% Mizar ND problem: t5_amistd_1,amistd_1,129,26 fof(dh_c1_8__amistd_1,definition, ( ( ~ v1_xboole_0(c1_8__amistd_1) => ! [A] : ( ( ~ v1_xboole_0(A) & m2_finseq_1(A,c1_8__amistd_1) ) => ! [B] : ( m2_finseq_1(B,c1_8__amistd_1) => k4_finseq_4(k5_numbers,c1_8__amistd_1,k4_graph_2(c1_8__amistd_1,A,B),1) = k4_finseq_4(k5_numbers,c1_8__amistd_1,A,1) ) ) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( ~ v1_xboole_0(D) & m2_finseq_1(D,C) ) => ! [E] : ( m2_finseq_1(E,C) => k4_finseq_4(k5_numbers,C,k4_graph_2(C,D,E),1) = k4_finseq_4(k5_numbers,C,D,1) ) ) ) ), introduced(definition,[new_symbol(c1_8__amistd_1),file(amistd_1,c1_8__amistd_1)]), [interesting(0.8),axiom,file(amistd_1,c1_8__amistd_1)]). fof(dh_c2_8__amistd_1,definition, ( ( ( ~ v1_xboole_0(c2_8__amistd_1) & m2_finseq_1(c2_8__amistd_1,c1_8__amistd_1) ) => ! [A] : ( m2_finseq_1(A,c1_8__amistd_1) => k4_finseq_4(k5_numbers,c1_8__amistd_1,k4_graph_2(c1_8__amistd_1,c2_8__amistd_1,A),1) = k4_finseq_4(k5_numbers,c1_8__amistd_1,c2_8__amistd_1,1) ) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,c1_8__amistd_1) ) => ! [C] : ( m2_finseq_1(C,c1_8__amistd_1) => k4_finseq_4(k5_numbers,c1_8__amistd_1,k4_graph_2(c1_8__amistd_1,B,C),1) = k4_finseq_4(k5_numbers,c1_8__amistd_1,B,1) ) ) ), introduced(definition,[new_symbol(c2_8__amistd_1),file(amistd_1,c2_8__amistd_1)]), [interesting(0.8),axiom,file(amistd_1,c2_8__amistd_1)]). fof(dh_c3_8__amistd_1,definition, ( ( m2_finseq_1(c3_8__amistd_1,c1_8__amistd_1) => k4_finseq_4(k5_numbers,c1_8__amistd_1,k4_graph_2(c1_8__amistd_1,c2_8__amistd_1,c3_8__amistd_1),1) = k4_finseq_4(k5_numbers,c1_8__amistd_1,c2_8__amistd_1,1) ) => ! [A] : ( m2_finseq_1(A,c1_8__amistd_1) => k4_finseq_4(k5_numbers,c1_8__amistd_1,k4_graph_2(c1_8__amistd_1,c2_8__amistd_1,A),1) = k4_finseq_4(k5_numbers,c1_8__amistd_1,c2_8__amistd_1,1) ) ), introduced(definition,[new_symbol(c3_8__amistd_1),file(amistd_1,c3_8__amistd_1)]), [interesting(0.8),axiom,file(amistd_1,c3_8__amistd_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(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(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(fc4_subset_1,theorem,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ), file(subset_1,fc4_subset_1), [interesting(0.9),axiom,file(subset_1,fc4_subset_1)]). fof(rc3_relat_1,theorem,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) ) ), file(relat_1,rc3_relat_1), [interesting(0.9),axiom,file(relat_1,rc3_relat_1)]). fof(rc4_funct_1,theorem,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc4_funct_1), [interesting(0.9),axiom,file(funct_1,rc4_funct_1)]). fof(reflexivity_r1_tarski,theorem,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), [interesting(0.9),axiom,file(tarski,r1_tarski)]). fof(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(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(redefinition_m2_relset_1,definition,( ! [A,B,C] : ( m2_relset_1(C,A,B) <=> m1_relset_1(C,A,B) ) ), file(relset_1,m2_relset_1), [interesting(0.9),axiom,file(relset_1,m2_relset_1)]). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]). fof(dt_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ), file(relset_1,m2_relset_1), [interesting(0.9),axiom,file(relset_1,m2_relset_1)]). fof(cc10_membered,theorem,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,A) => v1_xcmplx_0(B) ) ) ), file(membered,cc10_membered), [interesting(0.9),axiom,file(membered,cc10_membered)]). fof(cc11_membered,theorem,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) ) ) ) ), file(membered,cc11_membered), [interesting(0.9),axiom,file(membered,cc11_membered)]). fof(cc12_membered,theorem,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_rat_1(B) ) ) ) ), file(membered,cc12_membered), [interesting(0.9),axiom,file(membered,cc12_membered)]). fof(cc13_membered,theorem,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc13_membered), [interesting(0.9),axiom,file(membered,cc13_membered)]). fof(cc14_membered,theorem,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v4_ordinal2(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc14_membered), [interesting(0.9),axiom,file(membered,cc14_membered)]). fof(cc16_membered,theorem,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_membered(B) ) ) ), file(membered,cc16_membered), [interesting(0.9),axiom,file(membered,cc16_membered)]). fof(cc17_membered,theorem,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) ) ) ) ), file(membered,cc17_membered), [interesting(0.9),axiom,file(membered,cc17_membered)]). fof(cc18_membered,theorem,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) ) ) ) ), file(membered,cc18_membered), [interesting(0.9),axiom,file(membered,cc18_membered)]). fof(cc19_membered,theorem,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) ) ) ) ), file(membered,cc19_membered), [interesting(0.9),axiom,file(membered,cc19_membered)]). fof(cc1_funct_7,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_funct_7(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_funcop_1(A) ) ) ), file(funct_7,cc1_funct_7), [interesting(0.9),axiom,file(funct_7,cc1_funct_7)]). 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_realset1,theorem,( ! [A] : ( ~ v1_realset1(A) => ~ v1_xboole_0(A) ) ), file(realset1,cc1_realset1), [interesting(0.9),axiom,file(realset1,cc1_realset1)]). 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_membered,theorem,( ! [A] : ( v4_membered(A) => v3_membered(A) ) ), file(membered,cc2_membered), [interesting(0.9),axiom,file(membered,cc2_membered)]). fof(cc3_int_1,theorem,( ! [A] : ( v4_ordinal2(A) => v1_int_1(A) ) ), file(int_1,cc3_int_1), [interesting(0.9),axiom,file(int_1,cc3_int_1)]). fof(cc3_membered,theorem,( ! [A] : ( v3_membered(A) => v2_membered(A) ) ), file(membered,cc3_membered), [interesting(0.9),axiom,file(membered,cc3_membered)]). fof(cc3_nat_1,theorem,( ! [A] : ( v4_ordinal2(A) => ( v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(nat_1,cc3_nat_1), [interesting(0.9),axiom,file(nat_1,cc3_nat_1)]). fof(cc4_int_1,theorem,( ! [A] : ( v1_int_1(A) => ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(int_1,cc4_int_1), [interesting(0.9),axiom,file(int_1,cc4_int_1)]). fof(cc4_membered,theorem,( ! [A] : ( v2_membered(A) => v1_membered(A) ) ), file(membered,cc4_membered), [interesting(0.9),axiom,file(membered,cc4_membered)]). fof(fc12_relat_1,theorem, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) ), file(relat_1,fc12_relat_1), [interesting(0.9),axiom,file(relat_1,fc12_relat_1)]). fof(fc1_xboole_0,theorem,( v1_xboole_0(k1_xboole_0) ), file(xboole_0,fc1_xboole_0), [interesting(0.9),axiom,file(xboole_0,fc1_xboole_0)]). fof(fc2_finseq_1,theorem, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) & v1_funct_1(k1_xboole_0) & v2_funct_1(k1_xboole_0) & v1_finset_1(k1_xboole_0) & v1_finseq_1(k1_xboole_0) ), file(finseq_1,fc2_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc2_finseq_1)]). fof(fc3_funct_7,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) & v1_funcop_1(k1_xboole_0) ), file(funct_7,fc3_funct_7), [interesting(0.9),axiom,file(funct_7,fc3_funct_7)]). fof(fc4_relat_1,theorem, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) ), file(relat_1,fc4_relat_1), [interesting(0.9),axiom,file(relat_1,fc4_relat_1)]). fof(fc6_membered,theorem, ( v1_xboole_0(k1_xboole_0) & v1_membered(k1_xboole_0) & v2_membered(k1_xboole_0) & v3_membered(k1_xboole_0) & v4_membered(k1_xboole_0) & v5_membered(k1_xboole_0) ), file(membered,fc6_membered), [interesting(0.9),axiom,file(membered,fc6_membered)]). fof(fc8_funct_7,theorem,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_funcop_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_funcop_1(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)) & v1_funcop_1(k7_finseq_1(A,B)) ) ) ), file(funct_7,fc8_funct_7), [interesting(0.9),axiom,file(funct_7,fc8_funct_7)]). fof(rc1_amistd_1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & ~ v1_realset1(A) ) ), file(amistd_1,rc1_amistd_1), [interesting(0.9),axiom,file(amistd_1,rc1_amistd_1)]). fof(rc1_finseq_5,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_5,rc1_finseq_5), [interesting(0.9),axiom,file(finseq_5,rc1_finseq_5)]). fof(rc1_int_1,theorem,( ? [A] : ( m1_subset_1(A,k1_numbers) & v1_xcmplx_0(A) & v1_xreal_0(A) & v1_int_1(A) ) ), file(int_1,rc1_int_1), [interesting(0.9),axiom,file(int_1,rc1_int_1)]). fof(rc1_membered,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ), file(membered,rc1_membered), [interesting(0.9),axiom,file(membered,rc1_membered)]). fof(rc1_nat_1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(nat_1,rc1_nat_1), [interesting(0.9),axiom,file(nat_1,rc1_nat_1)]). fof(rc1_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_pre_circ,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ), file(pre_circ,rc1_pre_circ), [interesting(0.9),axiom,file(pre_circ,rc1_pre_circ)]). fof(rc1_realset1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_realset1(A) ) ), file(realset1,rc1_realset1), [interesting(0.9),axiom,file(realset1,rc1_realset1)]). fof(rc2_finseq_5,theorem,( ! [A] : ( ~ v1_xboole_0(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_5,rc2_finseq_5), [interesting(0.9),axiom,file(finseq_5,rc2_finseq_5)]). 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_int_1,theorem,( ? [A] : v1_int_1(A) ), file(int_1,rc2_int_1), [interesting(0.9),axiom,file(int_1,rc2_int_1)]). fof(rc2_nat_1,theorem,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(A) & v3_ordinal1(A) ) ), file(nat_1,rc2_nat_1), [interesting(0.9),axiom,file(nat_1,rc2_nat_1)]). fof(rc2_realset1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & ~ v1_realset1(A) ) ), file(realset1,rc2_realset1), [interesting(0.9),axiom,file(realset1,rc2_realset1)]). 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(rc3_funct_1,theorem,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ), file(funct_1,rc3_funct_1), [interesting(0.9),axiom,file(funct_1,rc3_funct_1)]). fof(rc3_nat_1,theorem,( ? [A] : ( m1_subset_1(A,k5_numbers) & ~ v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(nat_1,rc3_nat_1), [interesting(0.9),axiom,file(nat_1,rc3_nat_1)]). fof(rc4_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(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_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_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_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_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_numbers,axiom,( $true ), file(numbers,k1_numbers), [interesting(0.9),axiom,file(numbers,k1_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_k5_ordinal2,axiom,( $true ), file(ordinal2,k5_ordinal2), [interesting(0.9),axiom,file(ordinal2,k5_ordinal2)]). fof(dt_m1_finseq_1,axiom,( ! [A,B] : ( m1_finseq_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) ) ), file(finseq_1,m1_finseq_1), [interesting(0.9),axiom,file(finseq_1,m1_finseq_1)]). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), [interesting(0.9),axiom,file(relset_1,m1_relset_1)]). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), [interesting(0.9),axiom,file(subset_1,m1_subset_1)]). fof(dt_m2_finseq_1,axiom,( ! [A,B] : ( m2_finseq_1(B,A) => ( v1_funct_1(B) & v1_finseq_1(B) & m2_relset_1(B,k5_numbers,A) ) ) ), file(finseq_1,m2_finseq_1), [interesting(0.9),axiom,file(finseq_1,m2_finseq_1)]). fof(dt_m2_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(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_5,theorem,( ! [A] : ( v1_xboole_0(A) => v1_realset1(A) ) ), file(finseq_5,cc1_finseq_5), [interesting(0.9),axiom,file(finseq_5,cc1_finseq_5)]). 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_funct_1,theorem,( ! [A] : ( v1_xboole_0(A) => v1_funct_1(A) ) ), file(funct_1,cc1_funct_1), [interesting(0.9),axiom,file(funct_1,cc1_funct_1)]). fof(cc1_nat_1,theorem,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(nat_1,cc1_nat_1), [interesting(0.9),axiom,file(nat_1,cc1_nat_1)]). fof(cc1_relat_1,theorem,( ! [A] : ( v1_xboole_0(A) => v1_relat_1(A) ) ), file(relat_1,cc1_relat_1), [interesting(0.9),axiom,file(relat_1,cc1_relat_1)]). fof(cc1_scmring1,theorem,( ! [A] : ( ~ v1_finset_1(A) => ( ~ v1_xboole_0(A) & ~ v1_realset1(A) ) ) ), file(scmring1,cc1_scmring1), [interesting(0.9),axiom,file(scmring1,cc1_scmring1)]). fof(cc1_setfam_1,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_setfam_1(A) ) => ! [B] : ( m1_subset_1(B,A) => ~ v1_xboole_0(B) ) ) ), file(setfam_1,cc1_setfam_1), [interesting(0.9),axiom,file(setfam_1,cc1_setfam_1)]). 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_funct_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ) ), file(funct_1,cc2_funct_1), [interesting(0.9),axiom,file(funct_1,cc2_funct_1)]). fof(cc2_funct_7,theorem,( ! [A] : ( ( v1_xboole_0(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) & v1_finseq_1(A) & v1_funcop_1(A) & v1_funct_7(A) ) ) ), file(funct_7,cc2_funct_7), [interesting(0.9),axiom,file(funct_7,cc2_funct_7)]). fof(cc2_int_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) & v1_int_1(A) ) ) ), file(int_1,cc2_int_1), [interesting(0.9),axiom,file(int_1,cc2_int_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(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(fc1_ordinal2,theorem, ( v1_ordinal1(k5_ordinal2) & v2_ordinal1(k5_ordinal2) & v3_ordinal1(k5_ordinal2) & ~ v1_xboole_0(k5_ordinal2) ), file(ordinal2,fc1_ordinal2), [interesting(0.9),axiom,file(ordinal2,fc1_ordinal2)]). fof(fc1_subset_1,theorem,( ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ), file(subset_1,fc1_subset_1), [interesting(0.9),axiom,file(subset_1,fc1_subset_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(fc3_amistd_1,theorem,( ! [A,B] : ( ( ~ v1_xboole_0(A) & 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_xboole_0(k3_graph_2(A,B)) & v1_relat_1(k3_graph_2(A,B)) & v1_funct_1(k3_graph_2(A,B)) & v1_finset_1(k3_graph_2(A,B)) & v1_finseq_1(k3_graph_2(A,B)) & v1_setfam_1(k3_graph_2(A,B)) ) ) ), file(amistd_1,fc3_amistd_1), [interesting(0.9),axiom,file(amistd_1,fc3_amistd_1)]). 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_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_relat_1,theorem,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) ) ), file(relat_1,rc1_relat_1), [interesting(0.9),axiom,file(relat_1,rc1_relat_1)]). fof(rc1_setfam_1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_setfam_1(A) ) ), file(setfam_1,rc1_setfam_1), [interesting(0.9),axiom,file(setfam_1,rc1_setfam_1)]). fof(rc1_subset_1,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) ) ) ), file(subset_1,rc1_subset_1), [interesting(0.9),axiom,file(subset_1,rc1_subset_1)]). fof(rc1_xboole_0,theorem,( ? [A] : v1_xboole_0(A) ), file(xboole_0,rc1_xboole_0), [interesting(0.9),axiom,file(xboole_0,rc1_xboole_0)]). fof(rc2_finseq_1,theorem,( ! [A] : ? [B] : ( m1_relset_1(B,k5_numbers,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc2_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc2_finseq_1)]). fof(rc2_funct_1,theorem,( ? [A] : ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) ), file(funct_1,rc2_funct_1), [interesting(0.9),axiom,file(funct_1,rc2_funct_1)]). fof(rc2_partfun1,theorem,( ! [A,B] : ? [C] : ( m1_relset_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C) ) ), file(partfun1,rc2_partfun1), [interesting(0.9),axiom,file(partfun1,rc2_partfun1)]). fof(rc2_relat_1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) ) ), file(relat_1,rc2_relat_1), [interesting(0.9),axiom,file(relat_1,rc2_relat_1)]). fof(rc2_subset_1,theorem,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) ) ), file(subset_1,rc2_subset_1), [interesting(0.9),axiom,file(subset_1,rc2_subset_1)]). fof(rc2_xboole_0,theorem,( ? [A] : ~ v1_xboole_0(A) ), file(xboole_0,rc2_xboole_0), [interesting(0.9),axiom,file(xboole_0,rc2_xboole_0)]). 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(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(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(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(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(redefinition_k2_graph_2,definition,( ! [A,B,C,D] : ( ( m1_finseq_1(B,A) & m1_subset_1(C,k5_numbers) & m1_subset_1(D,k5_numbers) ) => k2_graph_2(A,B,C,D) = k1_graph_2(B,C,D) ) ), file(graph_2,k2_graph_2), [interesting(0.9),axiom,file(graph_2,k2_graph_2)]). fof(redefinition_k3_finseq_1,definition,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k3_finseq_1(A) = k1_card_1(A) ) ), file(finseq_1,k3_finseq_1), [interesting(0.9),axiom,file(finseq_1,k3_finseq_1)]). fof(redefinition_k4_graph_2,definition,( ! [A,B,C] : ( ( m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => k4_graph_2(A,B,C) = k3_graph_2(B,C) ) ), file(graph_2,k4_graph_2), [interesting(0.9),axiom,file(graph_2,k4_graph_2)]). fof(redefinition_k5_numbers,definition,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), [interesting(0.9),axiom,file(numbers,k5_numbers)]). 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_graph_2,axiom,( ! [A,B,C] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & m1_subset_1(B,k5_numbers) & m1_subset_1(C,k5_numbers) ) => ( v1_relat_1(k1_graph_2(A,B,C)) & v1_funct_1(k1_graph_2(A,B,C)) & v1_finseq_1(k1_graph_2(A,B,C)) ) ) ), file(graph_2,k1_graph_2), [interesting(0.9),axiom,file(graph_2,k1_graph_2)]). fof(dt_k2_graph_2,axiom,( ! [A,B,C,D] : ( ( m1_finseq_1(B,A) & m1_subset_1(C,k5_numbers) & m1_subset_1(D,k5_numbers) ) => m2_finseq_1(k2_graph_2(A,B,C,D),A) ) ), file(graph_2,k2_graph_2), [interesting(0.9),axiom,file(graph_2,k2_graph_2)]). fof(dt_k3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers) ) ), file(finseq_1,k3_finseq_1), [interesting(0.9),axiom,file(finseq_1,k3_finseq_1)]). fof(dt_k3_graph_2,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(k3_graph_2(A,B)) & v1_funct_1(k3_graph_2(A,B)) & v1_finseq_1(k3_graph_2(A,B)) ) ) ), file(graph_2,k3_graph_2), [interesting(0.9),axiom,file(graph_2,k3_graph_2)]). fof(dt_k4_finseq_4,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & m1_relset_1(C,A,B) ) => m1_subset_1(k4_finseq_4(A,B,C,D),B) ) ), file(finseq_4,k4_finseq_4), [interesting(0.9),axiom,file(finseq_4,k4_finseq_4)]). fof(dt_k4_graph_2,axiom,( ! [A,B,C] : ( ( m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => m2_finseq_1(k4_graph_2(A,B,C),A) ) ), file(graph_2,k4_graph_2), [interesting(0.9),axiom,file(graph_2,k4_graph_2)]). 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_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_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_8__amistd_1,assumption,( ~ v1_xboole_0(c1_8__amistd_1) ), introduced(assumption,[file(amistd_1,c1_8__amistd_1)]), [interesting(0.8),axiom,file(amistd_1,c1_8__amistd_1)]). fof(dt_c2_8__amistd_1,assumption, ( ~ v1_xboole_0(c2_8__amistd_1) & m2_finseq_1(c2_8__amistd_1,c1_8__amistd_1) ), introduced(assumption,[file(amistd_1,c2_8__amistd_1)]), [interesting(0.8),axiom,file(amistd_1,c2_8__amistd_1)]). fof(dt_c3_8__amistd_1,assumption,( m2_finseq_1(c3_8__amistd_1,c1_8__amistd_1) ), introduced(assumption,[file(amistd_1,c3_8__amistd_1)]), [interesting(0.8),axiom,file(amistd_1,c3_8__amistd_1)]). fof(cc1_amistd_1,theorem,( ! [A] : ( v1_relat_1(A) => ( v1_relat_1(A) & v1_setfam_1(A) ) ) ), file(amistd_1,cc1_amistd_1), [interesting(0.9),axiom,file(amistd_1,cc1_amistd_1)]). 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(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_funct_1,theorem,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc1_funct_1), [interesting(0.9),axiom,file(funct_1,rc1_funct_1)]). 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(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(spc1_boole,theorem,( ~ v1_xboole_0(1) ), file(boole,spc1_boole), [interesting(0.9),axiom,file(boole,spc1_boole)]). fof(spc2_boole,theorem,( ~ v1_xboole_0(2) ), file(boole,spc2_boole), [interesting(0.9),axiom,file(boole,spc2_boole)]). fof(d2_graph_2,definition,( ! [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) ) => k3_graph_2(A,B) = k7_finseq_1(A,k1_graph_2(B,2,k3_finseq_1(B))) ) ) ), file(graph_2,d2_graph_2), [interesting(0.9),axiom,file(graph_2,d2_graph_2)]). fof(e1_8_1__amistd_1,plain,( k4_finseq_4(k5_numbers,c1_8__amistd_1,k4_graph_2(c1_8__amistd_1,c2_8__amistd_1,c3_8__amistd_1),1) = k4_finseq_4(k5_numbers,c1_8__amistd_1,k8_finseq_1(c1_8__amistd_1,c2_8__amistd_1,k2_graph_2(c1_8__amistd_1,c3_8__amistd_1,2,k3_finseq_1(c3_8__amistd_1))),1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_8__amistd_1,dt_c2_8__amistd_1,dt_c3_8__amistd_1])],[dt_k2_zfmisc_1,cc1_relset_1,fc14_finset_1,fc4_subset_1,rc3_relat_1,rc4_funct_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_7,cc1_membered,cc1_realset1,cc20_membered,cc2_membered,cc3_int_1,cc3_membered,cc3_nat_1,cc4_int_1,cc4_membered,fc12_relat_1,fc1_xboole_0,fc2_finseq_1,fc3_funct_7,fc4_relat_1,fc6_membered,fc8_funct_7,rc1_amistd_1,rc1_finseq_5,rc1_int_1,rc1_membered,rc1_nat_1,rc1_partfun1,rc1_pre_circ,rc1_realset1,rc2_finseq_5,rc2_finset_1,rc2_int_1,rc2_nat_1,rc2_realset1,rc3_finseq_1,rc3_funct_1,rc3_nat_1,rc4_finseq_1,rc6_finseq_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_subset_1,redefinition_m2_finseq_1,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_subset_1,cc15_membered,cc1_finseq_5,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc1_relat_1,cc1_scmring1,cc1_setfam_1,cc2_finset_1,cc2_funct_1,cc2_funct_7,cc2_int_1,cc2_nat_1,cc6_membered,cc9_membered,fc13_finseq_1,fc14_finseq_1,fc1_ordinal2,fc1_subset_1,fc2_membered,fc3_amistd_1,fc5_membered,rc1_finset_1,rc1_relat_1,rc1_setfam_1,rc1_subset_1,rc1_xboole_0,rc2_finseq_1,rc2_funct_1,rc2_partfun1,rc2_relat_1,rc2_subset_1,rc2_xboole_0,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,redefinition_k2_graph_2,redefinition_k3_finseq_1,redefinition_k4_graph_2,redefinition_k5_numbers,redefinition_k8_finseq_1,dt_k1_graph_2,dt_k2_graph_2,dt_k3_finseq_1,dt_k3_graph_2,dt_k4_finseq_4,dt_k4_graph_2,dt_k5_numbers,dt_k7_finseq_1,dt_k8_finseq_1,dt_c1_8__amistd_1,dt_c2_8__amistd_1,dt_c3_8__amistd_1,cc1_amistd_1,cc1_finseq_1,rc1_finseq_1,rc1_funct_1,spc1_numerals,spc2_numerals,spc1_boole,spc2_boole,d2_graph_2]), [interesting(0.65),file(amistd_1,e1_8_1__amistd_1),[file(amistd_1,e1_8_1__amistd_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(fc5_relat_1,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) ) => ~ v1_xboole_0(k1_relat_1(A)) ) ), file(relat_1,fc5_relat_1), [interesting(0.9),axiom,file(relat_1,fc5_relat_1)]). fof(fc7_relat_1,theorem,( ! [A] : ( v1_xboole_0(A) => ( v1_xboole_0(k1_relat_1(A)) & v1_relat_1(k1_relat_1(A)) ) ) ), file(relat_1,fc7_relat_1), [interesting(0.9),axiom,file(relat_1,fc7_relat_1)]). fof(redefinition_k4_finseq_1,definition,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k4_finseq_1(A) = k1_relat_1(A) ) ), file(finseq_1,k4_finseq_1), [interesting(0.9),axiom,file(finseq_1,k4_finseq_1)]). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), [interesting(0.9),axiom,file(funct_1,k1_funct_1)]). fof(dt_k1_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), [interesting(0.9),axiom,file(relat_1,k1_relat_1)]). fof(dt_k4_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m1_subset_1(k4_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ), file(finseq_1,k4_finseq_1), [interesting(0.9),axiom,file(finseq_1,k4_finseq_1)]). fof(t6_finseq_5,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( r2_hidden(1,k4_finseq_1(A)) & r2_hidden(k3_finseq_1(A),k4_finseq_1(A)) ) ) ), file(finseq_5,t6_finseq_5), [interesting(0.9),axiom,file(finseq_5,t6_finseq_5)]). fof(e2_8__amistd_1,plain,( r2_hidden(1,k4_finseq_1(k8_finseq_1(c1_8__amistd_1,c2_8__amistd_1,k2_graph_2(c1_8__amistd_1,c3_8__amistd_1,2,k3_finseq_1(c3_8__amistd_1))))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_8__amistd_1,dt_c2_8__amistd_1,dt_c3_8__amistd_1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,fc4_subset_1,rc2_finseq_1,rc2_partfun1,reflexivity_r1_tarski,existence_m2_relset_1,redefinition_m2_relset_1,dt_k5_ordinal2,dt_m2_relset_1,cc3_int_1,cc3_nat_1,cc4_int_1,fc1_ordinal2,fc5_membered,rc1_int_1,rc1_nat_1,rc2_finset_1,rc2_int_1,rc2_nat_1,rc3_nat_1,rc3_relat_1,rc4_funct_1,existence_m1_finseq_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_graph_2,dt_k1_numbers,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_numbers,dt_k7_finseq_1,dt_m1_finseq_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_funct_7,cc1_membered,cc1_nat_1,cc1_realset1,cc1_scmring1,cc1_setfam_1,cc20_membered,cc2_finset_1,cc2_int_1,cc2_membered,cc2_nat_1,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc12_relat_1,fc13_finseq_1,fc14_finseq_1,fc17_finseq_1,fc1_subset_1,fc1_xboole_0,fc2_finseq_1,fc2_membered,fc3_funct_7,fc4_relat_1,fc5_relat_1,fc6_membered,fc7_relat_1,fc8_funct_7,rc1_amistd_1,rc1_finseq_5,rc1_finset_1,rc1_membered,rc1_partfun1,rc1_pre_circ,rc1_realset1,rc1_setfam_1,rc1_subset_1,rc2_finseq_5,rc2_realset1,rc2_subset_1,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc4_finseq_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t3_subset,t4_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,redefinition_k2_graph_2,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k8_finseq_1,dt_k2_graph_2,dt_k3_finseq_1,dt_k4_finseq_1,dt_k8_finseq_1,dt_c1_8__amistd_1,dt_c2_8__amistd_1,dt_c3_8__amistd_1,cc15_membered,cc1_amistd_1,cc1_finseq_1,cc1_finseq_5,cc1_finset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,cc2_funct_7,rc1_finseq_1,rc1_funct_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,spc1_boole,spc2_boole,t1_subset,t6_boole,t7_boole,spc1_numerals,spc2_numerals,spc1_boole,spc2_boole,t6_finseq_5]), [interesting(0.8),file(amistd_1,e2_8__amistd_1),[file(amistd_1,e2_8__amistd_1)]]). fof(d4_finseq_4,definition,( ! [A,B,C] : ( ( v1_funct_1(C) & m2_relset_1(C,A,B) ) => ! [D] : ( r2_hidden(D,k1_relat_1(C)) => k4_finseq_4(A,B,C,D) = k1_funct_1(C,D) ) ) ), file(finseq_4,d4_finseq_4), [interesting(0.9),axiom,file(finseq_4,d4_finseq_4)]). fof(e2_8_1__amistd_1,plain,( k4_finseq_4(k5_numbers,c1_8__amistd_1,k8_finseq_1(c1_8__amistd_1,c2_8__amistd_1,k2_graph_2(c1_8__amistd_1,c3_8__amistd_1,2,k3_finseq_1(c3_8__amistd_1))),1) = k1_funct_1(k8_finseq_1(c1_8__amistd_1,c2_8__amistd_1,k2_graph_2(c1_8__amistd_1,c3_8__amistd_1,2,k3_finseq_1(c3_8__amistd_1))),1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_8__amistd_1,dt_c2_8__amistd_1,dt_c3_8__amistd_1])],[rc3_relat_1,rc4_funct_1,reflexivity_r1_tarski,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_7,cc1_membered,cc1_realset1,cc1_scmring1,cc1_setfam_1,cc20_membered,cc2_finset_1,cc2_membered,cc3_int_1,cc3_membered,cc3_nat_1,cc4_int_1,cc4_membered,fc12_relat_1,fc14_finset_1,fc17_finseq_1,fc1_xboole_0,fc2_finseq_1,fc3_funct_7,fc4_relat_1,fc6_membered,fc8_funct_7,rc1_amistd_1,rc1_finseq_5,rc1_finset_1,rc1_int_1,rc1_membered,rc1_nat_1,rc1_partfun1,rc1_pre_circ,rc1_realset1,rc1_setfam_1,rc2_finseq_1,rc2_finseq_5,rc2_finset_1,rc2_int_1,rc2_nat_1,rc2_realset1,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc3_nat_1,rc4_finseq_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_subset_1,redefinition_m2_finseq_1,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_graph_2,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_k7_finseq_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_subset_1,cc15_membered,cc1_amistd_1,cc1_finseq_1,cc1_finseq_5,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc1_relat_1,cc1_relset_1,cc2_funct_1,cc2_funct_7,cc2_int_1,cc2_nat_1,cc6_membered,cc9_membered,fc13_finseq_1,fc14_finseq_1,fc1_ordinal2,fc1_subset_1,fc2_membered,fc4_subset_1,fc5_membered,fc5_relat_1,fc7_relat_1,rc1_finseq_1,rc1_funct_1,rc1_relat_1,rc1_subset_1,rc1_xboole_0,rc2_funct_1,rc2_partfun1,rc2_relat_1,rc2_subset_1,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_k2_graph_2,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_k8_finseq_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_relat_1,dt_k2_graph_2,dt_k3_finseq_1,dt_k4_finseq_1,dt_k4_finseq_4,dt_k5_numbers,dt_k8_finseq_1,dt_m2_relset_1,dt_c1_8__amistd_1,dt_c2_8__amistd_1,dt_c3_8__amistd_1,t1_subset,t7_boole,spc1_numerals,spc2_numerals,spc1_boole,spc2_boole,e2_8__amistd_1,d4_finseq_4]), [interesting(0.65),file(amistd_1,e2_8_1__amistd_1),[file(amistd_1,e2_8_1__amistd_1)]]). fof(fc1_int_1,theorem,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_int_1(k2_xcmplx_0(A,B)) ) ) ), file(int_1,fc1_int_1), [interesting(0.9),axiom,file(int_1,fc1_int_1)]). fof(fc6_int_1,theorem,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & v1_int_1(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v1_int_1(k2_xcmplx_0(B,A)) ) ) ), file(int_1,fc6_int_1), [interesting(0.9),axiom,file(int_1,fc6_int_1)]). 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(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_k1_finseq_1,axiom,( $true ), file(finseq_1,k1_finseq_1), [interesting(0.9),axiom,file(finseq_1,k1_finseq_1)]). fof(dt_k2_xcmplx_0,axiom,( $true ), file(xcmplx_0,k2_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k2_xcmplx_0)]). fof(fc1_finseq_1,theorem,( ! [A] : ( v4_ordinal2(A) => v1_finset_1(k1_finseq_1(A)) ) ), file(finseq_1,fc1_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc1_finseq_1)]). fof(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(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(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(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(redefinition_k2_finseq_1,definition,( ! [A] : ( v4_ordinal2(A) => k2_finseq_1(A) = k1_finseq_1(A) ) ), file(finseq_1,k2_finseq_1), [interesting(0.9),axiom,file(finseq_1,k2_finseq_1)]). fof(dt_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => m2_subset_1(k1_nat_1(A,B),k1_numbers,k5_numbers) ) ), file(nat_1,k1_nat_1), [interesting(0.9),axiom,file(nat_1,k1_nat_1)]). fof(dt_k2_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => m1_subset_1(k2_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ), file(finseq_1,k2_finseq_1), [interesting(0.9),axiom,file(finseq_1,k2_finseq_1)]). fof(e1_8__amistd_1,plain,( r2_hidden(1,k4_finseq_1(c2_8__amistd_1)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_8__amistd_1,dt_c2_8__amistd_1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,fc4_subset_1,rc2_finseq_1,rc2_partfun1,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,cc3_int_1,cc3_nat_1,cc4_int_1,fc1_ordinal2,fc5_membered,rc1_int_1,rc1_nat_1,rc2_finseq_5,rc2_finset_1,rc2_int_1,rc2_nat_1,rc3_nat_1,rc3_relat_1,rc4_finseq_1,rc4_funct_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_numbers,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_subset_1,dt_c1_8__amistd_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_7,cc1_membered,cc1_nat_1,cc1_realset1,cc1_scmring1,cc1_setfam_1,cc20_membered,cc2_finset_1,cc2_int_1,cc2_membered,cc2_nat_1,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc12_relat_1,fc17_finseq_1,fc1_subset_1,fc1_xboole_0,fc2_finseq_1,fc2_membered,fc3_funct_7,fc4_relat_1,fc5_relat_1,fc6_membered,fc7_relat_1,rc1_amistd_1,rc1_finseq_5,rc1_finset_1,rc1_membered,rc1_partfun1,rc1_pre_circ,rc1_realset1,rc1_setfam_1,rc1_subset_1,rc2_realset1,rc2_subset_1,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t3_subset,t4_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,redefinition_k3_finseq_1,redefinition_k4_finseq_1,dt_k3_finseq_1,dt_k4_finseq_1,dt_c2_8__amistd_1,cc15_membered,cc1_amistd_1,cc1_finseq_1,cc1_finseq_5,cc1_finset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,cc2_funct_7,rc1_finseq_1,rc1_funct_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,spc1_boole,t1_subset,t6_boole,t7_boole,spc1_numerals,spc1_boole,t6_finseq_5]), [interesting(0.8),file(amistd_1,e1_8__amistd_1),[file(amistd_1,e1_8__amistd_1)]]). fof(d7_finseq_1,definition,( ! [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) ) => ( C = k7_finseq_1(A,B) <=> ( k4_finseq_1(C) = k2_finseq_1(k1_nat_1(k3_finseq_1(A),k3_finseq_1(B))) & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( r2_hidden(D,k4_finseq_1(A)) => k1_funct_1(C,D) = k1_funct_1(A,D) ) ) & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( r2_hidden(D,k4_finseq_1(B)) => k1_funct_1(C,k1_nat_1(k3_finseq_1(A),D)) = k1_funct_1(B,D) ) ) ) ) ) ) ) ), file(finseq_1,d7_finseq_1), [interesting(0.9),axiom,file(finseq_1,d7_finseq_1)]). fof(e3_8_1__amistd_1,plain,( k1_funct_1(k8_finseq_1(c1_8__amistd_1,c2_8__amistd_1,k2_graph_2(c1_8__amistd_1,c3_8__amistd_1,2,k3_finseq_1(c3_8__amistd_1))),1) = k1_funct_1(c2_8__amistd_1,1) ), inference(mizar_by,[status(thm),assumptions([dt_c3_8__amistd_1,dt_c1_8__amistd_1,dt_c2_8__amistd_1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,fc4_subset_1,rc2_finseq_1,rc2_partfun1,rc3_relat_1,rc4_funct_1,reflexivity_r1_tarski,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_m2_relset_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_funct_7,cc1_membered,cc1_realset1,cc20_membered,cc2_membered,cc3_membered,cc4_int_1,fc12_relat_1,fc1_int_1,fc1_xboole_0,fc2_finseq_1,fc3_funct_7,fc4_relat_1,fc6_int_1,fc6_membered,fc8_funct_7,rc1_amistd_1,rc1_finseq_5,rc1_int_1,rc1_membered,rc1_nat_1,rc1_partfun1,rc1_pre_circ,rc1_realset1,rc2_finseq_5,rc2_finset_1,rc2_int_1,rc2_nat_1,rc2_realset1,rc3_finseq_1,rc3_funct_1,rc3_nat_1,rc4_finseq_1,rc6_finseq_1,spc6_arithm,commutativity_k2_xcmplx_0,existence_m1_finseq_1,existence_m1_subset_1,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_graph_2,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_xcmplx_0,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_finseq_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finseq_5,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc1_relat_1,cc1_scmring1,cc1_setfam_1,cc2_finset_1,cc2_funct_1,cc2_funct_7,cc2_int_1,cc2_nat_1,cc3_int_1,cc3_nat_1,cc4_membered,cc6_membered,cc9_membered,fc13_finseq_1,fc14_finseq_1,fc17_finseq_1,fc1_finseq_1,fc1_nat_1,fc1_ordinal2,fc1_subset_1,fc3_nat_1,fc4_nat_1,fc5_membered,fc5_relat_1,fc7_relat_1,rc1_finset_1,rc1_relat_1,rc1_setfam_1,rc1_subset_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_subset_1,rc2_xboole_0,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,rqRealAdd__k2_xcmplx_0__r1_r1_r2,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k1_nat_1,antisymmetry_r2_hidden,existence_m2_subset_1,redefinition_k1_nat_1,redefinition_k2_finseq_1,redefinition_k2_graph_2,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_k8_finseq_1,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_nat_1,dt_k1_numbers,dt_k2_finseq_1,dt_k2_graph_2,dt_k3_finseq_1,dt_k4_finseq_1,dt_k5_numbers,dt_k7_finseq_1,dt_k8_finseq_1,dt_m2_subset_1,dt_c1_8__amistd_1,dt_c2_8__amistd_1,dt_c3_8__amistd_1,cc1_amistd_1,cc1_finseq_1,fc2_membered,rc1_finseq_1,rc1_funct_1,t1_subset,t7_boole,spc1_numerals,spc2_numerals,spc1_boole,spc2_boole,e1_8__amistd_1,d7_finseq_1]), [interesting(0.65),file(amistd_1,e3_8_1__amistd_1),[file(amistd_1,e3_8_1__amistd_1)]]). fof(e4_8_1__amistd_1,plain,( k1_funct_1(c2_8__amistd_1,1) = k4_finseq_4(k5_numbers,c1_8__amistd_1,c2_8__amistd_1,1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_8__amistd_1,dt_c2_8__amistd_1])],[rc3_relat_1,rc4_funct_1,reflexivity_r1_tarski,existence_m1_finseq_1,dt_k1_xboole_0,dt_m1_finseq_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_7,cc1_membered,cc1_realset1,cc1_scmring1,cc1_setfam_1,cc20_membered,cc2_finset_1,cc2_membered,cc3_int_1,cc3_membered,cc3_nat_1,cc4_int_1,cc4_membered,fc12_relat_1,fc14_finset_1,fc17_finseq_1,fc1_xboole_0,fc2_finseq_1,fc3_funct_7,fc4_relat_1,fc6_membered,rc1_amistd_1,rc1_finseq_5,rc1_finset_1,rc1_int_1,rc1_membered,rc1_nat_1,rc1_partfun1,rc1_pre_circ,rc1_realset1,rc1_setfam_1,rc2_finseq_1,rc2_finseq_5,rc2_finset_1,rc2_int_1,rc2_nat_1,rc2_realset1,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc3_nat_1,rc4_finseq_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_subset_1,redefinition_m2_finseq_1,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_subset_1,cc15_membered,cc1_amistd_1,cc1_finseq_1,cc1_finseq_5,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc1_relat_1,cc1_relset_1,cc2_funct_1,cc2_funct_7,cc2_int_1,cc2_nat_1,cc6_membered,cc9_membered,fc1_ordinal2,fc1_subset_1,fc2_membered,fc4_subset_1,fc5_membered,fc5_relat_1,fc7_relat_1,rc1_finseq_1,rc1_funct_1,rc1_relat_1,rc1_subset_1,rc1_xboole_0,rc2_funct_1,rc2_partfun1,rc2_relat_1,rc2_subset_1,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_relat_1,dt_k4_finseq_1,dt_k4_finseq_4,dt_k5_numbers,dt_m2_relset_1,dt_c1_8__amistd_1,dt_c2_8__amistd_1,t1_subset,t7_boole,spc1_numerals,spc1_boole,e1_8__amistd_1,d4_finseq_4]), [interesting(0.65),file(amistd_1,e4_8_1__amistd_1),[file(amistd_1,e4_8_1__amistd_1)]]). fof(e3_8__amistd_1,plain,( k4_finseq_4(k5_numbers,c1_8__amistd_1,k4_graph_2(c1_8__amistd_1,c2_8__amistd_1,c3_8__amistd_1),1) = k4_finseq_4(k5_numbers,c1_8__amistd_1,c2_8__amistd_1,1) ), inference(iterative_eq,[status(thm),assumptions([dt_c3_8__amistd_1,dt_c1_8__amistd_1,dt_c2_8__amistd_1])],[e1_8_1__amistd_1,e2_8_1__amistd_1,e3_8_1__amistd_1,e4_8_1__amistd_1]), [interesting(0.8),file(amistd_1,e3_8__amistd_1),[file(amistd_1,e3_8__amistd_1)]]). fof(i4_8__amistd_1,theorem,( $true ), introduced(tautology,[file(amistd_1,i4_8__amistd_1)]), [interesting(0.8),trivial,file(amistd_1,i4_8__amistd_1)]). fof(i3_8__amistd_1,plain,( k4_finseq_4(k5_numbers,c1_8__amistd_1,k4_graph_2(c1_8__amistd_1,c2_8__amistd_1,c3_8__amistd_1),1) = k4_finseq_4(k5_numbers,c1_8__amistd_1,c2_8__amistd_1,1) ), inference(conclusion,[status(thm),assumptions([dt_c3_8__amistd_1,dt_c1_8__amistd_1,dt_c2_8__amistd_1])],[e3_8__amistd_1,i4_8__amistd_1]), [interesting(0.8),file(amistd_1,i3_8__amistd_1),[file(amistd_1,i3_8__amistd_1)]]). fof(i3_8_tmp__amistd_1,plain, ( m2_finseq_1(c3_8__amistd_1,c1_8__amistd_1) => k4_finseq_4(k5_numbers,c1_8__amistd_1,k4_graph_2(c1_8__amistd_1,c2_8__amistd_1,c3_8__amistd_1),1) = k4_finseq_4(k5_numbers,c1_8__amistd_1,c2_8__amistd_1,1) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_8__amistd_1,dt_c2_8__amistd_1]),discharge_asm(discharge,[dt_c3_8__amistd_1])],[dt_c3_8__amistd_1,i3_8__amistd_1]), [interesting(0.8),i2_8__amistd_1]). fof(i2_8__amistd_1,plain,( ! [A] : ( m2_finseq_1(A,c1_8__amistd_1) => k4_finseq_4(k5_numbers,c1_8__amistd_1,k4_graph_2(c1_8__amistd_1,c2_8__amistd_1,A),1) = k4_finseq_4(k5_numbers,c1_8__amistd_1,c2_8__amistd_1,1) ) ), inference(let,[status(thm),assumptions([dt_c1_8__amistd_1,dt_c2_8__amistd_1])],[i3_8_tmp__amistd_1,dh_c3_8__amistd_1]), [interesting(0.8),file(amistd_1,i2_8__amistd_1),[file(amistd_1,i2_8__amistd_1)]]). fof(i2_8_tmp__amistd_1,plain, ( ( ~ v1_xboole_0(c2_8__amistd_1) & m2_finseq_1(c2_8__amistd_1,c1_8__amistd_1) ) => ! [A] : ( m2_finseq_1(A,c1_8__amistd_1) => k4_finseq_4(k5_numbers,c1_8__amistd_1,k4_graph_2(c1_8__amistd_1,c2_8__amistd_1,A),1) = k4_finseq_4(k5_numbers,c1_8__amistd_1,c2_8__amistd_1,1) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_8__amistd_1]),discharge_asm(discharge,[dt_c2_8__amistd_1])],[dt_c2_8__amistd_1,i2_8__amistd_1]), [interesting(0.8),i1_8__amistd_1]). fof(i1_8__amistd_1,plain,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_finseq_1(A,c1_8__amistd_1) ) => ! [B] : ( m2_finseq_1(B,c1_8__amistd_1) => k4_finseq_4(k5_numbers,c1_8__amistd_1,k4_graph_2(c1_8__amistd_1,A,B),1) = k4_finseq_4(k5_numbers,c1_8__amistd_1,A,1) ) ) ), inference(let,[status(thm),assumptions([dt_c1_8__amistd_1])],[i2_8_tmp__amistd_1,dh_c2_8__amistd_1]), [interesting(0.8),file(amistd_1,i1_8__amistd_1),[file(amistd_1,i1_8__amistd_1)]]). fof(i1_8_tmp__amistd_1,plain, ( ~ v1_xboole_0(c1_8__amistd_1) => ! [A] : ( ( ~ v1_xboole_0(A) & m2_finseq_1(A,c1_8__amistd_1) ) => ! [B] : ( m2_finseq_1(B,c1_8__amistd_1) => k4_finseq_4(k5_numbers,c1_8__amistd_1,k4_graph_2(c1_8__amistd_1,A,B),1) = k4_finseq_4(k5_numbers,c1_8__amistd_1,A,1) ) ) ), inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_8__amistd_1])],[dt_c1_8__amistd_1,i1_8__amistd_1]), [interesting(1),t5_amistd_1]). fof(t5_amistd_1,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,A) ) => ! [C] : ( m2_finseq_1(C,A) => k4_finseq_4(k5_numbers,A,k4_graph_2(A,B,C),1) = k4_finseq_4(k5_numbers,A,B,1) ) ) ) ), inference(let,[status(thm),assumptions([])],[i1_8_tmp__amistd_1,dh_c1_8__amistd_1]), [interesting(1),file(amistd_1,t5_amistd_1),[file(amistd_1,t5_amistd_1)]]).