1,rc3_finset_1,rc4_finseq_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t1_numerals,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k3_xboole_0,idempotence_k3_xboole_0,existence_m2_relset_1,redefinition_k2_partfun1,redefinition_k4_card_1,redefinition_k4_relset_1,redefinition_k8_finseq_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k22_rfunct_3,dt_k2_partfun1,dt_k2_xboole_0,dt_k3_xboole_0,dt_k4_card_1,dt_k4_relset_1,dt_k8_finseq_1,dt_m2_relset_1,dt_c1_103__rfunct_3,dt_c1_103_1__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_1__rfunct_3,dt_c3_103__rfunct_3,cc15_membered,cc1_finset_1,fc10_finset_1,fc11_finset_1,fc2_finseq_1,fc2_membered,fc6_membered,fc9_finset_1,rc1_finset_1,spc0_boole,t1_boole,t2_boole,t6_boole,t7_boole,t8_boole,spc0_numerals,spc0_boole,e1_103_1__rfunct_3,t66_rfunct_3]), [interesting(0.5),file(rfunct_3,e5_103_1_2__rfunct_3),[file(rfunct_3,e5_103_1_2__rfunct_3)]]). fof(e6_103_1__rfunct_3,plain,( k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c1_103_1__rfunct_3)) = k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c1_103_1__rfunct_3)) ), inference(iterative_eq,[status(thm),assumptions([dt_c1_103__rfunct_3,dt_c1_103_1__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_1__rfunct_3,dt_c3_103__rfunct_3,e1_103_1__rfunct_3])],[e1_103_1_2__rfunct_3,e2_103_1_2__rfunct_3,e3_103_1_2__rfunct_3,e4_103_1_2__rfunct_3,e5_103_1_2__rfunct_3]), [interesting(0.65),file(rfunct_3,e6_103_1__rfunct_3),[file(rfunct_3,e6_103_1__rfunct_3)]]). fof(e7_103_1__rfunct_3,plain,( r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c1_103_1__rfunct_3)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c1_103_1__rfunct_3))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103__rfunct_3,dt_c1_103_1__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_1__rfunct_3,dt_c3_103__rfunct_3,e1_103_1__rfunct_3])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,reflexivity_r1_tarski,dt_k5_ordinal2,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc5_membered,rc1_nat_1,rc1_partfun1,rc1_xreal_0,rc2_finset_1,rc2_nat_1,rc3_finseq_1,rc3_nat_1,rc4_finseq_1,rc6_finseq_1,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k5_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_numbers,dt_m1_subset_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_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_nat_1,cc3_membered,cc6_membered,cc9_membered,fc13_finseq_1,fc14_finseq_1,fc14_finset_1,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc6_membered,fc9_finset_1,rc1_finseq_1,rc1_finset_1,rc1_membered,rc1_rfinseq,rc1_seq_1,rc2_finseq_1,rc2_rfunct_3,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t1_boole,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,existence_m1_finseq_1,existence_m1_relset_1,existence_m2_finseq_1,existence_m2_relset_1,redefinition_m2_finseq_1,redefinition_m2_relset_1,dt_k7_finseq_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m2_finseq_1,dt_m2_relset_1,cc15_membered,cc1_finset_1,cc1_seq_1,cc4_membered,fc22_membered,fc23_membered,rc2_partfun1,t6_boole,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,symmetry_r1_rfinseq,reflexivity_r1_rfinseq,redefinition_k8_finseq_1,dt_k1_numbers,dt_k22_rfunct_3,dt_k2_xboole_0,dt_k8_finseq_1,dt_c1_103__rfunct_3,dt_c1_103_1__rfunct_3,dt_c2_103__rfunct_3,dt_c3_103__rfunct_3,fc2_membered,e6_103_1__rfunct_3]), [interesting(0.65),file(rfunct_3,e7_103_1__rfunct_3),[file(rfunct_3,e7_103_1__rfunct_3)]]). fof(i4_103_1__rfunct_3,theorem,( $true ), introduced(tautology,[file(rfunct_3,i4_103_1__rfunct_3)]), [interesting(0.65),trivial,file(rfunct_3,i4_103_1__rfunct_3)]). fof(i3_103_1__rfunct_3,plain,( r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c1_103_1__rfunct_3)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c1_103_1__rfunct_3))) ), inference(conclusion,[status(thm),assumptions([dt_c1_103__rfunct_3,dt_c1_103_1__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_1__rfunct_3,dt_c3_103__rfunct_3,e1_103_1__rfunct_3])],[e7_103_1__rfunct_3,i4_103_1__rfunct_3]), [interesting(0.65),file(rfunct_3,i3_103_1__rfunct_3),[file(rfunct_3,i3_103_1__rfunct_3)]]). fof(i2_103_1__rfunct_3,plain, ( ( c2_103_1__rfunct_3 = k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c1_103_1__rfunct_3)) & v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c1_103_1__rfunct_3)))) & k3_xboole_0(c3_103__rfunct_3,c1_103_1__rfunct_3) = k1_xboole_0 & 0 = k4_card_1(c2_103_1__rfunct_3) ) => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c1_103_1__rfunct_3)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c1_103_1__rfunct_3))) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_103__rfunct_3,dt_c1_103_1__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_1__rfunct_3,dt_c3_103__rfunct_3]),discharge_asm(discharge,[e1_103_1__rfunct_3])],[e1_103_1__rfunct_3,i3_103_1__rfunct_3]), [interesting(0.65),file(rfunct_3,i2_103_1__rfunct_3),[file(rfunct_3,i2_103_1__rfunct_3)]]). fof(i2_103_1_tmp__rfunct_3,plain, ( v1_finset_1(c2_103_1__rfunct_3) => ( ( c2_103_1__rfunct_3 = k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c1_103_1__rfunct_3)) & v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c1_103_1__rfunct_3)))) & k3_xboole_0(c3_103__rfunct_3,c1_103_1__rfunct_3) = k1_xboole_0 & 0 = k4_card_1(c2_103_1__rfunct_3) ) => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c1_103_1__rfunct_3)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c1_103_1__rfunct_3))) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_103__rfunct_3,dt_c1_103_1__rfunct_3,dt_c2_103__rfunct_3,dt_c3_103__rfunct_3]),discharge_asm(discharge,[dt_c2_103_1__rfunct_3])],[dt_c2_103_1__rfunct_3,i2_103_1__rfunct_3]), [interesting(0.65),i1_103_1__rfunct_3]). fof(i1_103_1__rfunct_3,plain,( ! [A] : ( v1_finset_1(A) => ( ( A = k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c1_103_1__rfunct_3)) & v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c1_103_1__rfunct_3)))) & k3_xboole_0(c3_103__rfunct_3,c1_103_1__rfunct_3) = k1_xboole_0 & 0 = k4_card_1(A) ) => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c1_103_1__rfunct_3)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c1_103_1__rfunct_3))) ) ) ), inference(let,[status(thm),assumptions([dt_c1_103__rfunct_3,dt_c1_103_1__rfunct_3,dt_c2_103__rfunct_3,dt_c3_103__rfunct_3])],[i2_103_1_tmp__rfunct_3,dh_c2_103_1__rfunct_3]), [interesting(0.65),file(rfunct_3,i1_103_1__rfunct_3),[file(rfunct_3,i1_103_1__rfunct_3)]]). fof(i1_103_1_tmp__rfunct_3,plain,( ! [A] : ( v1_finset_1(A) => ( ( A = k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c1_103_1__rfunct_3)) & v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c1_103_1__rfunct_3)))) & k3_xboole_0(c3_103__rfunct_3,c1_103_1__rfunct_3) = k1_xboole_0 & 0 = k4_card_1(A) ) => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c1_103_1__rfunct_3)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c1_103_1__rfunct_3))) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c3_103__rfunct_3]),discharge_asm(discharge,[dt_c1_103_1__rfunct_3])],[dt_c1_103_1__rfunct_3,i1_103_1__rfunct_3]), [interesting(0.8),e6_103__rfunct_3]). fof(e6_103__rfunct_3,plain,( ! [A,B] : ( v1_finset_1(B) => ( ( B = k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,A)) & v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,A)))) & k3_xboole_0(c3_103__rfunct_3,A) = k1_xboole_0 & 0 = k4_card_1(B) ) => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,A)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,A))) ) ) ), inference(let,[status(thm),assumptions([dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c3_103__rfunct_3])],[i1_103_1_tmp__rfunct_3,dh_c1_103_1__rfunct_3]), [interesting(0.8),file(rfunct_3,e6_103__rfunct_3),[file(rfunct_3,e6_103__rfunct_3)]]). fof(dh_c1_103_2__rfunct_3,definition, ( ( m2_subset_1(c1_103_2__rfunct_3,k1_numbers,k5_numbers) => ( ! [A,B] : ( v1_finset_1(B) => ( ( B = k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,A)) & v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,A)))) & k3_xboole_0(c3_103__rfunct_3,A) = k1_xboole_0 & c1_103_2__rfunct_3 = k4_card_1(B) ) => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,A)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,A))) ) ) => ! [A,B] : ( v1_finset_1(B) => ( ( B = k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,A)) & v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,A)))) & k3_xboole_0(c3_103__rfunct_3,A) = k1_xboole_0 & k1_nat_1(c1_103_2__rfunct_3,1) = k4_card_1(B) ) => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,A)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,A))) ) ) ) ) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( ! [D,E] : ( v1_finset_1(E) => ( ( E = k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,D)) & v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,D)))) & k3_xboole_0(c3_103__rfunct_3,D) = k1_xboole_0 & C = k4_card_1(E) ) => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,D)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,D))) ) ) => ! [D,E] : ( v1_finset_1(E) => ( ( E = k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,D)) & v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,D)))) & k3_xboole_0(c3_103__rfunct_3,D) = k1_xboole_0 & k1_nat_1(C,1) = k4_card_1(E) ) => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,D)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,D))) ) ) ) ) ), introduced(definition,[new_symbol(c1_103_2__rfunct_3),file(rfunct_3,c1_103_2__rfunct_3)]), [interesting(0.65),axiom,file(rfunct_3,c1_103_2__rfunct_3)]). fof(e1_103_2__rfunct_3,assumption,( ! [A,B] : ( v1_finset_1(B) => ( ( B = k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,A)) & v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,A)))) & k3_xboole_0(c3_103__rfunct_3,A) = k1_xboole_0 & c1_103_2__rfunct_3 = k4_card_1(B) ) => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,A)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,A))) ) ) ), introduced(assumption,[file(rfunct_3,e1_103_2__rfunct_3)]), [interesting(0.65),axiom,file(rfunct_3,e1_103_2__rfunct_3)]). fof(dh_c2_103_2__rfunct_3,definition, ( ! [A] : ( v1_finset_1(A) => ( ( A = k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c2_103_2__rfunct_3)) & v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c2_103_2__rfunct_3)))) & k3_xboole_0(c3_103__rfunct_3,c2_103_2__rfunct_3) = k1_xboole_0 & k1_nat_1(c1_103_2__rfunct_3,1) = k4_card_1(A) ) => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c2_103_2__rfunct_3)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c2_103_2__rfunct_3))) ) ) => ! [B,C] : ( v1_finset_1(C) => ( ( C = k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,B)) & v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,B)))) & k3_xboole_0(c3_103__rfunct_3,B) = k1_xboole_0 & k1_nat_1(c1_103_2__rfunct_3,1) = k4_card_1(C) ) => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,B)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,B))) ) ) ), introduced(definition,[new_symbol(c2_103_2__rfunct_3),file(rfunct_3,c2_103_2__rfunct_3)]), [interesting(0.65),axiom,file(rfunct_3,c2_103_2__rfunct_3)]). fof(dh_c3_103_2__rfunct_3,definition, ( ( v1_finset_1(c3_103_2__rfunct_3) => ( ( c3_103_2__rfunct_3 = k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c2_103_2__rfunct_3)) & v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c2_103_2__rfunct_3)))) & k3_xboole_0(c3_103__rfunct_3,c2_103_2__rfunct_3) = k1_xboole_0 & k1_nat_1(c1_103_2__rfunct_3,1) = k4_card_1(c3_103_2__rfunct_3) ) => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c2_103_2__rfunct_3)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c2_103_2__rfunct_3))) ) ) => ! [A] : ( v1_finset_1(A) => ( ( A = k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c2_103_2__rfunct_3)) & v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c2_103_2__rfunct_3)))) & k3_xboole_0(c3_103__rfunct_3,c2_103_2__rfunct_3) = k1_xboole_0 & k1_nat_1(c1_103_2__rfunct_3,1) = k4_card_1(A) ) => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c2_103_2__rfunct_3)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c2_103_2__rfunct_3))) ) ) ), introduced(definition,[new_symbol(c3_103_2__rfunct_3),file(rfunct_3,c3_103_2__rfunct_3)]), [interesting(0.65),axiom,file(rfunct_3,c3_103_2__rfunct_3)]). fof(e2_103_2__rfunct_3,assumption, ( c3_103_2__rfunct_3 = k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c2_103_2__rfunct_3)) & v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c2_103_2__rfunct_3)))) & k3_xboole_0(c3_103__rfunct_3,c2_103_2__rfunct_3) = k1_xboole_0 & k1_nat_1(c1_103_2__rfunct_3,1) = k4_card_1(c3_103_2__rfunct_3) ), introduced(assumption,[file(rfunct_3,e2_103_2__rfunct_3)]), [interesting(0.65),axiom,file(rfunct_3,e2_103_2__rfunct_3)]). fof(fc10_membered,theorem,( ! [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), [interesting(0.9),axiom,file(membered,fc10_membered)]). fof(fc11_membered,theorem,( ! [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), [interesting(0.9),axiom,file(membered,fc11_membered)]). fof(fc9_membered,theorem,( ! [A] : ( v1_rat_1(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) ) ) ), file(membered,fc9_membered), [interesting(0.9),axiom,file(membered,fc9_membered)]). fof(fc12_finset_1,theorem,( ! [A,B] : ( v1_finset_1(A) => v1_finset_1(k4_xboole_0(A,B)) ) ), file(finset_1,fc12_finset_1), [interesting(0.9),axiom,file(finset_1,fc12_finset_1)]). fof(fc39_membered,theorem,( ! [A,B] : ( v3_membered(A) => ( v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) ) ) ), file(membered,fc39_membered), [interesting(0.9),axiom,file(membered,fc39_membered)]). fof(fc40_membered,theorem,( ! [A,B] : ( v4_membered(A) => ( v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) & v4_membered(k4_xboole_0(A,B)) ) ) ), file(membered,fc40_membered), [interesting(0.9),axiom,file(membered,fc40_membered)]). fof(fc41_membered,theorem,( ! [A,B] : ( v5_membered(A) => ( v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) & v4_membered(k4_xboole_0(A,B)) & v5_membered(k4_xboole_0(A,B)) ) ) ), file(membered,fc41_membered), [interesting(0.9),axiom,file(membered,fc41_membered)]). fof(fc7_membered,theorem,( ! [A] : ( v1_xcmplx_0(A) => v1_membered(k1_tarski(A)) ) ), file(membered,fc7_membered), [interesting(0.9),axiom,file(membered,fc7_membered)]). fof(fc8_membered,theorem,( ! [A] : ( v1_xreal_0(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) ) ) ), file(membered,fc8_membered), [interesting(0.9),axiom,file(membered,fc8_membered)]). fof(t3_boole,theorem,( ! [A] : k4_xboole_0(A,k1_xboole_0) = A ), file(boole,t3_boole), [interesting(0.9),axiom,file(boole,t3_boole)]). fof(t4_boole,theorem,( ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ), file(boole,t4_boole), [interesting(0.9),axiom,file(boole,t4_boole)]). fof(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), [interesting(0.9),axiom,file(tarski,k1_tarski)]). fof(dt_k5_finseq_1,axiom,( $true ), file(finseq_1,k5_finseq_1), [interesting(0.9),axiom,file(finseq_1,k5_finseq_1)]). fof(dt_k5_finsub_1,axiom,( ! [A] : v4_finsub_1(k5_finsub_1(A)) ), file(finsub_1,k5_finsub_1), [interesting(0.9),axiom,file(finsub_1,k5_finsub_1)]). fof(dh_c4_103_2__rfunct_3,definition, ( ? [A] : m1_subset_1(A,k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c2_103_2__rfunct_3))) => m1_subset_1(c4_103_2__rfunct_3,k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c2_103_2__rfunct_3))) ), introduced(definition,[new_symbol(c4_103_2__rfunct_3),file(rfunct_3,c4_103_2__rfunct_3)]), [interesting(0.65),axiom,file(rfunct_3,c4_103_2__rfunct_3)]). fof(dt_c2_103_2__rfunct_3,assumption,( $true ), introduced(assumption,[file(rfunct_3,c2_103_2__rfunct_3)]), [interesting(0.65),axiom,file(rfunct_3,c2_103_2__rfunct_3)]). fof(e4_103_2__rfunct_3,plain,( ? [A] : m1_subset_1(A,k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c2_103_2__rfunct_3))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3])],[cc1_finseq_1,cc1_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_partfun1,rc2_xreal_0,rc3_finseq_1,rc3_xreal_0,rc4_xreal_0,rc6_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc14_finset_1,fc17_finseq_1,fc1_rfinseq,fc2_finseq_1,fc2_seq_1,fc6_membered,rc1_finset_1,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_partfun1,rc2_rfunct_3,rc3_finset_1,rc4_finset_1,rc7_finseq_1,t1_subset,t4_subset,t5_subset,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k7_relat_1,dt_m1_relset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_seq_1,cc4_membered,cc6_membered,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,redefinition_k2_partfun1,redefinition_k4_relset_1,dt_k1_numbers,dt_k2_partfun1,dt_k4_relset_1,dt_m1_subset_1,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,fc2_membered]), [interesting(0.65),file(rfunct_3,e4_103_2__rfunct_3),[file(rfunct_3,e4_103_2__rfunct_3)]]). fof(dt_c4_103_2__rfunct_3,plain,( m1_subset_1(c4_103_2__rfunct_3,k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c2_103_2__rfunct_3))) ), inference(consider,[status(thm),assumptions([dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3])],[dh_c4_103_2__rfunct_3,e4_103_2__rfunct_3]), [interesting(0.65),file(rfunct_3,c4_103_2__rfunct_3),[file(rfunct_3,c4_103_2__rfunct_3)]]). fof(fc12_finseq_1,theorem,( ! [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), [interesting(0.9),axiom,file(finseq_1,fc12_finseq_1)]). fof(fc1_finset_1,theorem,( ! [A] : ( ~ v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)) ) ), file(finset_1,fc1_finset_1), [interesting(0.9),axiom,file(finset_1,fc1_finset_1)]). fof(fc37_membered,theorem,( ! [A,B] : ( v1_membered(A) => v1_membered(k4_xboole_0(A,B)) ) ), file(membered,fc37_membered), [interesting(0.9),axiom,file(membered,fc37_membered)]). fof(fc38_membered,theorem,( ! [A,B] : ( v2_membered(A) => ( v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) ) ) ), file(membered,fc38_membered), [interesting(0.9),axiom,file(membered,fc38_membered)]). fof(fc3_finseq_1,theorem,( ! [A] : ( v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) ) ), file(finseq_1,fc3_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc3_finseq_1)]). fof(fc4_finseq_1,theorem,( ! [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), [interesting(0.9),axiom,file(finseq_1,fc4_finseq_1)]). fof(redefinition_k12_finseq_1,definition,( ! [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), [interesting(0.9),axiom,file(finseq_1,k12_finseq_1)]). fof(redefinition_k2_seq_1,definition,( ! [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), [interesting(0.9),axiom,file(seq_1,k2_seq_1)]). fof(redefinition_k2_setwiseo,definition,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => k2_setwiseo(A,B) = k1_tarski(B) ) ), file(setwiseo,k2_setwiseo), [interesting(0.9),axiom,file(setwiseo,k2_setwiseo)]). 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), [interesting(0.9),axiom,file(finseq_1,k12_finseq_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), [interesting(0.9),axiom,file(seq_1,k2_seq_1)]). fof(dt_k2_setwiseo,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m1_subset_1(k2_setwiseo(A,B),k5_finsub_1(A)) ) ), file(setwiseo,k2_setwiseo), [interesting(0.9),axiom,file(setwiseo,k2_setwiseo)]). fof(dt_k4_xboole_0,axiom,( $true ), file(xboole_0,k4_xboole_0), [interesting(0.9),axiom,file(xboole_0,k4_xboole_0)]). fof(de_c5_103_2__rfunct_3,definition,( c5_103_2__rfunct_3 = c4_103_2__rfunct_3 ), introduced(definition,[new_symbol(c5_103_2__rfunct_3),file(rfunct_3,c5_103_2__rfunct_3)]), [interesting(0.65),axiom,file(rfunct_3,c5_103_2__rfunct_3)]). fof(fc13_xreal_0,theorem,( ! [A] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) ) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & ~ v3_xreal_0(k4_xcmplx_0(A)) ) ) ), file(xreal_0,fc13_xreal_0), [interesting(0.9),axiom,file(xreal_0,fc13_xreal_0)]). fof(fc14_xreal_0,theorem,( ! [A] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & ~ v2_xreal_0(k4_xcmplx_0(A)) ) ) ), file(xreal_0,fc14_xreal_0), [interesting(0.9),axiom,file(xreal_0,fc14_xreal_0)]). fof(fc15_xreal_0,theorem,( ! [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), [interesting(0.9),axiom,file(xreal_0,fc15_xreal_0)]). fof(fc16_xreal_0,theorem,( ! [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), [interesting(0.9),axiom,file(xreal_0,fc16_xreal_0)]). fof(fc17_xreal_0,theorem,( ! [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), [interesting(0.9),axiom,file(xreal_0,fc17_xreal_0)]). fof(fc18_xreal_0,theorem,( ! [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), [interesting(0.9),axiom,file(xreal_0,fc18_xreal_0)]). fof(fc19_xreal_0,theorem,( ! [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), [interesting(0.9),axiom,file(xreal_0,fc19_xreal_0)]). fof(fc1_xreal_0,theorem,( ! [A] : ( v1_xreal_0(A) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) ) ) ), file(xreal_0,fc1_xreal_0), [interesting(0.9),axiom,file(xreal_0,fc1_xreal_0)]). fof(fc20_xreal_0,theorem,( ! [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), [interesting(0.9),axiom,file(xreal_0,fc20_xreal_0)]). fof(fc27_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) & ~ v2_xreal_0(k7_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc27_xreal_0), [interesting(0.9),axiom,file(xreal_0,fc27_xreal_0)]). fof(fc28_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k7_xcmplx_0(B,A)) & v1_xreal_0(k7_xcmplx_0(B,A)) & ~ v2_xreal_0(k7_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc28_xreal_0), [interesting(0.9),axiom,file(xreal_0,fc28_xreal_0)]). fof(fc29_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) & ~ v3_xreal_0(k7_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc29_xreal_0), [interesting(0.9),axiom,file(xreal_0,fc29_xreal_0)]). fof(fc30_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) & ~ v3_xreal_0(k7_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc30_xreal_0), [interesting(0.9),axiom,file(xreal_0,fc30_xreal_0)]). fof(fc5_xreal_0,theorem,( ! [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), [interesting(0.9),axiom,file(xreal_0,fc5_xreal_0)]). fof(fc6_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc6_xreal_0), [interesting(0.9),axiom,file(xreal_0,fc6_xreal_0)]). 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(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__r0_rm1_rm1,theorem,( k2_xcmplx_0(0,k4_xcmplx_0(1)) = k4_xcmplx_0(1) ), file(arithm,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1)]). 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(rqRealAdd__k2_xcmplx_0__r1_rm1_r0,theorem,( k2_xcmplx_0(1,k4_xcmplx_0(1)) = 0 ), file(arithm,rqRealAdd__k2_xcmplx_0__r1_rm1_r0), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_rm1_r0)]). fof(rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,theorem,( k2_xcmplx_0(k4_xcmplx_0(1),0) = k4_xcmplx_0(1) ), file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1)]). fof(rqRealAdd__k2_xcmplx_0__rm1_r1_r0,theorem,( k2_xcmplx_0(k4_xcmplx_0(1),1) = 0 ), file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r1_r0), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r1_r0)]). fof(spc1_arithm,theorem,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k2_xcmplx_0(A,k4_xcmplx_0(B)) = k6_xcmplx_0(A,B) ) ), file(arithm,spc1_arithm), [interesting(0.9),axiom,file(arithm,spc1_arithm)]). 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(spc8_arithm,theorem,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k2_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(B)) = k4_xcmplx_0(k2_xcmplx_0(A,B)) ) ), file(arithm,spc8_arithm), [interesting(0.9),axiom,file(arithm,spc8_arithm)]). fof(spc9_arithm,theorem,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k6_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(B)) = k6_xcmplx_0(B,A) ) ), file(arithm,spc9_arithm), [interesting(0.9),axiom,file(arithm,spc9_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(t4_arithm,theorem,( ! [A] : ( v1_xcmplx_0(A) => k6_xcmplx_0(A,0) = A ) ), file(arithm,t4_arithm), [interesting(0.9),axiom,file(arithm,t4_arithm)]). fof(t5_arithm,theorem,( ! [A] : ( v1_xcmplx_0(A) => k7_xcmplx_0(0,A) = 0 ) ), file(arithm,t5_arithm), [interesting(0.9),axiom,file(arithm,t5_arithm)]). fof(t6_arithm,theorem,( ! [A] : ( v1_xcmplx_0(A) => k7_xcmplx_0(A,1) = A ) ), file(arithm,t6_arithm), [interesting(0.9),axiom,file(arithm,t6_arithm)]). fof(involutiveness_k4_xcmplx_0,theorem,( ! [A] : ( v1_xcmplx_0(A) => k4_xcmplx_0(k4_xcmplx_0(A)) = A ) ), file(xcmplx_0,k4_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k4_xcmplx_0)]). fof(dt_k4_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_xcmplx_0(k4_xcmplx_0(A)) ) ), file(xcmplx_0,k4_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k4_xcmplx_0)]). fof(dt_k6_xcmplx_0,axiom,( $true ), file(xcmplx_0,k6_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k6_xcmplx_0)]). fof(dt_k7_xcmplx_0,axiom,( $true ), file(xcmplx_0,k7_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k7_xcmplx_0)]). fof(dt_c1_103_2__rfunct_3,assumption,( m2_subset_1(c1_103_2__rfunct_3,k1_numbers,k5_numbers) ), introduced(assumption,[file(rfunct_3,c1_103_2__rfunct_3)]), [interesting(0.65),axiom,file(rfunct_3,c1_103_2__rfunct_3)]). fof(dt_c3_103_2__rfunct_3,assumption,( v1_finset_1(c3_103_2__rfunct_3) ), introduced(assumption,[file(rfunct_3,c3_103_2__rfunct_3)]), [interesting(0.65),axiom,file(rfunct_3,c3_103_2__rfunct_3)]). fof(rqRealDiff__k6_xcmplx_0__r0_r0_r0,theorem,( k6_xcmplx_0(0,0) = 0 ), file(arithm,rqRealDiff__k6_xcmplx_0__r0_r0_r0), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_r0_r0)]). fof(rqRealDiff__k6_xcmplx_0__r0_rm1_r1,theorem,( k6_xcmplx_0(0,k4_xcmplx_0(1)) = 1 ), file(arithm,rqRealDiff__k6_xcmplx_0__r0_rm1_r1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_rm1_r1)]). fof(rqRealDiff__k6_xcmplx_0__r1_r0_r1,theorem,( k6_xcmplx_0(1,0) = 1 ), file(arithm,rqRealDiff__k6_xcmplx_0__r1_r0_r1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_r0_r1)]). fof(rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,theorem,( k6_xcmplx_0(k4_xcmplx_0(1),0) = k4_xcmplx_0(1) ), file(arithm,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1)]). fof(rqRealDiv__k7_xcmplx_0__r0_r1_r0,theorem,( k7_xcmplx_0(0,1) = 0 ), file(arithm,rqRealDiv__k7_xcmplx_0__r0_r1_r0), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r0_r1_r0)]). fof(rqRealDiv__k7_xcmplx_0__r1_r1_r1,theorem,( k7_xcmplx_0(1,1) = 1 ), file(arithm,rqRealDiv__k7_xcmplx_0__r1_r1_r1), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_r1_r1)]). fof(rqRealDiv__k7_xcmplx_0__rm1_r1_rm1,theorem,( k7_xcmplx_0(k4_xcmplx_0(1),1) = k4_xcmplx_0(1) ), file(arithm,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1)]). fof(rqRealNeg__k4_xcmplx_0__r0_r0,theorem,( k4_xcmplx_0(0) = 0 ), file(arithm,rqRealNeg__k4_xcmplx_0__r0_r0), [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__r0_r0)]). fof(t47_card_1,theorem,( k1_card_1(k1_xboole_0) = k1_xboole_0 ), file(card_1,t47_card_1), [interesting(0.9),axiom,file(card_1,t47_card_1)]). fof(d3_tarski,definition,( ! [A,B] : ( r1_tarski(A,B) <=> ! [C] : ( r2_hidden(C,A) => r2_hidden(C,B) ) ) ), file(tarski,d3_tarski), [interesting(0.9),axiom,file(tarski,d3_tarski)]). fof(rqRealNeg__k4_xcmplx_0__r1_rm1,theorem,( k4_xcmplx_0(1) = k4_xcmplx_0(1) ), file(arithm,rqRealNeg__k4_xcmplx_0__r1_rm1), [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__r1_rm1)]). fof(rqRealDiv__k7_xcmplx_0__r1_rm1_rm1,theorem,( k7_xcmplx_0(1,k4_xcmplx_0(1)) = k4_xcmplx_0(1) ), file(arithm,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1)]). fof(rqRealNeg__k4_xcmplx_0__rm1_r1,theorem,( k4_xcmplx_0(k4_xcmplx_0(1)) = 1 ), file(arithm,rqRealNeg__k4_xcmplx_0__rm1_r1), [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rm1_r1)]). fof(rqRealDiff__k6_xcmplx_0__r0_r1_rm1,theorem,( k6_xcmplx_0(0,1) = k4_xcmplx_0(1) ), file(arithm,rqRealDiff__k6_xcmplx_0__r0_r1_rm1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_r1_rm1)]). fof(rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,theorem,( k6_xcmplx_0(k4_xcmplx_0(1),k4_xcmplx_0(1)) = 0 ), file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0)]). fof(rqRealDiff__k6_xcmplx_0__r1_r1_r0,theorem,( k6_xcmplx_0(1,1) = 0 ), file(arithm,rqRealDiff__k6_xcmplx_0__r1_r1_r0), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_r1_r0)]). fof(e5_103_2__rfunct_3,plain,( m1_subset_1(c4_103_2__rfunct_3,c1_103__rfunct_3) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[dt_k2_zfmisc_1,dt_k5_ordinal2,cc1_relset_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,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,fc13_xreal_0,fc14_finset_1,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc17_xreal_0,fc18_xreal_0,fc19_xreal_0,fc1_nat_1,fc1_xreal_0,fc20_xreal_0,fc27_xreal_0,fc28_xreal_0,fc29_xreal_0,fc2_seq_1,fc30_xreal_0,fc3_nat_1,fc3_xreal_0,fc4_nat_1,fc5_membered,fc5_xreal_0,fc6_xreal_0,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,rc1_nat_1,rc1_seq_1,rc1_xreal_0,rc2_finset_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,commutativity_k2_xcmplx_0,existence_m1_relset_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_xcmplx_0,dt_k5_numbers,dt_k7_relat_1,dt_m1_relset_1,dt_m2_relset_1,dt_m2_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finseq_1,cc1_finset_1,cc1_membered,cc1_nat_1,cc1_seq_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_nat_1,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc17_finseq_1,fc1_rfinseq,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,rc1_finseq_1,rc1_finset_1,rc1_membered,rc1_partfun1,rc2_finseq_1,rc2_partfun1,rc2_rfunct_3,rc3_finseq_1,rc3_finset_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_rm1_r0,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,rqRealAdd__k2_xcmplx_0__rm1_r1_r0,spc1_arithm,spc6_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_numerals,t2_subset,t4_arithm,t4_subset,t5_arithm,t5_subset,t6_arithm,t8_boole,commutativity_k1_nat_1,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k3_xboole_0,idempotence_k3_xboole_0,involutiveness_k4_xcmplx_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k1_nat_1,redefinition_k2_partfun1,redefinition_k4_card_1,redefinition_k4_relset_1,dt_k1_card_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_xboole_0,dt_k2_partfun1,dt_k2_xboole_0,dt_k3_xboole_0,dt_k4_card_1,dt_k4_relset_1,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_k7_xcmplx_0,dt_m1_subset_1,dt_c1_103__rfunct_3,dt_c1_103_2__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c4_103_2__rfunct_3,fc10_finset_1,fc11_finset_1,fc2_finseq_1,fc2_membered,fc6_membered,fc9_finset_1,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealDiv__k7_xcmplx_0__r0_r1_r0,rqRealDiv__k7_xcmplx_0__r1_r1_r1,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1,rqRealNeg__k4_xcmplx_0__r0_r0,t1_boole,t1_subset,t2_boole,t3_subset,t6_boole,t7_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e2_103_2__rfunct_3,t47_card_1,d3_tarski,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealDiff__k6_xcmplx_0__r1_r1_r0]), [interesting(0.65),file(rfunct_3,e5_103_2__rfunct_3),[file(rfunct_3,e5_103_2__rfunct_3)]]). fof(dt_c5_103_2__rfunct_3,plain,( m1_subset_1(c5_103_2__rfunct_3,c1_103__rfunct_3) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,reflexivity_r1_tarski,dt_k2_zfmisc_1,cc1_finseq_1,cc1_relset_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc7_xreal_0,fc14_finset_1,fc17_finseq_1,fc1_rfinseq,fc2_seq_1,rc1_finseq_1,rc1_nat_1,rc1_partfun1,rc1_seq_1,rc1_xreal_0,rc2_partfun1,rc2_rfunct_3,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k7_relat_1,dt_m1_relset_1,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,cc3_membered,cc4_membered,cc6_membered,fc2_finseq_1,fc6_membered,rc1_finset_1,rc1_membered,rc3_finset_1,rc4_finset_1,t1_subset,t3_subset,t4_subset,t5_subset,redefinition_k2_partfun1,redefinition_k4_relset_1,dt_k1_numbers,dt_k2_partfun1,dt_k4_relset_1,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,cc15_membered,cc1_finset_1,fc2_membered,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_m1_subset_1,dt_c1_103__rfunct_3,dt_c4_103_2__rfunct_3,de_c5_103_2__rfunct_3,e5_103_2__rfunct_3]), [interesting(0.65),file(rfunct_3,c5_103_2__rfunct_3),[file(rfunct_3,c5_103_2__rfunct_3)]]). fof(d14_rfunct_3,definition,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m2_relset_1(B,A,k1_numbers) ) => ! [C] : ( v1_finset_1(k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,C))) => ! [D] : ( ( v1_rfinseq(D) & m2_finseq_1(D,k1_numbers) ) => ( D = k22_rfunct_3(A,B,C) <=> r1_rfinseq(k2_partfun1(A,k1_numbers,B,C),D) ) ) ) ) ) ), file(rfunct_3,d14_rfunct_3), [interesting(0.9),axiom,file(rfunct_3,d14_rfunct_3)]). fof(e35_103_2__rfunct_3,plain,( r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c2_103_2__rfunct_3)),k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c2_103_2__rfunct_3))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103__rfunct_3,dt_c1_103_2__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,e2_103_2__rfunct_3])],[reflexivity_r1_tarski,dt_k5_ordinal2,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,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,fc13_xreal_0,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc17_xreal_0,fc18_xreal_0,fc19_xreal_0,fc1_nat_1,fc1_xreal_0,fc20_xreal_0,fc27_xreal_0,fc28_xreal_0,fc29_xreal_0,fc2_seq_1,fc30_xreal_0,fc3_nat_1,fc3_xreal_0,fc4_nat_1,fc5_membered,fc5_xreal_0,fc6_xreal_0,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,rc1_nat_1,rc1_seq_1,rc1_xreal_0,rc2_finset_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,commutativity_k2_xcmplx_0,antisymmetry_r2_hidden,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k5_numbers,dt_k7_relat_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_subset_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_relset_1,cc1_seq_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_nat_1,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc14_finset_1,fc17_finseq_1,fc1_rfinseq,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,rc1_finseq_1,rc1_membered,rc1_partfun1,rc1_rfinseq,rc2_finseq_1,rc2_partfun1,rc2_rfunct_3,rc3_finseq_1,rc3_finset_1,rc4_finseq_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_rm1_r0,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,rqRealAdd__k2_xcmplx_0__rm1_r1_r0,spc1_arithm,spc6_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_numerals,t1_subset,t2_subset,t3_subset,t4_arithm,t4_subset,t5_arithm,t5_subset,t6_arithm,commutativity_k1_nat_1,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k3_xboole_0,idempotence_k3_xboole_0,involutiveness_k4_xcmplx_0,symmetry_r1_rfinseq,reflexivity_r1_rfinseq,existence_m2_finseq_1,existence_m2_relset_1,redefinition_k1_nat_1,redefinition_k2_partfun1,redefinition_k4_card_1,redefinition_k4_relset_1,redefinition_m2_finseq_1,redefinition_m2_relset_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_xboole_0,dt_k22_rfunct_3,dt_k2_partfun1,dt_k2_xboole_0,dt_k3_xboole_0,dt_k4_card_1,dt_k4_relset_1,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_k7_xcmplx_0,dt_m2_finseq_1,dt_m2_relset_1,dt_c1_103__rfunct_3,dt_c1_103_2__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,cc15_membered,cc1_finset_1,fc10_finset_1,fc11_finset_1,fc2_finseq_1,fc2_membered,fc6_membered,fc9_finset_1,rc1_finset_1,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealDiv__k7_xcmplx_0__r0_r1_r0,rqRealDiv__k7_xcmplx_0__r1_r1_r1,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1,rqRealNeg__k4_xcmplx_0__r0_r0,spc0_boole,spc1_boole,t1_boole,t2_boole,t6_boole,t7_boole,t8_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e2_103_2__rfunct_3,d14_rfunct_3,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealDiff__k6_xcmplx_0__r1_r1_r0]), [interesting(0.65),file(rfunct_3,e35_103_2__rfunct_3),[file(rfunct_3,e35_103_2__rfunct_3)]]). fof(e1_103_2_1__rfunct_3,plain,( k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c2_103_2__rfunct_3))) = k3_xboole_0(k4_relset_1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3),k2_xboole_0(c3_103__rfunct_3,c2_103_2__rfunct_3)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c3_103__rfunct_3])],[cc1_finseq_1,cc1_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_partfun1,rc2_xreal_0,rc3_finseq_1,rc3_xreal_0,rc4_xreal_0,rc6_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc10_finset_1,fc11_finset_1,fc14_finset_1,fc17_finseq_1,fc1_rfinseq,fc1_seq_1,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc2_seq_1,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc6_membered,fc9_finset_1,rc1_finset_1,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_rfunct_3,rc3_finset_1,rc4_finset_1,rc7_finseq_1,t1_boole,t2_boole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_seq_1,cc4_membered,cc6_membered,fc22_membered,fc23_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,rc2_partfun1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,redefinition_k2_partfun1,redefinition_k4_relset_1,dt_k1_funct_1,dt_k1_numbers,dt_k1_relat_1,dt_k2_partfun1,dt_k2_xboole_0,dt_k3_xboole_0,dt_k4_relset_1,dt_k7_relat_1,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c3_103__rfunct_3,fc2_membered,t1_subset,t7_boole,t68_funct_1]), [interesting(0.5),file(rfunct_3,e1_103_2_1__rfunct_3),[file(rfunct_3,e1_103_2_1__rfunct_3)]]). fof(e2_103_2_1__rfunct_3,plain,( k3_xboole_0(k4_relset_1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3),k2_xboole_0(c3_103__rfunct_3,c2_103_2__rfunct_3)) = k2_xboole_0(k3_xboole_0(k4_relset_1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3),c3_103__rfunct_3),k3_xboole_0(k4_relset_1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3),c2_103_2__rfunct_3)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c3_103__rfunct_3])],[cc1_finseq_1,cc1_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_partfun1,rc2_xreal_0,rc3_finseq_1,rc3_xreal_0,rc4_xreal_0,rc6_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc10_finset_1,fc11_finset_1,fc14_finset_1,fc17_finseq_1,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc6_membered,fc9_finset_1,rc1_finset_1,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_partfun1,rc2_rfunct_3,rc3_finset_1,rc4_finset_1,rc7_finseq_1,t1_boole,t1_subset,t2_boole,t4_subset,t5_subset,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_seq_1,cc4_membered,cc6_membered,fc22_membered,fc23_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k3_xboole_0,idempotence_k3_xboole_0,redefinition_k4_relset_1,dt_k1_numbers,dt_k2_xboole_0,dt_k3_xboole_0,dt_k4_relset_1,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c3_103__rfunct_3,fc2_membered,t23_xboole_1]), [interesting(0.5),file(rfunct_3,e2_103_2_1__rfunct_3),[file(rfunct_3,e2_103_2_1__rfunct_3)]]). fof(e3_103_2_1__rfunct_3,plain,( k2_xboole_0(k3_xboole_0(k4_relset_1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3),c3_103__rfunct_3),k3_xboole_0(k4_relset_1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3),c2_103_2__rfunct_3)) = k2_xboole_0(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c3_103__rfunct_3)),k3_xboole_0(k4_relset_1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3),c2_103_2__rfunct_3)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c3_103__rfunct_3])],[cc1_finseq_1,cc1_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_partfun1,rc2_xreal_0,rc3_finseq_1,rc3_xreal_0,rc4_xreal_0,rc6_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc10_finset_1,fc11_finset_1,fc14_finset_1,fc17_finseq_1,fc1_rfinseq,fc1_seq_1,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc2_seq_1,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc6_membered,fc9_finset_1,rc1_finset_1,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_rfunct_3,rc3_finset_1,rc4_finset_1,rc7_finseq_1,t1_boole,t2_boole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_seq_1,cc4_membered,cc6_membered,fc22_membered,fc23_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,rc2_partfun1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,redefinition_k2_partfun1,redefinition_k4_relset_1,dt_k1_funct_1,dt_k1_numbers,dt_k1_relat_1,dt_k2_partfun1,dt_k2_xboole_0,dt_k3_xboole_0,dt_k4_relset_1,dt_k7_relat_1,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c3_103__rfunct_3,fc2_membered,t1_subset,t7_boole,t68_funct_1]), [interesting(0.5),file(rfunct_3,e3_103_2_1__rfunct_3),[file(rfunct_3,e3_103_2_1__rfunct_3)]]). fof(e4_103_2_1__rfunct_3,plain,( k2_xboole_0(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c3_103__rfunct_3)),k3_xboole_0(k4_relset_1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3),c2_103_2__rfunct_3)) = k4_subset_1(c1_103__rfunct_3,k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c3_103__rfunct_3)),k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c2_103_2__rfunct_3))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c3_103__rfunct_3])],[cc1_finseq_1,cc1_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_partfun1,rc2_xreal_0,rc3_finseq_1,rc3_xreal_0,rc4_xreal_0,rc6_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc10_finset_1,fc11_finset_1,fc14_finset_1,fc17_finseq_1,fc1_rfinseq,fc1_seq_1,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc2_seq_1,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc6_membered,fc9_finset_1,rc1_finset_1,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_rfunct_3,rc3_finset_1,rc4_finset_1,rc7_finseq_1,t1_boole,t2_boole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_seq_1,cc4_membered,cc6_membered,fc22_membered,fc23_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,rc2_partfun1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k3_xboole_0,idempotence_k3_xboole_0,commutativity_k4_subset_1,idempotence_k4_subset_1,antisymmetry_r2_hidden,redefinition_k2_partfun1,redefinition_k4_relset_1,redefinition_k4_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k1_relat_1,dt_k2_partfun1,dt_k2_xboole_0,dt_k3_xboole_0,dt_k4_relset_1,dt_k4_subset_1,dt_k7_relat_1,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c3_103__rfunct_3,fc2_membered,t1_subset,t7_boole,t68_funct_1]), [interesting(0.5),file(rfunct_3,e4_103_2_1__rfunct_3),[file(rfunct_3,e4_103_2_1__rfunct_3)]]). fof(e3_103_2__rfunct_3,plain,( k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c2_103_2__rfunct_3))) = k4_subset_1(c1_103__rfunct_3,k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c3_103__rfunct_3)),k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c2_103_2__rfunct_3))) ), inference(iterative_eq,[status(thm),assumptions([dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c3_103__rfunct_3])],[cc1_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_nat_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc10_finset_1,fc11_finset_1,fc14_finset_1,fc17_finseq_1,fc1_rfinseq,fc24_membered,fc25_membered,fc26_membered,fc2_seq_1,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc9_finset_1,rc1_finset_1,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_partfun1,rc2_rfunct_3,rc3_finset_1,rc4_finset_1,rc7_finseq_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k7_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_seq_1,cc4_membered,cc6_membered,fc22_membered,fc23_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k3_xboole_0,idempotence_k3_xboole_0,commutativity_k4_subset_1,idempotence_k4_subset_1,redefinition_k2_partfun1,redefinition_k4_relset_1,redefinition_k4_subset_1,dt_k1_numbers,dt_k2_partfun1,dt_k2_xboole_0,dt_k3_xboole_0,dt_k4_relset_1,dt_k4_subset_1,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c3_103__rfunct_3,fc2_membered,e1_103_2_1__rfunct_3,e2_103_2_1__rfunct_3,e3_103_2_1__rfunct_3,e4_103_2_1__rfunct_3]), [interesting(0.65),file(rfunct_3,e3_103_2__rfunct_3),[file(rfunct_3,e3_103_2__rfunct_3)]]). fof(d2_xboole_0,definition,( ! [A,B,C] : ( C = k2_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) | r2_hidden(D,B) ) ) ) ), file(xboole_0,d2_xboole_0), [interesting(0.9),axiom,file(xboole_0,d2_xboole_0)]). fof(e33_103_2__rfunct_3,plain,( r2_hidden(c5_103_2__rfunct_3,k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c2_103_2__rfunct_3)))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103_2__rfunct_3,dt_c3_103_2__rfunct_3,e2_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c3_103__rfunct_3])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,dt_k5_ordinal2,cc1_relset_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,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,fc13_xreal_0,fc14_finset_1,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc17_xreal_0,fc18_xreal_0,fc19_xreal_0,fc1_nat_1,fc1_xreal_0,fc20_xreal_0,fc27_xreal_0,fc28_xreal_0,fc29_xreal_0,fc2_seq_1,fc30_xreal_0,fc3_nat_1,fc3_xreal_0,fc4_nat_1,fc5_membered,fc5_xreal_0,fc6_xreal_0,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,rc1_nat_1,rc1_seq_1,rc1_xreal_0,rc2_finset_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,commutativity_k2_xcmplx_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_xcmplx_0,dt_k5_numbers,dt_k7_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,dt_c4_103_2__rfunct_3,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finseq_1,cc1_finset_1,cc1_membered,cc1_nat_1,cc1_seq_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_nat_1,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc17_finseq_1,fc1_rfinseq,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,rc1_finseq_1,rc1_finset_1,rc1_membered,rc1_partfun1,rc2_finseq_1,rc2_partfun1,rc2_rfunct_3,rc3_finseq_1,rc3_finset_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_rm1_r0,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,rqRealAdd__k2_xcmplx_0__rm1_r1_r0,spc1_arithm,spc6_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_numerals,t2_subset,t3_subset,t4_arithm,t4_subset,t5_arithm,t5_subset,t6_arithm,t8_boole,commutativity_k1_nat_1,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k3_xboole_0,idempotence_k3_xboole_0,commutativity_k4_subset_1,idempotence_k4_subset_1,involutiveness_k4_xcmplx_0,antisymmetry_r2_hidden,redefinition_k1_nat_1,redefinition_k2_partfun1,redefinition_k4_card_1,redefinition_k4_relset_1,redefinition_k4_subset_1,dt_k1_card_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_xboole_0,dt_k2_partfun1,dt_k2_xboole_0,dt_k3_xboole_0,dt_k4_card_1,dt_k4_relset_1,dt_k4_subset_1,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_k7_xcmplx_0,dt_c1_103__rfunct_3,dt_c1_103_2__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c5_103_2__rfunct_3,de_c5_103_2__rfunct_3,fc10_finset_1,fc11_finset_1,fc2_finseq_1,fc2_membered,fc6_membered,fc9_finset_1,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealDiv__k7_xcmplx_0__r0_r1_r0,rqRealDiv__k7_xcmplx_0__r1_r1_r1,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1,rqRealNeg__k4_xcmplx_0__r0_r0,t1_boole,t1_subset,t2_boole,t6_boole,t7_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e2_103_2__rfunct_3,e3_103_2__rfunct_3,t47_card_1,d2_xboole_0,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealDiff__k6_xcmplx_0__r1_r1_r0]), [interesting(0.65),file(rfunct_3,e33_103_2__rfunct_3),[file(rfunct_3,e33_103_2__rfunct_3)]]). fof(e1_103_2_4__rfunct_3,assumption,( r2_hidden(c5_103_2__rfunct_3,c3_103__rfunct_3) ), introduced(assumption,[file(rfunct_3,e1_103_2_4__rfunct_3)]), [interesting(0.5),axiom,file(rfunct_3,e1_103_2_4__rfunct_3)]). fof(e15_103_2__rfunct_3,plain, ( k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3)))) = k3_xboole_0(k4_relset_1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3),k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))) & k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c2_103_2__rfunct_3)) = k3_xboole_0(k4_relset_1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3),c2_103_2__rfunct_3) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[cc1_finseq_1,cc1_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc10_membered,fc11_membered,fc9_membered,rc1_finseq_1,rc1_nat_1,rc1_partfun1,rc2_xreal_0,rc3_finseq_1,rc3_xreal_0,rc4_xreal_0,rc6_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc10_finset_1,fc11_finset_1,fc12_finset_1,fc14_finset_1,fc17_finseq_1,fc1_rfinseq,fc1_seq_1,fc2_finseq_1,fc2_seq_1,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc39_membered,fc40_membered,fc41_membered,fc6_membered,fc7_membered,fc8_membered,rc1_finset_1,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_rfunct_3,rc3_finset_1,rc4_finset_1,rc7_finseq_1,t2_boole,t3_boole,t4_boole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k5_finsub_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_c4_103_2__rfunct_3,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_seq_1,cc4_membered,cc6_membered,fc1_finset_1,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc37_membered,fc38_membered,rc2_partfun1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,redefinition_k2_partfun1,redefinition_k2_setwiseo,redefinition_k4_relset_1,dt_k1_funct_1,dt_k1_numbers,dt_k1_relat_1,dt_k2_partfun1,dt_k2_setwiseo,dt_k3_xboole_0,dt_k4_relset_1,dt_k4_xboole_0,dt_k7_relat_1,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c5_103_2__rfunct_3,de_c5_103_2__rfunct_3,fc2_membered,t1_subset,t7_boole,t68_funct_1]), [interesting(0.65),file(rfunct_3,e15_103_2__rfunct_3),[file(rfunct_3,e15_103_2__rfunct_3)]]). fof(d3_xboole_0,definition,( ! [A,B,C] : ( C = k3_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) & r2_hidden(D,B) ) ) ) ), file(xboole_0,d3_xboole_0), [interesting(0.9),axiom,file(xboole_0,d3_xboole_0)]). fof(e2_103_2_4__rfunct_3,plain,( r2_hidden(c5_103_2__rfunct_3,c2_103_2__rfunct_3) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,dt_k5_ordinal2,cc1_relset_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc10_membered,fc10_xreal_0,fc11_membered,fc11_xreal_0,fc12_xreal_0,fc13_xreal_0,fc14_finset_1,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc17_xreal_0,fc18_xreal_0,fc19_xreal_0,fc1_nat_1,fc1_xreal_0,fc20_xreal_0,fc27_xreal_0,fc28_xreal_0,fc29_xreal_0,fc2_seq_1,fc30_xreal_0,fc3_nat_1,fc3_xreal_0,fc4_nat_1,fc5_membered,fc5_xreal_0,fc6_xreal_0,fc7_xreal_0,fc8_membered,fc8_xreal_0,fc9_membered,fc9_xreal_0,rc1_nat_1,rc1_seq_1,rc1_xreal_0,rc2_finset_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,commutativity_k2_xcmplx_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_xcmplx_0,dt_k5_finsub_1,dt_k5_numbers,dt_k7_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,dt_c4_103_2__rfunct_3,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finseq_1,cc1_finset_1,cc1_membered,cc1_nat_1,cc1_seq_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_nat_1,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc17_finseq_1,fc1_finset_1,fc1_rfinseq,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc37_membered,fc38_membered,fc39_membered,fc40_membered,fc41_membered,fc7_membered,rc1_finseq_1,rc1_finset_1,rc1_membered,rc1_partfun1,rc2_finseq_1,rc2_partfun1,rc2_rfunct_3,rc3_finseq_1,rc3_finset_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_rm1_r0,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,rqRealAdd__k2_xcmplx_0__rm1_r1_r0,spc1_arithm,spc6_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_numerals,t2_subset,t3_subset,t4_arithm,t4_subset,t5_arithm,t5_subset,t6_arithm,t8_boole,commutativity_k1_nat_1,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k3_xboole_0,idempotence_k3_xboole_0,involutiveness_k4_xcmplx_0,antisymmetry_r2_hidden,redefinition_k1_nat_1,redefinition_k2_partfun1,redefinition_k2_setwiseo,redefinition_k4_card_1,redefinition_k4_relset_1,dt_k1_card_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_xboole_0,dt_k2_partfun1,dt_k2_setwiseo,dt_k2_xboole_0,dt_k3_xboole_0,dt_k4_card_1,dt_k4_relset_1,dt_k4_xboole_0,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_k7_xcmplx_0,dt_c1_103__rfunct_3,dt_c1_103_2__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c5_103_2__rfunct_3,de_c5_103_2__rfunct_3,fc10_finset_1,fc11_finset_1,fc12_finset_1,fc2_finseq_1,fc2_membered,fc6_membered,fc9_finset_1,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealDiv__k7_xcmplx_0__r0_r1_r0,rqRealDiv__k7_xcmplx_0__r1_r1_r1,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1,rqRealNeg__k4_xcmplx_0__r0_r0,t1_boole,t1_subset,t2_boole,t3_boole,t4_boole,t6_boole,t7_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e2_103_2__rfunct_3,e15_103_2__rfunct_3,t47_card_1,d3_xboole_0,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealDiff__k6_xcmplx_0__r1_r1_r0]), [interesting(0.5),file(rfunct_3,e2_103_2_4__rfunct_3),[file(rfunct_3,e2_103_2_4__rfunct_3)]]). fof(e3_103_2_4__rfunct_3,plain,( ~ $true ), inference(mizar_by,[status(thm),assumptions([dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3,e1_103_2_4__rfunct_3])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,dt_k5_ordinal2,cc1_relset_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,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,fc13_xreal_0,fc14_finset_1,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc17_xreal_0,fc18_xreal_0,fc19_xreal_0,fc1_nat_1,fc1_xreal_0,fc20_xreal_0,fc27_xreal_0,fc28_xreal_0,fc29_xreal_0,fc2_seq_1,fc30_xreal_0,fc3_nat_1,fc3_xreal_0,fc4_nat_1,fc5_membered,fc5_xreal_0,fc6_xreal_0,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,rc1_nat_1,rc1_seq_1,rc1_xreal_0,rc2_finset_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,commutativity_k2_xcmplx_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_xcmplx_0,dt_k5_numbers,dt_k7_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,dt_c4_103_2__rfunct_3,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finseq_1,cc1_finset_1,cc1_membered,cc1_nat_1,cc1_seq_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_nat_1,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc17_finseq_1,fc1_rfinseq,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,rc1_finseq_1,rc1_finset_1,rc1_membered,rc1_partfun1,rc2_finseq_1,rc2_partfun1,rc2_rfunct_3,rc3_finseq_1,rc3_finset_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_rm1_r0,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,rqRealAdd__k2_xcmplx_0__rm1_r1_r0,spc1_arithm,spc6_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_numerals,t2_subset,t3_subset,t4_arithm,t4_subset,t5_arithm,t5_subset,t6_arithm,t8_boole,commutativity_k1_nat_1,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k3_xboole_0,idempotence_k3_xboole_0,involutiveness_k4_xcmplx_0,antisymmetry_r2_hidden,redefinition_k1_nat_1,redefinition_k2_partfun1,redefinition_k4_card_1,redefinition_k4_relset_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_xboole_0,dt_k2_partfun1,dt_k2_xboole_0,dt_k3_xboole_0,dt_k4_card_1,dt_k4_relset_1,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_k7_xcmplx_0,dt_c1_103__rfunct_3,dt_c1_103_2__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c5_103_2__rfunct_3,de_c5_103_2__rfunct_3,fc10_finset_1,fc11_finset_1,fc2_finseq_1,fc2_membered,fc6_membered,fc9_finset_1,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealDiv__k7_xcmplx_0__r0_r1_r0,rqRealDiv__k7_xcmplx_0__r1_r1_r1,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1,rqRealNeg__k4_xcmplx_0__r0_r0,t1_boole,t1_subset,t2_boole,t6_boole,t7_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e2_103_2_4__rfunct_3,e2_103_2__rfunct_3,e1_103_2_4__rfunct_3,d3_xboole_0,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealDiff__k6_xcmplx_0__r1_r1_r0]), [interesting(0.5),file(rfunct_3,e3_103_2_4__rfunct_3),[file(rfunct_3,e3_103_2_4__rfunct_3)]]). fof(i2_103_2_4__rfunct_3,theorem,( $true ), introduced(tautology,[file(rfunct_3,i2_103_2_4__rfunct_3)]), [interesting(0.5),trivial,file(rfunct_3,i2_103_2_4__rfunct_3)]). fof(i1_103_2_4__rfunct_3,plain,( ~ $true ), inference(conclusion,[status(thm),assumptions([dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3,e1_103_2_4__rfunct_3])],[e3_103_2_4__rfunct_3,i2_103_2_4__rfunct_3]), [interesting(0.5),file(rfunct_3,i1_103_2_4__rfunct_3),[file(rfunct_3,i1_103_2_4__rfunct_3)]]). fof(e30_103_2__rfunct_3,plain,( ~ r2_hidden(c5_103_2__rfunct_3,c3_103__rfunct_3) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3]),discharge_asm(discharge,[e1_103_2_4__rfunct_3])],[e1_103_2_4__rfunct_3,i1_103_2_4__rfunct_3]), [interesting(0.65),file(rfunct_3,e30_103_2__rfunct_3),[file(rfunct_3,e30_103_2__rfunct_3)]]). fof(t65_zfmisc_1,theorem,( ! [A,B] : ( k4_xboole_0(A,k1_tarski(B)) = A <=> ~ r2_hidden(B,A) ) ), file(zfmisc_1,t65_zfmisc_1), [interesting(0.9),axiom,file(zfmisc_1,t65_zfmisc_1)]). fof(e31_103_2__rfunct_3,plain,( k4_xboole_0(c3_103__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3)) = c3_103__rfunct_3 ), inference(mizar_by,[status(thm),assumptions([dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,cc1_relset_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc14_finset_1,fc2_seq_1,rc1_seq_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k7_relat_1,dt_m1_relset_1,dt_m2_relset_1,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finseq_1,cc1_seq_1,cc1_xreal_0,cc20_membered,cc2_finset_1,cc2_xreal_0,cc3_nat_1,cc6_membered,cc7_xreal_0,fc10_membered,fc11_membered,fc17_finseq_1,fc1_rfinseq,fc7_membered,fc8_membered,fc9_membered,rc1_finseq_1,rc1_nat_1,rc1_partfun1,rc1_xreal_0,rc2_partfun1,rc2_rfunct_3,rc3_finseq_1,rc3_finset_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t3_subset,t4_subset,t5_subset,redefinition_k2_partfun1,redefinition_k4_relset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k2_partfun1,dt_k4_relset_1,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc2_finseq_1,fc2_membered,fc37_membered,fc38_membered,fc39_membered,fc40_membered,fc41_membered,fc6_membered,rc1_membered,t3_boole,t4_boole,existence_m1_subset_1,dt_k5_finsub_1,dt_m1_subset_1,dt_c4_103_2__rfunct_3,cc15_membered,cc1_finset_1,fc12_finset_1,rc1_finset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k2_setwiseo,dt_k1_tarski,dt_k2_setwiseo,dt_k4_xboole_0,dt_c1_103__rfunct_3,dt_c3_103__rfunct_3,dt_c5_103_2__rfunct_3,de_c5_103_2__rfunct_3,fc1_finset_1,t1_subset,t7_boole,e30_103_2__rfunct_3,t65_zfmisc_1]), [interesting(0.65),file(rfunct_3,e31_103_2__rfunct_3),[file(rfunct_3,e31_103_2__rfunct_3)]]). fof(t42_xboole_1,theorem,( ! [A,B,C] : k4_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(k4_xboole_0(A,C),k4_xboole_0(B,C)) ), file(xboole_1,t42_xboole_1), [interesting(0.9),axiom,file(xboole_1,t42_xboole_1)]). fof(e32_103_2__rfunct_3,plain,( k4_xboole_0(k2_xboole_0(c3_103__rfunct_3,c2_103_2__rfunct_3),k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3)) = k2_xboole_0(c3_103__rfunct_3,k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,cc1_relset_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc14_finset_1,fc2_seq_1,rc1_seq_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k7_relat_1,dt_m1_relset_1,dt_m2_relset_1,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finseq_1,cc1_seq_1,cc1_xreal_0,cc20_membered,cc2_finset_1,cc2_xreal_0,cc3_nat_1,cc6_membered,cc7_xreal_0,fc10_membered,fc11_membered,fc17_finseq_1,fc1_rfinseq,fc7_membered,fc8_membered,fc9_membered,rc1_finseq_1,rc1_nat_1,rc1_partfun1,rc1_xreal_0,rc2_partfun1,rc2_rfunct_3,rc3_finseq_1,rc3_finset_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t3_subset,t4_subset,t5_subset,antisymmetry_r2_hidden,redefinition_k2_partfun1,redefinition_k4_relset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k2_partfun1,dt_k4_relset_1,dt_c2_103__rfunct_3,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc12_finset_1,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc2_membered,fc37_membered,fc38_membered,fc39_membered,fc40_membered,fc41_membered,fc6_membered,fc9_finset_1,rc1_finset_1,rc1_membered,t1_boole,t1_subset,t3_boole,t4_boole,existence_m1_subset_1,dt_k1_tarski,dt_k5_finsub_1,dt_m1_subset_1,dt_c4_103_2__rfunct_3,cc15_membered,cc1_finset_1,fc1_finset_1,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,redefinition_k2_setwiseo,dt_k2_setwiseo,dt_k2_xboole_0,dt_k4_xboole_0,dt_c1_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c5_103_2__rfunct_3,de_c5_103_2__rfunct_3,e31_103_2__rfunct_3,t42_xboole_1]), [interesting(0.65),file(rfunct_3,e32_103_2__rfunct_3),[file(rfunct_3,e32_103_2__rfunct_3)]]). fof(t69_rfunct_3,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C,D] : ( ( v1_funct_1(D) & m2_relset_1(D,A,k1_numbers) ) => ( ( v1_finset_1(k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,D,C))) & r2_hidden(B,k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,D,C))) ) => r1_rfinseq(k8_finseq_1(k1_numbers,k22_rfunct_3(A,D,k4_xboole_0(C,k2_setwiseo(A,B))),k12_finseq_1(k1_numbers,k2_seq_1(A,k1_numbers,D,B))),k2_partfun1(A,k1_numbers,D,C)) ) ) ) ) ), file(rfunct_3,t69_rfunct_3), [interesting(0.9),axiom,file(rfunct_3,t69_rfunct_3)]). fof(e34_103_2__rfunct_3,plain,( r1_rfinseq(k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3)))),k12_finseq_1(k1_numbers,k2_seq_1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c5_103_2__rfunct_3))),k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c2_103_2__rfunct_3))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[reflexivity_r1_tarski,dt_k5_ordinal2,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc10_membered,fc10_xreal_0,fc11_membered,fc11_xreal_0,fc12_xreal_0,fc13_xreal_0,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc17_xreal_0,fc18_xreal_0,fc19_xreal_0,fc1_nat_1,fc1_seq_1,fc1_xreal_0,fc20_xreal_0,fc27_xreal_0,fc28_xreal_0,fc29_xreal_0,fc2_seq_1,fc30_xreal_0,fc3_nat_1,fc3_xreal_0,fc4_nat_1,fc5_membered,fc5_xreal_0,fc6_xreal_0,fc7_xreal_0,fc8_membered,fc8_xreal_0,fc9_membered,fc9_xreal_0,rc1_nat_1,rc1_seq_1,rc1_xreal_0,rc2_finset_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,commutativity_k2_xcmplx_0,existence_m1_finseq_1,existence_m1_relset_1,existence_m2_finseq_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_funct_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k5_finseq_1,dt_k5_finsub_1,dt_k5_numbers,dt_k7_finseq_1,dt_k7_relat_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m2_finseq_1,dt_m2_subset_1,dt_c4_103_2__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_relset_1,cc1_seq_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_nat_1,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc14_finset_1,fc17_finseq_1,fc1_finset_1,fc1_rfinseq,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc37_membered,fc38_membered,fc39_membered,fc3_finseq_1,fc40_membered,fc41_membered,fc4_finseq_1,fc7_membered,rc1_finseq_1,rc1_membered,rc1_partfun1,rc1_rfinseq,rc2_finseq_1,rc2_partfun1,rc2_rfunct_3,rc3_finseq_1,rc3_finset_1,rc4_finseq_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_rm1_r0,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,rqRealAdd__k2_xcmplx_0__rm1_r1_r0,spc1_arithm,spc6_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_numerals,t3_subset,t4_arithm,t4_subset,t5_arithm,t5_subset,t6_arithm,commutativity_k1_nat_1,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k3_xboole_0,idempotence_k3_xboole_0,involutiveness_k4_xcmplx_0,symmetry_r1_rfinseq,reflexivity_r1_rfinseq,antisymmetry_r2_hidden,existence_m1_subset_1,existence_m2_relset_1,redefinition_k12_finseq_1,redefinition_k1_nat_1,redefinition_k2_partfun1,redefinition_k2_seq_1,redefinition_k2_setwiseo,redefinition_k4_card_1,redefinition_k4_relset_1,redefinition_k8_finseq_1,redefinition_m2_relset_1,dt_k12_finseq_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_xboole_0,dt_k22_rfunct_3,dt_k2_partfun1,dt_k2_seq_1,dt_k2_setwiseo,dt_k2_xboole_0,dt_k3_xboole_0,dt_k4_card_1,dt_k4_relset_1,dt_k4_xboole_0,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_k7_xcmplx_0,dt_k8_finseq_1,dt_m1_subset_1,dt_m2_relset_1,dt_c1_103__rfunct_3,dt_c1_103_2__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c5_103_2__rfunct_3,de_c5_103_2__rfunct_3,cc15_membered,cc1_finset_1,fc10_finset_1,fc11_finset_1,fc12_finset_1,fc2_finseq_1,fc2_membered,fc6_membered,fc9_finset_1,rc1_finset_1,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealDiv__k7_xcmplx_0__r0_r1_r0,rqRealDiv__k7_xcmplx_0__r1_r1_r1,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1,rqRealNeg__k4_xcmplx_0__r0_r0,spc0_boole,spc1_boole,t1_boole,t1_subset,t2_boole,t2_subset,t3_boole,t4_boole,t6_boole,t7_boole,t8_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e33_103_2__rfunct_3,e2_103_2__rfunct_3,e32_103_2__rfunct_3,t69_rfunct_3,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealDiff__k6_xcmplx_0__r1_r1_r0]), [interesting(0.65),file(rfunct_3,e34_103_2__rfunct_3),[file(rfunct_3,e34_103_2__rfunct_3)]]). fof(t2_rfinseq,theorem,( ! [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) ) => ( ( r1_rfinseq(A,B) & r1_rfinseq(A,C) ) => r1_rfinseq(B,C) ) ) ) ) ), file(rfinseq,t2_rfinseq), [interesting(0.9),axiom,file(rfinseq,t2_rfinseq)]). fof(e36_103_2__rfunct_3,plain,( r1_rfinseq(k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3)))),k12_finseq_1(k1_numbers,k2_seq_1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c5_103_2__rfunct_3))),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c2_103_2__rfunct_3))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[reflexivity_r1_tarski,dt_k1_relat_1,dt_k5_ordinal2,cc1_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc10_membered,fc11_membered,fc17_finseq_1,fc5_membered,fc9_membered,rc1_nat_1,rc1_partfun1,rc2_finset_1,rc2_nat_1,rc2_xreal_0,rc3_finseq_1,rc3_nat_1,rc3_xreal_0,rc4_finseq_1,rc4_xreal_0,rc6_finseq_1,antisymmetry_r2_hidden,redefinition_k4_relset_1,redefinition_k5_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k4_relset_1,dt_k5_numbers,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finseq_1,cc1_membered,cc1_nat_1,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_nat_1,cc2_xreal_0,cc3_membered,cc6_membered,cc7_xreal_0,cc9_membered,fc12_finset_1,fc13_finseq_1,fc14_finseq_1,fc14_finset_1,fc1_rfinseq,fc1_seq_1,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc2_seq_1,fc39_membered,fc40_membered,fc41_membered,fc6_membered,fc7_membered,fc8_membered,fc9_finset_1,rc1_finseq_1,rc1_finset_1,rc1_membered,rc1_rfinseq,rc1_seq_1,rc1_xreal_0,rc2_finseq_1,rc2_rfunct_3,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t1_boole,t1_subset,t3_boole,t3_subset,t4_boole,t4_subset,t5_subset,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_relset_1,redefinition_m2_finseq_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_tarski,dt_k5_finseq_1,dt_k5_finsub_1,dt_k7_finseq_1,dt_k7_relat_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_relset_1,dt_c4_103_2__rfunct_3,cc10_membered,cc11_membered,cc15_membered,cc1_finset_1,cc1_seq_1,cc4_membered,fc12_finseq_1,fc1_finset_1,fc22_membered,fc23_membered,fc37_membered,fc38_membered,fc3_finseq_1,fc4_finseq_1,rc2_partfun1,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,symmetry_r1_rfinseq,reflexivity_r1_rfinseq,redefinition_k12_finseq_1,redefinition_k2_partfun1,redefinition_k2_seq_1,redefinition_k2_setwiseo,redefinition_k8_finseq_1,dt_k12_finseq_1,dt_k1_numbers,dt_k22_rfunct_3,dt_k2_partfun1,dt_k2_seq_1,dt_k2_setwiseo,dt_k2_xboole_0,dt_k4_xboole_0,dt_k8_finseq_1,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c5_103_2__rfunct_3,de_c5_103_2__rfunct_3,fc2_membered,e35_103_2__rfunct_3,e34_103_2__rfunct_3,t2_rfinseq]), [interesting(0.65),file(rfunct_3,e36_103_2__rfunct_3),[file(rfunct_3,e36_103_2__rfunct_3)]]). fof(t15_rfinseq,theorem,( ! [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) ) => r1_rfinseq(k7_finseq_1(A,B),k7_finseq_1(B,A)) ) ) ), file(rfinseq,t15_rfinseq), [interesting(0.9),axiom,file(rfinseq,t15_rfinseq)]). fof(e26_103_2__rfunct_3,plain, ( r1_rfinseq(k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))),k12_finseq_1(k1_numbers,k2_seq_1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c5_103_2__rfunct_3)))),k8_finseq_1(k1_numbers,k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))),k12_finseq_1(k1_numbers,k2_seq_1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c5_103_2__rfunct_3))),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3))) & r1_rfinseq(k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c2_103_2__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c2_103_2__rfunct_3))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[reflexivity_r1_tarski,dt_k1_relat_1,dt_k5_ordinal2,dt_k7_relat_1,cc1_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc10_membered,fc11_membered,fc17_finseq_1,fc1_rfinseq,fc2_seq_1,fc5_membered,fc9_membered,rc1_nat_1,rc1_partfun1,rc2_finset_1,rc2_nat_1,rc2_xreal_0,rc3_finseq_1,rc3_nat_1,rc3_xreal_0,rc4_finseq_1,rc4_xreal_0,rc6_finseq_1,antisymmetry_r2_hidden,redefinition_k2_partfun1,redefinition_k4_relset_1,redefinition_k5_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_partfun1,dt_k2_zfmisc_1,dt_k4_relset_1,dt_k5_numbers,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_nat_1,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_nat_1,cc2_xreal_0,cc3_membered,cc6_membered,cc7_xreal_0,cc9_membered,fc14_finset_1,fc1_seq_1,fc2_finseq_1,fc39_membered,fc40_membered,fc41_membered,fc6_membered,fc7_membered,fc8_membered,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_finseq_1,rc3_finset_1,rc4_finset_1,t1_subset,t3_boole,t3_subset,t4_boole,t4_subset,t5_subset,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_relset_1,redefinition_m2_finseq_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_tarski,dt_k5_finseq_1,dt_k5_finsub_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_relset_1,dt_c4_103_2__rfunct_3,cc10_membered,cc11_membered,cc15_membered,cc1_finset_1,cc1_seq_1,cc4_membered,fc12_finseq_1,fc12_finset_1,fc13_finseq_1,fc14_finseq_1,fc1_finset_1,fc37_membered,fc38_membered,fc3_finseq_1,fc4_finseq_1,rc1_finset_1,rc1_rfinseq,rc2_partfun1,rc2_rfunct_3,rc7_finseq_1,rc8_finseq_1,t2_subset,t6_boole,t7_boole,t8_boole,symmetry_r1_rfinseq,reflexivity_r1_rfinseq,redefinition_k12_finseq_1,redefinition_k2_seq_1,redefinition_k2_setwiseo,redefinition_k8_finseq_1,dt_k12_finseq_1,dt_k1_numbers,dt_k22_rfunct_3,dt_k2_seq_1,dt_k2_setwiseo,dt_k4_xboole_0,dt_k7_finseq_1,dt_k8_finseq_1,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c5_103_2__rfunct_3,de_c5_103_2__rfunct_3,cc1_finseq_1,fc2_membered,rc1_finseq_1,t15_rfinseq]), [interesting(0.65),file(rfunct_3,e26_103_2__rfunct_3),[file(rfunct_3,e26_103_2__rfunct_3)]]). fof(e23_103_2__rfunct_3,plain,( r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c2_103_2__rfunct_3),k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c2_103_2__rfunct_3)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103__rfunct_3,dt_c1_103_2__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,e2_103_2__rfunct_3])],[reflexivity_r1_tarski,dt_k5_ordinal2,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,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,fc13_xreal_0,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc17_xreal_0,fc18_xreal_0,fc19_xreal_0,fc1_nat_1,fc1_xreal_0,fc20_xreal_0,fc27_xreal_0,fc28_xreal_0,fc29_xreal_0,fc2_seq_1,fc30_xreal_0,fc3_nat_1,fc3_xreal_0,fc4_nat_1,fc5_membered,fc5_xreal_0,fc6_xreal_0,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,rc1_nat_1,rc1_seq_1,rc1_xreal_0,rc2_finset_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,commutativity_k2_xcmplx_0,antisymmetry_r2_hidden,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k5_numbers,dt_k7_relat_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_subset_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_relset_1,cc1_seq_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_nat_1,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc14_finset_1,fc17_finseq_1,fc1_rfinseq,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,rc1_finseq_1,rc1_membered,rc1_partfun1,rc1_rfinseq,rc2_finseq_1,rc2_partfun1,rc2_rfunct_3,rc3_finseq_1,rc3_finset_1,rc4_finseq_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_rm1_r0,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,rqRealAdd__k2_xcmplx_0__rm1_r1_r0,spc1_arithm,spc6_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_numerals,t1_subset,t2_subset,t3_subset,t4_arithm,t4_subset,t5_arithm,t5_subset,t6_arithm,commutativity_k1_nat_1,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k3_xboole_0,idempotence_k3_xboole_0,involutiveness_k4_xcmplx_0,symmetry_r1_rfinseq,reflexivity_r1_rfinseq,existence_m2_finseq_1,existence_m2_relset_1,redefinition_k1_nat_1,redefinition_k2_partfun1,redefinition_k4_card_1,redefinition_k4_relset_1,redefinition_m2_finseq_1,redefinition_m2_relset_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_xboole_0,dt_k22_rfunct_3,dt_k2_partfun1,dt_k2_xboole_0,dt_k3_xboole_0,dt_k4_card_1,dt_k4_relset_1,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_k7_xcmplx_0,dt_m2_finseq_1,dt_m2_relset_1,dt_c1_103__rfunct_3,dt_c1_103_2__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,cc15_membered,cc1_finset_1,fc10_finset_1,fc11_finset_1,fc2_finseq_1,fc2_membered,fc6_membered,fc9_finset_1,rc1_finset_1,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealDiv__k7_xcmplx_0__r0_r1_r0,rqRealDiv__k7_xcmplx_0__r1_r1_r1,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1,rqRealNeg__k4_xcmplx_0__r0_r0,spc0_boole,spc1_boole,t1_boole,t2_boole,t6_boole,t7_boole,t8_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e2_103_2__rfunct_3,d14_rfunct_3,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealDiff__k6_xcmplx_0__r1_r1_r0]), [interesting(0.65),file(rfunct_3,e23_103_2__rfunct_3),[file(rfunct_3,e23_103_2__rfunct_3)]]). fof(e22_103_2__rfunct_3,plain,( r1_rfinseq(k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))),k12_finseq_1(k1_numbers,k2_seq_1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c5_103_2__rfunct_3))),k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c2_103_2__rfunct_3)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[reflexivity_r1_tarski,dt_k5_ordinal2,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc10_membered,fc10_xreal_0,fc11_membered,fc11_xreal_0,fc12_xreal_0,fc13_xreal_0,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc17_xreal_0,fc18_xreal_0,fc19_xreal_0,fc1_nat_1,fc1_seq_1,fc1_xreal_0,fc20_xreal_0,fc27_xreal_0,fc28_xreal_0,fc29_xreal_0,fc2_seq_1,fc30_xreal_0,fc3_nat_1,fc3_xreal_0,fc4_nat_1,fc5_membered,fc5_xreal_0,fc6_xreal_0,fc7_xreal_0,fc8_membered,fc8_xreal_0,fc9_membered,fc9_xreal_0,rc1_nat_1,rc1_seq_1,rc1_xreal_0,rc2_finset_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,commutativity_k2_xcmplx_0,existence_m1_finseq_1,existence_m1_relset_1,existence_m2_finseq_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k5_finseq_1,dt_k5_finsub_1,dt_k5_numbers,dt_k7_finseq_1,dt_k7_relat_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m2_finseq_1,dt_m2_subset_1,dt_c4_103_2__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_relset_1,cc1_seq_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_nat_1,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc14_finset_1,fc17_finseq_1,fc1_finset_1,fc1_rfinseq,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc37_membered,fc38_membered,fc39_membered,fc3_finseq_1,fc40_membered,fc41_membered,fc4_finseq_1,fc7_membered,rc1_finseq_1,rc1_membered,rc1_partfun1,rc1_rfinseq,rc2_finseq_1,rc2_partfun1,rc2_rfunct_3,rc3_finseq_1,rc3_finset_1,rc4_finseq_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_rm1_r0,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,rqRealAdd__k2_xcmplx_0__rm1_r1_r0,spc1_arithm,spc6_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_numerals,t3_subset,t4_arithm,t4_subset,t5_arithm,t5_subset,t6_arithm,commutativity_k1_nat_1,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k3_xboole_0,idempotence_k3_xboole_0,involutiveness_k4_xcmplx_0,symmetry_r1_rfinseq,reflexivity_r1_rfinseq,antisymmetry_r2_hidden,existence_m1_subset_1,existence_m2_relset_1,redefinition_k12_finseq_1,redefinition_k1_nat_1,redefinition_k2_partfun1,redefinition_k2_seq_1,redefinition_k2_setwiseo,redefinition_k4_card_1,redefinition_k4_relset_1,redefinition_k8_finseq_1,redefinition_m2_relset_1,dt_k12_finseq_1,dt_k1_card_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_xboole_0,dt_k22_rfunct_3,dt_k2_partfun1,dt_k2_seq_1,dt_k2_setwiseo,dt_k2_xboole_0,dt_k3_xboole_0,dt_k4_card_1,dt_k4_relset_1,dt_k4_xboole_0,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_k7_xcmplx_0,dt_k8_finseq_1,dt_m1_subset_1,dt_m2_relset_1,dt_c1_103__rfunct_3,dt_c1_103_2__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c5_103_2__rfunct_3,de_c5_103_2__rfunct_3,cc15_membered,cc1_finset_1,fc10_finset_1,fc11_finset_1,fc12_finset_1,fc2_finseq_1,fc2_membered,fc6_membered,fc9_finset_1,rc1_finset_1,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealDiv__k7_xcmplx_0__r0_r1_r0,rqRealDiv__k7_xcmplx_0__r1_r1_r1,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1,rqRealNeg__k4_xcmplx_0__r0_r0,spc0_boole,spc1_boole,t1_boole,t1_subset,t2_boole,t2_subset,t3_boole,t4_boole,t6_boole,t7_boole,t8_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e2_103_2__rfunct_3,t69_rfunct_3,t47_card_1,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealDiff__k6_xcmplx_0__r1_r1_r0]), [interesting(0.65),file(rfunct_3,e22_103_2__rfunct_3),[file(rfunct_3,e22_103_2__rfunct_3)]]). fof(e24_103_2__rfunct_3,plain,( r1_rfinseq(k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))),k12_finseq_1(k1_numbers,k2_seq_1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c5_103_2__rfunct_3))),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c2_103_2__rfunct_3)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[reflexivity_r1_tarski,dt_k1_relat_1,dt_k5_ordinal2,cc1_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc10_membered,fc11_membered,fc17_finseq_1,fc5_membered,fc9_membered,rc1_nat_1,rc1_partfun1,rc2_finset_1,rc2_nat_1,rc2_xreal_0,rc3_finseq_1,rc3_nat_1,rc3_xreal_0,rc4_finseq_1,rc4_xreal_0,rc6_finseq_1,antisymmetry_r2_hidden,redefinition_k4_relset_1,redefinition_k5_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k4_relset_1,dt_k5_numbers,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finseq_1,cc1_membered,cc1_nat_1,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_nat_1,cc2_xreal_0,cc3_membered,cc6_membered,cc7_xreal_0,cc9_membered,fc12_finset_1,fc13_finseq_1,fc14_finseq_1,fc14_finset_1,fc1_rfinseq,fc1_seq_1,fc2_finseq_1,fc2_seq_1,fc39_membered,fc40_membered,fc41_membered,fc6_membered,fc7_membered,fc8_membered,rc1_finseq_1,rc1_finset_1,rc1_membered,rc1_rfinseq,rc1_seq_1,rc1_xreal_0,rc2_finseq_1,rc2_rfunct_3,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t1_subset,t3_boole,t3_subset,t4_boole,t4_subset,t5_subset,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_relset_1,redefinition_m2_finseq_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_tarski,dt_k5_finseq_1,dt_k5_finsub_1,dt_k7_finseq_1,dt_k7_relat_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_relset_1,dt_c4_103_2__rfunct_3,cc10_membered,cc11_membered,cc15_membered,cc1_finset_1,cc1_seq_1,cc4_membered,fc12_finseq_1,fc1_finset_1,fc37_membered,fc38_membered,fc3_finseq_1,fc4_finseq_1,rc2_partfun1,t2_subset,t6_boole,t7_boole,t8_boole,symmetry_r1_rfinseq,reflexivity_r1_rfinseq,redefinition_k12_finseq_1,redefinition_k2_partfun1,redefinition_k2_seq_1,redefinition_k2_setwiseo,redefinition_k8_finseq_1,dt_k12_finseq_1,dt_k1_numbers,dt_k22_rfunct_3,dt_k2_partfun1,dt_k2_seq_1,dt_k2_setwiseo,dt_k4_xboole_0,dt_k8_finseq_1,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c5_103_2__rfunct_3,de_c5_103_2__rfunct_3,fc2_membered,e23_103_2__rfunct_3,e22_103_2__rfunct_3,t2_rfinseq]), [interesting(0.65),file(rfunct_3,e24_103_2__rfunct_3),[file(rfunct_3,e24_103_2__rfunct_3)]]). fof(t14_rfinseq,theorem,( ! [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] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( r1_rfinseq(A,B) <=> r1_rfinseq(k7_finseq_1(A,C),k7_finseq_1(B,C)) ) ) ) ) ), file(rfinseq,t14_rfinseq), [interesting(0.9),axiom,file(rfinseq,t14_rfinseq)]). fof(e25_103_2__rfunct_3,plain,( r1_rfinseq(k8_finseq_1(k1_numbers,k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))),k12_finseq_1(k1_numbers,k2_seq_1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c5_103_2__rfunct_3))),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c2_103_2__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[reflexivity_r1_tarski,dt_k1_relat_1,dt_k5_ordinal2,dt_k7_relat_1,cc1_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc10_membered,fc11_membered,fc17_finseq_1,fc1_rfinseq,fc2_seq_1,fc5_membered,fc9_membered,rc1_nat_1,rc1_partfun1,rc2_finset_1,rc2_nat_1,rc2_xreal_0,rc3_finseq_1,rc3_nat_1,rc3_xreal_0,rc4_finseq_1,rc4_xreal_0,rc6_finseq_1,antisymmetry_r2_hidden,redefinition_k2_partfun1,redefinition_k4_relset_1,redefinition_k5_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_partfun1,dt_k2_zfmisc_1,dt_k4_relset_1,dt_k5_numbers,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_nat_1,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_nat_1,cc2_xreal_0,cc3_membered,cc6_membered,cc7_xreal_0,cc9_membered,fc14_finset_1,fc1_seq_1,fc2_finseq_1,fc39_membered,fc40_membered,fc41_membered,fc6_membered,fc7_membered,fc8_membered,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_finseq_1,rc3_finset_1,rc4_finset_1,t1_subset,t3_boole,t3_subset,t4_boole,t4_subset,t5_subset,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_relset_1,redefinition_m2_finseq_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_tarski,dt_k5_finseq_1,dt_k5_finsub_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_relset_1,dt_c4_103_2__rfunct_3,cc10_membered,cc11_membered,cc15_membered,cc1_finset_1,cc1_seq_1,cc4_membered,fc12_finseq_1,fc12_finset_1,fc13_finseq_1,fc14_finseq_1,fc1_finset_1,fc37_membered,fc38_membered,fc3_finseq_1,fc4_finseq_1,rc1_finset_1,rc1_rfinseq,rc2_partfun1,rc2_rfunct_3,rc7_finseq_1,rc8_finseq_1,t2_subset,t6_boole,t7_boole,t8_boole,symmetry_r1_rfinseq,reflexivity_r1_rfinseq,redefinition_k12_finseq_1,redefinition_k2_seq_1,redefinition_k2_setwiseo,redefinition_k8_finseq_1,dt_k12_finseq_1,dt_k1_numbers,dt_k22_rfunct_3,dt_k2_seq_1,dt_k2_setwiseo,dt_k4_xboole_0,dt_k7_finseq_1,dt_k8_finseq_1,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c5_103_2__rfunct_3,de_c5_103_2__rfunct_3,cc1_finseq_1,fc2_membered,rc1_finseq_1,e24_103_2__rfunct_3,t14_rfinseq]), [interesting(0.65),file(rfunct_3,e25_103_2__rfunct_3),[file(rfunct_3,e25_103_2__rfunct_3)]]). fof(e27_103_2__rfunct_3,plain,( r1_rfinseq(k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))),k12_finseq_1(k1_numbers,k2_seq_1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c5_103_2__rfunct_3)))),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c2_103_2__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[reflexivity_r1_tarski,dt_k1_relat_1,dt_k5_ordinal2,dt_k7_relat_1,cc1_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc10_membered,fc11_membered,fc17_finseq_1,fc1_rfinseq,fc2_seq_1,fc5_membered,fc9_membered,rc1_nat_1,rc1_partfun1,rc2_finset_1,rc2_nat_1,rc2_xreal_0,rc3_finseq_1,rc3_nat_1,rc3_xreal_0,rc4_finseq_1,rc4_xreal_0,rc6_finseq_1,antisymmetry_r2_hidden,redefinition_k2_partfun1,redefinition_k4_relset_1,redefinition_k5_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_partfun1,dt_k2_zfmisc_1,dt_k4_relset_1,dt_k5_numbers,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finseq_1,cc1_membered,cc1_nat_1,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_nat_1,cc2_xreal_0,cc3_membered,cc6_membered,cc7_xreal_0,cc9_membered,fc12_finset_1,fc13_finseq_1,fc14_finseq_1,fc14_finset_1,fc1_seq_1,fc2_finseq_1,fc39_membered,fc40_membered,fc41_membered,fc6_membered,fc7_membered,fc8_membered,rc1_finseq_1,rc1_finset_1,rc1_membered,rc1_rfinseq,rc1_seq_1,rc1_xreal_0,rc2_finseq_1,rc2_rfunct_3,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t1_subset,t3_boole,t3_subset,t4_boole,t4_subset,t5_subset,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_relset_1,redefinition_m2_finseq_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_tarski,dt_k5_finseq_1,dt_k5_finsub_1,dt_k7_finseq_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_relset_1,dt_c4_103_2__rfunct_3,cc10_membered,cc11_membered,cc15_membered,cc1_finset_1,cc1_seq_1,cc4_membered,fc12_finseq_1,fc1_finset_1,fc37_membered,fc38_membered,fc3_finseq_1,fc4_finseq_1,rc2_partfun1,t2_subset,t6_boole,t7_boole,t8_boole,symmetry_r1_rfinseq,reflexivity_r1_rfinseq,redefinition_k12_finseq_1,redefinition_k2_seq_1,redefinition_k2_setwiseo,redefinition_k8_finseq_1,dt_k12_finseq_1,dt_k1_numbers,dt_k22_rfunct_3,dt_k2_seq_1,dt_k2_setwiseo,dt_k4_xboole_0,dt_k8_finseq_1,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c5_103_2__rfunct_3,de_c5_103_2__rfunct_3,fc2_membered,e26_103_2__rfunct_3,e25_103_2__rfunct_3,t2_rfinseq]), [interesting(0.65),file(rfunct_3,e27_103_2__rfunct_3),[file(rfunct_3,e27_103_2__rfunct_3)]]). fof(e28_103_2__rfunct_3,plain,( r1_rfinseq(k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))),k12_finseq_1(k1_numbers,k2_seq_1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c5_103_2__rfunct_3)))),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c2_103_2__rfunct_3))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[reflexivity_r1_tarski,dt_k1_relat_1,dt_k5_ordinal2,dt_k7_relat_1,cc1_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc10_membered,fc11_membered,fc17_finseq_1,fc1_rfinseq,fc2_seq_1,fc5_membered,fc9_membered,rc1_nat_1,rc1_partfun1,rc2_finset_1,rc2_nat_1,rc2_xreal_0,rc3_finseq_1,rc3_nat_1,rc3_xreal_0,rc4_finseq_1,rc4_xreal_0,rc6_finseq_1,antisymmetry_r2_hidden,redefinition_k2_partfun1,redefinition_k4_relset_1,redefinition_k5_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_partfun1,dt_k2_zfmisc_1,dt_k4_relset_1,dt_k5_numbers,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finseq_1,cc1_membered,cc1_nat_1,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_nat_1,cc2_xreal_0,cc3_membered,cc6_membered,cc7_xreal_0,cc9_membered,fc12_finset_1,fc13_finseq_1,fc14_finseq_1,fc14_finset_1,fc1_seq_1,fc2_finseq_1,fc39_membered,fc40_membered,fc41_membered,fc6_membered,fc7_membered,fc8_membered,rc1_finseq_1,rc1_finset_1,rc1_membered,rc1_rfinseq,rc1_seq_1,rc1_xreal_0,rc2_finseq_1,rc2_rfunct_3,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t1_subset,t3_boole,t3_subset,t4_boole,t4_subset,t5_subset,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_relset_1,redefinition_m2_finseq_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_tarski,dt_k5_finseq_1,dt_k5_finsub_1,dt_k7_finseq_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_relset_1,dt_c4_103_2__rfunct_3,cc10_membered,cc11_membered,cc15_membered,cc1_finset_1,cc1_seq_1,cc4_membered,fc12_finseq_1,fc1_finset_1,fc37_membered,fc38_membered,fc3_finseq_1,fc4_finseq_1,rc2_partfun1,t2_subset,t6_boole,t7_boole,t8_boole,symmetry_r1_rfinseq,reflexivity_r1_rfinseq,redefinition_k12_finseq_1,redefinition_k2_seq_1,redefinition_k2_setwiseo,redefinition_k8_finseq_1,dt_k12_finseq_1,dt_k1_numbers,dt_k22_rfunct_3,dt_k2_seq_1,dt_k2_setwiseo,dt_k4_xboole_0,dt_k8_finseq_1,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c5_103_2__rfunct_3,de_c5_103_2__rfunct_3,fc2_membered,e27_103_2__rfunct_3,e26_103_2__rfunct_3,t2_rfinseq]), [interesting(0.65),file(rfunct_3,e28_103_2__rfunct_3),[file(rfunct_3,e28_103_2__rfunct_3)]]). fof(de_c7_103_2__rfunct_3,definition,( c7_103_2__rfunct_3 = k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3)))) ), introduced(definition,[new_symbol(c7_103_2__rfunct_3),file(rfunct_3,c7_103_2__rfunct_3)]), [interesting(0.65),axiom,file(rfunct_3,c7_103_2__rfunct_3)]). fof(d10_xboole_0,definition,( ! [A,B] : ( A = B <=> ( r1_tarski(A,B) & r1_tarski(B,A) ) ) ), file(xboole_0,d10_xboole_0), [interesting(0.9),axiom,file(xboole_0,d10_xboole_0)]). fof(dt_c1_103_2_2_1__rfunct_3,assumption,( $true ), introduced(assumption,[file(rfunct_3,c1_103_2_2_1__rfunct_3)]), [interesting(0.35),axiom,file(rfunct_3,c1_103_2_2_1__rfunct_3)]). fof(dh_c1_103_2_2_1__rfunct_3,definition, ( ~ ( r2_hidden(c1_103_2_2_1__rfunct_3,k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))))) & ~ r2_hidden(c1_103_2_2_1__rfunct_3,k4_xboole_0(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c2_103_2__rfunct_3)),k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))) ) => ! [A] : ~ ( r2_hidden(A,k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))))) & ~ r2_hidden(A,k4_xboole_0(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c2_103_2__rfunct_3)),k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))) ) ), introduced(definition,[new_symbol(c1_103_2_2_1__rfunct_3),file(rfunct_3,c1_103_2_2_1__rfunct_3)]), [interesting(0.35),axiom,file(rfunct_3,c1_103_2_2_1__rfunct_3)]). fof(e1_103_2_2_1__rfunct_3,assumption,( r2_hidden(c1_103_2_2_1__rfunct_3,k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))))) ), introduced(assumption,[file(rfunct_3,e1_103_2_2_1__rfunct_3)]), [interesting(0.35),axiom,file(rfunct_3,e1_103_2_2_1__rfunct_3)]). fof(e2_103_2_2_1__rfunct_3,plain, ( r2_hidden(c1_103_2_2_1__rfunct_3,k4_relset_1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3)) & r2_hidden(c1_103_2_2_1__rfunct_3,k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103_2_2_1__rfunct_3,e1_103_2_2_1__rfunct_3,dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[cc1_finseq_1,cc1_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc10_membered,fc11_membered,fc9_membered,rc1_finseq_1,rc1_nat_1,rc1_partfun1,rc2_xreal_0,rc3_finseq_1,rc3_xreal_0,rc4_xreal_0,rc6_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc10_finset_1,fc11_finset_1,fc12_finset_1,fc14_finset_1,fc17_finseq_1,fc1_rfinseq,fc2_finseq_1,fc2_seq_1,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc39_membered,fc40_membered,fc41_membered,fc6_membered,fc7_membered,fc8_membered,rc1_finset_1,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_partfun1,rc2_rfunct_3,rc3_finset_1,rc4_finset_1,rc7_finseq_1,t2_boole,t3_boole,t4_boole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k5_finsub_1,dt_k7_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_c4_103_2__rfunct_3,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_seq_1,cc4_membered,cc6_membered,fc1_finset_1,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc37_membered,fc38_membered,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,redefinition_k2_partfun1,redefinition_k2_setwiseo,redefinition_k4_relset_1,dt_k1_numbers,dt_k2_partfun1,dt_k2_setwiseo,dt_k3_xboole_0,dt_k4_relset_1,dt_k4_xboole_0,dt_c1_103__rfunct_3,dt_c1_103_2_2_1__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c5_103_2__rfunct_3,de_c5_103_2__rfunct_3,fc2_membered,t1_subset,t7_boole,e1_103_2_2_1__rfunct_3,e15_103_2__rfunct_3,d3_xboole_0]), [interesting(0.35),file(rfunct_3,e2_103_2_2_1__rfunct_3),[file(rfunct_3,e2_103_2_2_1__rfunct_3)]]). fof(d4_xboole_0,definition,( ! [A,B,C] : ( C = k4_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) & ~ r2_hidden(D,B) ) ) ) ), file(xboole_0,d4_xboole_0), [interesting(0.9),axiom,file(xboole_0,d4_xboole_0)]). fof(e3_103_2_2_1__rfunct_3,plain, ( r2_hidden(c1_103_2_2_1__rfunct_3,c2_103_2__rfunct_3) & ~ r2_hidden(c1_103_2_2_1__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103_2_2_1__rfunct_3,e1_103_2_2_1__rfunct_3,dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[dt_k7_relat_1,cc1_finseq_1,cc1_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc10_membered,fc11_membered,fc1_rfinseq,fc2_seq_1,fc9_membered,rc1_finseq_1,rc1_nat_1,rc1_partfun1,rc2_xreal_0,rc3_finseq_1,rc3_xreal_0,rc4_xreal_0,rc6_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,redefinition_k2_partfun1,dt_k1_xboole_0,dt_k2_partfun1,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc12_finset_1,fc14_finset_1,fc17_finseq_1,fc2_finseq_1,fc39_membered,fc40_membered,fc41_membered,fc6_membered,fc7_membered,fc8_membered,rc1_finset_1,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_partfun1,rc2_rfunct_3,rc3_finset_1,rc4_finset_1,rc7_finseq_1,t3_boole,t4_boole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k5_finsub_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_c4_103_2__rfunct_3,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_seq_1,cc4_membered,cc6_membered,fc1_finset_1,fc37_membered,fc38_membered,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k2_setwiseo,redefinition_k4_relset_1,dt_k1_numbers,dt_k2_setwiseo,dt_k4_relset_1,dt_k4_xboole_0,dt_c1_103__rfunct_3,dt_c1_103_2_2_1__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c5_103_2__rfunct_3,de_c5_103_2__rfunct_3,fc2_membered,t1_subset,t7_boole,e2_103_2_2_1__rfunct_3,d4_xboole_0]), [interesting(0.35),file(rfunct_3,e3_103_2_2_1__rfunct_3),[file(rfunct_3,e3_103_2_2_1__rfunct_3)]]). fof(e4_103_2_2_1__rfunct_3,plain,( r2_hidden(c1_103_2_2_1__rfunct_3,k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c2_103_2__rfunct_3))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103_2_2_1__rfunct_3,e1_103_2_2_1__rfunct_3,dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[cc1_finseq_1,cc1_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc10_membered,fc11_membered,fc9_membered,rc1_finseq_1,rc1_nat_1,rc1_partfun1,rc2_xreal_0,rc3_finseq_1,rc3_xreal_0,rc4_xreal_0,rc6_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc10_finset_1,fc11_finset_1,fc12_finset_1,fc14_finset_1,fc17_finseq_1,fc1_rfinseq,fc2_finseq_1,fc2_seq_1,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc39_membered,fc40_membered,fc41_membered,fc6_membered,fc7_membered,fc8_membered,rc1_finset_1,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_partfun1,rc2_rfunct_3,rc3_finset_1,rc4_finset_1,rc7_finseq_1,t2_boole,t3_boole,t4_boole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k5_finsub_1,dt_k7_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_c4_103_2__rfunct_3,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_seq_1,cc4_membered,cc6_membered,fc1_finset_1,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc37_membered,fc38_membered,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,redefinition_k2_partfun1,redefinition_k2_setwiseo,redefinition_k4_relset_1,dt_k1_numbers,dt_k2_partfun1,dt_k2_setwiseo,dt_k3_xboole_0,dt_k4_relset_1,dt_k4_xboole_0,dt_c1_103__rfunct_3,dt_c1_103_2_2_1__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c5_103_2__rfunct_3,de_c5_103_2__rfunct_3,fc2_membered,t1_subset,t7_boole,e3_103_2_2_1__rfunct_3,e15_103_2__rfunct_3,e2_103_2_2_1__rfunct_3,d3_xboole_0]), [interesting(0.35),file(rfunct_3,e4_103_2_2_1__rfunct_3),[file(rfunct_3,e4_103_2_2_1__rfunct_3)]]). fof(e5_103_2_2_1__rfunct_3,plain,( r2_hidden(c1_103_2_2_1__rfunct_3,k4_xboole_0(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c2_103_2__rfunct_3)),k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103_2_2_1__rfunct_3,e1_103_2_2_1__rfunct_3,dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[cc1_finseq_1,cc1_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc10_membered,fc11_membered,fc9_membered,rc1_finseq_1,rc1_nat_1,rc1_partfun1,rc2_xreal_0,rc3_finseq_1,rc3_xreal_0,rc4_xreal_0,rc6_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc12_finset_1,fc14_finset_1,fc17_finseq_1,fc1_rfinseq,fc2_finseq_1,fc2_seq_1,fc39_membered,fc40_membered,fc41_membered,fc6_membered,fc7_membered,fc8_membered,rc1_finset_1,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_partfun1,rc2_rfunct_3,rc3_finset_1,rc4_finset_1,rc7_finseq_1,t3_boole,t4_boole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k5_finsub_1,dt_k7_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_c4_103_2__rfunct_3,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_seq_1,cc4_membered,cc6_membered,fc1_finset_1,fc37_membered,fc38_membered,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k2_partfun1,redefinition_k2_setwiseo,redefinition_k4_relset_1,dt_k1_numbers,dt_k2_partfun1,dt_k2_setwiseo,dt_k4_relset_1,dt_k4_xboole_0,dt_c1_103__rfunct_3,dt_c1_103_2_2_1__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c5_103_2__rfunct_3,de_c5_103_2__rfunct_3,fc2_membered,t1_subset,t7_boole,e4_103_2_2_1__rfunct_3,e3_103_2_2_1__rfunct_3,d4_xboole_0]), [interesting(0.35),file(rfunct_3,e5_103_2_2_1__rfunct_3),[file(rfunct_3,e5_103_2_2_1__rfunct_3)]]). fof(i3_103_2_2_1__rfunct_3,theorem,( $true ), introduced(tautology,[file(rfunct_3,i3_103_2_2_1__rfunct_3)]), [interesting(0.35),trivial,file(rfunct_3,i3_103_2_2_1__rfunct_3)]). fof(i2_103_2_2_1__rfunct_3,plain,( r2_hidden(c1_103_2_2_1__rfunct_3,k4_xboole_0(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c2_103_2__rfunct_3)),k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))) ), inference(conclusion,[status(thm),assumptions([dt_c1_103_2_2_1__rfunct_3,e1_103_2_2_1__rfunct_3,dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[e5_103_2_2_1__rfunct_3,i3_103_2_2_1__rfunct_3]), [interesting(0.35),file(rfunct_3,i2_103_2_2_1__rfunct_3),[file(rfunct_3,i2_103_2_2_1__rfunct_3)]]). fof(i1_103_2_2_1__rfunct_3,plain,( ~ ( r2_hidden(c1_103_2_2_1__rfunct_3,k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))))) & ~ r2_hidden(c1_103_2_2_1__rfunct_3,k4_xboole_0(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c2_103_2__rfunct_3)),k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_103_2_2_1__rfunct_3,dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3]),discharge_asm(discharge,[e1_103_2_2_1__rfunct_3])],[e1_103_2_2_1__rfunct_3,i2_103_2_2_1__rfunct_3]), [interesting(0.35),file(rfunct_3,i1_103_2_2_1__rfunct_3),[file(rfunct_3,i1_103_2_2_1__rfunct_3)]]). fof(i1_103_2_2_1_tmp__rfunct_3,plain,( ~ ( r2_hidden(c1_103_2_2_1__rfunct_3,k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))))) & ~ r2_hidden(c1_103_2_2_1__rfunct_3,k4_xboole_0(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c2_103_2__rfunct_3)),k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3]),discharge_asm(discharge,[dt_c1_103_2_2_1__rfunct_3])],[dt_c1_103_2_2_1__rfunct_3,i1_103_2_2_1__rfunct_3]), [interesting(0.5),e1_103_2_2__rfunct_3]). fof(e1_103_2_2__rfunct_3,plain,( r1_tarski(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3)))),k4_xboole_0(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c2_103_2__rfunct_3)),k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))) ), inference(let,[status(thm),assumptions([dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[i1_103_2_2_1_tmp__rfunct_3,cc1_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc10_membered,fc11_membered,fc9_membered,rc1_nat_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc12_finset_1,fc14_finset_1,fc17_finseq_1,fc1_rfinseq,fc2_seq_1,fc39_membered,fc40_membered,fc41_membered,fc7_membered,fc8_membered,rc1_finset_1,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_partfun1,rc2_rfunct_3,rc3_finset_1,rc4_finset_1,rc7_finseq_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k5_finsub_1,dt_k7_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_seq_1,cc4_membered,cc6_membered,fc1_finset_1,fc37_membered,fc38_membered,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k2_partfun1,redefinition_k2_setwiseo,redefinition_k4_relset_1,dt_k1_numbers,dt_k2_partfun1,dt_k2_setwiseo,dt_k4_relset_1,dt_k4_xboole_0,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c5_103_2__rfunct_3,fc2_membered,d3_tarski,dh_c1_103_2_2_1__rfunct_3]), [interesting(0.5),file(rfunct_3,e1_103_2_2__rfunct_3),[file(rfunct_3,e1_103_2_2__rfunct_3)]]). fof(dt_c1_103_2_2__rfunct_3,assumption,( $true ), introduced(assumption,[file(rfunct_3,c1_103_2_2__rfunct_3)]), [interesting(0.5),axiom,file(rfunct_3,c1_103_2_2__rfunct_3)]). fof(dh_c1_103_2_2__rfunct_3,definition, ( ~ ( r2_hidden(c1_103_2_2__rfunct_3,k4_xboole_0(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c2_103_2__rfunct_3)),k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))) & ~ r2_hidden(c1_103_2_2__rfunct_3,k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))))) ) => ! [A] : ~ ( r2_hidden(A,k4_xboole_0(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c2_103_2__rfunct_3)),k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))) & ~ r2_hidden(A,k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))))) ) ), introduced(definition,[new_symbol(c1_103_2_2__rfunct_3),file(rfunct_3,c1_103_2_2__rfunct_3)]), [interesting(0.5),axiom,file(rfunct_3,c1_103_2_2__rfunct_3)]). fof(e2_103_2_2__rfunct_3,assumption,( r2_hidden(c1_103_2_2__rfunct_3,k4_xboole_0(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c2_103_2__rfunct_3)),k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))) ), introduced(assumption,[file(rfunct_3,e2_103_2_2__rfunct_3)]), [interesting(0.5),axiom,file(rfunct_3,e2_103_2_2__rfunct_3)]). fof(e3_103_2_2__rfunct_3,plain, ( r2_hidden(c1_103_2_2__rfunct_3,k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c2_103_2__rfunct_3))) & ~ r2_hidden(c1_103_2_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103_2_2__rfunct_3,dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3,e2_103_2_2__rfunct_3])],[cc1_finseq_1,cc1_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc10_membered,fc11_membered,fc9_membered,rc1_finseq_1,rc1_nat_1,rc1_partfun1,rc2_xreal_0,rc3_finseq_1,rc3_xreal_0,rc4_xreal_0,rc6_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc12_finset_1,fc14_finset_1,fc17_finseq_1,fc1_rfinseq,fc2_finseq_1,fc2_seq_1,fc39_membered,fc40_membered,fc41_membered,fc6_membered,fc7_membered,fc8_membered,rc1_finset_1,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_partfun1,rc2_rfunct_3,rc3_finset_1,rc4_finset_1,rc7_finseq_1,t3_boole,t4_boole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k5_finsub_1,dt_k7_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_c4_103_2__rfunct_3,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_seq_1,cc4_membered,cc6_membered,fc1_finset_1,fc37_membered,fc38_membered,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k2_partfun1,redefinition_k2_setwiseo,redefinition_k4_relset_1,dt_k1_numbers,dt_k2_partfun1,dt_k2_setwiseo,dt_k4_relset_1,dt_k4_xboole_0,dt_c1_103__rfunct_3,dt_c1_103_2_2__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c5_103_2__rfunct_3,de_c5_103_2__rfunct_3,fc2_membered,t1_subset,t7_boole,e2_103_2_2__rfunct_3,d4_xboole_0]), [interesting(0.5),file(rfunct_3,e3_103_2_2__rfunct_3),[file(rfunct_3,e3_103_2_2__rfunct_3)]]). fof(e4_103_2_2__rfunct_3,plain, ( r2_hidden(c1_103_2_2__rfunct_3,k4_relset_1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3)) & r2_hidden(c1_103_2_2__rfunct_3,c2_103_2__rfunct_3) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103_2_2__rfunct_3,e2_103_2_2__rfunct_3,dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[cc1_finseq_1,cc1_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc10_membered,fc11_membered,fc9_membered,rc1_finseq_1,rc1_nat_1,rc1_partfun1,rc2_xreal_0,rc3_finseq_1,rc3_xreal_0,rc4_xreal_0,rc6_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc10_finset_1,fc11_finset_1,fc12_finset_1,fc14_finset_1,fc17_finseq_1,fc1_rfinseq,fc2_finseq_1,fc2_seq_1,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc39_membered,fc40_membered,fc41_membered,fc6_membered,fc7_membered,fc8_membered,rc1_finset_1,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_partfun1,rc2_rfunct_3,rc3_finset_1,rc4_finset_1,rc7_finseq_1,t2_boole,t3_boole,t4_boole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k5_finsub_1,dt_k7_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_c4_103_2__rfunct_3,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_seq_1,cc4_membered,cc6_membered,fc1_finset_1,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc37_membered,fc38_membered,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,redefinition_k2_partfun1,redefinition_k2_setwiseo,redefinition_k4_relset_1,dt_k1_numbers,dt_k2_partfun1,dt_k2_setwiseo,dt_k3_xboole_0,dt_k4_relset_1,dt_k4_xboole_0,dt_c1_103__rfunct_3,dt_c1_103_2_2__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c5_103_2__rfunct_3,de_c5_103_2__rfunct_3,fc2_membered,t1_subset,t7_boole,e3_103_2_2__rfunct_3,e15_103_2__rfunct_3,d3_xboole_0]), [interesting(0.5),file(rfunct_3,e4_103_2_2__rfunct_3),[file(rfunct_3,e4_103_2_2__rfunct_3)]]). fof(e5_103_2_2__rfunct_3,plain,( r2_hidden(c1_103_2_2__rfunct_3,k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103_2_2__rfunct_3,dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3,e2_103_2_2__rfunct_3])],[cc1_finseq_1,cc1_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc10_membered,fc11_membered,fc9_membered,rc1_finseq_1,rc1_nat_1,rc1_partfun1,rc2_xreal_0,rc3_finseq_1,rc3_xreal_0,rc4_xreal_0,rc6_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc12_finset_1,fc14_finset_1,fc17_finseq_1,fc1_rfinseq,fc2_finseq_1,fc2_seq_1,fc39_membered,fc40_membered,fc41_membered,fc6_membered,fc7_membered,fc8_membered,rc1_finset_1,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_partfun1,rc2_rfunct_3,rc3_finset_1,rc4_finset_1,rc7_finseq_1,t3_boole,t4_boole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k5_finsub_1,dt_k7_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_c4_103_2__rfunct_3,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_seq_1,cc4_membered,cc6_membered,fc1_finset_1,fc37_membered,fc38_membered,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k2_partfun1,redefinition_k2_setwiseo,redefinition_k4_relset_1,dt_k1_numbers,dt_k2_partfun1,dt_k2_setwiseo,dt_k4_relset_1,dt_k4_xboole_0,dt_c1_103__rfunct_3,dt_c1_103_2_2__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c5_103_2__rfunct_3,de_c5_103_2__rfunct_3,fc2_membered,t1_subset,t7_boole,e4_103_2_2__rfunct_3,e3_103_2_2__rfunct_3,d4_xboole_0]), [interesting(0.5),file(rfunct_3,e5_103_2_2__rfunct_3),[file(rfunct_3,e5_103_2_2__rfunct_3)]]). fof(e6_103_2_2__rfunct_3,plain,( r2_hidden(c1_103_2_2__rfunct_3,k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103_2_2__rfunct_3,e2_103_2_2__rfunct_3,dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[cc1_finseq_1,cc1_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc10_membered,fc11_membered,fc9_membered,rc1_finseq_1,rc1_nat_1,rc1_partfun1,rc2_xreal_0,rc3_finseq_1,rc3_xreal_0,rc4_xreal_0,rc6_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc10_finset_1,fc11_finset_1,fc12_finset_1,fc14_finset_1,fc17_finseq_1,fc1_rfinseq,fc2_finseq_1,fc2_seq_1,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc39_membered,fc40_membered,fc41_membered,fc6_membered,fc7_membered,fc8_membered,rc1_finset_1,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_partfun1,rc2_rfunct_3,rc3_finset_1,rc4_finset_1,rc7_finseq_1,t2_boole,t3_boole,t4_boole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k5_finsub_1,dt_k7_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_c4_103_2__rfunct_3,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_seq_1,cc4_membered,cc6_membered,fc1_finset_1,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc37_membered,fc38_membered,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,redefinition_k2_partfun1,redefinition_k2_setwiseo,redefinition_k4_relset_1,dt_k1_numbers,dt_k2_partfun1,dt_k2_setwiseo,dt_k3_xboole_0,dt_k4_relset_1,dt_k4_xboole_0,dt_c1_103__rfunct_3,dt_c1_103_2_2__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c5_103_2__rfunct_3,de_c5_103_2__rfunct_3,fc2_membered,t1_subset,t7_boole,e5_103_2_2__rfunct_3,e15_103_2__rfunct_3,e4_103_2_2__rfunct_3,d3_xboole_0]), [interesting(0.5),file(rfunct_3,e6_103_2_2__rfunct_3),[file(rfunct_3,e6_103_2_2__rfunct_3)]]). fof(i4_103_2_2__rfunct_3,theorem,( $true ), introduced(tautology,[file(rfunct_3,i4_103_2_2__rfunct_3)]), [interesting(0.5),trivial,file(rfunct_3,i4_103_2_2__rfunct_3)]). fof(i3_103_2_2__rfunct_3,plain,( r2_hidden(c1_103_2_2__rfunct_3,k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))))) ), inference(conclusion,[status(thm),assumptions([dt_c1_103_2_2__rfunct_3,e2_103_2_2__rfunct_3,dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[e6_103_2_2__rfunct_3,i4_103_2_2__rfunct_3]), [interesting(0.5),file(rfunct_3,i3_103_2_2__rfunct_3),[file(rfunct_3,i3_103_2_2__rfunct_3)]]). fof(i2_103_2_2__rfunct_3,plain,( ~ ( r2_hidden(c1_103_2_2__rfunct_3,k4_xboole_0(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c2_103_2__rfunct_3)),k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))) & ~ r2_hidden(c1_103_2_2__rfunct_3,k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))))) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_103_2_2__rfunct_3,dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3]),discharge_asm(discharge,[e2_103_2_2__rfunct_3])],[e2_103_2_2__rfunct_3,i3_103_2_2__rfunct_3]), [interesting(0.5),file(rfunct_3,i2_103_2_2__rfunct_3),[file(rfunct_3,i2_103_2_2__rfunct_3)]]). fof(i2_103_2_2_tmp__rfunct_3,plain,( ~ ( r2_hidden(c1_103_2_2__rfunct_3,k4_xboole_0(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c2_103_2__rfunct_3)),k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))) & ~ r2_hidden(c1_103_2_2__rfunct_3,k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))))) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3]),discharge_asm(discharge,[dt_c1_103_2_2__rfunct_3])],[dt_c1_103_2_2__rfunct_3,i2_103_2_2__rfunct_3]), [interesting(0.5),i1_103_2_2__rfunct_3]). fof(i1_103_2_2__rfunct_3,plain,( r1_tarski(k4_xboole_0(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c2_103_2__rfunct_3)),k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3)),k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))))) ), inference(let,[status(thm),assumptions([dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[i2_103_2_2_tmp__rfunct_3,cc1_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc10_membered,fc11_membered,fc9_membered,rc1_nat_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc12_finset_1,fc14_finset_1,fc17_finseq_1,fc1_rfinseq,fc2_seq_1,fc39_membered,fc40_membered,fc41_membered,fc7_membered,fc8_membered,rc1_finset_1,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_partfun1,rc2_rfunct_3,rc3_finset_1,rc4_finset_1,rc7_finseq_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k5_finsub_1,dt_k7_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_seq_1,cc4_membered,cc6_membered,fc1_finset_1,fc37_membered,fc38_membered,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k2_partfun1,redefinition_k2_setwiseo,redefinition_k4_relset_1,dt_k1_numbers,dt_k2_partfun1,dt_k2_setwiseo,dt_k4_relset_1,dt_k4_xboole_0,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c5_103_2__rfunct_3,fc2_membered,d3_tarski,dh_c1_103_2_2__rfunct_3]), [interesting(0.5),file(rfunct_3,i1_103_2_2__rfunct_3),[file(rfunct_3,i1_103_2_2__rfunct_3)]]). fof(e16_103_2__rfunct_3,plain,( k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3)))) = k4_xboole_0(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c2_103_2__rfunct_3)),k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3)) ), inference(conclusion,[status(thm),assumptions([dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[cc1_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc10_membered,fc11_membered,fc9_membered,rc1_nat_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc12_finset_1,fc14_finset_1,fc17_finseq_1,fc1_rfinseq,fc2_seq_1,fc39_membered,fc40_membered,fc41_membered,fc7_membered,fc8_membered,rc1_finset_1,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_partfun1,rc2_rfunct_3,rc3_finset_1,rc4_finset_1,rc7_finseq_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k5_finsub_1,dt_k7_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_seq_1,cc4_membered,cc6_membered,fc1_finset_1,fc37_membered,fc38_membered,reflexivity_r1_tarski,redefinition_k2_partfun1,redefinition_k2_setwiseo,redefinition_k4_relset_1,dt_k1_numbers,dt_k2_partfun1,dt_k2_setwiseo,dt_k4_relset_1,dt_k4_xboole_0,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c5_103_2__rfunct_3,fc2_membered,d10_xboole_0,e1_103_2_2__rfunct_3,i1_103_2_2__rfunct_3]), [interesting(0.65),file(rfunct_3,e16_103_2__rfunct_3),[file(rfunct_3,e16_103_2__rfunct_3)]]). fof(t16_finset_1,theorem,( ! [A,B] : ( v1_finset_1(A) => v1_finset_1(k4_xboole_0(A,B)) ) ), file(finset_1,t16_finset_1), [interesting(0.9),axiom,file(finset_1,t16_finset_1)]). fof(e17_103_2__rfunct_3,plain,( v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k2_zfmisc_1,dt_k5_ordinal2,cc1_relset_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc10_membered,fc10_xreal_0,fc11_membered,fc11_xreal_0,fc12_xreal_0,fc13_xreal_0,fc14_finset_1,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc17_xreal_0,fc18_xreal_0,fc19_xreal_0,fc1_nat_1,fc1_xreal_0,fc20_xreal_0,fc27_xreal_0,fc28_xreal_0,fc29_xreal_0,fc2_seq_1,fc30_xreal_0,fc3_nat_1,fc3_xreal_0,fc4_nat_1,fc5_membered,fc5_xreal_0,fc6_xreal_0,fc7_xreal_0,fc8_membered,fc8_xreal_0,fc9_membered,fc9_xreal_0,rc1_nat_1,rc1_seq_1,rc1_xreal_0,rc2_finset_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,t1_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_xcmplx_0,dt_k5_finsub_1,dt_k5_numbers,dt_k7_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,dt_c4_103_2__rfunct_3,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finseq_1,cc1_finset_1,cc1_membered,cc1_nat_1,cc1_seq_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_nat_1,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc17_finseq_1,fc1_finset_1,fc1_rfinseq,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc37_membered,fc38_membered,fc39_membered,fc40_membered,fc41_membered,fc7_membered,rc1_finseq_1,rc1_finset_1,rc1_membered,rc1_partfun1,rc2_finseq_1,rc2_partfun1,rc2_rfunct_3,rc3_finseq_1,rc3_finset_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_rm1_r0,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,rqRealAdd__k2_xcmplx_0__rm1_r1_r0,spc1_arithm,spc6_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_numerals,t2_subset,t3_subset,t4_arithm,t5_arithm,t6_arithm,t7_boole,t8_boole,commutativity_k1_nat_1,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k3_xboole_0,idempotence_k3_xboole_0,involutiveness_k4_xcmplx_0,redefinition_k1_nat_1,redefinition_k2_partfun1,redefinition_k2_setwiseo,redefinition_k4_card_1,redefinition_k4_relset_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_xboole_0,dt_k2_partfun1,dt_k2_setwiseo,dt_k2_xboole_0,dt_k3_xboole_0,dt_k4_card_1,dt_k4_relset_1,dt_k4_xboole_0,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_k7_xcmplx_0,dt_c1_103__rfunct_3,dt_c1_103_2__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c5_103_2__rfunct_3,de_c5_103_2__rfunct_3,fc10_finset_1,fc11_finset_1,fc12_finset_1,fc2_finseq_1,fc2_membered,fc6_membered,fc9_finset_1,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealDiv__k7_xcmplx_0__r0_r1_r0,rqRealDiv__k7_xcmplx_0__r1_r1_r1,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1,rqRealNeg__k4_xcmplx_0__r0_r0,t1_boole,t2_boole,t3_boole,t4_boole,t6_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e16_103_2__rfunct_3,e2_103_2__rfunct_3,t16_finset_1,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealDiff__k6_xcmplx_0__r1_r1_r0]), [interesting(0.65),file(rfunct_3,e17_103_2__rfunct_3),[file(rfunct_3,e17_103_2__rfunct_3)]]). fof(dt_c7_103_2__rfunct_3,plain,( v1_finset_1(c7_103_2__rfunct_3) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[cc1_finseq_1,cc1_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc10_membered,fc11_membered,fc9_membered,rc1_finseq_1,rc1_nat_1,rc1_partfun1,rc2_xreal_0,rc3_finseq_1,rc3_xreal_0,rc4_xreal_0,rc6_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc14_finset_1,fc17_finseq_1,fc1_rfinseq,fc2_finseq_1,fc2_seq_1,fc39_membered,fc40_membered,fc41_membered,fc6_membered,fc7_membered,fc8_membered,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_partfun1,rc2_rfunct_3,rc7_finseq_1,t1_subset,t3_boole,t4_boole,t4_subset,t5_subset,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k5_finsub_1,dt_k7_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_c4_103_2__rfunct_3,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_seq_1,cc2_finset_1,cc4_membered,cc6_membered,fc1_finset_1,fc37_membered,fc38_membered,rc1_finset_1,rc3_finset_1,rc4_finset_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,redefinition_k2_partfun1,redefinition_k2_setwiseo,redefinition_k4_relset_1,dt_k1_numbers,dt_k2_partfun1,dt_k2_setwiseo,dt_k4_relset_1,dt_k4_xboole_0,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c5_103_2__rfunct_3,de_c5_103_2__rfunct_3,fc12_finset_1,fc2_membered,de_c7_103_2__rfunct_3,e17_103_2__rfunct_3]), [interesting(0.65),file(rfunct_3,c7_103_2__rfunct_3),[file(rfunct_3,c7_103_2__rfunct_3)]]). fof(rqRealAdd__k2_xcmplx_0__r0_r2_r2,theorem,( k2_xcmplx_0(0,2) = 2 ), file(arithm,rqRealAdd__k2_xcmplx_0__r0_r2_r2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_r2_r2)]). fof(rqRealAdd__k2_xcmplx_0__r0_rm2_rm2,theorem,( k2_xcmplx_0(0,k4_xcmplx_0(2)) = k4_xcmplx_0(2) ), file(arithm,rqRealAdd__k2_xcmplx_0__r0_rm2_rm2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_rm2_rm2)]). fof(rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2,theorem,( k2_xcmplx_0(0,k7_xcmplx_0(1,2)) = k7_xcmplx_0(1,2) ), file(arithm,rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2)]). fof(rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2,theorem,( k2_xcmplx_0(0,k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ), file(arithm,rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2)]). fof(rqRealAdd__k2_xcmplx_0__r1_r1_r2,theorem,( k2_xcmplx_0(1,1) = 2 ), file(arithm,rqRealAdd__k2_xcmplx_0__r1_r1_r2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_r1_r2)]). fof(rqRealAdd__k2_xcmplx_0__r1_rm2_rm1,theorem,( k2_xcmplx_0(1,k4_xcmplx_0(2)) = k4_xcmplx_0(1) ), file(arithm,rqRealAdd__k2_xcmplx_0__r1_rm2_rm1), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_rm2_rm1)]). fof(rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2,theorem,( k2_xcmplx_0(1,k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(1,2) ), file(arithm,rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2)]). fof(rqRealAdd__k2_xcmplx_0__r2_r0_r2,theorem,( k2_xcmplx_0(2,0) = 2 ), file(arithm,rqRealAdd__k2_xcmplx_0__r2_r0_r2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r2_r0_r2)]). fof(rqRealAdd__k2_xcmplx_0__r2_rm1_r1,theorem,( k2_xcmplx_0(2,k4_xcmplx_0(1)) = 1 ), file(arithm,rqRealAdd__k2_xcmplx_0__r2_rm1_r1), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r2_rm1_r1)]). fof(rqRealAdd__k2_xcmplx_0__r2_rm2_r0,theorem,( k2_xcmplx_0(2,k4_xcmplx_0(2)) = 0 ), file(arithm,rqRealAdd__k2_xcmplx_0__r2_rm2_r0), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r2_rm2_r0)]). fof(rqRealAdd__k2_xcmplx_0__rm1_r2_r1,theorem,( k2_xcmplx_0(k4_xcmplx_0(1),2) = 1 ), file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r2_r1), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r2_r1)]). fof(rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2,theorem,( k2_xcmplx_0(k4_xcmplx_0(1),k4_xcmplx_0(1)) = k4_xcmplx_0(2) ), file(arithm,rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2)]). fof(rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2,theorem,( k2_xcmplx_0(k4_xcmplx_0(1),k7_xcmplx_0(1,2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ), file(arithm,rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2)]). fof(rqRealAdd__k2_xcmplx_0__rm2_r0_rm2,theorem,( k2_xcmplx_0(k4_xcmplx_0(2),0) = k4_xcmplx_0(2) ), file(arithm,rqRealAdd__k2_xcmplx_0__rm2_r0_rm2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm2_r0_rm2)]). fof(rqRealAdd__k2_xcmplx_0__rm2_r1_rm1,theorem,( k2_xcmplx_0(k4_xcmplx_0(2),1) = k4_xcmplx_0(1) ), file(arithm,rqRealAdd__k2_xcmplx_0__rm2_r1_rm1), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm2_r1_rm1)]). fof(rqRealAdd__k2_xcmplx_0__rm2_r2_r0,theorem,( k2_xcmplx_0(k4_xcmplx_0(2),2) = 0 ), file(arithm,rqRealAdd__k2_xcmplx_0__rm2_r2_r0), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm2_r2_r0)]). fof(rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2,theorem,( k2_xcmplx_0(k7_xcmplx_0(1,2),0) = k7_xcmplx_0(1,2) ), file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2)]). fof(rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2,theorem,( k2_xcmplx_0(k7_xcmplx_0(1,2),k4_xcmplx_0(1)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ), file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2)]). fof(rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1,theorem,( k2_xcmplx_0(k7_xcmplx_0(1,2),k7_xcmplx_0(1,2)) = 1 ), file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1)]). fof(rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0,theorem,( k2_xcmplx_0(k7_xcmplx_0(1,2),k7_xcmplx_0(k4_xcmplx_0(1),2)) = 0 ), file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0)]). fof(rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2,theorem,( k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),1) = k7_xcmplx_0(1,2) ), file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2)]). fof(rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0,theorem,( k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(1,2)) = 0 ), file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0)]). fof(rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1,theorem,( k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(k4_xcmplx_0(1),2)) = k4_xcmplx_0(1) ), file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1)]). fof(redefinition_k5_real_1,definition,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k5_real_1(A,B) = k6_xcmplx_0(A,B) ) ), file(real_1,k5_real_1), [interesting(0.9),axiom,file(real_1,k5_real_1)]). fof(dt_k5_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k5_real_1(A,B),k1_numbers) ) ), file(real_1,k5_real_1), [interesting(0.9),axiom,file(real_1,k5_real_1)]). fof(rqRealDiff__k6_xcmplx_0__r0_r2_rm2,theorem,( k6_xcmplx_0(0,2) = k4_xcmplx_0(2) ), file(arithm,rqRealDiff__k6_xcmplx_0__r0_r2_rm2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_r2_rm2)]). fof(rqRealDiff__k6_xcmplx_0__r0_rm2_r2,theorem,( k6_xcmplx_0(0,k4_xcmplx_0(2)) = 2 ), file(arithm,rqRealDiff__k6_xcmplx_0__r0_rm2_r2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_rm2_r2)]). fof(rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2,theorem,( k6_xcmplx_0(0,k7_xcmplx_0(1,2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ), file(arithm,rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2)]). fof(rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2,theorem,( k6_xcmplx_0(0,k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(1,2) ), file(arithm,rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2)]). fof(rqRealDiff__k6_xcmplx_0__r1_r2_rm1,theorem,( k6_xcmplx_0(1,2) = k4_xcmplx_0(1) ), file(arithm,rqRealDiff__k6_xcmplx_0__r1_r2_rm1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_r2_rm1)]). fof(rqRealDiff__k6_xcmplx_0__r1_rm1_r2,theorem,( k6_xcmplx_0(1,k4_xcmplx_0(1)) = 2 ), file(arithm,rqRealDiff__k6_xcmplx_0__r1_rm1_r2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_rm1_r2)]). fof(rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2,theorem,( k6_xcmplx_0(1,k7_xcmplx_0(1,2)) = k7_xcmplx_0(1,2) ), file(arithm,rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2)]). fof(rqRealDiff__k6_xcmplx_0__r2_r0_r2,theorem,( k6_xcmplx_0(2,0) = 2 ), file(arithm,rqRealDiff__k6_xcmplx_0__r2_r0_r2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r2_r0_r2)]). fof(rqRealDiff__k6_xcmplx_0__r2_r1_r1,theorem,( k6_xcmplx_0(2,1) = 1 ), file(arithm,rqRealDiff__k6_xcmplx_0__r2_r1_r1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r2_r1_r1)]). fof(rqRealDiff__k6_xcmplx_0__r2_r2_r0,theorem,( k6_xcmplx_0(2,2) = 0 ), file(arithm,rqRealDiff__k6_xcmplx_0__r2_r2_r0), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r2_r2_r0)]). fof(rqRealDiff__k6_xcmplx_0__rm1_rm2_r1,theorem,( k6_xcmplx_0(k4_xcmplx_0(1),k4_xcmplx_0(2)) = 1 ), file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm2_r1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm2_r1)]). fof(rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2,theorem,( k6_xcmplx_0(k4_xcmplx_0(1),k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ), file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2)]). fof(rqRealDiff__k6_xcmplx_0__rm2_r0_rm2,theorem,( k6_xcmplx_0(k4_xcmplx_0(2),0) = k4_xcmplx_0(2) ), file(arithm,rqRealDiff__k6_xcmplx_0__rm2_r0_rm2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm2_r0_rm2)]). fof(rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1,theorem,( k6_xcmplx_0(k4_xcmplx_0(2),k4_xcmplx_0(1)) = k4_xcmplx_0(1) ), file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1)]). fof(rqRealDiff__k6_xcmplx_0__rm2_rm2_r0,theorem,( k6_xcmplx_0(k4_xcmplx_0(2),k4_xcmplx_0(2)) = 0 ), file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rm2_r0), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rm2_r0)]). fof(rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2,theorem,( k6_xcmplx_0(k7_xcmplx_0(1,2),0) = k7_xcmplx_0(1,2) ), file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2)]). fof(rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2,theorem,( k6_xcmplx_0(k7_xcmplx_0(1,2),1) = k7_xcmplx_0(k4_xcmplx_0(1),2) ), file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2)]). fof(rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0,theorem,( k6_xcmplx_0(k7_xcmplx_0(1,2),k7_xcmplx_0(1,2)) = 0 ), file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0)]). fof(rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1,theorem,( k6_xcmplx_0(k7_xcmplx_0(1,2),k7_xcmplx_0(k4_xcmplx_0(1),2)) = 1 ), file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1)]). fof(rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2,theorem,( k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),0) = k7_xcmplx_0(k4_xcmplx_0(1),2) ), file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2)]). fof(rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2,theorem,( k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k4_xcmplx_0(1)) = k7_xcmplx_0(1,2) ), file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2)]). fof(rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1,theorem,( k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(1,2)) = k4_xcmplx_0(1) ), file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1)]). fof(rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0,theorem,( k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(k4_xcmplx_0(1),2)) = 0 ), file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0)]). fof(rqRealDiv__k7_xcmplx_0__r0_r2_r0,theorem,( k7_xcmplx_0(0,2) = 0 ), file(arithm,rqRealDiv__k7_xcmplx_0__r0_r2_r0), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r0_r2_r0)]). fof(rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2,theorem,( k7_xcmplx_0(1,2) = k7_xcmplx_0(1,2) ), file(arithm,rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2)]). fof(rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2,theorem,( k7_xcmplx_0(1,k4_xcmplx_0(2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ), file(arithm,rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2)]). fof(rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2,theorem,( k7_xcmplx_0(1,k7_xcmplx_0(1,2)) = 2 ), file(arithm,rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2)]). fof(rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2,theorem,( k7_xcmplx_0(1,k7_xcmplx_0(k4_xcmplx_0(1),2)) = k4_xcmplx_0(2) ), file(arithm,rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2)]). fof(rqRealDiv__k7_xcmplx_0__r2_r1_r2,theorem,( k7_xcmplx_0(2,1) = 2 ), file(arithm,rqRealDiv__k7_xcmplx_0__r2_r1_r2), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r2_r1_r2)]). fof(rqRealDiv__k7_xcmplx_0__r2_r2_r1,theorem,( k7_xcmplx_0(2,2) = 1 ), file(arithm,rqRealDiv__k7_xcmplx_0__r2_r2_r1), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r2_r2_r1)]). fof(rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2,theorem,( k7_xcmplx_0(k4_xcmplx_0(1),2) = k7_xcmplx_0(k4_xcmplx_0(1),2) ), file(arithm,rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2)]). fof(rqRealNeg__k4_xcmplx_0__r2_rm2,theorem,( k4_xcmplx_0(2) = k4_xcmplx_0(2) ), file(arithm,rqRealNeg__k4_xcmplx_0__r2_rm2), [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__r2_rm2)]). fof(rqRealNeg__k4_xcmplx_0__rm2_r2,theorem,( k4_xcmplx_0(k4_xcmplx_0(2)) = 2 ), file(arithm,rqRealNeg__k4_xcmplx_0__rm2_r2), [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rm2_r2)]). fof(rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2,theorem,( k4_xcmplx_0(k7_xcmplx_0(1,2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ), file(arithm,rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2), [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2)]). fof(rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2,theorem,( k4_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(1,2) ), file(arithm,rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2), [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2)]). fof(spc2_numerals,theorem, ( v2_xreal_0(2) & m2_subset_1(2,k1_numbers,k5_numbers) & m1_subset_1(2,k5_numbers) & m1_subset_1(2,k1_numbers) ), file(numerals,spc2_numerals), [interesting(0.9),axiom,file(numerals,spc2_numerals)]). fof(spc2_boole,theorem,( ~ v1_xboole_0(2) ), file(boole,spc2_boole), [interesting(0.9),axiom,file(boole,spc2_boole)]). fof(t37_zfmisc_1,theorem,( ! [A,B] : ( r1_tarski(k1_tarski(A),B) <=> r2_hidden(A,B) ) ), file(zfmisc_1,t37_zfmisc_1), [interesting(0.9),axiom,file(zfmisc_1,t37_zfmisc_1)]). fof(e14_103_2__rfunct_3,plain,( r1_tarski(k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3),k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c2_103_2__rfunct_3))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[dt_k2_zfmisc_1,dt_k5_ordinal2,cc1_relset_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc10_membered,fc10_xreal_0,fc11_membered,fc11_xreal_0,fc12_xreal_0,fc13_xreal_0,fc14_finset_1,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc17_xreal_0,fc18_xreal_0,fc19_xreal_0,fc1_nat_1,fc1_xreal_0,fc20_xreal_0,fc27_xreal_0,fc28_xreal_0,fc29_xreal_0,fc2_seq_1,fc30_xreal_0,fc3_nat_1,fc3_xreal_0,fc4_nat_1,fc5_membered,fc5_xreal_0,fc6_xreal_0,fc7_xreal_0,fc8_membered,fc8_xreal_0,fc9_membered,fc9_xreal_0,rc1_nat_1,rc1_seq_1,rc1_xreal_0,rc2_finset_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,commutativity_k2_xcmplx_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_xcmplx_0,dt_k5_finsub_1,dt_k5_numbers,dt_k7_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,dt_c4_103_2__rfunct_3,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finseq_1,cc1_finset_1,cc1_membered,cc1_nat_1,cc1_seq_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_nat_1,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc17_finseq_1,fc1_rfinseq,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc7_membered,rc1_finseq_1,rc1_finset_1,rc1_membered,rc1_partfun1,rc2_finseq_1,rc2_partfun1,rc2_rfunct_3,rc3_finseq_1,rc3_finset_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_rm1_r0,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,rqRealAdd__k2_xcmplx_0__rm1_r1_r0,spc1_arithm,spc6_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_numerals,t2_subset,t4_arithm,t4_subset,t5_arithm,t5_subset,t6_arithm,t8_boole,commutativity_k1_nat_1,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k3_xboole_0,idempotence_k3_xboole_0,involutiveness_k4_xcmplx_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k1_nat_1,redefinition_k2_partfun1,redefinition_k2_setwiseo,redefinition_k4_card_1,redefinition_k4_relset_1,dt_k1_card_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_tarski,dt_k1_xboole_0,dt_k2_partfun1,dt_k2_setwiseo,dt_k2_xboole_0,dt_k3_xboole_0,dt_k4_card_1,dt_k4_relset_1,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_k7_xcmplx_0,dt_c1_103__rfunct_3,dt_c1_103_2__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c5_103_2__rfunct_3,de_c5_103_2__rfunct_3,fc10_finset_1,fc11_finset_1,fc1_finset_1,fc2_finseq_1,fc2_membered,fc6_membered,fc9_finset_1,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealDiv__k7_xcmplx_0__r0_r1_r0,rqRealDiv__k7_xcmplx_0__r1_r1_r1,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1,rqRealNeg__k4_xcmplx_0__r0_r0,t1_boole,t1_subset,t2_boole,t3_subset,t6_boole,t7_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e2_103_2__rfunct_3,t47_card_1,t37_zfmisc_1,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealDiff__k6_xcmplx_0__r1_r1_r0]), [interesting(0.65),file(rfunct_3,e14_103_2__rfunct_3),[file(rfunct_3,e14_103_2__rfunct_3)]]). fof(t63_card_2,theorem,( ! [A] : ( v1_finset_1(A) => ! [B] : ( v1_finset_1(B) => ( r1_tarski(B,A) => k4_card_1(k4_xboole_0(A,B)) = k5_real_1(k4_card_1(A),k4_card_1(B)) ) ) ) ), file(card_2,t63_card_2), [interesting(0.9),axiom,file(card_2,t63_card_2)]). fof(rqRealDiff__k6_xcmplx_0__rm1_r1_rm2,theorem,( k6_xcmplx_0(k4_xcmplx_0(1),1) = k4_xcmplx_0(2) ), file(arithm,rqRealDiff__k6_xcmplx_0__rm1_r1_rm2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_r1_rm2)]). fof(e1_103_2_3__rfunct_3,plain,( k4_card_1(c7_103_2__rfunct_3) = k5_real_1(k1_nat_1(c1_103_2__rfunct_3,1),k4_card_1(k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[antisymmetry_r2_hidden,dt_k2_zfmisc_1,dt_k5_ordinal2,cc1_relset_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc10_membered,fc10_xreal_0,fc11_membered,fc11_xreal_0,fc12_xreal_0,fc13_xreal_0,fc14_finset_1,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc17_xreal_0,fc18_xreal_0,fc19_xreal_0,fc1_nat_1,fc1_xreal_0,fc20_xreal_0,fc27_xreal_0,fc28_xreal_0,fc29_xreal_0,fc2_seq_1,fc30_xreal_0,fc3_nat_1,fc3_xreal_0,fc4_nat_1,fc5_membered,fc5_xreal_0,fc6_xreal_0,fc7_xreal_0,fc8_membered,fc8_xreal_0,fc9_membered,fc9_xreal_0,rc1_nat_1,rc1_seq_1,rc1_xreal_0,rc2_finset_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,t1_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_xcmplx_0,dt_k5_finsub_1,dt_k5_numbers,dt_k7_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,dt_c4_103_2__rfunct_3,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finseq_1,cc1_finset_1,cc1_membered,cc1_nat_1,cc1_seq_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_nat_1,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc17_finseq_1,fc1_finset_1,fc1_rfinseq,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc37_membered,fc38_membered,fc39_membered,fc40_membered,fc41_membered,fc7_membered,rc1_finseq_1,rc1_finset_1,rc1_membered,rc1_partfun1,rc2_finseq_1,rc2_partfun1,rc2_rfunct_3,rc3_finseq_1,rc3_finset_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_r2_r2,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r0_rm2_rm2,rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2,rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_r1_r2,rqRealAdd__k2_xcmplx_0__r1_rm1_r0,rqRealAdd__k2_xcmplx_0__r1_rm2_rm1,rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2,rqRealAdd__k2_xcmplx_0__r2_r0_r2,rqRealAdd__k2_xcmplx_0__r2_rm1_r1,rqRealAdd__k2_xcmplx_0__r2_rm2_r0,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,rqRealAdd__k2_xcmplx_0__rm1_r1_r0,rqRealAdd__k2_xcmplx_0__rm1_r2_r1,rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2,rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2,rqRealAdd__k2_xcmplx_0__rm2_r0_rm2,rqRealAdd__k2_xcmplx_0__rm2_r1_rm1,rqRealAdd__k2_xcmplx_0__rm2_r2_r0,rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2,rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2,rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1,rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0,rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2,rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0,rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1,spc1_arithm,spc6_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_numerals,t2_subset,t4_arithm,t5_arithm,t6_arithm,t7_boole,t8_boole,commutativity_k1_nat_1,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k3_xboole_0,idempotence_k3_xboole_0,involutiveness_k4_xcmplx_0,reflexivity_r1_tarski,redefinition_k1_nat_1,redefinition_k2_partfun1,redefinition_k2_setwiseo,redefinition_k4_card_1,redefinition_k4_relset_1,redefinition_k5_real_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_xboole_0,dt_k2_partfun1,dt_k2_setwiseo,dt_k2_xboole_0,dt_k3_xboole_0,dt_k4_card_1,dt_k4_relset_1,dt_k4_xboole_0,dt_k4_xcmplx_0,dt_k5_real_1,dt_k6_xcmplx_0,dt_k7_xcmplx_0,dt_c1_103__rfunct_3,dt_c1_103_2__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c5_103_2__rfunct_3,dt_c7_103_2__rfunct_3,de_c5_103_2__rfunct_3,de_c7_103_2__rfunct_3,fc10_finset_1,fc11_finset_1,fc12_finset_1,fc2_finseq_1,fc2_membered,fc6_membered,fc9_finset_1,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_r2_rm2,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r0_rm2_r2,rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2,rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__r1_r2_rm1,rqRealDiff__k6_xcmplx_0__r1_rm1_r2,rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2,rqRealDiff__k6_xcmplx_0__r2_r0_r2,rqRealDiff__k6_xcmplx_0__r2_r1_r1,rqRealDiff__k6_xcmplx_0__r2_r2_r0,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealDiff__k6_xcmplx_0__rm1_rm2_r1,rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2,rqRealDiff__k6_xcmplx_0__rm2_r0_rm2,rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1,rqRealDiff__k6_xcmplx_0__rm2_rm2_r0,rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2,rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2,rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0,rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1,rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2,rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2,rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1,rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0,rqRealDiv__k7_xcmplx_0__r0_r1_r0,rqRealDiv__k7_xcmplx_0__r0_r2_r0,rqRealDiv__k7_xcmplx_0__r1_r1_r1,rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2,rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2,rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2,rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2,rqRealDiv__k7_xcmplx_0__r2_r1_r2,rqRealDiv__k7_xcmplx_0__r2_r2_r1,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1,rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealNeg__k4_xcmplx_0__r2_rm2,rqRealNeg__k4_xcmplx_0__rm2_r2,rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2,rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2,t1_boole,t2_boole,t3_boole,t3_subset,t4_boole,t6_boole,spc0_numerals,spc1_numerals,spc2_numerals,spc0_boole,spc1_boole,spc2_boole,e2_103_2__rfunct_3,e14_103_2__rfunct_3,e16_103_2__rfunct_3,t63_card_2,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqRealDiff__k6_xcmplx_0__rm1_r1_rm2]), [interesting(0.5),file(rfunct_3,e1_103_2_3__rfunct_3),[file(rfunct_3,e1_103_2_3__rfunct_3)]]). fof(t79_card_1,theorem,( ! [A] : k4_card_1(k1_tarski(A)) = 1 ), file(card_1,t79_card_1), [interesting(0.9),axiom,file(card_1,t79_card_1)]). fof(e2_103_2_3__rfunct_3,plain,( k5_real_1(k1_nat_1(c1_103_2__rfunct_3,1),k4_card_1(k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))) = k5_real_1(k1_nat_1(c1_103_2__rfunct_3,1),1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[dt_k2_zfmisc_1,cc1_relset_1,fc14_finset_1,fc2_seq_1,rc1_seq_1,reflexivity_r1_tarski,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k7_relat_1,dt_m1_relset_1,dt_m2_relset_1,cc1_finseq_1,cc1_seq_1,fc10_membered,fc17_finseq_1,fc1_rfinseq,fc9_membered,rc1_finseq_1,rc1_partfun1,rc2_finseq_1,rc2_finset_1,rc2_partfun1,rc2_rfunct_3,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,redefinition_k2_partfun1,redefinition_k4_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_partfun1,dt_k4_relset_1,dt_k5_ordinal2,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,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,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,fc10_xreal_0,fc11_membered,fc11_xreal_0,fc12_xreal_0,fc13_xreal_0,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc17_xreal_0,fc18_xreal_0,fc19_xreal_0,fc1_nat_1,fc1_xreal_0,fc20_xreal_0,fc2_finseq_1,fc3_nat_1,fc3_xreal_0,fc4_nat_1,fc5_membered,fc5_xreal_0,fc6_membered,fc7_xreal_0,fc8_membered,fc8_xreal_0,fc9_xreal_0,rc1_membered,rc1_nat_1,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,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_numbers,dt_k5_finsub_1,dt_k5_numbers,dt_k6_xcmplx_0,dt_m1_subset_1,dt_m2_subset_1,dt_c4_103_2__rfunct_3,cc15_membered,cc1_finset_1,cc1_nat_1,cc2_nat_1,fc2_membered,fc7_membered,rc1_finset_1,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,spc1_arithm,spc6_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_numerals,t2_subset,t4_arithm,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,commutativity_k2_xcmplx_0,involutiveness_k4_xcmplx_0,redefinition_k1_nat_1,redefinition_k2_setwiseo,redefinition_k4_card_1,redefinition_k5_real_1,dt_k1_nat_1,dt_k1_tarski,dt_k2_setwiseo,dt_k2_xcmplx_0,dt_k4_card_1,dt_k4_xcmplx_0,dt_k5_real_1,dt_c1_103__rfunct_3,dt_c1_103_2__rfunct_3,dt_c5_103_2__rfunct_3,de_c5_103_2__rfunct_3,fc1_finset_1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_rm1_r0,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealNeg__k4_xcmplx_0__rm1_r1,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,t79_card_1,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealAdd__k2_xcmplx_0__rm1_r1_r0]), [interesting(0.5),file(rfunct_3,e2_103_2_3__rfunct_3),[file(rfunct_3,e2_103_2_3__rfunct_3)]]). fof(e3_103_2_3__rfunct_3,plain,( k5_real_1(k1_nat_1(c1_103_2__rfunct_3,1),1) = c1_103_2__rfunct_3 ), inference(mizar_by,[status(thm),assumptions([dt_c1_103_2__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,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,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc13_xreal_0,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc17_xreal_0,fc18_xreal_0,fc19_xreal_0,fc1_nat_1,fc1_xreal_0,fc20_xreal_0,fc2_finseq_1,fc3_nat_1,fc3_xreal_0,fc4_nat_1,fc5_membered,fc5_xreal_0,fc6_membered,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,rc1_finset_1,rc1_membered,rc1_nat_1,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,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_k6_xcmplx_0,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc1_finset_1,cc1_nat_1,cc2_nat_1,fc2_membered,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,spc1_arithm,spc6_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_numerals,t2_subset,t4_arithm,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,commutativity_k2_xcmplx_0,involutiveness_k4_xcmplx_0,redefinition_k1_nat_1,redefinition_k5_real_1,dt_k1_nat_1,dt_k2_xcmplx_0,dt_k4_xcmplx_0,dt_k5_real_1,dt_c1_103_2__rfunct_3,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_rm1_r0,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealNeg__k4_xcmplx_0__rm1_r1,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealAdd__k2_xcmplx_0__rm1_r1_r0]), [interesting(0.5),file(rfunct_3,e3_103_2_3__rfunct_3),[file(rfunct_3,e3_103_2_3__rfunct_3)]]). fof(e18_103_2__rfunct_3,plain,( k4_card_1(c7_103_2__rfunct_3) = c1_103_2__rfunct_3 ), inference(iterative_eq,[status(thm),assumptions([dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3,dt_c1_103_2__rfunct_3])],[e1_103_2_3__rfunct_3,e2_103_2_3__rfunct_3,e3_103_2_3__rfunct_3]), [interesting(0.65),file(rfunct_3,e18_103_2__rfunct_3),[file(rfunct_3,e18_103_2__rfunct_3)]]). fof(t36_xboole_1,theorem,( ! [A,B] : r1_tarski(k4_xboole_0(A,B),A) ), file(xboole_1,t36_xboole_1), [interesting(0.9),axiom,file(xboole_1,t36_xboole_1)]). fof(e6_103_2__rfunct_3,plain,( r1_tarski(k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3)),c2_103_2__rfunct_3) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[dt_k2_zfmisc_1,cc1_relset_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc14_finset_1,fc2_seq_1,rc1_seq_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k7_relat_1,dt_m1_relset_1,dt_m2_relset_1,cc1_finseq_1,cc1_seq_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc7_xreal_0,fc10_membered,fc11_membered,fc17_finseq_1,fc1_rfinseq,fc7_membered,fc8_membered,fc9_membered,rc1_finseq_1,rc1_nat_1,rc1_partfun1,rc1_xreal_0,rc2_partfun1,rc2_rfunct_3,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,redefinition_k2_partfun1,redefinition_k4_relset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k2_partfun1,dt_k4_relset_1,dt_c2_103__rfunct_3,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,fc12_finset_1,fc2_finseq_1,fc2_membered,fc37_membered,fc38_membered,fc39_membered,fc40_membered,fc41_membered,fc6_membered,rc1_finset_1,rc1_membered,rc3_finset_1,rc4_finset_1,t1_subset,t3_boole,t4_boole,t4_subset,t5_subset,existence_m1_subset_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k5_finsub_1,dt_m1_subset_1,dt_c4_103_2__rfunct_3,cc15_membered,cc1_finset_1,fc1_finset_1,t2_subset,t6_boole,t7_boole,t8_boole,reflexivity_r1_tarski,redefinition_k2_setwiseo,dt_k2_setwiseo,dt_k4_xboole_0,dt_c1_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c5_103_2__rfunct_3,de_c5_103_2__rfunct_3,t3_subset,t36_xboole_1]), [interesting(0.65),file(rfunct_3,e6_103_2__rfunct_3),[file(rfunct_3,e6_103_2__rfunct_3)]]). fof(t13_xboole_1,theorem,( ! [A,B,C,D] : ( ( r1_tarski(A,B) & r1_tarski(C,D) ) => r1_tarski(k2_xboole_0(A,C),k2_xboole_0(B,D)) ) ), file(xboole_1,t13_xboole_1), [interesting(0.9),axiom,file(xboole_1,t13_xboole_1)]). fof(e7_103_2__rfunct_3,plain,( r1_tarski(k2_xboole_0(c3_103__rfunct_3,k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))),k2_xboole_0(c3_103__rfunct_3,c2_103_2__rfunct_3)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[dt_k2_zfmisc_1,cc1_relset_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc14_finset_1,fc2_seq_1,rc1_seq_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k7_relat_1,dt_m1_relset_1,dt_m2_relset_1,cc1_finseq_1,cc1_seq_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc7_xreal_0,fc10_membered,fc11_membered,fc17_finseq_1,fc1_rfinseq,fc7_membered,fc8_membered,fc9_membered,rc1_finseq_1,rc1_nat_1,rc1_partfun1,rc1_xreal_0,rc2_partfun1,rc2_rfunct_3,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,redefinition_k2_partfun1,redefinition_k4_relset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k2_partfun1,dt_k4_relset_1,dt_c2_103__rfunct_3,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,fc12_finset_1,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc2_membered,fc37_membered,fc38_membered,fc39_membered,fc40_membered,fc41_membered,fc6_membered,fc9_finset_1,rc1_finset_1,rc1_membered,rc3_finset_1,rc4_finset_1,t1_boole,t1_subset,t3_boole,t4_boole,t4_subset,t5_subset,existence_m1_subset_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k5_finsub_1,dt_m1_subset_1,dt_c4_103_2__rfunct_3,cc15_membered,cc1_finset_1,fc1_finset_1,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,redefinition_k2_setwiseo,dt_k2_setwiseo,dt_k2_xboole_0,dt_k4_xboole_0,dt_c1_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c5_103_2__rfunct_3,de_c5_103_2__rfunct_3,t3_subset,e6_103_2__rfunct_3,t13_xboole_1]), [interesting(0.65),file(rfunct_3,e7_103_2__rfunct_3),[file(rfunct_3,e7_103_2__rfunct_3)]]). fof(t27_xboole_1,theorem,( ! [A,B,C,D] : ( ( r1_tarski(A,B) & r1_tarski(C,D) ) => r1_tarski(k3_xboole_0(A,C),k3_xboole_0(B,D)) ) ), file(xboole_1,t27_xboole_1), [interesting(0.9),axiom,file(xboole_1,t27_xboole_1)]). fof(e8_103_2__rfunct_3,plain,( r1_tarski(k3_xboole_0(k4_relset_1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3),k2_xboole_0(c3_103__rfunct_3,k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3)))),k3_xboole_0(k4_relset_1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3),k2_xboole_0(c3_103__rfunct_3,c2_103_2__rfunct_3))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[dt_k7_relat_1,cc1_finseq_1,cc1_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc10_membered,fc11_membered,fc1_rfinseq,fc2_seq_1,fc9_membered,rc1_finseq_1,rc1_nat_1,rc1_partfun1,rc2_xreal_0,rc3_finseq_1,rc3_xreal_0,rc4_xreal_0,rc6_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,redefinition_k2_partfun1,dt_k1_xboole_0,dt_k2_partfun1,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc10_finset_1,fc11_finset_1,fc12_finset_1,fc14_finset_1,fc17_finseq_1,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc39_membered,fc40_membered,fc41_membered,fc6_membered,fc7_membered,fc8_membered,fc9_finset_1,rc1_finset_1,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_partfun1,rc2_rfunct_3,rc3_finset_1,rc4_finset_1,rc7_finseq_1,t1_boole,t1_subset,t2_boole,t3_boole,t4_boole,t4_subset,t5_subset,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k5_finsub_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_c4_103_2__rfunct_3,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_seq_1,cc4_membered,cc6_membered,fc1_finset_1,fc22_membered,fc23_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc37_membered,fc38_membered,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k3_xboole_0,idempotence_k3_xboole_0,reflexivity_r1_tarski,redefinition_k2_setwiseo,redefinition_k4_relset_1,dt_k1_numbers,dt_k2_setwiseo,dt_k2_xboole_0,dt_k3_xboole_0,dt_k4_relset_1,dt_k4_xboole_0,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c5_103_2__rfunct_3,de_c5_103_2__rfunct_3,fc2_membered,t3_subset,e7_103_2__rfunct_3,t27_xboole_1]), [interesting(0.65),file(rfunct_3,e8_103_2__rfunct_3),[file(rfunct_3,e8_103_2__rfunct_3)]]). fof(e9_103_2__rfunct_3,plain,( r1_tarski(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))))),k3_xboole_0(k4_relset_1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3),k2_xboole_0(c3_103__rfunct_3,c2_103_2__rfunct_3))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[cc1_finseq_1,cc1_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc10_membered,fc11_membered,fc9_membered,rc1_finseq_1,rc1_nat_1,rc1_partfun1,rc2_xreal_0,rc3_finseq_1,rc3_xreal_0,rc4_xreal_0,rc6_finseq_1,rc8_finseq_1,dt_k1_xboole_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc10_finset_1,fc11_finset_1,fc12_finset_1,fc14_finset_1,fc17_finseq_1,fc1_rfinseq,fc1_seq_1,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc2_seq_1,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc39_membered,fc40_membered,fc41_membered,fc6_membered,fc7_membered,fc8_membered,fc9_finset_1,rc1_finset_1,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_rfunct_3,rc3_finset_1,rc4_finset_1,rc7_finseq_1,t1_boole,t2_boole,t3_boole,t4_boole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k5_finsub_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_c4_103_2__rfunct_3,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_seq_1,cc4_membered,cc6_membered,fc1_finset_1,fc22_membered,fc23_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc37_membered,fc38_membered,rc2_partfun1,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k3_xboole_0,idempotence_k3_xboole_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k2_partfun1,redefinition_k2_setwiseo,redefinition_k4_relset_1,dt_k1_funct_1,dt_k1_numbers,dt_k1_relat_1,dt_k2_partfun1,dt_k2_setwiseo,dt_k2_xboole_0,dt_k3_xboole_0,dt_k4_relset_1,dt_k4_xboole_0,dt_k7_relat_1,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c5_103_2__rfunct_3,de_c5_103_2__rfunct_3,fc2_membered,t1_subset,t3_subset,t7_boole,e8_103_2__rfunct_3,t68_funct_1]), [interesting(0.65),file(rfunct_3,e9_103_2__rfunct_3),[file(rfunct_3,e9_103_2__rfunct_3)]]). fof(e10_103_2__rfunct_3,plain,( r1_tarski(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))))),k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c2_103_2__rfunct_3)))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[cc1_finseq_1,cc1_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc10_membered,fc11_membered,fc9_membered,rc1_finseq_1,rc1_nat_1,rc1_partfun1,rc2_xreal_0,rc3_finseq_1,rc3_xreal_0,rc4_xreal_0,rc6_finseq_1,rc8_finseq_1,dt_k1_xboole_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc10_finset_1,fc11_finset_1,fc12_finset_1,fc14_finset_1,fc17_finseq_1,fc1_rfinseq,fc1_seq_1,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc2_seq_1,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc39_membered,fc40_membered,fc41_membered,fc6_membered,fc7_membered,fc8_membered,fc9_finset_1,rc1_finset_1,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_rfunct_3,rc3_finset_1,rc4_finset_1,rc7_finseq_1,t1_boole,t2_boole,t3_boole,t4_boole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k5_finsub_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_c4_103_2__rfunct_3,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_seq_1,cc4_membered,cc6_membered,fc1_finset_1,fc22_membered,fc23_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc37_membered,fc38_membered,rc2_partfun1,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k3_xboole_0,idempotence_k3_xboole_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k2_partfun1,redefinition_k2_setwiseo,redefinition_k4_relset_1,dt_k1_funct_1,dt_k1_numbers,dt_k1_relat_1,dt_k2_partfun1,dt_k2_setwiseo,dt_k2_xboole_0,dt_k3_xboole_0,dt_k4_relset_1,dt_k4_xboole_0,dt_k7_relat_1,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c5_103_2__rfunct_3,de_c5_103_2__rfunct_3,fc2_membered,t1_subset,t3_subset,t7_boole,e9_103_2__rfunct_3,t68_funct_1]), [interesting(0.65),file(rfunct_3,e10_103_2__rfunct_3),[file(rfunct_3,e10_103_2__rfunct_3)]]). fof(e11_103_2__rfunct_3,plain,( v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3)))))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[antisymmetry_r2_hidden,dt_k2_zfmisc_1,dt_k5_ordinal2,cc1_relset_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc10_membered,fc10_xreal_0,fc11_membered,fc11_xreal_0,fc12_xreal_0,fc13_xreal_0,fc14_finset_1,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc17_xreal_0,fc18_xreal_0,fc19_xreal_0,fc1_nat_1,fc1_xreal_0,fc20_xreal_0,fc27_xreal_0,fc28_xreal_0,fc29_xreal_0,fc2_seq_1,fc30_xreal_0,fc3_nat_1,fc3_xreal_0,fc4_nat_1,fc5_membered,fc5_xreal_0,fc6_xreal_0,fc7_xreal_0,fc8_membered,fc8_xreal_0,fc9_membered,fc9_xreal_0,rc1_nat_1,rc1_seq_1,rc1_xreal_0,rc2_finset_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,t1_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_xcmplx_0,dt_k5_finsub_1,dt_k5_numbers,dt_k7_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,dt_c4_103_2__rfunct_3,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finseq_1,cc1_finset_1,cc1_membered,cc1_nat_1,cc1_seq_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_nat_1,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc17_finseq_1,fc1_finset_1,fc1_rfinseq,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc37_membered,fc38_membered,fc39_membered,fc40_membered,fc41_membered,fc7_membered,rc1_finseq_1,rc1_finset_1,rc1_membered,rc1_partfun1,rc2_finseq_1,rc2_partfun1,rc2_rfunct_3,rc3_finseq_1,rc3_finset_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_rm1_r0,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,rqRealAdd__k2_xcmplx_0__rm1_r1_r0,spc1_arithm,spc6_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_numerals,t2_subset,t4_arithm,t5_arithm,t6_arithm,t7_boole,t8_boole,commutativity_k1_nat_1,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k3_xboole_0,idempotence_k3_xboole_0,involutiveness_k4_xcmplx_0,reflexivity_r1_tarski,redefinition_k1_nat_1,redefinition_k2_partfun1,redefinition_k2_setwiseo,redefinition_k4_card_1,redefinition_k4_relset_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_xboole_0,dt_k2_partfun1,dt_k2_setwiseo,dt_k2_xboole_0,dt_k3_xboole_0,dt_k4_card_1,dt_k4_relset_1,dt_k4_xboole_0,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_k7_xcmplx_0,dt_c1_103__rfunct_3,dt_c1_103_2__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c5_103_2__rfunct_3,de_c5_103_2__rfunct_3,fc10_finset_1,fc11_finset_1,fc12_finset_1,fc2_finseq_1,fc2_membered,fc6_membered,fc9_finset_1,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealDiv__k7_xcmplx_0__r0_r1_r0,rqRealDiv__k7_xcmplx_0__r1_r1_r1,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1,rqRealNeg__k4_xcmplx_0__r0_r0,t1_boole,t2_boole,t3_boole,t3_subset,t4_boole,t6_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e10_103_2__rfunct_3,e2_103_2__rfunct_3,t13_finset_1,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealDiff__k6_xcmplx_0__r1_r1_r0]), [interesting(0.65),file(rfunct_3,e11_103_2__rfunct_3),[file(rfunct_3,e11_103_2__rfunct_3)]]). fof(e12_103_2__rfunct_3,plain,( r1_tarski(k3_xboole_0(c3_103__rfunct_3,k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))),k3_xboole_0(c3_103__rfunct_3,c2_103_2__rfunct_3)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[dt_k2_zfmisc_1,cc1_relset_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc14_finset_1,fc2_seq_1,rc1_seq_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k7_relat_1,dt_m1_relset_1,dt_m2_relset_1,cc1_finseq_1,cc1_seq_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc7_xreal_0,fc10_membered,fc11_membered,fc17_finseq_1,fc1_rfinseq,fc7_membered,fc8_membered,fc9_membered,rc1_finseq_1,rc1_nat_1,rc1_partfun1,rc1_xreal_0,rc2_partfun1,rc2_rfunct_3,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,redefinition_k2_partfun1,redefinition_k4_relset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k2_partfun1,dt_k4_relset_1,dt_c2_103__rfunct_3,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,fc10_finset_1,fc11_finset_1,fc12_finset_1,fc27_membered,fc28_membered,fc29_membered,fc2_finseq_1,fc2_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc37_membered,fc38_membered,fc39_membered,fc40_membered,fc41_membered,fc6_membered,rc1_finset_1,rc1_membered,rc3_finset_1,rc4_finset_1,t1_subset,t2_boole,t3_boole,t4_boole,t4_subset,t5_subset,existence_m1_subset_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k5_finsub_1,dt_m1_subset_1,dt_c4_103_2__rfunct_3,cc15_membered,cc1_finset_1,fc1_finset_1,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,reflexivity_r1_tarski,redefinition_k2_setwiseo,dt_k2_setwiseo,dt_k3_xboole_0,dt_k4_xboole_0,dt_c1_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c5_103_2__rfunct_3,de_c5_103_2__rfunct_3,t3_subset,e6_103_2__rfunct_3,t27_xboole_1]), [interesting(0.65),file(rfunct_3,e12_103_2__rfunct_3),[file(rfunct_3,e12_103_2__rfunct_3)]]). fof(t3_xboole_1,theorem,( ! [A] : ( r1_tarski(A,k1_xboole_0) => A = k1_xboole_0 ) ), file(xboole_1,t3_xboole_1), [interesting(0.9),axiom,file(xboole_1,t3_xboole_1)]). fof(e13_103_2__rfunct_3,plain,( k3_xboole_0(c3_103__rfunct_3,k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))) = k1_xboole_0 ), inference(mizar_by,[status(thm),assumptions([dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[antisymmetry_r2_hidden,dt_k2_zfmisc_1,dt_k5_ordinal2,cc1_relset_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc10_membered,fc10_xreal_0,fc11_membered,fc11_xreal_0,fc12_xreal_0,fc13_xreal_0,fc14_finset_1,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc17_xreal_0,fc18_xreal_0,fc19_xreal_0,fc1_nat_1,fc1_xreal_0,fc20_xreal_0,fc27_xreal_0,fc28_xreal_0,fc29_xreal_0,fc2_seq_1,fc30_xreal_0,fc3_nat_1,fc3_xreal_0,fc4_nat_1,fc5_membered,fc5_xreal_0,fc6_xreal_0,fc7_xreal_0,fc8_membered,fc8_xreal_0,fc9_membered,fc9_xreal_0,rc1_nat_1,rc1_seq_1,rc1_xreal_0,rc2_finset_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,t1_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_xcmplx_0,dt_k5_finsub_1,dt_k5_numbers,dt_k7_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,dt_c4_103_2__rfunct_3,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finseq_1,cc1_finset_1,cc1_membered,cc1_nat_1,cc1_seq_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_nat_1,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc17_finseq_1,fc1_finset_1,fc1_rfinseq,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc37_membered,fc38_membered,fc39_membered,fc40_membered,fc41_membered,fc7_membered,rc1_finseq_1,rc1_finset_1,rc1_membered,rc1_partfun1,rc2_finseq_1,rc2_partfun1,rc2_rfunct_3,rc3_finseq_1,rc3_finset_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_rm1_r0,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,rqRealAdd__k2_xcmplx_0__rm1_r1_r0,spc1_arithm,spc6_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_numerals,t2_subset,t4_arithm,t5_arithm,t6_arithm,t7_boole,t8_boole,commutativity_k1_nat_1,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k3_xboole_0,idempotence_k3_xboole_0,involutiveness_k4_xcmplx_0,reflexivity_r1_tarski,redefinition_k1_nat_1,redefinition_k2_partfun1,redefinition_k2_setwiseo,redefinition_k4_card_1,redefinition_k4_relset_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_xboole_0,dt_k2_partfun1,dt_k2_setwiseo,dt_k2_xboole_0,dt_k3_xboole_0,dt_k4_card_1,dt_k4_relset_1,dt_k4_xboole_0,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_k7_xcmplx_0,dt_c1_103__rfunct_3,dt_c1_103_2__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c5_103_2__rfunct_3,de_c5_103_2__rfunct_3,fc10_finset_1,fc11_finset_1,fc12_finset_1,fc2_finseq_1,fc2_membered,fc6_membered,fc9_finset_1,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealDiv__k7_xcmplx_0__r0_r1_r0,rqRealDiv__k7_xcmplx_0__r1_r1_r1,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1,rqRealNeg__k4_xcmplx_0__r0_r0,t1_boole,t2_boole,t3_boole,t3_subset,t4_boole,t6_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e12_103_2__rfunct_3,e2_103_2__rfunct_3,t3_xboole_1,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealDiff__k6_xcmplx_0__r1_r1_r0]), [interesting(0.65),file(rfunct_3,e13_103_2__rfunct_3),[file(rfunct_3,e13_103_2__rfunct_3)]]). fof(e19_103_2__rfunct_3,plain,( r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3)))),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))))) ), inference(mizar_by,[status(thm),assumptions([e1_103_2__rfunct_3,dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k2_zfmisc_1,dt_k5_ordinal2,cc1_relset_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc10_membered,fc11_membered,fc14_finset_1,fc2_seq_1,fc5_membered,fc7_membered,fc8_membered,fc9_membered,rc1_nat_1,rc1_seq_1,rc1_xreal_0,rc2_finset_1,rc2_nat_1,rc3_nat_1,t1_subset,t4_subset,t5_subset,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k5_finsub_1,dt_k5_numbers,dt_k7_finseq_1,dt_k7_relat_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_relset_1,dt_m2_subset_1,dt_c4_103_2__rfunct_3,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finseq_1,cc1_finset_1,cc1_membered,cc1_nat_1,cc1_seq_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_nat_1,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc13_finseq_1,fc14_finseq_1,fc17_finseq_1,fc1_finset_1,fc1_rfinseq,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc37_membered,fc38_membered,fc39_membered,fc40_membered,fc41_membered,rc1_finseq_1,rc1_finset_1,rc1_membered,rc1_partfun1,rc1_rfinseq,rc2_finseq_1,rc2_partfun1,rc2_rfunct_3,rc3_finseq_1,rc3_finset_1,rc4_finseq_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t3_subset,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k3_xboole_0,idempotence_k3_xboole_0,symmetry_r1_rfinseq,reflexivity_r1_rfinseq,redefinition_k2_partfun1,redefinition_k2_setwiseo,redefinition_k4_card_1,redefinition_k4_relset_1,redefinition_k8_finseq_1,dt_k1_numbers,dt_k1_xboole_0,dt_k22_rfunct_3,dt_k2_partfun1,dt_k2_setwiseo,dt_k2_xboole_0,dt_k3_xboole_0,dt_k4_card_1,dt_k4_relset_1,dt_k4_xboole_0,dt_k8_finseq_1,dt_c1_103__rfunct_3,dt_c1_103_2__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c5_103_2__rfunct_3,dt_c7_103_2__rfunct_3,de_c5_103_2__rfunct_3,de_c7_103_2__rfunct_3,fc10_finset_1,fc11_finset_1,fc12_finset_1,fc2_finseq_1,fc2_membered,fc6_membered,fc9_finset_1,t1_boole,t2_boole,t3_boole,t4_boole,t6_boole,e18_103_2__rfunct_3,e1_103_2__rfunct_3,e11_103_2__rfunct_3,e13_103_2__rfunct_3]), [interesting(0.65),file(rfunct_3,e19_103_2__rfunct_3),[file(rfunct_3,e19_103_2__rfunct_3)]]). fof(e20_103_2__rfunct_3,plain,( r1_rfinseq(k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3)))),k12_finseq_1(k1_numbers,k2_seq_1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c5_103_2__rfunct_3))),k8_finseq_1(k1_numbers,k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3)))),k12_finseq_1(k1_numbers,k2_seq_1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c5_103_2__rfunct_3)))) ), inference(mizar_by,[status(thm),assumptions([e1_103_2__rfunct_3,dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[reflexivity_r1_tarski,dt_k1_relat_1,dt_k5_ordinal2,dt_k7_relat_1,cc1_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc10_membered,fc11_membered,fc17_finseq_1,fc1_rfinseq,fc2_seq_1,fc5_membered,fc9_membered,rc1_nat_1,rc1_partfun1,rc2_finset_1,rc2_nat_1,rc2_xreal_0,rc3_finseq_1,rc3_nat_1,rc3_xreal_0,rc4_finseq_1,rc4_xreal_0,rc6_finseq_1,antisymmetry_r2_hidden,redefinition_k2_partfun1,redefinition_k4_relset_1,redefinition_k5_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_partfun1,dt_k2_zfmisc_1,dt_k4_relset_1,dt_k5_numbers,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_nat_1,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_nat_1,cc2_xreal_0,cc3_membered,cc6_membered,cc7_xreal_0,cc9_membered,fc14_finset_1,fc1_seq_1,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc39_membered,fc40_membered,fc41_membered,fc6_membered,fc7_membered,fc8_membered,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_finseq_1,rc3_finset_1,rc4_finset_1,t1_boole,t1_subset,t3_boole,t3_subset,t4_boole,t4_subset,t5_subset,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_relset_1,redefinition_m2_finseq_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_tarski,dt_k5_finseq_1,dt_k5_finsub_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_relset_1,dt_c4_103_2__rfunct_3,cc10_membered,cc11_membered,cc15_membered,cc1_finset_1,cc1_seq_1,cc4_membered,fc12_finseq_1,fc12_finset_1,fc13_finseq_1,fc14_finseq_1,fc1_finset_1,fc22_membered,fc23_membered,fc37_membered,fc38_membered,fc3_finseq_1,fc4_finseq_1,fc9_finset_1,rc1_finset_1,rc1_rfinseq,rc2_partfun1,rc2_rfunct_3,rc7_finseq_1,rc8_finseq_1,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,symmetry_r1_rfinseq,reflexivity_r1_rfinseq,redefinition_k12_finseq_1,redefinition_k2_seq_1,redefinition_k2_setwiseo,redefinition_k8_finseq_1,dt_k12_finseq_1,dt_k1_numbers,dt_k22_rfunct_3,dt_k2_seq_1,dt_k2_setwiseo,dt_k2_xboole_0,dt_k4_xboole_0,dt_k7_finseq_1,dt_k8_finseq_1,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c5_103_2__rfunct_3,de_c5_103_2__rfunct_3,cc1_finseq_1,fc2_membered,rc1_finseq_1,e19_103_2__rfunct_3,t14_rfinseq]), [interesting(0.65),file(rfunct_3,e20_103_2__rfunct_3),[file(rfunct_3,e20_103_2__rfunct_3)]]). fof(t45_finseq_1,theorem,( ! [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] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => k7_finseq_1(k7_finseq_1(A,B),C) = k7_finseq_1(A,k7_finseq_1(B,C)) ) ) ) ), file(finseq_1,t45_finseq_1), [interesting(0.9),axiom,file(finseq_1,t45_finseq_1)]). fof(e21_103_2__rfunct_3,plain,( r1_rfinseq(k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3)))),k12_finseq_1(k1_numbers,k2_seq_1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c5_103_2__rfunct_3))),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3))),k12_finseq_1(k1_numbers,k2_seq_1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c5_103_2__rfunct_3))))) ), inference(mizar_by,[status(thm),assumptions([e1_103_2__rfunct_3,dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[reflexivity_r1_tarski,dt_k1_relat_1,dt_k5_ordinal2,dt_k7_relat_1,cc1_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc10_membered,fc11_membered,fc17_finseq_1,fc1_rfinseq,fc2_seq_1,fc5_membered,fc9_membered,rc1_nat_1,rc1_partfun1,rc2_finset_1,rc2_nat_1,rc2_xreal_0,rc3_finseq_1,rc3_nat_1,rc3_xreal_0,rc4_finseq_1,rc4_xreal_0,rc6_finseq_1,antisymmetry_r2_hidden,redefinition_k2_partfun1,redefinition_k4_relset_1,redefinition_k5_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_partfun1,dt_k2_zfmisc_1,dt_k4_relset_1,dt_k5_numbers,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_nat_1,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_nat_1,cc2_xreal_0,cc3_membered,cc6_membered,cc7_xreal_0,cc9_membered,fc14_finset_1,fc1_seq_1,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc39_membered,fc40_membered,fc41_membered,fc6_membered,fc7_membered,fc8_membered,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_finseq_1,rc3_finset_1,rc4_finset_1,t1_boole,t1_subset,t3_boole,t3_subset,t4_boole,t4_subset,t5_subset,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_relset_1,redefinition_m2_finseq_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_tarski,dt_k5_finseq_1,dt_k5_finsub_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_relset_1,dt_c4_103_2__rfunct_3,cc10_membered,cc11_membered,cc15_membered,cc1_finset_1,cc1_seq_1,cc4_membered,fc12_finseq_1,fc12_finset_1,fc13_finseq_1,fc14_finseq_1,fc1_finset_1,fc22_membered,fc23_membered,fc37_membered,fc38_membered,fc3_finseq_1,fc4_finseq_1,fc9_finset_1,rc1_finset_1,rc1_rfinseq,rc2_partfun1,rc2_rfunct_3,rc7_finseq_1,rc8_finseq_1,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,symmetry_r1_rfinseq,reflexivity_r1_rfinseq,redefinition_k12_finseq_1,redefinition_k2_seq_1,redefinition_k2_setwiseo,redefinition_k8_finseq_1,dt_k12_finseq_1,dt_k1_numbers,dt_k22_rfunct_3,dt_k2_seq_1,dt_k2_setwiseo,dt_k2_xboole_0,dt_k4_xboole_0,dt_k7_finseq_1,dt_k8_finseq_1,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c5_103_2__rfunct_3,de_c5_103_2__rfunct_3,cc1_finseq_1,fc2_membered,rc1_finseq_1,e20_103_2__rfunct_3,t45_finseq_1]), [interesting(0.65),file(rfunct_3,e21_103_2__rfunct_3),[file(rfunct_3,e21_103_2__rfunct_3)]]). fof(e29_103_2__rfunct_3,plain,( r1_rfinseq(k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,k4_xboole_0(c2_103_2__rfunct_3,k2_setwiseo(c1_103__rfunct_3,c5_103_2__rfunct_3)))),k12_finseq_1(k1_numbers,k2_seq_1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c5_103_2__rfunct_3))),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c2_103_2__rfunct_3))) ), inference(mizar_by,[status(thm),assumptions([e1_103_2__rfunct_3,dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[reflexivity_r1_tarski,dt_k1_relat_1,dt_k5_ordinal2,dt_k7_relat_1,cc1_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc10_membered,fc11_membered,fc17_finseq_1,fc1_rfinseq,fc2_seq_1,fc5_membered,fc9_membered,rc1_nat_1,rc1_partfun1,rc2_finset_1,rc2_nat_1,rc2_xreal_0,rc3_finseq_1,rc3_nat_1,rc3_xreal_0,rc4_finseq_1,rc4_xreal_0,rc6_finseq_1,antisymmetry_r2_hidden,redefinition_k2_partfun1,redefinition_k4_relset_1,redefinition_k5_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_partfun1,dt_k2_zfmisc_1,dt_k4_relset_1,dt_k5_numbers,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finseq_1,cc1_membered,cc1_nat_1,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_nat_1,cc2_xreal_0,cc3_membered,cc6_membered,cc7_xreal_0,cc9_membered,fc12_finset_1,fc13_finseq_1,fc14_finseq_1,fc14_finset_1,fc1_seq_1,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc39_membered,fc40_membered,fc41_membered,fc6_membered,fc7_membered,fc8_membered,fc9_finset_1,rc1_finseq_1,rc1_finset_1,rc1_membered,rc1_rfinseq,rc1_seq_1,rc1_xreal_0,rc2_finseq_1,rc2_rfunct_3,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t1_boole,t1_subset,t3_boole,t3_subset,t4_boole,t4_subset,t5_subset,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_relset_1,redefinition_m2_finseq_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_tarski,dt_k5_finseq_1,dt_k5_finsub_1,dt_k7_finseq_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_relset_1,dt_c4_103_2__rfunct_3,cc10_membered,cc11_membered,cc15_membered,cc1_finset_1,cc1_seq_1,cc4_membered,fc12_finseq_1,fc1_finset_1,fc22_membered,fc23_membered,fc37_membered,fc38_membered,fc3_finseq_1,fc4_finseq_1,rc2_partfun1,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,symmetry_r1_rfinseq,reflexivity_r1_rfinseq,redefinition_k12_finseq_1,redefinition_k2_seq_1,redefinition_k2_setwiseo,redefinition_k8_finseq_1,dt_k12_finseq_1,dt_k1_numbers,dt_k22_rfunct_3,dt_k2_seq_1,dt_k2_setwiseo,dt_k2_xboole_0,dt_k4_xboole_0,dt_k8_finseq_1,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c5_103_2__rfunct_3,de_c5_103_2__rfunct_3,fc2_membered,e28_103_2__rfunct_3,e21_103_2__rfunct_3,t2_rfinseq]), [interesting(0.65),file(rfunct_3,e29_103_2__rfunct_3),[file(rfunct_3,e29_103_2__rfunct_3)]]). fof(e37_103_2__rfunct_3,plain,( r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c2_103_2__rfunct_3)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c2_103_2__rfunct_3))) ), inference(mizar_by,[status(thm),assumptions([e1_103_2__rfunct_3,dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[reflexivity_r1_tarski,dt_k1_relat_1,dt_k5_ordinal2,dt_k7_relat_1,cc1_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc10_membered,fc11_membered,fc17_finseq_1,fc1_rfinseq,fc2_seq_1,fc5_membered,fc9_membered,rc1_nat_1,rc1_partfun1,rc2_finset_1,rc2_nat_1,rc2_xreal_0,rc3_finseq_1,rc3_nat_1,rc3_xreal_0,rc4_finseq_1,rc4_xreal_0,rc6_finseq_1,antisymmetry_r2_hidden,redefinition_k2_partfun1,redefinition_k4_relset_1,redefinition_k5_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_partfun1,dt_k2_zfmisc_1,dt_k4_relset_1,dt_k5_numbers,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finseq_1,cc1_membered,cc1_nat_1,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_nat_1,cc2_xreal_0,cc3_membered,cc6_membered,cc7_xreal_0,cc9_membered,fc12_finset_1,fc13_finseq_1,fc14_finseq_1,fc14_finset_1,fc1_seq_1,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc39_membered,fc40_membered,fc41_membered,fc6_membered,fc7_membered,fc8_membered,fc9_finset_1,rc1_finseq_1,rc1_finset_1,rc1_membered,rc1_rfinseq,rc1_seq_1,rc1_xreal_0,rc2_finseq_1,rc2_rfunct_3,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t1_boole,t1_subset,t3_boole,t3_subset,t4_boole,t4_subset,t5_subset,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_relset_1,redefinition_m2_finseq_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_tarski,dt_k5_finseq_1,dt_k5_finsub_1,dt_k7_finseq_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_relset_1,dt_c4_103_2__rfunct_3,cc10_membered,cc11_membered,cc15_membered,cc1_finset_1,cc1_seq_1,cc4_membered,fc12_finseq_1,fc1_finset_1,fc22_membered,fc23_membered,fc37_membered,fc38_membered,fc3_finseq_1,fc4_finseq_1,rc2_partfun1,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,symmetry_r1_rfinseq,reflexivity_r1_rfinseq,redefinition_k12_finseq_1,redefinition_k2_seq_1,redefinition_k2_setwiseo,redefinition_k8_finseq_1,dt_k12_finseq_1,dt_k1_numbers,dt_k22_rfunct_3,dt_k2_seq_1,dt_k2_setwiseo,dt_k2_xboole_0,dt_k4_xboole_0,dt_k8_finseq_1,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c5_103_2__rfunct_3,de_c5_103_2__rfunct_3,fc2_membered,e36_103_2__rfunct_3,e29_103_2__rfunct_3,t2_rfinseq]), [interesting(0.65),file(rfunct_3,e37_103_2__rfunct_3),[file(rfunct_3,e37_103_2__rfunct_3)]]). fof(i6_103_2__rfunct_3,theorem,( $true ), introduced(tautology,[file(rfunct_3,i6_103_2__rfunct_3)]), [interesting(0.65),trivial,file(rfunct_3,i6_103_2__rfunct_3)]). fof(i5_103_2__rfunct_3,plain,( r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c2_103_2__rfunct_3)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c2_103_2__rfunct_3))) ), inference(conclusion,[status(thm),assumptions([e1_103_2__rfunct_3,dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3,e2_103_2__rfunct_3])],[e37_103_2__rfunct_3,i6_103_2__rfunct_3]), [interesting(0.65),file(rfunct_3,i5_103_2__rfunct_3),[file(rfunct_3,i5_103_2__rfunct_3)]]). fof(i4_103_2__rfunct_3,plain, ( ( c3_103_2__rfunct_3 = k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c2_103_2__rfunct_3)) & v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c2_103_2__rfunct_3)))) & k3_xboole_0(c3_103__rfunct_3,c2_103_2__rfunct_3) = k1_xboole_0 & k1_nat_1(c1_103_2__rfunct_3,1) = k4_card_1(c3_103_2__rfunct_3) ) => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c2_103_2__rfunct_3)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c2_103_2__rfunct_3))) ), inference(discharge_asm,[status(thm),assumptions([e1_103_2__rfunct_3,dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c3_103_2__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3]),discharge_asm(discharge,[e2_103_2__rfunct_3])],[e2_103_2__rfunct_3,i5_103_2__rfunct_3]), [interesting(0.65),file(rfunct_3,i4_103_2__rfunct_3),[file(rfunct_3,i4_103_2__rfunct_3)]]). fof(i4_103_2_tmp__rfunct_3,plain, ( v1_finset_1(c3_103_2__rfunct_3) => ( ( c3_103_2__rfunct_3 = k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c2_103_2__rfunct_3)) & v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c2_103_2__rfunct_3)))) & k3_xboole_0(c3_103__rfunct_3,c2_103_2__rfunct_3) = k1_xboole_0 & k1_nat_1(c1_103_2__rfunct_3,1) = k4_card_1(c3_103_2__rfunct_3) ) => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c2_103_2__rfunct_3)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c2_103_2__rfunct_3))) ) ), inference(discharge_asm,[status(thm),assumptions([e1_103_2__rfunct_3,dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3]),discharge_asm(discharge,[dt_c3_103_2__rfunct_3])],[dt_c3_103_2__rfunct_3,i4_103_2__rfunct_3]), [interesting(0.65),i3_103_2__rfunct_3]). fof(i3_103_2__rfunct_3,plain,( ! [A] : ( v1_finset_1(A) => ( ( A = k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c2_103_2__rfunct_3)) & v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c2_103_2__rfunct_3)))) & k3_xboole_0(c3_103__rfunct_3,c2_103_2__rfunct_3) = k1_xboole_0 & k1_nat_1(c1_103_2__rfunct_3,1) = k4_card_1(A) ) => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c2_103_2__rfunct_3)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c2_103_2__rfunct_3))) ) ) ), inference(let,[status(thm),assumptions([e1_103_2__rfunct_3,dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c2_103_2__rfunct_3])],[i4_103_2_tmp__rfunct_3,dh_c3_103_2__rfunct_3]), [interesting(0.65),file(rfunct_3,i3_103_2__rfunct_3),[file(rfunct_3,i3_103_2__rfunct_3)]]). fof(i3_103_2_tmp__rfunct_3,plain,( ! [A] : ( v1_finset_1(A) => ( ( A = k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,c2_103_2__rfunct_3)) & v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c2_103_2__rfunct_3)))) & k3_xboole_0(c3_103__rfunct_3,c2_103_2__rfunct_3) = k1_xboole_0 & k1_nat_1(c1_103_2__rfunct_3,1) = k4_card_1(A) ) => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c2_103_2__rfunct_3)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c2_103_2__rfunct_3))) ) ) ), inference(discharge_asm,[status(thm),assumptions([e1_103_2__rfunct_3,dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3]),discharge_asm(discharge,[dt_c2_103_2__rfunct_3])],[dt_c2_103_2__rfunct_3,i3_103_2__rfunct_3]), [interesting(0.65),i2_103_2__rfunct_3]). fof(i2_103_2__rfunct_3,plain,( ! [A,B] : ( v1_finset_1(B) => ( ( B = k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,A)) & v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,A)))) & k3_xboole_0(c3_103__rfunct_3,A) = k1_xboole_0 & k1_nat_1(c1_103_2__rfunct_3,1) = k4_card_1(B) ) => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,A)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,A))) ) ) ), inference(let,[status(thm),assumptions([e1_103_2__rfunct_3,dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3])],[i3_103_2_tmp__rfunct_3,dh_c2_103_2__rfunct_3]), [interesting(0.65),file(rfunct_3,i2_103_2__rfunct_3),[file(rfunct_3,i2_103_2__rfunct_3)]]). fof(i1_103_2__rfunct_3,plain, ( ! [A,B] : ( v1_finset_1(B) => ( ( B = k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,A)) & v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,A)))) & k3_xboole_0(c3_103__rfunct_3,A) = k1_xboole_0 & c1_103_2__rfunct_3 = k4_card_1(B) ) => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,A)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,A))) ) ) => ! [A,B] : ( v1_finset_1(B) => ( ( B = k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,A)) & v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,A)))) & k3_xboole_0(c3_103__rfunct_3,A) = k1_xboole_0 & k1_nat_1(c1_103_2__rfunct_3,1) = k4_card_1(B) ) => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,A)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,A))) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_103_2__rfunct_3,dt_c3_103__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3]),discharge_asm(discharge,[e1_103_2__rfunct_3])],[e1_103_2__rfunct_3,i2_103_2__rfunct_3]), [interesting(0.65),file(rfunct_3,i1_103_2__rfunct_3),[file(rfunct_3,i1_103_2__rfunct_3)]]). fof(i1_103_2_tmp__rfunct_3,plain, ( m2_subset_1(c1_103_2__rfunct_3,k1_numbers,k5_numbers) => ( ! [A,B] : ( v1_finset_1(B) => ( ( B = k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,A)) & v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,A)))) & k3_xboole_0(c3_103__rfunct_3,A) = k1_xboole_0 & c1_103_2__rfunct_3 = k4_card_1(B) ) => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,A)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,A))) ) ) => ! [A,B] : ( v1_finset_1(B) => ( ( B = k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,A)) & v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,A)))) & k3_xboole_0(c3_103__rfunct_3,A) = k1_xboole_0 & k1_nat_1(c1_103_2__rfunct_3,1) = k4_card_1(B) ) => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,A)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,A))) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c3_103__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3]),discharge_asm(discharge,[dt_c1_103_2__rfunct_3])],[dt_c1_103_2__rfunct_3,i1_103_2__rfunct_3]), [interesting(0.8),e7_103__rfunct_3]). fof(e7_103__rfunct_3,plain,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ( ! [B,C] : ( v1_finset_1(C) => ( ( C = k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,B)) & v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,B)))) & k3_xboole_0(c3_103__rfunct_3,B) = k1_xboole_0 & A = k4_card_1(C) ) => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,B)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,B))) ) ) => ! [B,C] : ( v1_finset_1(C) => ( ( C = k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,B)) & v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,B)))) & k3_xboole_0(c3_103__rfunct_3,B) = k1_xboole_0 & k1_nat_1(A,1) = k4_card_1(C) ) => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,B)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,B))) ) ) ) ) ), inference(let,[status(thm),assumptions([dt_c3_103__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3])],[i1_103_2_tmp__rfunct_3,dh_c1_103_2__rfunct_3]), [interesting(0.8),file(rfunct_3,e7_103__rfunct_3),[file(rfunct_3,e7_103__rfunct_3)]]). fof(e8_103__rfunct_3,plain,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B,C] : ( v1_finset_1(C) => ( ( C = k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,B)) & v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,B)))) & k3_xboole_0(c3_103__rfunct_3,B) = k1_xboole_0 & A = k4_card_1(C) ) => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,B)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,B))) ) ) ) ), inference(mizar_from,[status(thm),assumptions([dt_c3_103__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3])],[cc1_xreal_0,cc2_xreal_0,cc3_nat_1,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,fc1_nat_1,fc2_seq_1,fc3_nat_1,fc3_xreal_0,fc4_nat_1,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,rc1_nat_1,rc1_seq_1,rc1_xreal_0,rc2_finset_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,commutativity_k2_xcmplx_0,redefinition_m2_finseq_1,dt_k1_card_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_k7_finseq_1,dt_k7_relat_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_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_relset_1,cc1_seq_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_nat_1,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc13_finseq_1,fc14_finseq_1,fc14_finset_1,fc17_finseq_1,fc1_rfinseq,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc5_membered,rc1_finseq_1,rc1_membered,rc1_partfun1,rc1_rfinseq,rc2_finseq_1,rc2_partfun1,rc2_rfunct_3,rc3_finseq_1,rc3_finset_1,rc4_finseq_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,commutativity_k1_nat_1,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k3_xboole_0,idempotence_k3_xboole_0,symmetry_r1_rfinseq,reflexivity_r1_rfinseq,redefinition_k1_nat_1,redefinition_k2_partfun1,redefinition_k4_card_1,redefinition_k4_relset_1,redefinition_k5_numbers,redefinition_k8_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_xboole_0,dt_k22_rfunct_3,dt_k2_partfun1,dt_k2_xboole_0,dt_k3_xboole_0,dt_k4_card_1,dt_k4_relset_1,dt_k5_numbers,dt_k8_finseq_1,dt_m2_relset_1,dt_m2_subset_1,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c3_103__rfunct_3,cc15_membered,cc1_finset_1,fc10_finset_1,fc11_finset_1,fc2_finseq_1,fc2_membered,fc6_membered,fc9_finset_1,rc1_finset_1,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,s1_nat_1__e8_103__rfunct_3,e6_103__rfunct_3,e7_103__rfunct_3]), [interesting(0.8),file(rfunct_3,e8_103__rfunct_3),[file(rfunct_3,e8_103__rfunct_3)]]). fof(e11_103__rfunct_3,plain,( r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c4_103__rfunct_3)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c4_103__rfunct_3))) ), inference(mizar_by,[status(thm),assumptions([dt_c4_103__rfunct_3,e1_103__rfunct_3,dt_c3_103__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,e9_103__rfunct_3])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k2_zfmisc_1,cc1_relset_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc14_finset_1,fc2_seq_1,rc1_nat_1,rc1_seq_1,rc1_xreal_0,rc2_finset_1,rc2_nat_1,rc3_nat_1,t1_subset,t4_subset,t5_subset,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_relset_1,redefinition_m2_finseq_1,redefinition_m2_relset_1,dt_k1_card_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_k7_finseq_1,dt_k7_relat_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finseq_1,cc1_finset_1,cc1_membered,cc1_nat_1,cc1_seq_1,cc20_membered,cc2_finset_1,cc2_membered,cc2_nat_1,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc13_finseq_1,fc14_finseq_1,fc17_finseq_1,fc1_rfinseq,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc5_membered,rc1_finseq_1,rc1_finset_1,rc1_membered,rc1_partfun1,rc1_rfinseq,rc2_finseq_1,rc2_partfun1,rc2_rfunct_3,rc3_finseq_1,rc3_finset_1,rc4_finseq_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t3_subset,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k3_xboole_0,idempotence_k3_xboole_0,symmetry_r1_rfinseq,reflexivity_r1_rfinseq,existence_m2_subset_1,redefinition_k2_partfun1,redefinition_k4_card_1,redefinition_k4_relset_1,redefinition_k5_numbers,redefinition_k8_finseq_1,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k22_rfunct_3,dt_k2_partfun1,dt_k2_xboole_0,dt_k3_xboole_0,dt_k4_card_1,dt_k4_relset_1,dt_k5_numbers,dt_k8_finseq_1,dt_m2_subset_1,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c3_103__rfunct_3,dt_c4_103__rfunct_3,dt_c5_103__rfunct_3,de_c5_103__rfunct_3,fc10_finset_1,fc11_finset_1,fc2_finseq_1,fc2_membered,fc6_membered,fc9_finset_1,t1_boole,t2_boole,t6_boole,e10_103__rfunct_3,e1_103__rfunct_3,e8_103__rfunct_3,e9_103__rfunct_3]), [interesting(0.8),file(rfunct_3,e11_103__rfunct_3),[file(rfunct_3,e11_103__rfunct_3)]]). fof(i6_103__rfunct_3,theorem,( $true ), introduced(tautology,[file(rfunct_3,i6_103__rfunct_3)]), [interesting(0.8),trivial,file(rfunct_3,i6_103__rfunct_3)]). fof(i5_103__rfunct_3,plain,( r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c4_103__rfunct_3)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c4_103__rfunct_3))) ), inference(conclusion,[status(thm),assumptions([dt_c4_103__rfunct_3,e1_103__rfunct_3,dt_c3_103__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,e9_103__rfunct_3])],[e11_103__rfunct_3,i6_103__rfunct_3]), [interesting(0.8),file(rfunct_3,i5_103__rfunct_3),[file(rfunct_3,i5_103__rfunct_3)]]). fof(i5_103_tmp__rfunct_3,plain, ( k3_xboole_0(c3_103__rfunct_3,c4_103__rfunct_3) = k1_xboole_0 => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c4_103__rfunct_3)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c4_103__rfunct_3))) ), inference(discharge_asm,[status(thm),assumptions([dt_c4_103__rfunct_3,e1_103__rfunct_3,dt_c3_103__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3]),discharge_asm(discharge,[e9_103__rfunct_3])],[e9_103__rfunct_3,i5_103__rfunct_3]), [interesting(0.8),i4_103__rfunct_3]). fof(i4_103__rfunct_3,plain,( ~ ( r1_xboole_0(c3_103__rfunct_3,c4_103__rfunct_3) & ~ r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c4_103__rfunct_3)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c4_103__rfunct_3))) ) ), inference(mizar_def_expansion,[status(thm),assumptions([dt_c4_103__rfunct_3,e1_103__rfunct_3,dt_c3_103__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3])],[i5_103_tmp__rfunct_3,d7_xboole_0,cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,dt_k5_ordinal2,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc5_membered,rc1_nat_1,rc1_xreal_0,rc2_finset_1,rc2_nat_1,rc3_nat_1,redefinition_k5_numbers,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_nat_1,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_nat_1,cc6_membered,cc9_membered,fc14_finset_1,rc1_seq_1,rc2_finseq_1,rc3_finset_1,rc4_finset_1,redefinition_m2_finseq_1,redefinition_m2_relset_1,dt_k7_finseq_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m2_finseq_1,dt_m2_relset_1,cc15_membered,cc1_finseq_1,cc1_finset_1,cc1_membered,cc1_seq_1,cc2_membered,cc3_membered,cc4_membered,fc10_finset_1,fc11_finset_1,fc13_finseq_1,fc14_finseq_1,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc9_finset_1,rc1_finseq_1,rc1_finset_1,rc1_membered,rc1_partfun1,rc1_rfinseq,rc2_partfun1,rc2_rfunct_3,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k3_xboole_0,idempotence_k3_xboole_0,symmetry_r1_rfinseq,reflexivity_r1_rfinseq,symmetry_r1_xboole_0,redefinition_k8_finseq_1,dt_k1_numbers,dt_k1_xboole_0,dt_k22_rfunct_3,dt_k2_xboole_0,dt_k3_xboole_0,dt_k8_finseq_1,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3,dt_c3_103__rfunct_3,dt_c4_103__rfunct_3,fc2_finseq_1,fc2_membered,fc6_membered]), [interesting(0.8),file(rfunct_3,i4_103__rfunct_3),[file(rfunct_3,i4_103__rfunct_3)]]). fof(i3_103__rfunct_3,plain, ( ( v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c4_103__rfunct_3)))) & r1_xboole_0(c3_103__rfunct_3,c4_103__rfunct_3) ) => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c4_103__rfunct_3)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c4_103__rfunct_3))) ), inference(discharge_asm,[status(thm),assumptions([dt_c4_103__rfunct_3,dt_c3_103__rfunct_3,dt_c1_103__rfunct_3,dt_c2_103__rfunct_3]),discharge_asm(discharge,[e1_103__rfunct_3])],[e1_103__rfunct_3,i4_103__rfunct_3]), [interesting(0.8),file(rfunct_3,i3_103__rfunct_3),[file(rfunct_3,i3_103__rfunct_3)]]). fof(i3_103_tmp__rfunct_3,plain, ( ( v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c4_103__rfunct_3)))) & r1_xboole_0(c3_103__rfunct_3,c4_103__rfunct_3) ) => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(c3_103__rfunct_3,c4_103__rfunct_3)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c3_103__rfunct_3),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,c4_103__rfunct_3))) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_103__rfunct_3,dt_c2_103__rfunct_3]),discharge_asm(discharge,[dt_c3_103__rfunct_3,dt_c4_103__rfunct_3])],[dt_c3_103__rfunct_3,dt_c4_103__rfunct_3,i3_103__rfunct_3]), [interesting(0.8),i2_103__rfunct_3]). fof(i2_103__rfunct_3,plain,( ! [A,B] : ( ( v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(A,B)))) & r1_xboole_0(A,B) ) => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(A,B)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,A),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,B))) ) ), inference(let,[status(thm),assumptions([dt_c1_103__rfunct_3,dt_c2_103__rfunct_3])],[i3_103_tmp__rfunct_3,dh_c3_103__rfunct_3,dh_c4_103__rfunct_3]), [interesting(0.8),file(rfunct_3,i2_103__rfunct_3),[file(rfunct_3,i2_103__rfunct_3)]]). fof(i2_103_tmp__rfunct_3,plain, ( ( v1_funct_1(c2_103__rfunct_3) & m2_relset_1(c2_103__rfunct_3,c1_103__rfunct_3,k1_numbers) ) => ! [A,B] : ( ( v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,c2_103__rfunct_3,k2_xboole_0(A,B)))) & r1_xboole_0(A,B) ) => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,k2_xboole_0(A,B)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,A),k22_rfunct_3(c1_103__rfunct_3,c2_103__rfunct_3,B))) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_103__rfunct_3]),discharge_asm(discharge,[dt_c2_103__rfunct_3])],[dt_c2_103__rfunct_3,i2_103__rfunct_3]), [interesting(0.8),i1_103__rfunct_3]). fof(i1_103__rfunct_3,plain,( ! [A] : ( ( v1_funct_1(A) & m2_relset_1(A,c1_103__rfunct_3,k1_numbers) ) => ! [B,C] : ( ( v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,A,k2_xboole_0(B,C)))) & r1_xboole_0(B,C) ) => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,A,k2_xboole_0(B,C)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,A,B),k22_rfunct_3(c1_103__rfunct_3,A,C))) ) ) ), inference(let,[status(thm),assumptions([dt_c1_103__rfunct_3])],[i2_103_tmp__rfunct_3,dh_c2_103__rfunct_3]), [interesting(0.8),file(rfunct_3,i1_103__rfunct_3),[file(rfunct_3,i1_103__rfunct_3)]]). fof(i1_103_tmp__rfunct_3,plain, ( ~ v1_xboole_0(c1_103__rfunct_3) => ! [A] : ( ( v1_funct_1(A) & m2_relset_1(A,c1_103__rfunct_3,k1_numbers) ) => ! [B,C] : ( ( v1_finset_1(k4_relset_1(c1_103__rfunct_3,k1_numbers,k2_partfun1(c1_103__rfunct_3,k1_numbers,A,k2_xboole_0(B,C)))) & r1_xboole_0(B,C) ) => r1_rfinseq(k22_rfunct_3(c1_103__rfunct_3,A,k2_xboole_0(B,C)),k8_finseq_1(k1_numbers,k22_rfunct_3(c1_103__rfunct_3,A,B),k22_rfunct_3(c1_103__rfunct_3,A,C))) ) ) ), inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_103__rfunct_3])],[dt_c1_103__rfunct_3,i1_103__rfunct_3]), [interesting(1),t79_rfunct_3]). fof(t79_rfunct_3,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m2_relset_1(B,A,k1_numbers) ) => ! [C,D] : ( ( v1_finset_1(k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,k2_xboole_0(C,D)))) & r1_xboole_0(C,D) ) => r1_rfinseq(k22_rfunct_3(A,B,k2_xboole_0(C,D)),k8_finseq_1(k1_numbers,k22_rfunct_3(A,B,C),k22_rfunct_3(A,B,D))) ) ) ) ), inference(let,[status(thm),assumptions([])],[i1_103_tmp__rfunct_3,dh_c1_103__rfunct_3]), [interesting(1),file(rfunct_3,t79_rfunct_3),[file(rfunct_3,t79_rfunct_3)]]).