% Mizar ND problem: t9_amistd_1,amistd_1,184,45 fof(dh_c1_12__amistd_1,definition, ( ( ~ v1_xboole_0(c1_12__amistd_1) => ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_finseq_1(B,c1_12__amistd_1) => ! [C] : ( m2_finseq_1(C,c1_12__amistd_1) => ( ( r1_xreal_0(1,A) & r1_xreal_0(A,k3_finseq_1(B)) ) => k4_finseq_4(k5_numbers,c1_12__amistd_1,k4_graph_2(c1_12__amistd_1,B,C),A) = k4_finseq_4(k5_numbers,c1_12__amistd_1,B,A) ) ) ) ) ) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ! [F] : ( m2_finseq_1(F,D) => ! [G] : ( m2_finseq_1(G,D) => ( ( r1_xreal_0(1,E) & r1_xreal_0(E,k3_finseq_1(F)) ) => k4_finseq_4(k5_numbers,D,k4_graph_2(D,F,G),E) = k4_finseq_4(k5_numbers,D,F,E) ) ) ) ) ) ), introduced(definition,[new_symbol(c1_12__amistd_1),file(amistd_1,c1_12__amistd_1)]), [interesting(0.8),axiom,file(amistd_1,c1_12__amistd_1)]). fof(dh_c2_12__amistd_1,definition, ( ( m2_subset_1(c2_12__amistd_1,k1_numbers,k5_numbers) => ! [A] : ( m2_finseq_1(A,c1_12__amistd_1) => ! [B] : ( m2_finseq_1(B,c1_12__amistd_1) => ( ( r1_xreal_0(1,c2_12__amistd_1) & r1_xreal_0(c2_12__amistd_1,k3_finseq_1(A)) ) => k4_finseq_4(k5_numbers,c1_12__amistd_1,k4_graph_2(c1_12__amistd_1,A,B),c2_12__amistd_1) = k4_finseq_4(k5_numbers,c1_12__amistd_1,A,c2_12__amistd_1) ) ) ) ) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( m2_finseq_1(D,c1_12__amistd_1) => ! [E] : ( m2_finseq_1(E,c1_12__amistd_1) => ( ( r1_xreal_0(1,C) & r1_xreal_0(C,k3_finseq_1(D)) ) => k4_finseq_4(k5_numbers,c1_12__amistd_1,k4_graph_2(c1_12__amistd_1,D,E),C) = k4_finseq_4(k5_numbers,c1_12__amistd_1,D,C) ) ) ) ) ), introduced(definition,[new_symbol(c2_12__amistd_1),file(amistd_1,c2_12__amistd_1)]), [interesting(0.8),axiom,file(amistd_1,c2_12__amistd_1)]). fof(dh_c3_12__amistd_1,definition, ( ( m2_finseq_1(c3_12__amistd_1,c1_12__amistd_1) => ! [A] : ( m2_finseq_1(A,c1_12__amistd_1) => ( ( r1_xreal_0(1,c2_12__amistd_1) & r1_xreal_0(c2_12__amistd_1,k3_finseq_1(c3_12__amistd_1)) ) => k4_finseq_4(k5_numbers,c1_12__amistd_1,k4_graph_2(c1_12__amistd_1,c3_12__amistd_1,A),c2_12__amistd_1) = k4_finseq_4(k5_numbers,c1_12__amistd_1,c3_12__amistd_1,c2_12__amistd_1) ) ) ) => ! [B] : ( m2_finseq_1(B,c1_12__amistd_1) => ! [C] : ( m2_finseq_1(C,c1_12__amistd_1) => ( ( r1_xreal_0(1,c2_12__amistd_1) & r1_xreal_0(c2_12__amistd_1,k3_finseq_1(B)) ) => k4_finseq_4(k5_numbers,c1_12__amistd_1,k4_graph_2(c1_12__amistd_1,B,C),c2_12__amistd_1) = k4_finseq_4(k5_numbers,c1_12__amistd_1,B,c2_12__amistd_1) ) ) ) ), introduced(definition,[new_symbol(c3_12__amistd_1),file(amistd_1,c3_12__amistd_1)]), [interesting(0.8),axiom,file(amistd_1,c3_12__amistd_1)]). fof(dh_c4_12__amistd_1,definition, ( ( m2_finseq_1(c4_12__amistd_1,c1_12__amistd_1) => ( ( r1_xreal_0(1,c2_12__amistd_1) & r1_xreal_0(c2_12__amistd_1,k3_finseq_1(c3_12__amistd_1)) ) => k4_finseq_4(k5_numbers,c1_12__amistd_1,k4_graph_2(c1_12__amistd_1,c3_12__amistd_1,c4_12__amistd_1),c2_12__amistd_1) = k4_finseq_4(k5_numbers,c1_12__amistd_1,c3_12__amistd_1,c2_12__amistd_1) ) ) => ! [A] : ( m2_finseq_1(A,c1_12__amistd_1) => ( ( r1_xreal_0(1,c2_12__amistd_1) & r1_xreal_0(c2_12__amistd_1,k3_finseq_1(c3_12__amistd_1)) ) => k4_finseq_4(k5_numbers,c1_12__amistd_1,k4_graph_2(c1_12__amistd_1,c3_12__amistd_1,A),c2_12__amistd_1) = k4_finseq_4(k5_numbers,c1_12__amistd_1,c3_12__amistd_1,c2_12__amistd_1) ) ) ), introduced(definition,[new_symbol(c4_12__amistd_1),file(amistd_1,c4_12__amistd_1)]), [interesting(0.8),axiom,file(amistd_1,c4_12__amistd_1)]). fof(e1_12__amistd_1,assumption,( r1_xreal_0(1,c2_12__amistd_1) ), introduced(assumption,[file(amistd_1,e1_12__amistd_1)]), [interesting(0.8),axiom,file(amistd_1,e1_12__amistd_1)]). fof(e2_12__amistd_1,assumption,( r1_xreal_0(c2_12__amistd_1,k3_finseq_1(c3_12__amistd_1)) ), introduced(assumption,[file(amistd_1,e2_12__amistd_1)]), [interesting(0.8),axiom,file(amistd_1,e2_12__amistd_1)]). fof(e1_12_1_1__amistd_1,assumption,( c4_12__amistd_1 = k1_xboole_0 ), introduced(assumption,[file(amistd_1,e1_12_1_1__amistd_1)]), [interesting(0.5),axiom,file(amistd_1,e1_12_1_1__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(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_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(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_realset1,theorem,( ! [A] : ( ~ v1_realset1(A) => ~ v1_xboole_0(A) ) ), file(realset1,cc1_realset1), [interesting(0.9),axiom,file(realset1,cc1_realset1)]). 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_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(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_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_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_realset1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_realset1(A) ) ), file(realset1,rc1_realset1), [interesting(0.9),axiom,file(realset1,rc1_realset1)]). 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_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(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_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(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(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(cc16_membered,theorem,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_membered(B) ) ) ), file(membered,cc16_membered), [interesting(0.9),axiom,file(membered,cc16_membered)]). fof(cc17_membered,theorem,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) ) ) ) ), file(membered,cc17_membered), [interesting(0.9),axiom,file(membered,cc17_membered)]). fof(cc18_membered,theorem,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) ) ) ) ), file(membered,cc18_membered), [interesting(0.9),axiom,file(membered,cc18_membered)]). fof(cc19_membered,theorem,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) ) ) ) ), file(membered,cc19_membered), [interesting(0.9),axiom,file(membered,cc19_membered)]). fof(cc1_finseq_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_membered,theorem,( ! [A] : ( v5_membered(A) => v4_membered(A) ) ), file(membered,cc1_membered), [interesting(0.9),axiom,file(membered,cc1_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_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(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_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_membered,theorem,( ! [A] : ( v4_membered(A) => v3_membered(A) ) ), file(membered,cc2_membered), [interesting(0.9),axiom,file(membered,cc2_membered)]). 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(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(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(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_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_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_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_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_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_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_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_finset_1,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc3_finset_1), [interesting(0.9),axiom,file(finset_1,rc3_finset_1)]). fof(rc3_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_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_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(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(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(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(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(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(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]). 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_c1_12__amistd_1,assumption,( ~ v1_xboole_0(c1_12__amistd_1) ), introduced(assumption,[file(amistd_1,c1_12__amistd_1)]), [interesting(0.8),axiom,file(amistd_1,c1_12__amistd_1)]). fof(dt_c2_12__amistd_1,assumption,( m2_subset_1(c2_12__amistd_1,k1_numbers,k5_numbers) ), introduced(assumption,[file(amistd_1,c2_12__amistd_1)]), [interesting(0.8),axiom,file(amistd_1,c2_12__amistd_1)]). fof(dt_c3_12__amistd_1,assumption,( m2_finseq_1(c3_12__amistd_1,c1_12__amistd_1) ), introduced(assumption,[file(amistd_1,c3_12__amistd_1)]), [interesting(0.8),axiom,file(amistd_1,c3_12__amistd_1)]). fof(dt_c4_12__amistd_1,assumption,( m2_finseq_1(c4_12__amistd_1,c1_12__amistd_1) ), introduced(assumption,[file(amistd_1,c4_12__amistd_1)]), [interesting(0.8),axiom,file(amistd_1,c4_12__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(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(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(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_amistd_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k3_graph_2(A,k1_xboole_0) = A ) ), file(amistd_1,t7_amistd_1), [interesting(0.9),axiom,file(amistd_1,t7_amistd_1)]). fof(e2_12_1_1__amistd_1,plain,( k4_finseq_4(k5_numbers,c1_12__amistd_1,k4_graph_2(c1_12__amistd_1,c3_12__amistd_1,c4_12__amistd_1),c2_12__amistd_1) = k4_finseq_4(k5_numbers,c1_12__amistd_1,c3_12__amistd_1,c2_12__amistd_1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_12__amistd_1,dt_c2_12__amistd_1,dt_c3_12__amistd_1,dt_c4_12__amistd_1,e1_12_1_1__amistd_1])],[dt_k2_zfmisc_1,cc1_relset_1,fc14_finset_1,fc4_subset_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_m2_relset_1,cc1_funct_7,cc1_realset1,cc3_int_1,cc3_nat_1,cc4_int_1,rc1_amistd_1,rc1_int_1,rc1_nat_1,rc1_realset1,rc2_finset_1,rc2_int_1,rc2_nat_1,rc2_realset1,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_subset_1,redefinition_m2_finseq_1,redefinition_m2_subset_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,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finseq_5,cc1_finset_1,cc1_funct_1,cc1_membered,cc1_nat_1,cc1_relat_1,cc1_scmring1,cc1_setfam_1,cc20_membered,cc2_finset_1,cc2_funct_1,cc2_funct_7,cc2_int_1,cc2_membered,cc2_nat_1,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc1_subset_1,fc2_membered,fc3_amistd_1,fc5_membered,rc1_finseq_5,rc1_finset_1,rc1_membered,rc1_partfun1,rc1_pre_circ,rc1_relat_1,rc1_setfam_1,rc1_subset_1,rc1_xboole_0,rc2_finseq_1,rc2_finseq_5,rc2_funct_1,rc2_partfun1,rc2_relat_1,rc2_subset_1,rc2_xboole_0,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc3_relat_1,rc4_finseq_1,rc4_finset_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t3_subset,t7_boole,t8_boole,redefinition_k4_graph_2,redefinition_k5_numbers,dt_k1_xboole_0,dt_k3_graph_2,dt_k4_finseq_4,dt_k4_graph_2,dt_k5_numbers,dt_c1_12__amistd_1,dt_c2_12__amistd_1,dt_c3_12__amistd_1,dt_c4_12__amistd_1,cc1_amistd_1,cc1_finseq_1,fc12_relat_1,fc1_xboole_0,fc2_finseq_1,fc3_funct_7,fc4_relat_1,fc6_membered,rc1_finseq_1,rc1_funct_1,t6_boole,e1_12_1_1__amistd_1,t7_amistd_1]), [interesting(0.5),file(amistd_1,e2_12_1_1__amistd_1),[file(amistd_1,e2_12_1_1__amistd_1)]]). fof(i2_12_1_1__amistd_1,theorem,( $true ), introduced(tautology,[file(amistd_1,i2_12_1_1__amistd_1)]), [interesting(0.5),trivial,file(amistd_1,i2_12_1_1__amistd_1)]). fof(i1_12_1_1__amistd_1,plain,( k4_finseq_4(k5_numbers,c1_12__amistd_1,k4_graph_2(c1_12__amistd_1,c3_12__amistd_1,c4_12__amistd_1),c2_12__amistd_1) = k4_finseq_4(k5_numbers,c1_12__amistd_1,c3_12__amistd_1,c2_12__amistd_1) ), inference(conclusion,[status(thm),assumptions([dt_c1_12__amistd_1,dt_c2_12__amistd_1,dt_c3_12__amistd_1,dt_c4_12__amistd_1,e1_12_1_1__amistd_1])],[e2_12_1_1__amistd_1,i2_12_1_1__amistd_1]), [interesting(0.5),file(amistd_1,i1_12_1_1__amistd_1),[file(amistd_1,i1_12_1_1__amistd_1)]]). fof(i1_12_1__amistd_1,plain, ( c4_12__amistd_1 = k1_xboole_0 => k4_finseq_4(k5_numbers,c1_12__amistd_1,k4_graph_2(c1_12__amistd_1,c3_12__amistd_1,c4_12__amistd_1),c2_12__amistd_1) = k4_finseq_4(k5_numbers,c1_12__amistd_1,c3_12__amistd_1,c2_12__amistd_1) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_12__amistd_1,dt_c2_12__amistd_1,dt_c3_12__amistd_1,dt_c4_12__amistd_1]),discharge_asm(discharge,[e1_12_1_1__amistd_1])],[e1_12_1_1__amistd_1,i1_12_1_1__amistd_1]), [interesting(0.65),file(amistd_1,i1_12_1__amistd_1),[file(amistd_1,i1_12_1__amistd_1)]]). fof(e1_12_1_2__amistd_1,assumption,( c4_12__amistd_1 != k1_xboole_0 ), introduced(assumption,[file(amistd_1,e1_12_1_2__amistd_1)]), [interesting(0.5),axiom,file(amistd_1,e1_12_1_2__amistd_1)]). fof(t2_real,theorem,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & v3_xreal_0(B) ) => v3_xreal_0(A) ) ) ) ), file(real,t2_real), [interesting(0.9),axiom,file(real,t2_real)]). fof(t3_real,theorem,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xreal_0(A,B) & ~ v3_xreal_0(A) & v3_xreal_0(B) ) ) ) ), file(real,t3_real), [interesting(0.9),axiom,file(real,t3_real)]). fof(t5_real,theorem,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) => ( v1_xboole_0(B) | v3_xreal_0(A) | v2_xreal_0(B) ) ) ) ) ), file(real,t5_real), [interesting(0.9),axiom,file(real,t5_real)]). fof(t6_real,theorem,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) => ( v1_xboole_0(A) | v2_xreal_0(B) | v3_xreal_0(A) ) ) ) ) ), file(real,t6_real), [interesting(0.9),axiom,file(real,t6_real)]). fof(t7_real,theorem,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v2_xreal_0(A) & ~ v3_xreal_0(B) ) ) ) ), file(real,t7_real), [interesting(0.9),axiom,file(real,t7_real)]). fof(t8_real,theorem,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v3_xreal_0(B) & ~ v2_xreal_0(A) ) ) ) ), file(real,t8_real), [interesting(0.9),axiom,file(real,t8_real)]). fof(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(t1_real,theorem,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & v2_xreal_0(A) ) => v2_xreal_0(B) ) ) ) ), file(real,t1_real), [interesting(0.9),axiom,file(real,t1_real)]). fof(t4_real,theorem,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xreal_0(A,B) & ~ v2_xreal_0(B) & v2_xreal_0(A) ) ) ) ), file(real,t4_real), [interesting(0.9),axiom,file(real,t4_real)]). fof(reflexivity_r1_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => r1_xreal_0(A,A) ) ), file(xreal_0,r1_xreal_0), [interesting(0.9),axiom,file(xreal_0,r1_xreal_0)]). fof(connectedness_r1_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( r1_xreal_0(A,B) | r1_xreal_0(B,A) ) ) ), file(xreal_0,r1_xreal_0), [interesting(0.9),axiom,file(xreal_0,r1_xreal_0)]). fof(redefinition_k3_finseq_1,definition,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k3_finseq_1(A) = k1_card_1(A) ) ), file(finseq_1,k3_finseq_1), [interesting(0.9),axiom,file(finseq_1,k3_finseq_1)]). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), [interesting(0.9),axiom,file(funct_1,k1_funct_1)]). fof(dt_k3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers) ) ), file(finseq_1,k3_finseq_1), [interesting(0.9),axiom,file(finseq_1,k3_finseq_1)]). fof(spc1_numerals,theorem, ( v2_xreal_0(1) & m2_subset_1(1,k1_numbers,k5_numbers) & m1_subset_1(1,k5_numbers) & m1_subset_1(1,k1_numbers) ), file(numerals,spc1_numerals), [interesting(0.9),axiom,file(numerals,spc1_numerals)]). fof(spc1_boole,theorem,( ~ v1_xboole_0(1) ), file(boole,spc1_boole), [interesting(0.9),axiom,file(boole,spc1_boole)]). fof(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(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(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_k1_nat_1,theorem,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k1_nat_1(A,B) = k1_nat_1(B,A) ) ), file(nat_1,k1_nat_1), [interesting(0.9),axiom,file(nat_1,k1_nat_1)]). fof(commutativity_k2_xcmplx_0,theorem,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ), file(xcmplx_0,k2_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k2_xcmplx_0)]). fof(redefinition_k1_nat_1,definition,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k1_nat_1(A,B) = k2_xcmplx_0(A,B) ) ), file(nat_1,k1_nat_1), [interesting(0.9),axiom,file(nat_1,k1_nat_1)]). fof(dt_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => m2_subset_1(k1_nat_1(A,B),k1_numbers,k5_numbers) ) ), file(nat_1,k1_nat_1), [interesting(0.9),axiom,file(nat_1,k1_nat_1)]). fof(dt_k2_xcmplx_0,axiom,( $true ), file(xcmplx_0,k2_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k2_xcmplx_0)]). fof(fc1_nat_1,theorem,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => ( v4_ordinal2(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(nat_1,fc1_nat_1), [interesting(0.9),axiom,file(nat_1,fc1_nat_1)]). fof(rqLessOrEqual__r1_xreal_0__r1_r1,theorem,( r1_xreal_0(1,1) ), file(arithm,rqLessOrEqual__r1_xreal_0__r1_r1), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_r1)]). fof(fc3_int_1,theorem,( ! [A] : ( v1_int_1(A) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & v1_int_1(k4_xcmplx_0(A)) ) ) ), file(int_1,fc3_int_1), [interesting(0.9),axiom,file(int_1,fc3_int_1)]). fof(fc4_int_1,theorem,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_int_1(k6_xcmplx_0(A,B)) ) ) ), file(int_1,fc4_int_1), [interesting(0.9),axiom,file(int_1,fc4_int_1)]). fof(fc8_int_1,theorem,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & v1_int_1(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & v1_int_1(k6_xcmplx_0(B,A)) ) ) ), file(int_1,fc8_int_1), [interesting(0.9),axiom,file(int_1,fc8_int_1)]). fof(fc5_int_1,theorem,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & ~ v2_xreal_0(k4_xcmplx_0(A)) & v1_int_1(k4_xcmplx_0(A)) ) ) ), file(int_1,fc5_int_1), [interesting(0.9),axiom,file(int_1,fc5_int_1)]). fof(fc9_int_1,theorem,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_int_1(k6_xcmplx_0(A,B)) ) ) ), file(int_1,fc9_int_1), [interesting(0.9),axiom,file(int_1,fc9_int_1)]). 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_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_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__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_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_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_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__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_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(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(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(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(t1_numerals,theorem,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), [interesting(0.9),axiom,file(numerals,t1_numerals)]). 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(rqLessOrEqual__r1_xreal_0__r0_r2,theorem,( r1_xreal_0(0,2) ), file(arithm,rqLessOrEqual__r1_xreal_0__r0_r2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_r2)]). fof(rqLessOrEqual__r1_xreal_0__r0_rm1,theorem,( ~ r1_xreal_0(0,k4_xcmplx_0(1)) ), file(arithm,rqLessOrEqual__r1_xreal_0__r0_rm1), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_rm1)]). fof(rqLessOrEqual__r1_xreal_0__r0_rm2,theorem,( ~ r1_xreal_0(0,k4_xcmplx_0(2)) ), file(arithm,rqLessOrEqual__r1_xreal_0__r0_rm2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_rm2)]). fof(rqLessOrEqual__r1_xreal_0__r0_rn1d2,theorem,( r1_xreal_0(0,k7_xcmplx_0(1,2)) ), file(arithm,rqLessOrEqual__r1_xreal_0__r0_rn1d2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_rn1d2)]). fof(rqLessOrEqual__r1_xreal_0__r0_rnm1d2,theorem,( ~ r1_xreal_0(0,k7_xcmplx_0(k4_xcmplx_0(1),2)) ), file(arithm,rqLessOrEqual__r1_xreal_0__r0_rnm1d2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_rnm1d2)]). fof(rqLessOrEqual__r1_xreal_0__r1_r2,theorem,( r1_xreal_0(1,2) ), file(arithm,rqLessOrEqual__r1_xreal_0__r1_r2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_r2)]). fof(rqLessOrEqual__r1_xreal_0__r1_rm1,theorem,( ~ r1_xreal_0(1,k4_xcmplx_0(1)) ), file(arithm,rqLessOrEqual__r1_xreal_0__r1_rm1), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_rm1)]). fof(rqLessOrEqual__r1_xreal_0__r1_rm2,theorem,( ~ r1_xreal_0(1,k4_xcmplx_0(2)) ), file(arithm,rqLessOrEqual__r1_xreal_0__r1_rm2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_rm2)]). fof(rqLessOrEqual__r1_xreal_0__r1_rn1d2,theorem,( ~ r1_xreal_0(1,k7_xcmplx_0(1,2)) ), file(arithm,rqLessOrEqual__r1_xreal_0__r1_rn1d2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_rn1d2)]). fof(rqLessOrEqual__r1_xreal_0__r1_rnm1d2,theorem,( ~ r1_xreal_0(1,k7_xcmplx_0(k4_xcmplx_0(1),2)) ), file(arithm,rqLessOrEqual__r1_xreal_0__r1_rnm1d2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_rnm1d2)]). fof(rqLessOrEqual__r1_xreal_0__r2_r0,theorem,( ~ r1_xreal_0(2,0) ), file(arithm,rqLessOrEqual__r1_xreal_0__r2_r0), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_r0)]). fof(rqLessOrEqual__r1_xreal_0__r2_r1,theorem,( ~ r1_xreal_0(2,1) ), file(arithm,rqLessOrEqual__r1_xreal_0__r2_r1), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_r1)]). fof(rqLessOrEqual__r1_xreal_0__r2_r2,theorem,( r1_xreal_0(2,2) ), file(arithm,rqLessOrEqual__r1_xreal_0__r2_r2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_r2)]). fof(rqLessOrEqual__r1_xreal_0__r2_rm1,theorem,( ~ r1_xreal_0(2,k4_xcmplx_0(1)) ), file(arithm,rqLessOrEqual__r1_xreal_0__r2_rm1), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_rm1)]). fof(rqLessOrEqual__r1_xreal_0__r2_rm2,theorem,( ~ r1_xreal_0(2,k4_xcmplx_0(2)) ), file(arithm,rqLessOrEqual__r1_xreal_0__r2_rm2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_rm2)]). fof(rqLessOrEqual__r1_xreal_0__r2_rn1d2,theorem,( ~ r1_xreal_0(2,k7_xcmplx_0(1,2)) ), file(arithm,rqLessOrEqual__r1_xreal_0__r2_rn1d2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_rn1d2)]). fof(rqLessOrEqual__r1_xreal_0__r2_rnm1d2,theorem,( ~ r1_xreal_0(2,k7_xcmplx_0(k4_xcmplx_0(1),2)) ), file(arithm,rqLessOrEqual__r1_xreal_0__r2_rnm1d2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_rnm1d2)]). fof(rqLessOrEqual__r1_xreal_0__rm1_r0,theorem,( r1_xreal_0(k4_xcmplx_0(1),0) ), file(arithm,rqLessOrEqual__r1_xreal_0__rm1_r0), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm1_r0)]). fof(rqLessOrEqual__r1_xreal_0__rm1_r1,theorem,( r1_xreal_0(k4_xcmplx_0(1),1) ), file(arithm,rqLessOrEqual__r1_xreal_0__rm1_r1), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm1_r1)]). fof(rqLessOrEqual__r1_xreal_0__rm1_r2,theorem,( r1_xreal_0(k4_xcmplx_0(1),2) ), file(arithm,rqLessOrEqual__r1_xreal_0__rm1_r2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm1_r2)]). fof(rqLessOrEqual__r1_xreal_0__rm1_rm1,theorem,( r1_xreal_0(k4_xcmplx_0(1),k4_xcmplx_0(1)) ), file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rm1), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rm1)]). fof(rqLessOrEqual__r1_xreal_0__rm1_rm2,theorem,( ~ r1_xreal_0(k4_xcmplx_0(1),k4_xcmplx_0(2)) ), file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rm2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rm2)]). fof(rqLessOrEqual__r1_xreal_0__rm1_rn1d2,theorem,( r1_xreal_0(k4_xcmplx_0(1),k7_xcmplx_0(1,2)) ), file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rn1d2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rn1d2)]). fof(rqLessOrEqual__r1_xreal_0__rm1_rnm1d2,theorem,( r1_xreal_0(k4_xcmplx_0(1),k7_xcmplx_0(k4_xcmplx_0(1),2)) ), file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rnm1d2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rnm1d2)]). fof(rqLessOrEqual__r1_xreal_0__rm2_r0,theorem,( r1_xreal_0(k4_xcmplx_0(2),0) ), file(arithm,rqLessOrEqual__r1_xreal_0__rm2_r0), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm2_r0)]). fof(rqLessOrEqual__r1_xreal_0__rm2_r1,theorem,( r1_xreal_0(k4_xcmplx_0(2),1) ), file(arithm,rqLessOrEqual__r1_xreal_0__rm2_r1), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm2_r1)]). fof(rqLessOrEqual__r1_xreal_0__rm2_r2,theorem,( r1_xreal_0(k4_xcmplx_0(2),2) ), file(arithm,rqLessOrEqual__r1_xreal_0__rm2_r2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm2_r2)]). fof(rqLessOrEqual__r1_xreal_0__rm2_rm1,theorem,( r1_xreal_0(k4_xcmplx_0(2),k4_xcmplx_0(1)) ), file(arithm,rqLessOrEqual__r1_xreal_0__rm2_rm1), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm2_rm1)]). fof(rqLessOrEqual__r1_xreal_0__rm2_rm2,theorem,( r1_xreal_0(k4_xcmplx_0(2),k4_xcmplx_0(2)) ), file(arithm,rqLessOrEqual__r1_xreal_0__rm2_rm2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm2_rm2)]). fof(rqLessOrEqual__r1_xreal_0__rn1d2_r0,theorem,( ~ r1_xreal_0(k7_xcmplx_0(1,2),0) ), file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_r0), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_r0)]). fof(rqLessOrEqual__r1_xreal_0__rn1d2_r1,theorem,( r1_xreal_0(k7_xcmplx_0(1,2),1) ), file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_r1), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_r1)]). fof(rqLessOrEqual__r1_xreal_0__rn1d2_r2,theorem,( r1_xreal_0(k7_xcmplx_0(1,2),2) ), file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_r2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_r2)]). fof(rqLessOrEqual__r1_xreal_0__rn1d2_rm1,theorem,( ~ r1_xreal_0(k7_xcmplx_0(1,2),k4_xcmplx_0(1)) ), file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_rm1), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_rm1)]). fof(rqLessOrEqual__r1_xreal_0__rn1d2_rn1d2,theorem,( r1_xreal_0(k7_xcmplx_0(1,2),k7_xcmplx_0(1,2)) ), file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_rn1d2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_rn1d2)]). fof(rqLessOrEqual__r1_xreal_0__rn1d2_rnm1d2,theorem,( ~ r1_xreal_0(k7_xcmplx_0(1,2),k7_xcmplx_0(k4_xcmplx_0(1),2)) ), file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_rnm1d2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_rnm1d2)]). fof(rqLessOrEqual__r1_xreal_0__rnm1d2_r0,theorem,( r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(1),2),0) ), file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d2_r0), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d2_r0)]). fof(rqLessOrEqual__r1_xreal_0__rnm1d2_r1,theorem,( r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(1),2),1) ), file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d2_r1), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d2_r1)]). fof(rqLessOrEqual__r1_xreal_0__rnm1d2_r2,theorem,( r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(1),2),2) ), file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d2_r2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d2_r2)]). fof(rqLessOrEqual__r1_xreal_0__rnm1d2_rm1,theorem,( ~ r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k4_xcmplx_0(1)) ), file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d2_rm1), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d2_rm1)]). fof(rqLessOrEqual__r1_xreal_0__rnm1d2_rn1d2,theorem,( r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(1,2)) ), file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d2_rn1d2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d2_rn1d2)]). fof(rqLessOrEqual__r1_xreal_0__rnm1d2_rnm1d2,theorem,( r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(k4_xcmplx_0(1),2)) ), file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d2_rnm1d2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d2_rnm1d2)]). 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_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__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_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__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_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(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_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__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_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__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_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(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(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(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(spc0_boole,theorem,( v1_xboole_0(0) ), file(boole,spc0_boole), [interesting(0.9),axiom,file(boole,spc0_boole)]). fof(spc2_boole,theorem,( ~ v1_xboole_0(2) ), file(boole,spc2_boole), [interesting(0.9),axiom,file(boole,spc2_boole)]). fof(t25_finseq_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( k3_finseq_1(A) = 0 <=> A = k1_xboole_0 ) ) ), file(finseq_1,t25_finseq_1), [interesting(0.9),axiom,file(finseq_1,t25_finseq_1)]). fof(e3_12_1_2__amistd_1,plain,( k3_finseq_1(c4_12__amistd_1) != 0 ), inference(mizar_by,[status(thm),assumptions([dt_c1_12__amistd_1,dt_c4_12__amistd_1,e1_12_1_2__amistd_1])],[reflexivity_r1_tarski,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,antisymmetry_r2_hidden,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_7,cc1_realset1,cc20_membered,cc2_finset_1,cc3_int_1,cc3_nat_1,cc4_int_1,cc6_membered,cc9_membered,fc1_ordinal2,fc1_subset_1,fc5_membered,rc1_amistd_1,rc1_int_1,rc1_nat_1,rc1_realset1,rc1_subset_1,rc2_finseq_5,rc2_finset_1,rc2_int_1,rc2_nat_1,rc2_realset1,rc2_subset_1,rc3_finset_1,rc3_nat_1,rc4_finseq_1,rc4_finset_1,t1_subset,t3_subset,t4_subset,t5_subset,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_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_subset_1,dt_c1_12__amistd_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc1_finseq_5,cc1_finset_1,cc1_funct_1,cc1_membered,cc1_nat_1,cc1_relat_1,cc1_scmring1,cc1_setfam_1,cc2_funct_1,cc2_funct_7,cc2_int_1,cc2_membered,cc2_nat_1,cc3_membered,cc4_membered,fc2_membered,rc1_finseq_5,rc1_finset_1,rc1_membered,rc1_partfun1,rc1_pre_circ,rc1_relat_1,rc1_setfam_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,rc3_finseq_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t1_numerals,t2_subset,t7_boole,t8_boole,redefinition_k3_finseq_1,dt_k1_xboole_0,dt_k3_finseq_1,dt_c4_12__amistd_1,cc1_amistd_1,cc1_finseq_1,fc12_relat_1,fc1_xboole_0,fc2_finseq_1,fc3_funct_7,fc4_relat_1,fc6_membered,rc1_finseq_1,rc1_funct_1,t6_boole,spc0_numerals,spc0_boole,e1_12_1_2__amistd_1,t25_finseq_1]), [interesting(0.5),file(amistd_1,e3_12_1_2__amistd_1),[file(amistd_1,e3_12_1_2__amistd_1)]]). fof(t19_nat_1,theorem,( ! [A] : ( v4_ordinal2(A) => ~ ( 0 != A & r1_xreal_0(A,0) ) ) ), file(nat_1,t19_nat_1), [interesting(0.9),axiom,file(nat_1,t19_nat_1)]). fof(rqLessOrEqual__r1_xreal_0__r0_r0,theorem,( r1_xreal_0(0,0) ), file(arithm,rqLessOrEqual__r1_xreal_0__r0_r0), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_r0)]). fof(e4_12_1_2__amistd_1,plain,( ~ r1_xreal_0(k3_finseq_1(c4_12__amistd_1),0) ), inference(mizar_by,[status(thm),assumptions([dt_c1_12__amistd_1,dt_c4_12__amistd_1,e1_12_1_2__amistd_1])],[reflexivity_r1_tarski,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,antisymmetry_r2_hidden,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,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,cc1_scmring1,cc1_setfam_1,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc12_relat_1,fc1_ordinal2,fc1_subset_1,fc1_xboole_0,fc2_finseq_1,fc3_funct_7,fc4_relat_1,fc5_membered,fc6_membered,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_finset_1,rc2_nat_1,rc2_realset1,rc2_subset_1,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,t1_subset,t3_subset,t4_subset,t5_subset,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_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_subset_1,dt_c1_12__amistd_1,cc15_membered,cc1_amistd_1,cc1_finseq_1,cc1_finseq_5,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc1_relat_1,cc2_funct_1,cc2_funct_7,cc2_int_1,cc2_nat_1,cc4_int_1,fc2_membered,rc1_finseq_1,rc1_funct_1,rc1_int_1,rc1_nat_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_int_1,rc2_relat_1,rc2_xboole_0,t1_numerals,t1_real,t2_real,t2_subset,t3_real,t4_real,t5_real,t6_boole,t6_real,t7_boole,t7_real,t8_boole,t8_real,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k3_finseq_1,dt_k3_finseq_1,dt_c4_12__amistd_1,cc3_int_1,cc3_nat_1,spc0_numerals,spc0_boole,e3_12_1_2__amistd_1,t19_nat_1,rqLessOrEqual__r1_xreal_0__r0_r0]), [interesting(0.5),file(amistd_1,e4_12_1_2__amistd_1),[file(amistd_1,e4_12_1_2__amistd_1)]]). fof(t8_xreal_1,theorem,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xreal_0(A,B) <=> r1_xreal_0(k2_xcmplx_0(A,C),k2_xcmplx_0(B,C)) ) ) ) ) ), file(xreal_1,t8_xreal_1), [interesting(0.9),axiom,file(xreal_1,t8_xreal_1)]). fof(e5_12_1_2__amistd_1,plain,( ~ r1_xreal_0(k1_nat_1(k3_finseq_1(c3_12__amistd_1),k3_finseq_1(c4_12__amistd_1)),k1_nat_1(k3_finseq_1(c3_12__amistd_1),0)) ), inference(mizar_by,[status(thm),assumptions([dt_c3_12__amistd_1,dt_c1_12__amistd_1,dt_c4_12__amistd_1,e1_12_1_2__amistd_1])],[reflexivity_r1_tarski,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,antisymmetry_r2_hidden,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,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,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,cc6_membered,cc9_membered,fc12_relat_1,fc1_int_1,fc1_nat_1,fc1_ordinal2,fc1_subset_1,fc1_xboole_0,fc2_finseq_1,fc3_funct_7,fc3_nat_1,fc4_nat_1,fc4_relat_1,fc5_membered,fc6_int_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,rc1_subset_1,rc2_finseq_5,rc2_finset_1,rc2_int_1,rc2_nat_1,rc2_realset1,rc2_subset_1,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,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_subset_1,dt_c1_12__amistd_1,cc15_membered,cc1_amistd_1,cc1_finseq_1,cc1_finseq_5,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc1_relat_1,cc2_funct_1,cc2_funct_7,cc2_int_1,cc2_nat_1,fc2_membered,rc1_finseq_1,rc1_funct_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,rqRealAdd__k2_xcmplx_0__r0_r0_r0,spc6_arithm,t1_arithm,t1_numerals,t1_real,t2_subset,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,commutativity_k2_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k1_nat_1,redefinition_k3_finseq_1,dt_k1_nat_1,dt_k2_xcmplx_0,dt_k3_finseq_1,dt_c3_12__amistd_1,dt_c4_12__amistd_1,spc0_numerals,spc0_boole,e4_12_1_2__amistd_1,t8_xreal_1,rqLessOrEqual__r1_xreal_0__r0_r0]), [interesting(0.5),file(amistd_1,e5_12_1_2__amistd_1),[file(amistd_1,e5_12_1_2__amistd_1)]]). fof(t13_graph_2,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) ) => ( A != k1_xboole_0 => k1_nat_1(k3_finseq_1(k3_graph_2(B,A)),1) = k1_nat_1(k3_finseq_1(B),k3_finseq_1(A)) ) ) ) ), file(graph_2,t13_graph_2), [interesting(0.9),axiom,file(graph_2,t13_graph_2)]). fof(e2_12_1_2__amistd_1,plain,( k1_nat_1(k3_finseq_1(k4_graph_2(c1_12__amistd_1,c3_12__amistd_1,c4_12__amistd_1)),1) = k1_nat_1(k3_finseq_1(c3_12__amistd_1),k3_finseq_1(c4_12__amistd_1)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_12__amistd_1,dt_c3_12__amistd_1,dt_c4_12__amistd_1,e1_12_1_2__amistd_1])],[reflexivity_r1_tarski,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,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m2_relset_1,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_7,cc1_realset1,cc20_membered,cc2_finset_1,cc3_int_1,cc3_nat_1,cc4_int_1,cc6_membered,cc9_membered,fc1_int_1,fc1_nat_1,fc1_ordinal2,fc1_subset_1,fc3_nat_1,fc4_nat_1,fc5_membered,fc6_int_1,rc1_amistd_1,rc1_int_1,rc1_nat_1,rc1_realset1,rc1_subset_1,rc2_finset_1,rc2_int_1,rc2_nat_1,rc2_realset1,rc2_subset_1,rc3_finset_1,rc3_nat_1,rc4_finset_1,spc6_arithm,t1_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,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_numbers,dt_k2_xcmplx_0,dt_k5_numbers,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,cc15_membered,cc1_finseq_5,cc1_finset_1,cc1_funct_1,cc1_membered,cc1_nat_1,cc1_relat_1,cc1_scmring1,cc1_setfam_1,cc2_funct_1,cc2_funct_7,cc2_int_1,cc2_membered,cc2_nat_1,cc3_membered,cc4_membered,fc2_membered,fc3_amistd_1,rc1_finseq_5,rc1_finset_1,rc1_membered,rc1_partfun1,rc1_pre_circ,rc1_relat_1,rc1_setfam_1,rc1_xboole_0,rc2_finseq_5,rc2_funct_1,rc2_relat_1,rc2_xboole_0,rc3_finseq_1,rc3_funct_1,rc3_relat_1,rc4_finseq_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t7_boole,t8_boole,commutativity_k1_nat_1,redefinition_k1_nat_1,redefinition_k3_finseq_1,redefinition_k4_graph_2,dt_k1_nat_1,dt_k1_xboole_0,dt_k3_finseq_1,dt_k3_graph_2,dt_k4_graph_2,dt_c1_12__amistd_1,dt_c3_12__amistd_1,dt_c4_12__amistd_1,cc1_amistd_1,cc1_finseq_1,fc12_relat_1,fc1_xboole_0,fc2_finseq_1,fc3_funct_7,fc4_relat_1,fc6_membered,rc1_finseq_1,rc1_funct_1,t6_boole,spc1_numerals,spc1_boole,e1_12_1_2__amistd_1,t13_graph_2]), [interesting(0.5),file(amistd_1,e2_12_1_2__amistd_1),[file(amistd_1,e2_12_1_2__amistd_1)]]). fof(t2_xreal_1,theorem,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xreal_0(A,B) & r1_xreal_0(B,C) ) => r1_xreal_0(A,C) ) ) ) ) ), file(xreal_1,t2_xreal_1), [interesting(0.9),axiom,file(xreal_1,t2_xreal_1)]). 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__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(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(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(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(rqLessOrEqual__r1_xreal_0__r0_r1,theorem,( r1_xreal_0(0,1) ), file(arithm,rqLessOrEqual__r1_xreal_0__r0_r1), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_r1)]). fof(rqLessOrEqual__r1_xreal_0__r1_r0,theorem,( ~ r1_xreal_0(1,0) ), file(arithm,rqLessOrEqual__r1_xreal_0__r1_r0), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_r0)]). fof(e6_12_1_2__amistd_1,plain,( ~ r1_xreal_0(k1_nat_1(k3_finseq_1(k4_graph_2(c1_12__amistd_1,c3_12__amistd_1,c4_12__amistd_1)),1),c2_12__amistd_1) ), inference(mizar_by,[status(thm),assumptions([dt_c2_12__amistd_1,e2_12__amistd_1,dt_c1_12__amistd_1,dt_c3_12__amistd_1,dt_c4_12__amistd_1,e1_12_1_2__amistd_1])],[reflexivity_r1_tarski,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,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_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,cc6_membered,cc9_membered,fc12_relat_1,fc1_int_1,fc1_nat_1,fc1_ordinal2,fc1_subset_1,fc1_xboole_0,fc2_finseq_1,fc3_funct_7,fc3_int_1,fc3_nat_1,fc4_int_1,fc4_nat_1,fc4_relat_1,fc5_membered,fc6_int_1,fc6_membered,fc8_int_1,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,rc1_subset_1,rc2_finseq_5,rc2_finset_1,rc2_int_1,rc2_nat_1,rc2_realset1,rc2_subset_1,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,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,commutativity_k2_xcmplx_0,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_numbers,dt_k2_xcmplx_0,dt_k3_graph_2,dt_k5_numbers,dt_m1_finseq_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,cc2_funct_1,cc2_funct_7,cc2_int_1,cc2_nat_1,fc2_membered,fc3_amistd_1,fc5_int_1,fc9_int_1,rc1_finseq_1,rc1_funct_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,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,t1_real,t2_subset,t4_arithm,t4_real,t5_arithm,t6_arithm,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,involutiveness_k4_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k1_nat_1,redefinition_k3_finseq_1,redefinition_k4_graph_2,dt_k1_nat_1,dt_k3_finseq_1,dt_k4_graph_2,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_k7_xcmplx_0,dt_c1_12__amistd_1,dt_c2_12__amistd_1,dt_c3_12__amistd_1,dt_c4_12__amistd_1,rqLessOrEqual__r1_xreal_0__r0_r2,rqLessOrEqual__r1_xreal_0__r0_rm1,rqLessOrEqual__r1_xreal_0__r0_rm2,rqLessOrEqual__r1_xreal_0__r0_rn1d2,rqLessOrEqual__r1_xreal_0__r0_rnm1d2,rqLessOrEqual__r1_xreal_0__r1_r2,rqLessOrEqual__r1_xreal_0__r1_rm1,rqLessOrEqual__r1_xreal_0__r1_rm2,rqLessOrEqual__r1_xreal_0__r1_rn1d2,rqLessOrEqual__r1_xreal_0__r1_rnm1d2,rqLessOrEqual__r1_xreal_0__r2_r0,rqLessOrEqual__r1_xreal_0__r2_r1,rqLessOrEqual__r1_xreal_0__r2_r2,rqLessOrEqual__r1_xreal_0__r2_rm1,rqLessOrEqual__r1_xreal_0__r2_rm2,rqLessOrEqual__r1_xreal_0__r2_rn1d2,rqLessOrEqual__r1_xreal_0__r2_rnm1d2,rqLessOrEqual__r1_xreal_0__rm1_r0,rqLessOrEqual__r1_xreal_0__rm1_r1,rqLessOrEqual__r1_xreal_0__rm1_r2,rqLessOrEqual__r1_xreal_0__rm1_rm1,rqLessOrEqual__r1_xreal_0__rm1_rm2,rqLessOrEqual__r1_xreal_0__rm1_rn1d2,rqLessOrEqual__r1_xreal_0__rm1_rnm1d2,rqLessOrEqual__r1_xreal_0__rm2_r0,rqLessOrEqual__r1_xreal_0__rm2_r1,rqLessOrEqual__r1_xreal_0__rm2_r2,rqLessOrEqual__r1_xreal_0__rm2_rm1,rqLessOrEqual__r1_xreal_0__rm2_rm2,rqLessOrEqual__r1_xreal_0__rn1d2_r0,rqLessOrEqual__r1_xreal_0__rn1d2_r1,rqLessOrEqual__r1_xreal_0__rn1d2_r2,rqLessOrEqual__r1_xreal_0__rn1d2_rm1,rqLessOrEqual__r1_xreal_0__rn1d2_rn1d2,rqLessOrEqual__r1_xreal_0__rn1d2_rnm1d2,rqLessOrEqual__r1_xreal_0__rnm1d2_r0,rqLessOrEqual__r1_xreal_0__rnm1d2_r1,rqLessOrEqual__r1_xreal_0__rnm1d2_r2,rqLessOrEqual__r1_xreal_0__rnm1d2_rm1,rqLessOrEqual__r1_xreal_0__rnm1d2_rn1d2,rqLessOrEqual__r1_xreal_0__rnm1d2_rnm1d2,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,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_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__r2_rm2,rqRealNeg__k4_xcmplx_0__rm2_r2,rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2,rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2,spc0_numerals,spc1_numerals,spc2_numerals,spc0_boole,spc1_boole,spc2_boole,e5_12_1_2__amistd_1,e2_12__amistd_1,e2_12_1_2__amistd_1,t2_xreal_1,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealDiff__k6_xcmplx_0__rm1_r1_rm2,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r1_r0]), [interesting(0.5),file(amistd_1,e6_12_1_2__amistd_1),[file(amistd_1,e6_12_1_2__amistd_1)]]). fof(t38_nat_1,theorem,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ( ~ r1_xreal_0(k2_xcmplx_0(B,1),A) <=> r1_xreal_0(A,B) ) ) ) ), file(nat_1,t38_nat_1), [interesting(0.9),axiom,file(nat_1,t38_nat_1)]). fof(e7_12_1_2__amistd_1,plain,( r1_xreal_0(c2_12__amistd_1,k3_finseq_1(k4_graph_2(c1_12__amistd_1,c3_12__amistd_1,c4_12__amistd_1))) ), inference(mizar_by,[status(thm),assumptions([dt_c2_12__amistd_1,e2_12__amistd_1,dt_c1_12__amistd_1,dt_c3_12__amistd_1,dt_c4_12__amistd_1,e1_12_1_2__amistd_1])],[reflexivity_r1_tarski,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,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_7,cc1_membered,cc1_realset1,cc1_scmring1,cc1_setfam_1,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc12_relat_1,fc1_ordinal2,fc1_subset_1,fc1_xboole_0,fc2_finseq_1,fc3_funct_7,fc4_relat_1,fc5_membered,fc6_membered,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_finset_1,rc2_nat_1,rc2_realset1,rc2_subset_1,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,t1_subset,t3_subset,t4_subset,t5_subset,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_numbers,dt_k3_graph_2,dt_k5_numbers,dt_m1_finseq_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,cc2_funct_1,cc2_funct_7,cc2_int_1,cc2_nat_1,cc4_int_1,fc1_int_1,fc2_membered,fc3_amistd_1,fc3_nat_1,fc4_nat_1,fc6_int_1,rc1_finseq_1,rc1_funct_1,rc1_int_1,rc1_nat_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_int_1,rc2_relat_1,rc2_xboole_0,spc6_arithm,t1_real,t2_real,t2_subset,t3_real,t4_real,t5_real,t6_boole,t6_real,t7_boole,t7_real,t8_boole,t8_real,commutativity_k1_nat_1,commutativity_k2_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k1_nat_1,redefinition_k3_finseq_1,redefinition_k4_graph_2,dt_k1_nat_1,dt_k2_xcmplx_0,dt_k3_finseq_1,dt_k4_graph_2,dt_c1_12__amistd_1,dt_c2_12__amistd_1,dt_c3_12__amistd_1,dt_c4_12__amistd_1,cc3_int_1,cc3_nat_1,fc1_nat_1,rqLessOrEqual__r1_xreal_0__r1_r1,spc1_numerals,spc1_boole,e6_12_1_2__amistd_1,t38_nat_1]), [interesting(0.5),file(amistd_1,e7_12_1_2__amistd_1),[file(amistd_1,e7_12_1_2__amistd_1)]]). fof(t24_finseq_4,theorem,( ! [A,B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( ( r1_xreal_0(1,C) & r1_xreal_0(C,k3_finseq_1(B)) ) => k4_finseq_4(k5_numbers,A,B,C) = k1_funct_1(B,C) ) ) ) ), file(finseq_4,t24_finseq_4), [interesting(0.9),axiom,file(finseq_4,t24_finseq_4)]). fof(e1_12_1_2_1__amistd_1,plain,( k4_finseq_4(k5_numbers,c1_12__amistd_1,k4_graph_2(c1_12__amistd_1,c3_12__amistd_1,c4_12__amistd_1),c2_12__amistd_1) = k1_funct_1(k4_graph_2(c1_12__amistd_1,c3_12__amistd_1,c4_12__amistd_1),c2_12__amistd_1) ), inference(mizar_by,[status(thm),assumptions([dt_c2_12__amistd_1,e2_12__amistd_1,dt_c1_12__amistd_1,dt_c3_12__amistd_1,dt_c4_12__amistd_1,e1_12_1_2__amistd_1,e1_12__amistd_1])],[rc3_relat_1,rc4_funct_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_funct_7,cc1_membered,cc1_realset1,cc1_relset_1,cc1_scmring1,cc1_setfam_1,cc20_membered,cc2_finset_1,cc2_membered,cc3_int_1,cc3_membered,cc3_nat_1,cc4_int_1,fc12_relat_1,fc14_finset_1,fc1_xboole_0,fc2_finseq_1,fc3_funct_7,fc4_relat_1,fc4_subset_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,t1_subset,t2_real,t3_real,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_card_1,dt_k1_zfmisc_1,dt_k3_graph_2,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_amistd_1,cc1_finseq_1,cc1_finseq_5,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc1_relat_1,cc2_funct_1,cc2_funct_7,cc2_int_1,cc2_nat_1,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc1_subset_1,fc3_amistd_1,fc5_membered,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,t1_real,t2_subset,t3_subset,t4_real,t6_boole,t7_boole,t8_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m2_finseq_1,existence_m2_subset_1,redefinition_k3_finseq_1,redefinition_k4_graph_2,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k3_finseq_1,dt_k4_finseq_4,dt_k4_graph_2,dt_k5_numbers,dt_m2_finseq_1,dt_m2_subset_1,dt_c1_12__amistd_1,dt_c2_12__amistd_1,dt_c3_12__amistd_1,dt_c4_12__amistd_1,fc2_membered,spc1_numerals,spc1_boole,e7_12_1_2__amistd_1,e1_12__amistd_1,t24_finseq_4,rqLessOrEqual__r1_xreal_0__r1_r1]), [interesting(0.35),file(amistd_1,e1_12_1_2_1__amistd_1),[file(amistd_1,e1_12_1_2_1__amistd_1)]]). fof(t14_graph_2,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] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( ( r1_xreal_0(1,C) & r1_xreal_0(C,k3_finseq_1(A)) ) => k1_funct_1(k3_graph_2(A,B),C) = k1_funct_1(A,C) ) ) ) ) ), file(graph_2,t14_graph_2), [interesting(0.9),axiom,file(graph_2,t14_graph_2)]). fof(e2_12_1_2_1__amistd_1,plain,( k1_funct_1(k4_graph_2(c1_12__amistd_1,c3_12__amistd_1,c4_12__amistd_1),c2_12__amistd_1) = k1_funct_1(c3_12__amistd_1,c2_12__amistd_1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_12__amistd_1,dt_c2_12__amistd_1,dt_c3_12__amistd_1,dt_c4_12__amistd_1,e1_12__amistd_1,e2_12__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,antisymmetry_r2_hidden,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_int_1,cc3_membered,cc3_nat_1,cc4_int_1,fc12_relat_1,fc1_xboole_0,fc2_finseq_1,fc3_funct_7,fc4_relat_1,fc6_membered,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,t2_real,t3_real,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_finseq_1,existence_m1_subset_1,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_card_1,dt_k1_zfmisc_1,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,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc1_subset_1,fc3_amistd_1,fc5_membered,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,t1_real,t2_subset,t3_subset,t4_real,t6_boole,t7_boole,t8_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m2_subset_1,redefinition_k3_finseq_1,redefinition_k4_graph_2,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k3_finseq_1,dt_k3_graph_2,dt_k4_graph_2,dt_k5_numbers,dt_m2_subset_1,dt_c1_12__amistd_1,dt_c2_12__amistd_1,dt_c3_12__amistd_1,dt_c4_12__amistd_1,cc1_amistd_1,cc1_finseq_1,fc2_membered,rc1_finseq_1,rc1_funct_1,spc1_numerals,spc1_boole,e1_12__amistd_1,e2_12__amistd_1,t14_graph_2,rqLessOrEqual__r1_xreal_0__r1_r1]), [interesting(0.35),file(amistd_1,e2_12_1_2_1__amistd_1),[file(amistd_1,e2_12_1_2_1__amistd_1)]]). fof(e3_12_1_2_1__amistd_1,plain,( k1_funct_1(c3_12__amistd_1,c2_12__amistd_1) = k4_finseq_4(k5_numbers,c1_12__amistd_1,c3_12__amistd_1,c2_12__amistd_1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_12__amistd_1,dt_c2_12__amistd_1,dt_c3_12__amistd_1,e1_12__amistd_1,e2_12__amistd_1])],[rc3_relat_1,rc4_funct_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_funct_7,cc1_membered,cc1_realset1,cc1_relset_1,cc1_scmring1,cc1_setfam_1,cc20_membered,cc2_finset_1,cc2_membered,cc3_int_1,cc3_membered,cc3_nat_1,cc4_int_1,fc12_relat_1,fc14_finset_1,fc1_xboole_0,fc2_finseq_1,fc3_funct_7,fc4_relat_1,fc4_subset_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,t1_subset,t2_real,t3_real,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_card_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_amistd_1,cc1_finseq_1,cc1_finseq_5,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc1_relat_1,cc2_funct_1,cc2_funct_7,cc2_int_1,cc2_nat_1,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc1_subset_1,fc5_membered,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,t1_real,t2_subset,t3_subset,t4_real,t6_boole,t7_boole,t8_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m2_finseq_1,existence_m2_subset_1,redefinition_k3_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k3_finseq_1,dt_k4_finseq_4,dt_k5_numbers,dt_m2_finseq_1,dt_m2_subset_1,dt_c1_12__amistd_1,dt_c2_12__amistd_1,dt_c3_12__amistd_1,fc2_membered,spc1_numerals,spc1_boole,e1_12__amistd_1,e2_12__amistd_1,t24_finseq_4,rqLessOrEqual__r1_xreal_0__r1_r1]), [interesting(0.35),file(amistd_1,e3_12_1_2_1__amistd_1),[file(amistd_1,e3_12_1_2_1__amistd_1)]]). fof(e8_12_1_2__amistd_1,plain,( k4_finseq_4(k5_numbers,c1_12__amistd_1,k4_graph_2(c1_12__amistd_1,c3_12__amistd_1,c4_12__amistd_1),c2_12__amistd_1) = k4_finseq_4(k5_numbers,c1_12__amistd_1,c3_12__amistd_1,c2_12__amistd_1) ), inference(iterative_eq,[status(thm),assumptions([e1_12_1_2__amistd_1,dt_c4_12__amistd_1,dt_c1_12__amistd_1,dt_c2_12__amistd_1,dt_c3_12__amistd_1,e1_12__amistd_1,e2_12__amistd_1])],[e1_12_1_2_1__amistd_1,e2_12_1_2_1__amistd_1,e3_12_1_2_1__amistd_1]), [interesting(0.5),file(amistd_1,e8_12_1_2__amistd_1),[file(amistd_1,e8_12_1_2__amistd_1)]]). fof(i2_12_1_2__amistd_1,theorem,( $true ), introduced(tautology,[file(amistd_1,i2_12_1_2__amistd_1)]), [interesting(0.5),trivial,file(amistd_1,i2_12_1_2__amistd_1)]). fof(i1_12_1_2__amistd_1,plain,( k4_finseq_4(k5_numbers,c1_12__amistd_1,k4_graph_2(c1_12__amistd_1,c3_12__amistd_1,c4_12__amistd_1),c2_12__amistd_1) = k4_finseq_4(k5_numbers,c1_12__amistd_1,c3_12__amistd_1,c2_12__amistd_1) ), inference(conclusion,[status(thm),assumptions([e1_12_1_2__amistd_1,dt_c4_12__amistd_1,dt_c1_12__amistd_1,dt_c2_12__amistd_1,dt_c3_12__amistd_1,e1_12__amistd_1,e2_12__amistd_1])],[e8_12_1_2__amistd_1,i2_12_1_2__amistd_1]), [interesting(0.5),file(amistd_1,i1_12_1_2__amistd_1),[file(amistd_1,i1_12_1_2__amistd_1)]]). fof(i2_12_1__amistd_1,plain, ( c4_12__amistd_1 != k1_xboole_0 => k4_finseq_4(k5_numbers,c1_12__amistd_1,k4_graph_2(c1_12__amistd_1,c3_12__amistd_1,c4_12__amistd_1),c2_12__amistd_1) = k4_finseq_4(k5_numbers,c1_12__amistd_1,c3_12__amistd_1,c2_12__amistd_1) ), inference(discharge_asm,[status(thm),assumptions([dt_c4_12__amistd_1,dt_c1_12__amistd_1,dt_c2_12__amistd_1,dt_c3_12__amistd_1,e1_12__amistd_1,e2_12__amistd_1]),discharge_asm(discharge,[e1_12_1_2__amistd_1])],[e1_12_1_2__amistd_1,i1_12_1_2__amistd_1]), [interesting(0.65),file(amistd_1,i2_12_1__amistd_1),[file(amistd_1,i2_12_1__amistd_1)]]). fof(e1_12_1__amistd_1,plain,( ~ ( c4_12__amistd_1 != k1_xboole_0 & c4_12__amistd_1 = k1_xboole_0 ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_12__amistd_1,dt_c4_12__amistd_1])],[reflexivity_r1_tarski,cc3_int_1,cc3_nat_1,cc4_int_1,rc1_int_1,rc1_nat_1,rc2_finset_1,rc2_int_1,rc2_nat_1,rc3_nat_1,existence_m1_relset_1,existence_m1_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_m1_relset_1,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,cc1_setfam_1,cc20_membered,cc2_finset_1,cc2_int_1,cc2_nat_1,cc6_membered,cc9_membered,fc14_finset_1,fc1_ordinal2,fc1_subset_1,fc2_membered,fc4_subset_1,fc5_membered,rc1_subset_1,rc2_finseq_1,rc2_partfun1,rc2_subset_1,rc3_finset_1,rc4_finset_1,t2_subset,t3_subset,t4_subset,t5_subset,antisymmetry_r2_hidden,existence_m1_finseq_1,existence_m2_relset_1,redefinition_k5_numbers,redefinition_m2_relset_1,dt_k5_numbers,dt_m1_finseq_1,dt_m2_relset_1,cc1_funct_7,cc1_realset1,rc1_amistd_1,rc1_realset1,rc1_setfam_1,rc2_finseq_5,rc2_realset1,rc4_finseq_1,t1_subset,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_m2_finseq_1,dt_c1_12__amistd_1,cc15_membered,cc1_amistd_1,cc1_finseq_1,cc1_finseq_5,cc1_finset_1,cc1_funct_1,cc1_membered,cc1_relat_1,cc1_scmring1,cc2_funct_1,cc2_funct_7,cc2_membered,cc3_membered,cc4_membered,rc1_finseq_1,rc1_finseq_5,rc1_finset_1,rc1_funct_1,rc1_membered,rc1_partfun1,rc1_pre_circ,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,rc3_finseq_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t7_boole,t8_boole,dt_k1_xboole_0,dt_c4_12__amistd_1,fc12_relat_1,fc1_xboole_0,fc2_finseq_1,fc3_funct_7,fc4_relat_1,fc6_membered,t6_boole]), [interesting(0.65),file(amistd_1,e1_12_1__amistd_1),[file(amistd_1,e1_12_1__amistd_1)]]). fof(i4_12__amistd_1,plain,( k4_finseq_4(k5_numbers,c1_12__amistd_1,k4_graph_2(c1_12__amistd_1,c3_12__amistd_1,c4_12__amistd_1),c2_12__amistd_1) = k4_finseq_4(k5_numbers,c1_12__amistd_1,c3_12__amistd_1,c2_12__amistd_1) ), inference(percases,[status(thm),assumptions([dt_c2_12__amistd_1,dt_c3_12__amistd_1,e1_12__amistd_1,e2_12__amistd_1,dt_c1_12__amistd_1,dt_c4_12__amistd_1])],[i1_12_1__amistd_1,i2_12_1__amistd_1,e1_12_1__amistd_1]), [interesting(0.8),file(amistd_1,i4_12__amistd_1),[file(amistd_1,i4_12__amistd_1)]]). fof(i3_12__amistd_1,plain, ( ( r1_xreal_0(1,c2_12__amistd_1) & r1_xreal_0(c2_12__amistd_1,k3_finseq_1(c3_12__amistd_1)) ) => k4_finseq_4(k5_numbers,c1_12__amistd_1,k4_graph_2(c1_12__amistd_1,c3_12__amistd_1,c4_12__amistd_1),c2_12__amistd_1) = k4_finseq_4(k5_numbers,c1_12__amistd_1,c3_12__amistd_1,c2_12__amistd_1) ), inference(discharge_asm,[status(thm),assumptions([dt_c2_12__amistd_1,dt_c3_12__amistd_1,dt_c1_12__amistd_1,dt_c4_12__amistd_1]),discharge_asm(discharge,[e1_12__amistd_1,e2_12__amistd_1])],[e1_12__amistd_1,e2_12__amistd_1,i4_12__amistd_1]), [interesting(0.8),file(amistd_1,i3_12__amistd_1),[file(amistd_1,i3_12__amistd_1)]]). fof(i3_12_tmp__amistd_1,plain, ( ( m2_finseq_1(c3_12__amistd_1,c1_12__amistd_1) & m2_finseq_1(c4_12__amistd_1,c1_12__amistd_1) ) => ( ( r1_xreal_0(1,c2_12__amistd_1) & r1_xreal_0(c2_12__amistd_1,k3_finseq_1(c3_12__amistd_1)) ) => k4_finseq_4(k5_numbers,c1_12__amistd_1,k4_graph_2(c1_12__amistd_1,c3_12__amistd_1,c4_12__amistd_1),c2_12__amistd_1) = k4_finseq_4(k5_numbers,c1_12__amistd_1,c3_12__amistd_1,c2_12__amistd_1) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c2_12__amistd_1,dt_c1_12__amistd_1]),discharge_asm(discharge,[dt_c3_12__amistd_1,dt_c4_12__amistd_1])],[dt_c3_12__amistd_1,dt_c4_12__amistd_1,i3_12__amistd_1]), [interesting(0.8),i2_12__amistd_1]). fof(i2_12__amistd_1,plain,( ! [A] : ( m2_finseq_1(A,c1_12__amistd_1) => ! [B] : ( m2_finseq_1(B,c1_12__amistd_1) => ( ( r1_xreal_0(1,c2_12__amistd_1) & r1_xreal_0(c2_12__amistd_1,k3_finseq_1(A)) ) => k4_finseq_4(k5_numbers,c1_12__amistd_1,k4_graph_2(c1_12__amistd_1,A,B),c2_12__amistd_1) = k4_finseq_4(k5_numbers,c1_12__amistd_1,A,c2_12__amistd_1) ) ) ) ), inference(let,[status(thm),assumptions([dt_c2_12__amistd_1,dt_c1_12__amistd_1])],[i3_12_tmp__amistd_1,dh_c3_12__amistd_1,dh_c4_12__amistd_1]), [interesting(0.8),file(amistd_1,i2_12__amistd_1),[file(amistd_1,i2_12__amistd_1)]]). fof(i2_12_tmp__amistd_1,plain, ( m2_subset_1(c2_12__amistd_1,k1_numbers,k5_numbers) => ! [A] : ( m2_finseq_1(A,c1_12__amistd_1) => ! [B] : ( m2_finseq_1(B,c1_12__amistd_1) => ( ( r1_xreal_0(1,c2_12__amistd_1) & r1_xreal_0(c2_12__amistd_1,k3_finseq_1(A)) ) => k4_finseq_4(k5_numbers,c1_12__amistd_1,k4_graph_2(c1_12__amistd_1,A,B),c2_12__amistd_1) = k4_finseq_4(k5_numbers,c1_12__amistd_1,A,c2_12__amistd_1) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_12__amistd_1]),discharge_asm(discharge,[dt_c2_12__amistd_1])],[dt_c2_12__amistd_1,i2_12__amistd_1]), [interesting(0.8),i1_12__amistd_1]). fof(i1_12__amistd_1,plain,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_finseq_1(B,c1_12__amistd_1) => ! [C] : ( m2_finseq_1(C,c1_12__amistd_1) => ( ( r1_xreal_0(1,A) & r1_xreal_0(A,k3_finseq_1(B)) ) => k4_finseq_4(k5_numbers,c1_12__amistd_1,k4_graph_2(c1_12__amistd_1,B,C),A) = k4_finseq_4(k5_numbers,c1_12__amistd_1,B,A) ) ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_12__amistd_1])],[i2_12_tmp__amistd_1,dh_c2_12__amistd_1]), [interesting(0.8),file(amistd_1,i1_12__amistd_1),[file(amistd_1,i1_12__amistd_1)]]). fof(i1_12_tmp__amistd_1,plain, ( ~ v1_xboole_0(c1_12__amistd_1) => ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_finseq_1(B,c1_12__amistd_1) => ! [C] : ( m2_finseq_1(C,c1_12__amistd_1) => ( ( r1_xreal_0(1,A) & r1_xreal_0(A,k3_finseq_1(B)) ) => k4_finseq_4(k5_numbers,c1_12__amistd_1,k4_graph_2(c1_12__amistd_1,B,C),A) = k4_finseq_4(k5_numbers,c1_12__amistd_1,B,A) ) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_12__amistd_1])],[dt_c1_12__amistd_1,i1_12__amistd_1]), [interesting(1),t9_amistd_1]). fof(t9_amistd_1,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m2_finseq_1(D,A) => ( ( r1_xreal_0(1,B) & r1_xreal_0(B,k3_finseq_1(C)) ) => k4_finseq_4(k5_numbers,A,k4_graph_2(A,C,D),B) = k4_finseq_4(k5_numbers,A,C,B) ) ) ) ) ) ), inference(let,[status(thm),assumptions([])],[i1_12_tmp__amistd_1,dh_c1_12__amistd_1]), [interesting(1),file(amistd_1,t9_amistd_1),[file(amistd_1,t9_amistd_1)]]).