% Mizar ND problem: t7_bintree1,bintree1,86,31 fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), [interesting(0.9),axiom,file(zfmisc_1,k2_zfmisc_1)]). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), [interesting(0.9),axiom,file(relset_1,m1_relset_1)]). fof(cc1_arytm_3,theorem,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_ordinal1(B) & v2_ordinal1(B) & v3_ordinal1(B) ) ) ) ), file(arytm_3,cc1_arytm_3), [interesting(0.9),axiom,file(arytm_3,cc1_arytm_3)]). fof(cc1_fraenkel,theorem,( ! [A] : ( v1_fraenkel(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ) ), file(fraenkel,cc1_fraenkel), [interesting(0.9),axiom,file(fraenkel,cc1_fraenkel)]). 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(cc2_arytm_3,theorem,( ! [A] : ( ( v1_xboole_0(A) & v3_ordinal1(A) ) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ) ), file(arytm_3,cc2_arytm_3), [interesting(0.9),axiom,file(arytm_3,cc2_arytm_3)]). 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(rc1_arytm_3,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ), file(arytm_3,rc1_arytm_3), [interesting(0.9),axiom,file(arytm_3,rc1_arytm_3)]). fof(rc1_fraenkel,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_fraenkel(A) ) ), file(fraenkel,rc1_fraenkel), [interesting(0.9),axiom,file(fraenkel,rc1_fraenkel)]). 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(rc9_trees_2,theorem,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ? [C] : ( m1_relset_1(C,A,B) & v1_relat_1(C) & ~ v1_xboole_0(C) ) ) ), file(trees_2,rc9_trees_2), [interesting(0.9),axiom,file(trees_2,rc9_trees_2)]). 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_k13_finseq_1,axiom,( $true ), file(finseq_1,k13_finseq_1), [interesting(0.9),axiom,file(finseq_1,k13_finseq_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_finseq_2,axiom,( $true ), file(finseq_2,m1_finseq_2), [interesting(0.9),axiom,file(finseq_2,m1_finseq_2)]). fof(dt_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ), file(relset_1,m2_relset_1), [interesting(0.9),axiom,file(relset_1,m2_relset_1)]). fof(cc3_arytm_3,theorem,( ! [A] : ( m1_subset_1(A,k5_ordinal2) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ) ), file(arytm_3,cc3_arytm_3), [interesting(0.9),axiom,file(arytm_3,cc3_arytm_3)]). fof(cc7_trees_3,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_trees_3(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v4_trees_3(A) ) ) ), file(trees_3,cc7_trees_3), [interesting(0.9),axiom,file(trees_3,cc7_trees_3)]). fof(fc12_membered,theorem,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => v1_membered(k2_tarski(A,B)) ) ), file(membered,fc12_membered), [interesting(0.9),axiom,file(membered,fc12_membered)]). fof(fc13_membered,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) ) ) ), file(membered,fc13_membered), [interesting(0.9),axiom,file(membered,fc13_membered)]). fof(fc14_membered,theorem,( ! [A,B] : ( ( v1_rat_1(A) & v1_rat_1(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) ) ) ), file(membered,fc14_membered), [interesting(0.9),axiom,file(membered,fc14_membered)]). fof(fc15_membered,theorem,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) ) ) ), file(membered,fc15_membered), [interesting(0.9),axiom,file(membered,fc15_membered)]). fof(fc16_finseq_1,theorem,( ! [A] : ( ~ v1_xboole_0(k13_finseq_1(A)) & v1_fraenkel(k13_finseq_1(A)) ) ), file(finseq_1,fc16_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc16_finseq_1)]). fof(fc16_membered,theorem,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) & v5_membered(k2_tarski(A,B)) ) ) ), file(membered,fc16_membered), [interesting(0.9),axiom,file(membered,fc16_membered)]). 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(fc7_trees_3,theorem,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v4_trees_3(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v4_trees_3(B) ) => ( v1_relat_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finset_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) & v4_trees_3(k7_finseq_1(A,B)) ) ) ), file(trees_3,fc7_trees_3), [interesting(0.9),axiom,file(trees_3,fc7_trees_3)]). fof(fc8_trees_3,theorem,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v5_trees_3(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v5_trees_3(B) ) => ( v1_relat_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finset_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) & v4_trees_3(k7_finseq_1(A,B)) & v5_trees_3(k7_finseq_1(A,B)) ) ) ), file(trees_3,fc8_trees_3), [interesting(0.9),axiom,file(trees_3,fc8_trees_3)]). fof(fc9_finseq_1,theorem,( ! [A] : ~ v1_xboole_0(k13_finseq_1(A)) ), file(finseq_1,fc9_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc9_finseq_1)]). fof(rc5_trees_3,theorem,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finset_1(A) & v1_finseq_1(A) & v4_trees_3(A) & v5_trees_3(A) ) ), file(trees_3,rc5_trees_3), [interesting(0.9),axiom,file(trees_3,rc5_trees_3)]). fof(rc7_trees_3,theorem,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v4_trees_3(A) & v5_trees_3(A) ) ), file(trees_3,rc7_trees_3), [interesting(0.9),axiom,file(trees_3,rc7_trees_3)]). fof(redefinition_k3_finseq_2,definition,( ! [A] : k3_finseq_2(A) = k13_finseq_1(A) ), file(finseq_2,k3_finseq_2), [interesting(0.9),axiom,file(finseq_2,k3_finseq_2)]). fof(redefinition_k5_numbers,definition,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), [interesting(0.9),axiom,file(numbers,k5_numbers)]). fof(redefinition_m2_finseq_1,definition,( ! [A,B] : ( m2_finseq_1(B,A) <=> m1_finseq_1(B,A) ) ), file(finseq_1,m2_finseq_1), [interesting(0.9),axiom,file(finseq_1,m2_finseq_1)]). fof(redefinition_m2_finseq_2,definition,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) ) => ! [C] : ( m2_finseq_2(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(finseq_2,m2_finseq_2), [interesting(0.9),axiom,file(finseq_2,m2_finseq_2)]). 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_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]). fof(dt_k3_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(k3_finseq_2(A)) & m1_finseq_2(k3_finseq_2(A),A) ) ), file(finseq_2,k3_finseq_2), [interesting(0.9),axiom,file(finseq_2,k3_finseq_2)]). fof(dt_k5_finseq_1,axiom,( $true ), file(finseq_1,k5_finseq_1), [interesting(0.9),axiom,file(finseq_1,k5_finseq_1)]). fof(dt_k5_numbers,axiom,( m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ), file(numbers,k5_numbers), [interesting(0.9),axiom,file(numbers,k5_numbers)]). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), [interesting(0.9),axiom,file(subset_1,m1_subset_1)]). fof(dt_m2_finseq_1,axiom,( ! [A,B] : ( m2_finseq_1(B,A) => ( v1_funct_1(B) & v1_finseq_1(B) & m2_relset_1(B,k5_numbers,A) ) ) ), file(finseq_1,m2_finseq_1), [interesting(0.9),axiom,file(finseq_1,m2_finseq_1)]). fof(dt_m2_finseq_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) ) => ! [C] : ( m2_finseq_2(C,A,B) => m2_finseq_1(C,A) ) ) ), file(finseq_2,m2_finseq_2), [interesting(0.9),axiom,file(finseq_2,m2_finseq_2)]). 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(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_dtconstr,theorem,( ! [A,B] : ( m1_subset_1(B,k3_finseq_2(A)) => v1_finseq_1(B) ) ), file(dtconstr,cc1_dtconstr), [interesting(0.9),axiom,file(dtconstr,cc1_dtconstr)]). fof(cc1_finseq_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ) ), file(finseq_1,cc1_finseq_1), [interesting(0.9),axiom,file(finseq_1,cc1_finseq_1)]). fof(cc1_membered,theorem,( ! [A] : ( v5_membered(A) => v4_membered(A) ) ), file(membered,cc1_membered), [interesting(0.9),axiom,file(membered,cc1_membered)]). fof(cc20_membered,theorem,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) ) ) ) ), file(membered,cc20_membered), [interesting(0.9),axiom,file(membered,cc20_membered)]). fof(cc2_membered,theorem,( ! [A] : ( v4_membered(A) => v3_membered(A) ) ), file(membered,cc2_membered), [interesting(0.9),axiom,file(membered,cc2_membered)]). fof(cc3_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(fc10_trees_3,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ( v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & ~ v1_xboole_0(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) & v4_trees_3(k5_finseq_1(A)) ) ) ), file(trees_3,fc10_trees_3), [interesting(0.9),axiom,file(trees_3,fc10_trees_3)]). fof(fc12_finseq_1,theorem,( ! [A] : ( ~ v1_xboole_0(k5_finseq_1(A)) & v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) ) ), file(finseq_1,fc12_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc12_finseq_1)]). fof(fc13_finseq_1,theorem,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ~ v1_xboole_0(k7_finseq_1(A,B)) & v1_relat_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finset_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) ) ) ), file(finseq_1,fc13_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc13_finseq_1)]). fof(fc13_trees_3,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) => ( v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & ~ v1_xboole_0(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) & v4_trees_3(k5_finseq_1(A)) & v5_trees_3(k5_finseq_1(A)) ) ) ), file(trees_3,fc13_trees_3), [interesting(0.9),axiom,file(trees_3,fc13_trees_3)]). fof(fc14_finseq_1,theorem,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ~ v1_xboole_0(k7_finseq_1(B,A)) & v1_relat_1(k7_finseq_1(B,A)) & v1_funct_1(k7_finseq_1(B,A)) & v1_finset_1(k7_finseq_1(B,A)) & v1_finseq_1(k7_finseq_1(B,A)) ) ) ), file(finseq_1,fc14_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc14_finseq_1)]). fof(fc1_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(fc21_trees_3,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) => ( ~ v1_xboole_0(k3_trees_1(A)) & v1_finset_1(k3_trees_1(A)) ) ) ), file(trees_3,fc21_trees_3), [interesting(0.9),axiom,file(trees_3,fc21_trees_3)]). fof(fc3_finseq_1,theorem,( ! [A] : ( v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) ) ), file(finseq_1,fc3_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc3_finseq_1)]). fof(fc4_finseq_1,theorem,( ! [A] : ( v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) ) ), file(finseq_1,fc4_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc4_finseq_1)]). fof(fc4_trees_2,theorem,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) & m1_subset_1(B,A) ) => v1_finset_1(k1_trees_2(A,B)) ) ), file(trees_2,fc4_trees_2), [interesting(0.9),axiom,file(trees_2,fc4_trees_2)]). 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_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_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(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(rc7_finseq_1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc7_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc7_finseq_1)]). fof(rc8_finseq_1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc8_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc8_finseq_1)]). fof(commutativity_k2_tarski,theorem,( ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ), file(tarski,k2_tarski), [interesting(0.9),axiom,file(tarski,k2_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(redefinition_k3_lang1,definition,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => k3_lang1(A,B) = k5_finseq_1(B) ) ), file(lang1,k3_lang1), [interesting(0.9),axiom,file(lang1,k3_lang1)]). fof(redefinition_m1_trees_1,definition,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m1_trees_1(B,A) <=> m1_subset_1(B,A) ) ) ), file(trees_1,m1_trees_1), [interesting(0.9),axiom,file(trees_1,m1_trees_1)]). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), [interesting(0.9),axiom,file(numbers,k1_numbers)]). fof(dt_k1_trees_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & m1_subset_1(B,A) ) => m1_subset_1(k1_trees_2(A,B),k1_zfmisc_1(A)) ) ), file(trees_2,k1_trees_2), [interesting(0.9),axiom,file(trees_2,k1_trees_2)]). fof(dt_k2_tarski,axiom,( $true ), file(tarski,k2_tarski), [interesting(0.9),axiom,file(tarski,k2_tarski)]). fof(dt_k2_trees_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( ~ v1_xboole_0(k2_trees_1(A)) & v1_finset_1(k2_trees_1(A)) & v1_trees_1(k2_trees_1(A)) ) ) ), file(trees_1,k2_trees_1), [interesting(0.9),axiom,file(trees_1,k2_trees_1)]). fof(dt_k3_lang1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m2_finseq_2(k3_lang1(A,B),A,k3_finseq_2(A)) ) ), file(lang1,k3_lang1), [interesting(0.9),axiom,file(lang1,k3_lang1)]). fof(dt_k3_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => m1_subset_1(k3_trees_1(A),k1_zfmisc_1(A)) ) ), file(trees_1,k3_trees_1), [interesting(0.9),axiom,file(trees_1,k3_trees_1)]). fof(dt_k7_finseq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( v1_relat_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) ) ) ), file(finseq_1,k7_finseq_1), [interesting(0.9),axiom,file(finseq_1,k7_finseq_1)]). fof(dt_m1_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m1_trees_1(B,A) => m2_finseq_1(B,k5_numbers) ) ) ), file(trees_1,m1_trees_1), [interesting(0.9),axiom,file(trees_1,m1_trees_1)]). fof(dt_c2_5__bintree1,assumption,( m1_trees_1(c2_5__bintree1,k2_trees_1(2)) ), introduced(assumption,[file(bintree1,c2_5__bintree1)]), [interesting(0.8),axiom,file(bintree1,c2_5__bintree1)]). 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(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_subset_1,theorem,( ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ), file(subset_1,fc3_subset_1), [interesting(0.9),axiom,file(subset_1,fc3_subset_1)]). fof(spc0_numerals,theorem, ( v2_xreal_0(0) & m2_subset_1(0,k1_numbers,k5_numbers) & m1_subset_1(0,k5_numbers) & m1_subset_1(0,k1_numbers) ), file(numerals,spc0_numerals), [interesting(0.9),axiom,file(numerals,spc0_numerals)]). fof(spc1_numerals,theorem, ( v2_xreal_0(1) & m2_subset_1(1,k1_numbers,k5_numbers) & m1_subset_1(1,k5_numbers) & m1_subset_1(1,k1_numbers) ), file(numerals,spc1_numerals), [interesting(0.9),axiom,file(numerals,spc1_numerals)]). fof(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(spc1_boole,theorem,( ~ v1_xboole_0(1) ), file(boole,spc1_boole), [interesting(0.9),axiom,file(boole,spc1_boole)]). fof(spc2_boole,theorem,( ~ v1_xboole_0(2) ), file(boole,spc2_boole), [interesting(0.9),axiom,file(boole,spc2_boole)]). fof(d2_bintree1,definition,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ( v1_bintree1(A) <=> ! [B] : ( m1_trees_1(B,A) => ( ~ r2_hidden(B,k3_trees_1(A)) => k1_trees_2(A,B) = k2_tarski(k7_finseq_1(B,k3_lang1(k1_numbers,0)),k7_finseq_1(B,k3_lang1(k1_numbers,1))) ) ) ) ) ), file(bintree1,d2_bintree1), [interesting(0.9),axiom,file(bintree1,d2_bintree1)]). fof(dh_c2_5__bintree1,definition, ( ( m1_trees_1(c2_5__bintree1,k2_trees_1(2)) => ( ~ r2_hidden(c2_5__bintree1,k3_trees_1(k2_trees_1(2))) => k1_trees_2(k2_trees_1(2),c2_5__bintree1) = k2_tarski(k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)),k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,1))) ) ) => ! [A] : ( m1_trees_1(A,k2_trees_1(2)) => ( ~ r2_hidden(A,k3_trees_1(k2_trees_1(2))) => k1_trees_2(k2_trees_1(2),A) = k2_tarski(k7_finseq_1(A,k3_lang1(k1_numbers,0)),k7_finseq_1(A,k3_lang1(k1_numbers,1))) ) ) ), introduced(definition,[new_symbol(c2_5__bintree1),file(bintree1,c2_5__bintree1)]), [interesting(0.8),axiom,file(bintree1,c2_5__bintree1)]). fof(e1_5__bintree1,assumption,( ~ r2_hidden(c2_5__bintree1,k3_trees_1(k2_trees_1(2))) ), introduced(assumption,[file(bintree1,e1_5__bintree1)]), [interesting(0.8),axiom,file(bintree1,e1_5__bintree1)]). fof(e1_5_1_1__bintree1,assumption,( c2_5__bintree1 = k1_xboole_0 ), introduced(assumption,[file(bintree1,e1_5_1_1__bintree1)]), [interesting(0.5),axiom,file(bintree1,e1_5_1_1__bintree1)]). 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_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_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(rc3_finseq_1,theorem,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc3_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc3_finseq_1)]). fof(rc4_finseq_1,theorem,( ! [A] : ? [B] : ( m1_finseq_1(B,A) & v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc4_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc4_finseq_1)]). fof(rc6_finseq_1,theorem,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc6_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc6_finseq_1)]). fof(reflexivity_r1_tarski,theorem,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), [interesting(0.9),axiom,file(tarski,r1_tarski)]). fof(existence_m1_finseq_2,axiom,( ! [A] : ? [B] : m1_finseq_2(B,A) ), file(finseq_2,m1_finseq_2), [interesting(0.9),axiom,file(finseq_2,m1_finseq_2)]). 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(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]). fof(fc2_finseq_1,theorem, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) & v1_funct_1(k1_xboole_0) & v2_funct_1(k1_xboole_0) & v1_finset_1(k1_xboole_0) & v1_finseq_1(k1_xboole_0) ), file(finseq_1,fc2_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc2_finseq_1)]). fof(fc6_membered,theorem, ( v1_xboole_0(k1_xboole_0) & v1_membered(k1_xboole_0) & v2_membered(k1_xboole_0) & v3_membered(k1_xboole_0) & v4_membered(k1_xboole_0) & v5_membered(k1_xboole_0) ), file(membered,fc6_membered), [interesting(0.9),axiom,file(membered,fc6_membered)]). fof(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_m1_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ? [B] : m1_trees_1(B,A) ) ), file(trees_1,m1_trees_1), [interesting(0.9),axiom,file(trees_1,m1_trees_1)]). fof(existence_m2_finseq_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) ) => ? [C] : m2_finseq_2(C,A,B) ) ), file(finseq_2,m2_finseq_2), [interesting(0.9),axiom,file(finseq_2,m2_finseq_2)]). 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(t1_numerals,theorem,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), [interesting(0.9),axiom,file(numerals,t1_numerals)]). fof(t2_subset,theorem,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), [interesting(0.9),axiom,file(subset,t2_subset)]). fof(t3_subset,theorem,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), [interesting(0.9),axiom,file(subset,t3_subset)]). fof(t4_subset,theorem,( ! [A,B,C] : ( ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) ) => m1_subset_1(A,C) ) ), file(subset,t4_subset), [interesting(0.9),axiom,file(subset,t4_subset)]). fof(t5_subset,theorem,( ! [A,B,C] : ~ ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C) ) ), file(subset,t5_subset), [interesting(0.9),axiom,file(subset,t5_subset)]). fof(t6_boole,theorem,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), [interesting(0.9),axiom,file(boole,t6_boole)]). fof(t8_boole,theorem,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), [interesting(0.9),axiom,file(boole,t8_boole)]). fof(t1_subset,theorem,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), [interesting(0.9),axiom,file(subset,t1_subset)]). fof(t7_boole,theorem,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), [interesting(0.9),axiom,file(boole,t7_boole)]). fof(fraenkel_a_1_0_bintree1,definition,( ! [A,B] : ( m1_trees_1(B,k2_trees_1(2)) => ( r2_hidden(A,a_1_0_bintree1(B)) <=> ? [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) & A = k7_finseq_1(B,k3_lang1(k1_numbers,C)) & r2_hidden(k7_finseq_1(B,k3_lang1(k1_numbers,C)),k2_trees_1(2)) ) ) ) ), file(bintree1,a_1_0_bintree1), [interesting(0.9),axiom,file(bintree1,a_1_0_bintree1)]). fof(dh_c1_5_1_1_1__bintree1,definition, ( ( r2_hidden(c1_5_1_1_1__bintree1,a_1_0_bintree1(c2_5__bintree1)) <=> r2_hidden(c1_5_1_1_1__bintree1,k2_tarski(k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)),k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,1)))) ) => ! [A] : ( r2_hidden(A,a_1_0_bintree1(c2_5__bintree1)) <=> r2_hidden(A,k2_tarski(k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)),k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,1)))) ) ), introduced(definition,[new_symbol(c1_5_1_1_1__bintree1),file(bintree1,c1_5_1_1_1__bintree1)]), [interesting(0.35),axiom,file(bintree1,c1_5_1_1_1__bintree1)]). fof(e1_5_1_1_1_1__bintree1,assumption,( r2_hidden(c1_5_1_1_1__bintree1,a_1_0_bintree1(c2_5__bintree1)) ), introduced(assumption,[file(bintree1,e1_5_1_1_1_1__bintree1)]), [interesting(0.2),axiom,file(bintree1,e1_5_1_1_1_1__bintree1)]). fof(e1_5_1_1_1_1_1_1__bintree1,assumption,( c1_5_1_1_1__bintree1 = k1_xboole_0 ), introduced(assumption,[file(bintree1,e1_5_1_1_1_1_1_1__bintree1)]), [interesting(0.02),axiom,file(bintree1,e1_5_1_1_1_1_1_1__bintree1)]). 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(redefinition_k3_finseq_1,definition,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k3_finseq_1(A) = k1_card_1(A) ) ), file(finseq_1,k3_finseq_1), [interesting(0.9),axiom,file(finseq_1,k3_finseq_1)]). fof(dt_k3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers) ) ), file(finseq_1,k3_finseq_1), [interesting(0.9),axiom,file(finseq_1,k3_finseq_1)]). fof(dt_c1_5_1_1_1__bintree1,assumption,( $true ), introduced(assumption,[file(bintree1,c1_5_1_1_1__bintree1)]), [interesting(0.35),axiom,file(bintree1,c1_5_1_1_1__bintree1)]). fof(de_c2_5_1_1_1_1__bintree1,definition,( c2_5_1_1_1_1__bintree1 = c1_5_1_1_1__bintree1 ), introduced(definition,[new_symbol(c2_5_1_1_1_1__bintree1),file(bintree1,c2_5_1_1_1_1__bintree1)]), [interesting(0.2),axiom,file(bintree1,c2_5_1_1_1_1__bintree1)]). fof(dh_c1_5_1_1_1_1__bintree1,definition, ( ? [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) & c1_5_1_1_1__bintree1 = k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,A)) & r2_hidden(k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,A)),k2_trees_1(2)) ) => ( m2_subset_1(c1_5_1_1_1_1__bintree1,k1_numbers,k5_numbers) & c1_5_1_1_1__bintree1 = k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,c1_5_1_1_1_1__bintree1)) & r2_hidden(k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,c1_5_1_1_1_1__bintree1)),k2_trees_1(2)) ) ), introduced(definition,[new_symbol(c1_5_1_1_1_1__bintree1),file(bintree1,c1_5_1_1_1_1__bintree1)]), [interesting(0.2),axiom,file(bintree1,c1_5_1_1_1_1__bintree1)]). fof(t2_tarski,theorem,( ! [A,B] : ( ! [C] : ( r2_hidden(C,A) <=> r2_hidden(C,B) ) => A = B ) ), file(tarski,t2_tarski), [interesting(0.9),axiom,file(tarski,t2_tarski)]). fof(e2_5_1_1_1_1__bintree1,plain,( ? [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) & c1_5_1_1_1__bintree1 = k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,A)) & r2_hidden(k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,A)),k2_trees_1(2)) ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5_1_1_1__bintree1,dt_c2_5__bintree1,e1_5_1_1_1_1__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc4_subset_1,rc2_finseq_1,rc9_trees_2,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_fraenkel,rc1_fraenkel,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,reflexivity_r1_tarski,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_m1_finseq_2,dt_m2_finseq_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_arytm_3,cc1_membered,cc20_membered,cc2_arytm_3,cc2_membered,cc3_membered,cc7_trees_3,fc16_finseq_1,fc2_finseq_1,fc6_membered,fc7_trees_3,fc8_trees_3,fc9_finseq_1,rc1_arytm_3,rc1_membered,rc5_trees_3,rc7_trees_3,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_2,redefinition_k3_finseq_2,redefinition_m1_trees_1,redefinition_m2_finseq_2,dt_k1_zfmisc_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_2,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_dtconstr,cc1_finseq_1,cc3_arytm_3,cc4_membered,cc6_membered,cc9_membered,fc10_trees_3,fc12_finseq_1,fc13_finseq_1,fc13_trees_3,fc14_finseq_1,fc1_subset_1,fc3_finseq_1,fc4_finseq_1,fc5_membered,rc1_finseq_1,rc1_subset_1,rc2_subset_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m2_subset_1,redefinition_k3_lang1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_trees_1,dt_k3_lang1,dt_k5_numbers,dt_k7_finseq_1,dt_m2_subset_1,dt_c1_5_1_1_1__bintree1,dt_c2_5__bintree1,fc2_membered,t1_subset,t7_boole,t2_tarski,fraenkel_a_1_0_bintree1,spc2_numerals,spc2_boole,e1_5_1_1_1_1__bintree1]), [interesting(0.2),file(bintree1,e2_5_1_1_1_1__bintree1),[file(bintree1,e2_5_1_1_1_1__bintree1)]]). fof(dt_c1_5_1_1_1_1__bintree1,plain,( m2_subset_1(c1_5_1_1_1_1__bintree1,k1_numbers,k5_numbers) ), inference(consider,[status(thm),assumptions([dt_c1_5_1_1_1__bintree1,dt_c2_5__bintree1,e1_5_1_1_1_1__bintree1])],[dh_c1_5_1_1_1_1__bintree1,e2_5_1_1_1_1__bintree1]), [interesting(0.2),file(bintree1,c1_5_1_1_1_1__bintree1),[file(bintree1,c1_5_1_1_1_1__bintree1)]]). fof(e3_5_1_1_1_1__bintree1,plain, ( c1_5_1_1_1__bintree1 = k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,c1_5_1_1_1_1__bintree1)) & r2_hidden(k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,c1_5_1_1_1_1__bintree1)),k2_trees_1(2)) ), inference(consider,[status(thm),assumptions([dt_c1_5_1_1_1__bintree1,dt_c2_5__bintree1,e1_5_1_1_1_1__bintree1])],[dh_c1_5_1_1_1_1__bintree1,e2_5_1_1_1_1__bintree1]), [interesting(0.2),file(bintree1,e3_5_1_1_1_1__bintree1),[file(bintree1,e3_5_1_1_1_1__bintree1)]]). fof(e5_5_1_1_1_1__bintree1,plain, ( v1_relat_1(c1_5_1_1_1__bintree1) & v1_funct_1(c1_5_1_1_1__bintree1) & v1_finseq_1(c1_5_1_1_1__bintree1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5_1_1_1__bintree1,dt_c2_5__bintree1,e1_5_1_1_1_1__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc4_subset_1,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_arytm_3,cc1_fraenkel,cc2_arytm_3,rc1_arytm_3,rc1_fraenkel,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_2,dt_m2_finseq_1,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc6_membered,cc7_trees_3,cc9_membered,fc16_finseq_1,fc1_subset_1,fc2_finseq_1,fc5_membered,fc6_membered,fc7_trees_3,fc8_trees_3,fc9_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,rc5_trees_3,rc7_trees_3,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m1_trees_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_dtconstr,cc4_membered,fc10_trees_3,fc12_finseq_1,fc13_finseq_1,fc13_trees_3,fc14_finseq_1,fc3_finseq_1,fc4_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k3_lang1,dt_k1_numbers,dt_k2_trees_1,dt_k3_lang1,dt_k7_finseq_1,dt_c1_5_1_1_1__bintree1,dt_c1_5_1_1_1_1__bintree1,dt_c2_5__bintree1,cc1_finseq_1,fc2_membered,rc1_finseq_1,t1_subset,t7_boole,spc2_numerals,spc2_boole,e3_5_1_1_1_1__bintree1]), [interesting(0.2),file(bintree1,e5_5_1_1_1_1__bintree1),[file(bintree1,e5_5_1_1_1_1__bintree1)]]). fof(dt_c2_5_1_1_1_1__bintree1,plain, ( v1_relat_1(c2_5_1_1_1_1__bintree1) & v1_funct_1(c2_5_1_1_1_1__bintree1) & v1_finseq_1(c2_5_1_1_1_1__bintree1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5_1_1_1__bintree1,dt_c2_5__bintree1,e1_5_1_1_1_1__bintree1])],[dt_c1_5_1_1_1__bintree1,cc1_finseq_1,rc1_finseq_1,de_c2_5_1_1_1_1__bintree1,e5_5_1_1_1_1__bintree1]), [interesting(0.2),file(bintree1,c2_5_1_1_1_1__bintree1),[file(bintree1,c2_5_1_1_1_1__bintree1)]]). fof(t47_finseq_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( k7_finseq_1(A,k1_xboole_0) = A & k7_finseq_1(k1_xboole_0,A) = A ) ) ), file(finseq_1,t47_finseq_1), [interesting(0.9),axiom,file(finseq_1,t47_finseq_1)]). fof(e4_5_1_1_1_1__bintree1,plain,( c1_5_1_1_1__bintree1 = k3_lang1(k1_numbers,c1_5_1_1_1_1__bintree1) ), inference(mizar_by,[status(thm),assumptions([e1_5_1_1__bintree1,dt_c1_5_1_1_1__bintree1,dt_c2_5__bintree1,e1_5_1_1_1_1__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc4_subset_1,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_arytm_3,cc1_fraenkel,cc2_arytm_3,rc1_arytm_3,rc1_fraenkel,rc4_finseq_1,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_2,dt_m2_finseq_1,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc20_membered,cc3_arytm_3,cc6_membered,cc7_trees_3,cc9_membered,fc16_finseq_1,fc1_subset_1,fc5_membered,fc7_trees_3,fc8_trees_3,fc9_finseq_1,rc1_subset_1,rc2_subset_1,rc5_trees_3,rc7_trees_3,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m1_trees_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc1_dtconstr,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc10_trees_3,fc12_finseq_1,fc13_finseq_1,fc13_trees_3,fc14_finseq_1,fc3_finseq_1,fc4_finseq_1,rc1_membered,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t8_boole,antisymmetry_r2_hidden,redefinition_k3_lang1,dt_k1_numbers,dt_k1_xboole_0,dt_k2_trees_1,dt_k3_lang1,dt_k7_finseq_1,dt_c1_5_1_1_1__bintree1,dt_c1_5_1_1_1_1__bintree1,dt_c2_5__bintree1,cc1_finseq_1,fc2_finseq_1,fc2_membered,fc6_membered,rc1_finseq_1,t1_subset,t6_boole,t7_boole,spc2_numerals,spc2_boole,e1_5_1_1__bintree1,e3_5_1_1_1_1__bintree1,t47_finseq_1]), [interesting(0.2),file(bintree1,e4_5_1_1_1_1__bintree1),[file(bintree1,e4_5_1_1_1_1__bintree1)]]). fof(e2_5_1_1_1_1_1_1__bintree1,plain, ( k3_finseq_1(c2_5_1_1_1_1__bintree1) = 0 & k3_finseq_1(c2_5_1_1_1_1__bintree1) = 1 ), inference(mizar_by,[status(thm),assumptions([e1_5_1_1_1_1_1_1__bintree1,e1_5_1_1__bintree1,dt_c1_5_1_1_1__bintree1,dt_c2_5__bintree1,e1_5_1_1_1_1__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc4_subset_1,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_arytm_3,cc1_fraenkel,cc2_arytm_3,rc1_arytm_3,rc1_fraenkel,rc4_finseq_1,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_2,dt_m2_finseq_1,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc20_membered,cc3_arytm_3,cc6_membered,cc9_membered,fc16_finseq_1,fc1_subset_1,fc5_membered,fc9_finseq_1,rc1_subset_1,rc2_subset_1,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_card_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc1_dtconstr,cc1_finseq_1,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc12_finseq_1,fc3_finseq_1,fc4_finseq_1,rc1_finseq_1,rc1_membered,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t1_numerals,t2_subset,t7_boole,t8_boole,redefinition_k3_finseq_1,redefinition_k3_lang1,dt_k1_numbers,dt_k1_xboole_0,dt_k3_finseq_1,dt_k3_lang1,dt_c1_5_1_1_1__bintree1,dt_c1_5_1_1_1_1__bintree1,dt_c2_5_1_1_1_1__bintree1,de_c2_5_1_1_1_1__bintree1,fc2_finseq_1,fc2_membered,fc6_membered,t6_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e1_5_1_1_1_1_1_1__bintree1,e4_5_1_1_1_1__bintree1]), [interesting(0.02),file(bintree1,e2_5_1_1_1_1_1_1__bintree1),[file(bintree1,e2_5_1_1_1_1_1_1__bintree1)]]). fof(e3_5_1_1_1_1_1_1__bintree1,plain,( r2_hidden(c1_5_1_1_1__bintree1,k2_tarski(k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)),k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,1)))) ), inference(mizar_by,[status(thm),assumptions([e1_5_1_1_1_1_1_1__bintree1,e1_5_1_1__bintree1,dt_c1_5_1_1_1__bintree1,dt_c2_5__bintree1,e1_5_1_1_1_1__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc4_subset_1,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_arytm_3,cc1_fraenkel,cc2_arytm_3,cc7_trees_3,fc14_membered,fc15_membered,fc16_membered,fc7_trees_3,fc8_trees_3,rc1_arytm_3,rc1_fraenkel,rc3_finseq_1,rc4_finseq_1,rc5_trees_3,rc6_finseq_1,rc7_trees_3,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_2,dt_m2_finseq_1,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc6_membered,cc9_membered,fc10_trees_3,fc12_membered,fc13_membered,fc13_trees_3,fc16_finseq_1,fc1_subset_1,fc2_finseq_1,fc5_membered,fc6_membered,fc9_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,rc7_finseq_1,rc8_finseq_1,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m1_trees_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_card_1,dt_k2_trees_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_dtconstr,cc1_finseq_1,cc4_membered,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc3_finseq_1,fc4_finseq_1,rc1_finseq_1,spc2_boole,spc2_numerals,t1_numerals,t2_subset,t6_boole,t8_boole,spc2_numerals,spc2_boole,commutativity_k2_tarski,antisymmetry_r2_hidden,redefinition_k3_finseq_1,redefinition_k3_lang1,dt_k1_numbers,dt_k2_tarski,dt_k3_finseq_1,dt_k3_lang1,dt_k7_finseq_1,dt_c1_5_1_1_1__bintree1,dt_c2_5__bintree1,dt_c2_5_1_1_1_1__bintree1,de_c2_5_1_1_1_1__bintree1,fc2_membered,fc3_subset_1,t1_subset,t7_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e2_5_1_1_1_1_1_1__bintree1]), [interesting(0.02),file(bintree1,e3_5_1_1_1_1_1_1__bintree1),[file(bintree1,e3_5_1_1_1_1_1_1__bintree1)]]). fof(i2_5_1_1_1_1_1_1__bintree1,theorem,( $true ), introduced(tautology,[file(bintree1,i2_5_1_1_1_1_1_1__bintree1)]), [interesting(0.02),trivial,file(bintree1,i2_5_1_1_1_1_1_1__bintree1)]). fof(i1_5_1_1_1_1_1_1__bintree1,plain,( r2_hidden(c1_5_1_1_1__bintree1,k2_tarski(k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)),k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,1)))) ), inference(conclusion,[status(thm),assumptions([e1_5_1_1_1_1_1_1__bintree1,e1_5_1_1__bintree1,dt_c1_5_1_1_1__bintree1,dt_c2_5__bintree1,e1_5_1_1_1_1__bintree1])],[e3_5_1_1_1_1_1_1__bintree1,i2_5_1_1_1_1_1_1__bintree1]), [interesting(0.02),file(bintree1,i1_5_1_1_1_1_1_1__bintree1),[file(bintree1,i1_5_1_1_1_1_1_1__bintree1)]]). fof(i1_5_1_1_1_1_1__bintree1,plain, ( c1_5_1_1_1__bintree1 = k1_xboole_0 => r2_hidden(c1_5_1_1_1__bintree1,k2_tarski(k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)),k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,1)))) ), inference(discharge_asm,[status(thm),assumptions([e1_5_1_1__bintree1,dt_c1_5_1_1_1__bintree1,dt_c2_5__bintree1,e1_5_1_1_1_1__bintree1]),discharge_asm(discharge,[e1_5_1_1_1_1_1_1__bintree1])],[e1_5_1_1_1_1_1_1__bintree1,i1_5_1_1_1_1_1_1__bintree1]), [interesting(0.05),file(bintree1,i1_5_1_1_1_1_1__bintree1),[file(bintree1,i1_5_1_1_1_1_1__bintree1)]]). fof(e1_5_1_1_1_1_1_2__bintree1,assumption,( c1_5_1_1_1__bintree1 = k3_lang1(k1_numbers,0) ), introduced(assumption,[file(bintree1,e1_5_1_1_1_1_1_2__bintree1)]), [interesting(0.02),axiom,file(bintree1,e1_5_1_1_1_1_1_2__bintree1)]). fof(e2_5_1_1_1_1_1_2__bintree1,plain,( c2_5_1_1_1_1__bintree1 = k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5_1_1_1__bintree1,dt_c2_5__bintree1,e1_5_1_1_1_1__bintree1,e1_5_1_1_1_1_1_2__bintree1,e1_5_1_1__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc4_subset_1,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_arytm_3,cc1_fraenkel,cc2_arytm_3,cc7_trees_3,fc7_trees_3,fc8_trees_3,rc1_arytm_3,rc1_fraenkel,rc4_finseq_1,rc5_trees_3,rc7_trees_3,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_2,dt_m2_finseq_1,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc20_membered,cc3_arytm_3,cc6_membered,cc9_membered,fc10_trees_3,fc13_trees_3,fc16_finseq_1,fc1_subset_1,fc5_membered,fc9_finseq_1,rc1_subset_1,rc2_subset_1,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m1_trees_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k2_trees_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc1_dtconstr,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc3_finseq_1,fc4_finseq_1,rc1_membered,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,spc2_boole,spc2_numerals,t1_numerals,t2_subset,t7_boole,t8_boole,spc2_numerals,spc2_boole,redefinition_k3_lang1,dt_k1_numbers,dt_k1_xboole_0,dt_k3_lang1,dt_k7_finseq_1,dt_c1_5_1_1_1__bintree1,dt_c2_5__bintree1,dt_c2_5_1_1_1_1__bintree1,de_c2_5_1_1_1_1__bintree1,cc1_finseq_1,fc2_finseq_1,fc2_membered,fc6_membered,rc1_finseq_1,t6_boole,spc0_numerals,spc0_boole,e1_5_1_1_1_1_1_2__bintree1,e1_5_1_1__bintree1,t47_finseq_1]), [interesting(0.02),file(bintree1,e2_5_1_1_1_1_1_2__bintree1),[file(bintree1,e2_5_1_1_1_1_1_2__bintree1)]]). fof(d2_tarski,definition,( ! [A,B,C] : ( C = k2_tarski(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( D = A | D = B ) ) ) ), file(tarski,d2_tarski), [interesting(0.9),axiom,file(tarski,d2_tarski)]). fof(e3_5_1_1_1_1_1_2__bintree1,plain,( r2_hidden(c1_5_1_1_1__bintree1,k2_tarski(k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)),k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,1)))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5_1_1_1__bintree1,dt_c2_5__bintree1,e1_5_1_1_1_1__bintree1,e1_5_1_1_1_1_1_2__bintree1,e1_5_1_1__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc4_subset_1,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_arytm_3,cc1_fraenkel,cc2_arytm_3,cc7_trees_3,fc14_membered,fc15_membered,fc16_membered,fc7_trees_3,fc8_trees_3,rc1_arytm_3,rc1_fraenkel,rc3_finseq_1,rc4_finseq_1,rc5_trees_3,rc6_finseq_1,rc7_trees_3,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_2,dt_m2_finseq_1,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc6_membered,cc9_membered,fc10_trees_3,fc12_membered,fc13_membered,fc13_trees_3,fc16_finseq_1,fc1_subset_1,fc2_finseq_1,fc5_membered,fc6_membered,fc9_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,rc7_finseq_1,rc8_finseq_1,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m1_trees_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k2_trees_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_dtconstr,cc1_finseq_1,cc4_membered,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc3_finseq_1,fc4_finseq_1,rc1_finseq_1,spc2_boole,spc2_numerals,t1_numerals,t2_subset,t6_boole,t8_boole,spc2_numerals,spc2_boole,commutativity_k2_tarski,antisymmetry_r2_hidden,redefinition_k3_lang1,dt_k1_numbers,dt_k2_tarski,dt_k3_lang1,dt_k7_finseq_1,dt_c1_5_1_1_1__bintree1,dt_c2_5__bintree1,dt_c2_5_1_1_1_1__bintree1,de_c2_5_1_1_1_1__bintree1,fc2_membered,fc3_subset_1,t1_subset,t7_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e2_5_1_1_1_1_1_2__bintree1,d2_tarski]), [interesting(0.02),file(bintree1,e3_5_1_1_1_1_1_2__bintree1),[file(bintree1,e3_5_1_1_1_1_1_2__bintree1)]]). fof(i2_5_1_1_1_1_1_2__bintree1,theorem,( $true ), introduced(tautology,[file(bintree1,i2_5_1_1_1_1_1_2__bintree1)]), [interesting(0.02),trivial,file(bintree1,i2_5_1_1_1_1_1_2__bintree1)]). fof(i1_5_1_1_1_1_1_2__bintree1,plain,( r2_hidden(c1_5_1_1_1__bintree1,k2_tarski(k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)),k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,1)))) ), inference(conclusion,[status(thm),assumptions([dt_c1_5_1_1_1__bintree1,dt_c2_5__bintree1,e1_5_1_1_1_1__bintree1,e1_5_1_1_1_1_1_2__bintree1,e1_5_1_1__bintree1])],[e3_5_1_1_1_1_1_2__bintree1,i2_5_1_1_1_1_1_2__bintree1]), [interesting(0.02),file(bintree1,i1_5_1_1_1_1_1_2__bintree1),[file(bintree1,i1_5_1_1_1_1_1_2__bintree1)]]). fof(i2_5_1_1_1_1_1__bintree1,plain, ( c1_5_1_1_1__bintree1 = k3_lang1(k1_numbers,0) => r2_hidden(c1_5_1_1_1__bintree1,k2_tarski(k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)),k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,1)))) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_5_1_1_1__bintree1,dt_c2_5__bintree1,e1_5_1_1_1_1__bintree1,e1_5_1_1__bintree1]),discharge_asm(discharge,[e1_5_1_1_1_1_1_2__bintree1])],[e1_5_1_1_1_1_1_2__bintree1,i1_5_1_1_1_1_1_2__bintree1]), [interesting(0.05),file(bintree1,i2_5_1_1_1_1_1__bintree1),[file(bintree1,i2_5_1_1_1_1_1__bintree1)]]). fof(e1_5_1_1_1_1_1_3__bintree1,assumption,( c1_5_1_1_1__bintree1 = k3_lang1(k1_numbers,1) ), introduced(assumption,[file(bintree1,e1_5_1_1_1_1_1_3__bintree1)]), [interesting(0.02),axiom,file(bintree1,e1_5_1_1_1_1_1_3__bintree1)]). fof(e2_5_1_1_1_1_1_3__bintree1,plain,( c2_5_1_1_1_1__bintree1 = k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,1)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5_1_1_1__bintree1,dt_c2_5__bintree1,e1_5_1_1_1_1__bintree1,e1_5_1_1_1_1_1_3__bintree1,e1_5_1_1__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc4_subset_1,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_arytm_3,cc1_fraenkel,cc2_arytm_3,cc7_trees_3,fc7_trees_3,fc8_trees_3,rc1_arytm_3,rc1_fraenkel,rc4_finseq_1,rc5_trees_3,rc7_trees_3,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_2,dt_m2_finseq_1,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc20_membered,cc3_arytm_3,cc6_membered,cc9_membered,fc10_trees_3,fc13_trees_3,fc16_finseq_1,fc1_subset_1,fc5_membered,fc9_finseq_1,rc1_subset_1,rc2_subset_1,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m1_trees_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k2_trees_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc1_dtconstr,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc3_finseq_1,fc4_finseq_1,rc1_membered,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,spc2_boole,spc2_numerals,t2_subset,t7_boole,t8_boole,spc2_numerals,spc2_boole,redefinition_k3_lang1,dt_k1_numbers,dt_k1_xboole_0,dt_k3_lang1,dt_k7_finseq_1,dt_c1_5_1_1_1__bintree1,dt_c2_5__bintree1,dt_c2_5_1_1_1_1__bintree1,de_c2_5_1_1_1_1__bintree1,cc1_finseq_1,fc2_finseq_1,fc2_membered,fc6_membered,rc1_finseq_1,t6_boole,spc1_numerals,spc1_boole,e1_5_1_1_1_1_1_3__bintree1,e1_5_1_1__bintree1,t47_finseq_1]), [interesting(0.02),file(bintree1,e2_5_1_1_1_1_1_3__bintree1),[file(bintree1,e2_5_1_1_1_1_1_3__bintree1)]]). fof(e3_5_1_1_1_1_1_3__bintree1,plain,( r2_hidden(c1_5_1_1_1__bintree1,k2_tarski(k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)),k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,1)))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5_1_1_1__bintree1,dt_c2_5__bintree1,e1_5_1_1_1_1__bintree1,e1_5_1_1_1_1_1_3__bintree1,e1_5_1_1__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc4_subset_1,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_arytm_3,cc1_fraenkel,cc2_arytm_3,cc7_trees_3,fc14_membered,fc15_membered,fc16_membered,fc7_trees_3,fc8_trees_3,rc1_arytm_3,rc1_fraenkel,rc3_finseq_1,rc4_finseq_1,rc5_trees_3,rc6_finseq_1,rc7_trees_3,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_2,dt_m2_finseq_1,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc6_membered,cc9_membered,fc10_trees_3,fc12_membered,fc13_membered,fc13_trees_3,fc16_finseq_1,fc1_subset_1,fc2_finseq_1,fc5_membered,fc6_membered,fc9_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,rc7_finseq_1,rc8_finseq_1,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m1_trees_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k2_trees_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_dtconstr,cc1_finseq_1,cc4_membered,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc3_finseq_1,fc4_finseq_1,rc1_finseq_1,spc2_boole,spc2_numerals,t1_numerals,t2_subset,t6_boole,t8_boole,spc2_numerals,spc2_boole,commutativity_k2_tarski,antisymmetry_r2_hidden,redefinition_k3_lang1,dt_k1_numbers,dt_k2_tarski,dt_k3_lang1,dt_k7_finseq_1,dt_c1_5_1_1_1__bintree1,dt_c2_5__bintree1,dt_c2_5_1_1_1_1__bintree1,de_c2_5_1_1_1_1__bintree1,fc2_membered,fc3_subset_1,t1_subset,t7_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e2_5_1_1_1_1_1_3__bintree1,d2_tarski]), [interesting(0.02),file(bintree1,e3_5_1_1_1_1_1_3__bintree1),[file(bintree1,e3_5_1_1_1_1_1_3__bintree1)]]). fof(i2_5_1_1_1_1_1_3__bintree1,theorem,( $true ), introduced(tautology,[file(bintree1,i2_5_1_1_1_1_1_3__bintree1)]), [interesting(0.02),trivial,file(bintree1,i2_5_1_1_1_1_1_3__bintree1)]). fof(i1_5_1_1_1_1_1_3__bintree1,plain,( r2_hidden(c1_5_1_1_1__bintree1,k2_tarski(k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)),k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,1)))) ), inference(conclusion,[status(thm),assumptions([dt_c1_5_1_1_1__bintree1,dt_c2_5__bintree1,e1_5_1_1_1_1__bintree1,e1_5_1_1_1_1_1_3__bintree1,e1_5_1_1__bintree1])],[e3_5_1_1_1_1_1_3__bintree1,i2_5_1_1_1_1_1_3__bintree1]), [interesting(0.02),file(bintree1,i1_5_1_1_1_1_1_3__bintree1),[file(bintree1,i1_5_1_1_1_1_1_3__bintree1)]]). fof(i3_5_1_1_1_1_1__bintree1,plain, ( c1_5_1_1_1__bintree1 = k3_lang1(k1_numbers,1) => r2_hidden(c1_5_1_1_1__bintree1,k2_tarski(k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)),k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,1)))) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_5_1_1_1__bintree1,dt_c2_5__bintree1,e1_5_1_1_1_1__bintree1,e1_5_1_1__bintree1]),discharge_asm(discharge,[e1_5_1_1_1_1_1_3__bintree1])],[e1_5_1_1_1_1_1_3__bintree1,i1_5_1_1_1_1_1_3__bintree1]), [interesting(0.05),file(bintree1,i3_5_1_1_1_1_1__bintree1),[file(bintree1,i3_5_1_1_1_1_1__bintree1)]]). fof(fc17_membered,theorem,( ! [A,B,C] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) ) => v1_membered(k1_enumset1(A,B,C)) ) ), file(membered,fc17_membered), [interesting(0.9),axiom,file(membered,fc17_membered)]). fof(fc18_membered,theorem,( ! [A,B,C] : ( ( v1_xreal_0(A) & v1_xreal_0(B) & v1_xreal_0(C) ) => ( v1_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)) ) ) ), file(membered,fc18_membered), [interesting(0.9),axiom,file(membered,fc18_membered)]). fof(fc19_membered,theorem,( ! [A,B,C] : ( ( v1_rat_1(A) & v1_rat_1(B) & v1_rat_1(C) ) => ( v1_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)) & v3_membered(k1_enumset1(A,B,C)) ) ) ), file(membered,fc19_membered), [interesting(0.9),axiom,file(membered,fc19_membered)]). fof(fc20_membered,theorem,( ! [A,B,C] : ( ( v1_int_1(A) & v1_int_1(B) & v1_int_1(C) ) => ( v1_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)) & v3_membered(k1_enumset1(A,B,C)) & v4_membered(k1_enumset1(A,B,C)) ) ) ), file(membered,fc20_membered), [interesting(0.9),axiom,file(membered,fc20_membered)]). fof(fc21_membered,theorem,( ! [A,B,C] : ( ( v4_ordinal2(A) & v4_ordinal2(B) & v4_ordinal2(C) ) => ( v1_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)) & v3_membered(k1_enumset1(A,B,C)) & v4_membered(k1_enumset1(A,B,C)) & v5_membered(k1_enumset1(A,B,C)) ) ) ), file(membered,fc21_membered), [interesting(0.9),axiom,file(membered,fc21_membered)]). fof(redefinition_k12_finseq_1,definition,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => k12_finseq_1(A,B) = k5_finseq_1(B) ) ), file(finseq_1,k12_finseq_1), [interesting(0.9),axiom,file(finseq_1,k12_finseq_1)]). fof(dt_k12_finseq_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m2_finseq_1(k12_finseq_1(A,B),A) ) ), file(finseq_1,k12_finseq_1), [interesting(0.9),axiom,file(finseq_1,k12_finseq_1)]). fof(dt_k1_enumset1,axiom,( $true ), file(enumset1,k1_enumset1), [interesting(0.9),axiom,file(enumset1,k1_enumset1)]). fof(d1_enumset1,definition,( ! [A,B,C,D] : ( D = k1_enumset1(A,B,C) <=> ! [E] : ( r2_hidden(E,D) <=> ~ ( E != A & E != B & E != C ) ) ) ), file(enumset1,d1_enumset1), [interesting(0.9),axiom,file(enumset1,d1_enumset1)]). fof(t10_modal_1,theorem,( k2_trees_1(2) = k1_enumset1(k1_xboole_0,k12_finseq_1(k5_numbers,0),k12_finseq_1(k5_numbers,1)) ), file(modal_1,t10_modal_1), [interesting(0.9),axiom,file(modal_1,t10_modal_1)]). fof(e1_5_1_1_1_1_1__bintree1,plain,( ~ ( c1_5_1_1_1__bintree1 != k1_xboole_0 & c1_5_1_1_1__bintree1 != k3_lang1(k1_numbers,0) & c1_5_1_1_1__bintree1 != k3_lang1(k1_numbers,1) ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5_1_1_1__bintree1,dt_c2_5__bintree1,e1_5_1_1_1_1__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_fraenkel,cc1_relset_1,fc4_subset_1,rc1_fraenkel,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m1_finseq_2,existence_m2_relset_1,redefinition_m2_relset_1,dt_k13_finseq_1,dt_m1_finseq_1,dt_m1_finseq_2,dt_m2_relset_1,cc1_arytm_3,cc2_arytm_3,cc7_trees_3,fc16_finseq_1,fc17_membered,fc18_membered,fc19_membered,fc20_membered,fc21_membered,fc7_trees_3,fc8_trees_3,fc9_finseq_1,rc1_arytm_3,rc4_finseq_1,rc5_trees_3,rc7_trees_3,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_m1_trees_1,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_zfmisc_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_1,dt_m2_finseq_2,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_dtconstr,cc1_finseq_1,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc10_trees_3,fc12_finseq_1,fc13_finseq_1,fc13_trees_3,fc14_finseq_1,fc1_subset_1,fc3_finseq_1,fc4_finseq_1,fc5_membered,rc1_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,redefinition_k12_finseq_1,redefinition_k3_lang1,redefinition_k5_numbers,dt_k12_finseq_1,dt_k1_enumset1,dt_k1_numbers,dt_k1_xboole_0,dt_k2_trees_1,dt_k3_lang1,dt_k5_numbers,dt_k7_finseq_1,dt_c1_5_1_1_1__bintree1,dt_c1_5_1_1_1_1__bintree1,dt_c2_5__bintree1,fc2_finseq_1,fc2_membered,fc6_membered,t1_subset,t6_boole,t7_boole,spc0_numerals,spc1_numerals,spc2_numerals,spc0_boole,spc1_boole,spc2_boole,e3_5_1_1_1_1__bintree1,d1_enumset1,t10_modal_1]), [interesting(0.05),file(bintree1,e1_5_1_1_1_1_1__bintree1),[file(bintree1,e1_5_1_1_1_1_1__bintree1)]]). fof(i1_5_1_1_1_1__bintree1,plain,( r2_hidden(c1_5_1_1_1__bintree1,k2_tarski(k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)),k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,1)))) ), inference(percases,[status(thm),assumptions([e1_5_1_1__bintree1,dt_c1_5_1_1_1__bintree1,dt_c2_5__bintree1,e1_5_1_1_1_1__bintree1])],[i1_5_1_1_1_1_1__bintree1,i2_5_1_1_1_1_1__bintree1,i3_5_1_1_1_1_1__bintree1,e1_5_1_1_1_1_1__bintree1]), [interesting(0.2),file(bintree1,i1_5_1_1_1_1__bintree1),[file(bintree1,i1_5_1_1_1_1__bintree1)]]). fof(e1_5_1_1_1__bintree1,plain, ( r2_hidden(c1_5_1_1_1__bintree1,a_1_0_bintree1(c2_5__bintree1)) => r2_hidden(c1_5_1_1_1__bintree1,k2_tarski(k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)),k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,1)))) ), inference(discharge_asm,[status(thm),assumptions([e1_5_1_1__bintree1,dt_c1_5_1_1_1__bintree1,dt_c2_5__bintree1]),discharge_asm(discharge,[e1_5_1_1_1_1__bintree1])],[e1_5_1_1_1_1__bintree1,i1_5_1_1_1_1__bintree1]), [interesting(0.35),file(bintree1,e1_5_1_1_1__bintree1),[file(bintree1,e1_5_1_1_1__bintree1)]]). fof(e2_5_1_1_1__bintree1,assumption,( r2_hidden(c1_5_1_1_1__bintree1,k2_tarski(k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)),k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,1)))) ), introduced(assumption,[file(bintree1,e2_5_1_1_1__bintree1)]), [interesting(0.35),axiom,file(bintree1,e2_5_1_1_1__bintree1)]). fof(de_c2_5_1_1_1__bintree1,definition,( c2_5_1_1_1__bintree1 = c1_5_1_1_1__bintree1 ), introduced(definition,[new_symbol(c2_5_1_1_1__bintree1),file(bintree1,c2_5_1_1_1__bintree1)]), [interesting(0.35),axiom,file(bintree1,c2_5_1_1_1__bintree1)]). fof(e4_5_1_1_1__bintree1,plain, ( v1_relat_1(c1_5_1_1_1__bintree1) & v1_funct_1(c1_5_1_1_1__bintree1) & v1_finseq_1(c1_5_1_1_1__bintree1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5_1_1_1__bintree1,dt_c2_5__bintree1,e2_5_1_1_1__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc4_subset_1,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_arytm_3,cc1_fraenkel,cc2_arytm_3,cc7_trees_3,fc14_membered,fc15_membered,fc16_membered,fc7_trees_3,fc8_trees_3,rc1_arytm_3,rc1_fraenkel,rc3_finseq_1,rc4_finseq_1,rc5_trees_3,rc6_finseq_1,rc7_trees_3,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_2,dt_m2_finseq_1,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc6_membered,cc9_membered,fc10_trees_3,fc12_membered,fc13_membered,fc13_trees_3,fc16_finseq_1,fc1_subset_1,fc2_finseq_1,fc5_membered,fc6_membered,fc9_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m1_trees_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k2_trees_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_dtconstr,cc4_membered,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc3_finseq_1,fc4_finseq_1,rc7_finseq_1,rc8_finseq_1,spc2_boole,spc2_numerals,t1_numerals,t2_subset,t6_boole,t8_boole,spc2_numerals,spc2_boole,commutativity_k2_tarski,antisymmetry_r2_hidden,redefinition_k3_lang1,dt_k1_numbers,dt_k2_tarski,dt_k3_lang1,dt_k7_finseq_1,dt_c1_5_1_1_1__bintree1,dt_c2_5__bintree1,cc1_finseq_1,fc2_membered,fc3_subset_1,rc1_finseq_1,t1_subset,t7_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e2_5_1_1_1__bintree1,d2_tarski]), [interesting(0.35),file(bintree1,e4_5_1_1_1__bintree1),[file(bintree1,e4_5_1_1_1__bintree1)]]). fof(dt_c2_5_1_1_1__bintree1,plain, ( v1_relat_1(c2_5_1_1_1__bintree1) & v1_funct_1(c2_5_1_1_1__bintree1) & v1_finseq_1(c2_5_1_1_1__bintree1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5_1_1_1__bintree1,dt_c2_5__bintree1,e2_5_1_1_1__bintree1])],[dt_c1_5_1_1_1__bintree1,cc1_finseq_1,rc1_finseq_1,de_c2_5_1_1_1__bintree1,e4_5_1_1_1__bintree1]), [interesting(0.35),file(bintree1,c2_5_1_1_1__bintree1),[file(bintree1,c2_5_1_1_1__bintree1)]]). fof(e3_5_1_1_1__bintree1,plain, ( c1_5_1_1_1__bintree1 = k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)) | c1_5_1_1_1__bintree1 = k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,1)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5_1_1_1__bintree1,dt_c2_5__bintree1,e2_5_1_1_1__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc4_subset_1,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_arytm_3,cc1_fraenkel,cc2_arytm_3,cc7_trees_3,fc14_membered,fc15_membered,fc16_membered,fc7_trees_3,fc8_trees_3,rc1_arytm_3,rc1_fraenkel,rc3_finseq_1,rc4_finseq_1,rc5_trees_3,rc6_finseq_1,rc7_trees_3,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_2,dt_m2_finseq_1,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc6_membered,cc9_membered,fc10_trees_3,fc12_membered,fc13_membered,fc13_trees_3,fc16_finseq_1,fc1_subset_1,fc2_finseq_1,fc5_membered,fc6_membered,fc9_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,rc7_finseq_1,rc8_finseq_1,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m1_trees_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k2_trees_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_dtconstr,cc1_finseq_1,cc4_membered,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc3_finseq_1,fc4_finseq_1,rc1_finseq_1,spc2_boole,spc2_numerals,t1_numerals,t2_subset,t6_boole,t8_boole,spc2_numerals,spc2_boole,commutativity_k2_tarski,antisymmetry_r2_hidden,redefinition_k3_lang1,dt_k1_numbers,dt_k2_tarski,dt_k3_lang1,dt_k7_finseq_1,dt_c1_5_1_1_1__bintree1,dt_c2_5__bintree1,fc2_membered,fc3_subset_1,t1_subset,t7_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e2_5_1_1_1__bintree1,d2_tarski]), [interesting(0.35),file(bintree1,e3_5_1_1_1__bintree1),[file(bintree1,e3_5_1_1_1__bintree1)]]). fof(e5_5_1_1_1__bintree1,plain, ( c2_5_1_1_1__bintree1 = k3_lang1(k1_numbers,0) | c2_5_1_1_1__bintree1 = k3_lang1(k1_numbers,1) ), inference(mizar_by,[status(thm),assumptions([e1_5_1_1__bintree1,dt_c1_5_1_1_1__bintree1,dt_c2_5__bintree1,e2_5_1_1_1__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc4_subset_1,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_arytm_3,cc1_fraenkel,cc2_arytm_3,cc7_trees_3,fc7_trees_3,fc8_trees_3,rc1_arytm_3,rc1_fraenkel,rc4_finseq_1,rc5_trees_3,rc7_trees_3,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_2,dt_m2_finseq_1,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc20_membered,cc3_arytm_3,cc6_membered,cc9_membered,fc10_trees_3,fc13_trees_3,fc16_finseq_1,fc1_subset_1,fc5_membered,fc9_finseq_1,rc1_subset_1,rc2_subset_1,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m1_trees_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k2_trees_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc1_dtconstr,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc3_finseq_1,fc4_finseq_1,rc1_membered,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,spc2_boole,spc2_numerals,t1_numerals,t2_subset,t7_boole,t8_boole,spc2_numerals,spc2_boole,redefinition_k3_lang1,dt_k1_numbers,dt_k1_xboole_0,dt_k3_lang1,dt_k7_finseq_1,dt_c1_5_1_1_1__bintree1,dt_c2_5__bintree1,dt_c2_5_1_1_1__bintree1,de_c2_5_1_1_1__bintree1,cc1_finseq_1,fc2_finseq_1,fc2_membered,fc6_membered,rc1_finseq_1,t6_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e1_5_1_1__bintree1,e3_5_1_1_1__bintree1,t47_finseq_1]), [interesting(0.35),file(bintree1,e5_5_1_1_1__bintree1),[file(bintree1,e5_5_1_1_1__bintree1)]]). fof(e6_5_1_1_1__bintree1,plain,( r2_hidden(c2_5_1_1_1__bintree1,k2_trees_1(2)) ), inference(mizar_by,[status(thm),assumptions([e1_5_1_1__bintree1,dt_c1_5_1_1_1__bintree1,dt_c2_5__bintree1,e2_5_1_1_1__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_fraenkel,cc1_relset_1,fc4_subset_1,rc1_fraenkel,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m1_finseq_2,existence_m2_relset_1,redefinition_m2_relset_1,dt_k13_finseq_1,dt_m1_finseq_1,dt_m1_finseq_2,dt_m2_relset_1,cc1_arytm_3,cc2_arytm_3,cc7_trees_3,fc16_finseq_1,fc17_membered,fc18_membered,fc19_membered,fc20_membered,fc21_membered,fc9_finseq_1,rc1_arytm_3,rc4_finseq_1,rc5_trees_3,rc7_trees_3,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_zfmisc_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_subset_1,dt_c1_5_1_1_1__bintree1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_dtconstr,cc1_finseq_1,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc10_trees_3,fc12_finseq_1,fc13_trees_3,fc1_subset_1,fc3_finseq_1,fc4_finseq_1,fc5_membered,rc1_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,redefinition_k12_finseq_1,redefinition_k3_lang1,redefinition_k5_numbers,dt_k12_finseq_1,dt_k1_enumset1,dt_k1_numbers,dt_k1_xboole_0,dt_k2_trees_1,dt_k3_lang1,dt_k5_numbers,dt_c2_5_1_1_1__bintree1,de_c2_5_1_1_1__bintree1,fc2_finseq_1,fc2_membered,fc6_membered,t1_subset,t6_boole,t7_boole,spc0_numerals,spc1_numerals,spc2_numerals,spc0_boole,spc1_boole,spc2_boole,e5_5_1_1_1__bintree1,d1_enumset1,t10_modal_1]), [interesting(0.35),file(bintree1,e6_5_1_1_1__bintree1),[file(bintree1,e6_5_1_1_1__bintree1)]]). fof(e7_5_1_1_1__bintree1,plain,( r2_hidden(c1_5_1_1_1__bintree1,a_1_0_bintree1(c2_5__bintree1)) ), inference(mizar_by,[status(thm),assumptions([e1_5_1_1__bintree1,dt_c1_5_1_1_1__bintree1,dt_c2_5__bintree1,e2_5_1_1_1__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc4_subset_1,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_arytm_3,cc1_fraenkel,cc2_arytm_3,rc1_arytm_3,rc1_fraenkel,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_2,dt_m2_finseq_1,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc6_membered,cc7_trees_3,cc9_membered,fc16_finseq_1,fc1_subset_1,fc2_finseq_1,fc5_membered,fc6_membered,fc7_trees_3,fc8_trees_3,fc9_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,rc5_trees_3,rc7_trees_3,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m1_trees_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_dtconstr,cc1_finseq_1,cc4_membered,fc10_trees_3,fc12_finseq_1,fc13_finseq_1,fc13_trees_3,fc14_finseq_1,fc3_finseq_1,fc4_finseq_1,rc1_finseq_1,rc7_finseq_1,rc8_finseq_1,t1_numerals,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k3_lang1,dt_k1_numbers,dt_k2_trees_1,dt_k3_lang1,dt_k7_finseq_1,dt_c1_5_1_1_1__bintree1,dt_c2_5__bintree1,dt_c2_5_1_1_1__bintree1,de_c2_5_1_1_1__bintree1,fc2_membered,t1_subset,t7_boole,t2_tarski,fraenkel_a_1_0_bintree1,spc0_numerals,spc1_numerals,spc2_numerals,spc0_boole,spc1_boole,spc2_boole,e6_5_1_1_1__bintree1,e3_5_1_1_1__bintree1]), [interesting(0.35),file(bintree1,e7_5_1_1_1__bintree1),[file(bintree1,e7_5_1_1_1__bintree1)]]). fof(i4_5_1_1_1__bintree1,theorem,( $true ), introduced(tautology,[file(bintree1,i4_5_1_1_1__bintree1)]), [interesting(0.35),trivial,file(bintree1,i4_5_1_1_1__bintree1)]). fof(i3_5_1_1_1__bintree1,plain,( r2_hidden(c1_5_1_1_1__bintree1,a_1_0_bintree1(c2_5__bintree1)) ), inference(conclusion,[status(thm),assumptions([e1_5_1_1__bintree1,dt_c1_5_1_1_1__bintree1,dt_c2_5__bintree1,e2_5_1_1_1__bintree1])],[e7_5_1_1_1__bintree1,i4_5_1_1_1__bintree1]), [interesting(0.35),file(bintree1,i3_5_1_1_1__bintree1),[file(bintree1,i3_5_1_1_1__bintree1)]]). fof(i2_5_1_1_1__bintree1,plain, ( r2_hidden(c1_5_1_1_1__bintree1,k2_tarski(k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)),k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,1)))) => r2_hidden(c1_5_1_1_1__bintree1,a_1_0_bintree1(c2_5__bintree1)) ), inference(discharge_asm,[status(thm),assumptions([e1_5_1_1__bintree1,dt_c1_5_1_1_1__bintree1,dt_c2_5__bintree1]),discharge_asm(discharge,[e2_5_1_1_1__bintree1])],[e2_5_1_1_1__bintree1,i3_5_1_1_1__bintree1]), [interesting(0.35),file(bintree1,i2_5_1_1_1__bintree1),[file(bintree1,i2_5_1_1_1__bintree1)]]). fof(i1_5_1_1_1__bintree1,plain, ( r2_hidden(c1_5_1_1_1__bintree1,a_1_0_bintree1(c2_5__bintree1)) <=> r2_hidden(c1_5_1_1_1__bintree1,k2_tarski(k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)),k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,1)))) ), inference(conclusion,[status(thm),assumptions([e1_5_1_1__bintree1,dt_c1_5_1_1_1__bintree1,dt_c2_5__bintree1])],[e1_5_1_1_1__bintree1,i2_5_1_1_1__bintree1]), [interesting(0.35),file(bintree1,i1_5_1_1_1__bintree1),[file(bintree1,i1_5_1_1_1__bintree1)]]). fof(i1_5_1_1_1_tmp__bintree1,plain, ( r2_hidden(c1_5_1_1_1__bintree1,a_1_0_bintree1(c2_5__bintree1)) <=> r2_hidden(c1_5_1_1_1__bintree1,k2_tarski(k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)),k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,1)))) ), inference(discharge_asm,[status(thm),assumptions([e1_5_1_1__bintree1,dt_c2_5__bintree1]),discharge_asm(discharge,[dt_c1_5_1_1_1__bintree1])],[dt_c1_5_1_1_1__bintree1,i1_5_1_1_1__bintree1]), [interesting(0.5),e3_5_1_1__bintree1]). fof(e3_5_1_1__bintree1,plain,( ! [A] : ( r2_hidden(A,a_1_0_bintree1(c2_5__bintree1)) <=> r2_hidden(A,k2_tarski(k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)),k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,1)))) ) ), inference(let,[status(thm),assumptions([e1_5_1_1__bintree1,dt_c2_5__bintree1])],[i1_5_1_1_1_tmp__bintree1,dh_c1_5_1_1_1__bintree1]), [interesting(0.5),file(bintree1,e3_5_1_1__bintree1),[file(bintree1,e3_5_1_1__bintree1)]]). fof(redefinition_k8_finseq_1,definition,( ! [A,B,C] : ( ( m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => k8_finseq_1(A,B,C) = k7_finseq_1(B,C) ) ), file(finseq_1,k8_finseq_1), [interesting(0.9),axiom,file(finseq_1,k8_finseq_1)]). fof(dt_k8_finseq_1,axiom,( ! [A,B,C] : ( ( m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => m2_finseq_1(k8_finseq_1(A,B,C),A) ) ), file(finseq_1,k8_finseq_1), [interesting(0.9),axiom,file(finseq_1,k8_finseq_1)]). fof(fraenkel_a_2_1_trees_2,definition,( ! [A,B,C] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) & m1_trees_1(C,B) ) => ( r2_hidden(A,a_2_1_trees_2(B,C)) <=> ? [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) & A = k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,D)) & r2_hidden(k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,D)),B) ) ) ) ), file(trees_2,a_2_1_trees_2), [interesting(0.9),axiom,file(trees_2,a_2_1_trees_2)]). fof(d5_trees_2,definition,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m1_trees_1(B,A) => k1_trees_2(A,B) = a_2_1_trees_2(A,B) ) ) ), file(trees_2,d5_trees_2), [interesting(0.9),axiom,file(trees_2,d5_trees_2)]). fof(e2_5_1_1__bintree1,plain,( k1_trees_2(k2_trees_1(2),c2_5__bintree1) = a_1_0_bintree1(c2_5__bintree1) ), inference(mizar_by,[status(thm),assumptions([dt_c2_5__bintree1])],[cc1_fraenkel,rc1_fraenkel,existence_m1_finseq_2,existence_m1_relset_1,dt_k13_finseq_1,dt_k2_zfmisc_1,dt_m1_finseq_2,dt_m1_relset_1,cc1_arytm_3,cc1_relset_1,cc2_arytm_3,cc7_trees_3,fc16_finseq_1,fc4_subset_1,fc7_trees_3,fc8_trees_3,fc9_finseq_1,rc1_arytm_3,rc2_finseq_1,rc5_trees_3,rc7_trees_3,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_finseq_2,existence_m2_relset_1,redefinition_k3_finseq_2,redefinition_m2_finseq_2,redefinition_m2_relset_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_finseq_2,dt_m2_relset_1,cc1_dtconstr,cc1_finseq_1,cc3_arytm_3,fc10_trees_3,fc12_finseq_1,fc13_finseq_1,fc13_trees_3,fc14_finseq_1,fc3_finseq_1,fc4_finseq_1,fc5_membered,rc1_finseq_1,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_subset_1,redefinition_k12_finseq_1,redefinition_k3_lang1,redefinition_k5_numbers,redefinition_k8_finseq_1,redefinition_m2_finseq_1,redefinition_m2_subset_1,dt_k12_finseq_1,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k3_lang1,dt_k5_numbers,dt_k7_finseq_1,dt_k8_finseq_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc1_subset_1,fc2_finseq_1,fc2_membered,fc4_trees_2,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,existence_m1_trees_1,redefinition_m1_trees_1,dt_k1_trees_2,dt_k2_trees_1,dt_m1_trees_1,dt_c2_5__bintree1,cc15_membered,spc2_boole,t6_boole,t7_boole,t8_boole,t2_tarski,fraenkel_a_1_0_bintree1,fraenkel_a_2_1_trees_2,spc2_numerals,spc2_boole,d5_trees_2]), [interesting(0.5),file(bintree1,e2_5_1_1__bintree1),[file(bintree1,e2_5_1_1__bintree1)]]). fof(e4_5_1_1__bintree1,plain,( k1_trees_2(k2_trees_1(2),c2_5__bintree1) = k2_tarski(k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)),k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,1))) ), inference(mizar_by,[status(thm),assumptions([e1_5_1_1__bintree1,dt_c2_5__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc4_subset_1,rc2_finseq_1,rc9_trees_2,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_arytm_3,cc1_fraenkel,cc2_arytm_3,fc14_membered,fc15_membered,fc16_membered,rc1_arytm_3,rc1_fraenkel,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,reflexivity_r1_tarski,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_k5_ordinal2,dt_m1_finseq_2,dt_m2_finseq_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc7_trees_3,fc12_membered,fc13_membered,fc16_finseq_1,fc2_finseq_1,fc5_membered,fc6_membered,fc7_trees_3,fc8_trees_3,fc9_finseq_1,rc1_membered,rc5_trees_3,rc7_trees_3,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m1_trees_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_zfmisc_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_dtconstr,cc1_finseq_1,cc4_membered,cc6_membered,cc9_membered,fc10_trees_3,fc12_finseq_1,fc13_finseq_1,fc13_trees_3,fc14_finseq_1,fc1_subset_1,fc3_finseq_1,fc4_finseq_1,fc4_trees_2,rc1_finseq_1,rc1_subset_1,rc2_subset_1,rc7_finseq_1,rc8_finseq_1,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k2_tarski,antisymmetry_r2_hidden,redefinition_k3_lang1,dt_k1_numbers,dt_k1_trees_2,dt_k2_tarski,dt_k2_trees_1,dt_k3_lang1,dt_k7_finseq_1,dt_c2_5__bintree1,fc2_membered,fc3_subset_1,t1_subset,t7_boole,fraenkel_a_1_0_bintree1,spc0_numerals,spc1_numerals,spc2_numerals,spc0_boole,spc1_boole,spc2_boole,e3_5_1_1__bintree1,e2_5_1_1__bintree1,t2_tarski]), [interesting(0.5),file(bintree1,e4_5_1_1__bintree1),[file(bintree1,e4_5_1_1__bintree1)]]). fof(i2_5_1_1__bintree1,theorem,( $true ), introduced(tautology,[file(bintree1,i2_5_1_1__bintree1)]), [interesting(0.5),trivial,file(bintree1,i2_5_1_1__bintree1)]). fof(i1_5_1_1__bintree1,plain,( k1_trees_2(k2_trees_1(2),c2_5__bintree1) = k2_tarski(k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)),k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,1))) ), inference(conclusion,[status(thm),assumptions([e1_5_1_1__bintree1,dt_c2_5__bintree1])],[e4_5_1_1__bintree1,i2_5_1_1__bintree1]), [interesting(0.5),file(bintree1,i1_5_1_1__bintree1),[file(bintree1,i1_5_1_1__bintree1)]]). fof(i1_5_1__bintree1,plain, ( c2_5__bintree1 = k1_xboole_0 => k1_trees_2(k2_trees_1(2),c2_5__bintree1) = k2_tarski(k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)),k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,1))) ), inference(discharge_asm,[status(thm),assumptions([dt_c2_5__bintree1]),discharge_asm(discharge,[e1_5_1_1__bintree1])],[e1_5_1_1__bintree1,i1_5_1_1__bintree1]), [interesting(0.65),file(bintree1,i1_5_1__bintree1),[file(bintree1,i1_5_1__bintree1)]]). fof(e1_5_1_2__bintree1,assumption,( c2_5__bintree1 = k3_lang1(k1_numbers,0) ), introduced(assumption,[file(bintree1,e1_5_1_2__bintree1)]), [interesting(0.5),axiom,file(bintree1,e1_5_1_2__bintree1)]). fof(e1_5_1_2_1__bintree1,assumption,( r2_hidden(k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)),k2_trees_1(2)) ), introduced(assumption,[file(bintree1,e1_5_1_2_1__bintree1)]), [interesting(0.35),axiom,file(bintree1,e1_5_1_2_1__bintree1)]). fof(e1_5_1_2_1_1_1__bintree1,assumption,( k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)) = k1_xboole_0 ), introduced(assumption,[file(bintree1,e1_5_1_2_1_1_1__bintree1)]), [interesting(0.05),axiom,file(bintree1,e1_5_1_2_1_1_1__bintree1)]). fof(spc5_arithm,theorem,( ! [A,B,C] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) ) => k3_xcmplx_0(k2_xcmplx_0(A,B),C) = k2_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,C)) ) ), file(arithm,spc5_arithm), [interesting(0.9),axiom,file(arithm,spc5_arithm)]). fof(spc6_arithm,theorem,( ! [A,B,C] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) ) => k2_xcmplx_0(k2_xcmplx_0(A,B),C) = k2_xcmplx_0(A,k2_xcmplx_0(B,C)) ) ), file(arithm,spc6_arithm), [interesting(0.9),axiom,file(arithm,spc6_arithm)]). fof(spc7_arithm,theorem,( ! [A,B,C] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) ) => k3_xcmplx_0(k3_xcmplx_0(A,B),C) = k3_xcmplx_0(A,k3_xcmplx_0(B,C)) ) ), file(arithm,spc6_arithm), [interesting(0.9),axiom,file(arithm,spc6_arithm)]). fof(t1_arithm,theorem,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(A,0) = A ) ), file(arithm,t1_arithm), [interesting(0.9),axiom,file(arithm,t1_arithm)]). fof(t2_arithm,theorem,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(A,0) = 0 ) ), file(arithm,t2_arithm), [interesting(0.9),axiom,file(arithm,t2_arithm)]). fof(t3_arithm,theorem,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(1,A) = A ) ), file(arithm,t3_arithm), [interesting(0.9),axiom,file(arithm,t3_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(commutativity_k3_xcmplx_0,theorem,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k3_xcmplx_0(A,B) = k3_xcmplx_0(B,A) ) ), file(xcmplx_0,k3_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k3_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(dt_k3_xcmplx_0,axiom,( $true ), file(xcmplx_0,k3_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k3_xcmplx_0)]). fof(rqRealAdd__k2_xcmplx_0__r0_r0_r0,theorem,( k2_xcmplx_0(0,0) = 0 ), file(arithm,rqRealAdd__k2_xcmplx_0__r0_r0_r0), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_r0_r0)]). fof(rqRealAdd__k2_xcmplx_0__r0_r1_r1,theorem,( k2_xcmplx_0(0,1) = 1 ), file(arithm,rqRealAdd__k2_xcmplx_0__r0_r1_r1), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_r1_r1)]). fof(rqRealAdd__k2_xcmplx_0__r0_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__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__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(rqRealMult__k3_xcmplx_0__r0_r0_r0,theorem,( k3_xcmplx_0(0,0) = 0 ), file(arithm,rqRealMult__k3_xcmplx_0__r0_r0_r0), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r0_r0_r0)]). fof(rqRealMult__k3_xcmplx_0__r0_r1_r0,theorem,( k3_xcmplx_0(0,1) = 0 ), file(arithm,rqRealMult__k3_xcmplx_0__r0_r1_r0), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r0_r1_r0)]). fof(rqRealMult__k3_xcmplx_0__r0_r2_r0,theorem,( k3_xcmplx_0(0,2) = 0 ), file(arithm,rqRealMult__k3_xcmplx_0__r0_r2_r0), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r0_r2_r0)]). fof(rqRealMult__k3_xcmplx_0__r1_r0_r0,theorem,( k3_xcmplx_0(1,0) = 0 ), file(arithm,rqRealMult__k3_xcmplx_0__r1_r0_r0), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_r0_r0)]). fof(rqRealMult__k3_xcmplx_0__r1_r1_r1,theorem,( k3_xcmplx_0(1,1) = 1 ), file(arithm,rqRealMult__k3_xcmplx_0__r1_r1_r1), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_r1_r1)]). fof(rqRealMult__k3_xcmplx_0__r1_r2_r2,theorem,( k3_xcmplx_0(1,2) = 2 ), file(arithm,rqRealMult__k3_xcmplx_0__r1_r2_r2), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_r2_r2)]). fof(rqRealMult__k3_xcmplx_0__r2_r0_r0,theorem,( k3_xcmplx_0(2,0) = 0 ), file(arithm,rqRealMult__k3_xcmplx_0__r2_r0_r0), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r2_r0_r0)]). fof(fc10_membered,theorem,( ! [A] : ( v1_int_1(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) ) ) ), file(membered,fc10_membered), [interesting(0.9),axiom,file(membered,fc10_membered)]). fof(fc11_membered,theorem,( ! [A] : ( v4_ordinal2(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) & v5_membered(k1_tarski(A)) ) ) ), file(membered,fc11_membered), [interesting(0.9),axiom,file(membered,fc11_membered)]). fof(fc9_membered,theorem,( ! [A] : ( v1_rat_1(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) ) ) ), file(membered,fc9_membered), [interesting(0.9),axiom,file(membered,fc9_membered)]). fof(fc8_membered,theorem,( ! [A] : ( v1_xreal_0(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) ) ) ), file(membered,fc8_membered), [interesting(0.9),axiom,file(membered,fc8_membered)]). fof(fc11_finseq_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_finset_1(A) ) => v1_finset_1(k2_relat_1(A)) ) ), file(finseq_1,fc11_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc11_finseq_1)]). fof(fc7_membered,theorem,( ! [A] : ( v1_xcmplx_0(A) => v1_membered(k1_tarski(A)) ) ), file(membered,fc7_membered), [interesting(0.9),axiom,file(membered,fc7_membered)]). fof(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(spc2_arithm,theorem,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(A,k4_xcmplx_0(1)) = k4_xcmplx_0(A) ) ), file(arithm,spc2_arithm), [interesting(0.9),axiom,file(arithm,spc2_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(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(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(redefinition_k9_finseq_1,definition,( ! [A] : k9_finseq_1(A) = k5_finseq_1(A) ), file(finseq_1,k9_finseq_1), [interesting(0.9),axiom,file(finseq_1,k9_finseq_1)]). fof(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), [interesting(0.9),axiom,file(tarski,k1_tarski)]). fof(dt_k2_relat_1,axiom,( $true ), file(relat_1,k2_relat_1), [interesting(0.9),axiom,file(relat_1,k2_relat_1)]). 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_k9_finseq_1,axiom,( ! [A] : ( v1_relat_1(k9_finseq_1(A)) & v1_funct_1(k9_finseq_1(A)) ) ), file(finseq_1,k9_finseq_1), [interesting(0.9),axiom,file(finseq_1,k9_finseq_1)]). fof(fc2_subset_1,theorem,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) ), file(subset_1,fc2_subset_1), [interesting(0.9),axiom,file(subset_1,fc2_subset_1)]). fof(rqRealAdd__k2_xcmplx_0__r0_r3_r3,theorem,( k2_xcmplx_0(0,3) = 3 ), file(arithm,rqRealAdd__k2_xcmplx_0__r0_r3_r3), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_r3_r3)]). 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_rm3_rm3,theorem,( k2_xcmplx_0(0,k4_xcmplx_0(3)) = k4_xcmplx_0(3) ), file(arithm,rqRealAdd__k2_xcmplx_0__r0_rm3_rm3), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_rm3_rm3)]). fof(rqRealAdd__k2_xcmplx_0__r1_r2_r3,theorem,( k2_xcmplx_0(1,2) = 3 ), file(arithm,rqRealAdd__k2_xcmplx_0__r1_r2_r3), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_r2_r3)]). 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_rm3_rm2,theorem,( k2_xcmplx_0(1,k4_xcmplx_0(3)) = k4_xcmplx_0(2) ), file(arithm,rqRealAdd__k2_xcmplx_0__r1_rm3_rm2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_rm3_rm2)]). fof(rqRealAdd__k2_xcmplx_0__r2_r1_r3,theorem,( k2_xcmplx_0(2,1) = 3 ), file(arithm,rqRealAdd__k2_xcmplx_0__r2_r1_r3), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r2_r1_r3)]). 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__r2_rm3_rm1,theorem,( k2_xcmplx_0(2,k4_xcmplx_0(3)) = k4_xcmplx_0(1) ), file(arithm,rqRealAdd__k2_xcmplx_0__r2_rm3_rm1), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r2_rm3_rm1)]). fof(rqRealAdd__k2_xcmplx_0__r3_r0_r3,theorem,( k2_xcmplx_0(3,0) = 3 ), file(arithm,rqRealAdd__k2_xcmplx_0__r3_r0_r3), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r3_r0_r3)]). fof(rqRealAdd__k2_xcmplx_0__r3_rm1_r2,theorem,( k2_xcmplx_0(3,k4_xcmplx_0(1)) = 2 ), file(arithm,rqRealAdd__k2_xcmplx_0__r3_rm1_r2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r3_rm1_r2)]). fof(rqRealAdd__k2_xcmplx_0__r3_rm2_r1,theorem,( k2_xcmplx_0(3,k4_xcmplx_0(2)) = 1 ), file(arithm,rqRealAdd__k2_xcmplx_0__r3_rm2_r1), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r3_rm2_r1)]). fof(rqRealAdd__k2_xcmplx_0__r3_rm3_r0,theorem,( k2_xcmplx_0(3,k4_xcmplx_0(3)) = 0 ), file(arithm,rqRealAdd__k2_xcmplx_0__r3_rm3_r0), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r3_rm3_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_r3_r2,theorem,( k2_xcmplx_0(k4_xcmplx_0(1),3) = 2 ), file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r3_r2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r3_r2)]). 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_rm2_rm3,theorem,( k2_xcmplx_0(k4_xcmplx_0(1),k4_xcmplx_0(2)) = k4_xcmplx_0(3) ), file(arithm,rqRealAdd__k2_xcmplx_0__rm1_rm2_rm3), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm1_rm2_rm3)]). 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__rm2_r3_r1,theorem,( k2_xcmplx_0(k4_xcmplx_0(2),3) = 1 ), file(arithm,rqRealAdd__k2_xcmplx_0__rm2_r3_r1), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm2_r3_r1)]). fof(rqRealAdd__k2_xcmplx_0__rm2_rm1_rm3,theorem,( k2_xcmplx_0(k4_xcmplx_0(2),k4_xcmplx_0(1)) = k4_xcmplx_0(3) ), file(arithm,rqRealAdd__k2_xcmplx_0__rm2_rm1_rm3), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm2_rm1_rm3)]). fof(rqRealAdd__k2_xcmplx_0__rm3_r1_rm2,theorem,( k2_xcmplx_0(k4_xcmplx_0(3),1) = k4_xcmplx_0(2) ), file(arithm,rqRealAdd__k2_xcmplx_0__rm3_r1_rm2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm3_r1_rm2)]). fof(rqRealAdd__k2_xcmplx_0__rm3_r2_rm1,theorem,( k2_xcmplx_0(k4_xcmplx_0(3),2) = k4_xcmplx_0(1) ), file(arithm,rqRealAdd__k2_xcmplx_0__rm3_r2_rm1), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm3_r2_rm1)]). fof(rqRealAdd__k2_xcmplx_0__rm3_r3_r0,theorem,( k2_xcmplx_0(k4_xcmplx_0(3),3) = 0 ), file(arithm,rqRealAdd__k2_xcmplx_0__rm3_r3_r0), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm3_r3_r0)]). 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_r3_rm3,theorem,( k6_xcmplx_0(0,3) = k4_xcmplx_0(3) ), file(arithm,rqRealDiff__k6_xcmplx_0__r0_r3_rm3), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_r3_rm3)]). 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_rm3_r3,theorem,( k6_xcmplx_0(0,k4_xcmplx_0(3)) = 3 ), file(arithm,rqRealDiff__k6_xcmplx_0__r0_rm3_r3), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_rm3_r3)]). fof(rqRealDiff__k6_xcmplx_0__r1_r3_rm2,theorem,( k6_xcmplx_0(1,3) = k4_xcmplx_0(2) ), file(arithm,rqRealDiff__k6_xcmplx_0__r1_r3_rm2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_r3_rm2)]). fof(rqRealDiff__k6_xcmplx_0__r1_rm2_r3,theorem,( k6_xcmplx_0(1,k4_xcmplx_0(2)) = 3 ), file(arithm,rqRealDiff__k6_xcmplx_0__r1_rm2_r3), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_rm2_r3)]). 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__r2_r3_rm1,theorem,( k6_xcmplx_0(2,3) = k4_xcmplx_0(1) ), file(arithm,rqRealDiff__k6_xcmplx_0__r2_r3_rm1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r2_r3_rm1)]). fof(rqRealDiff__k6_xcmplx_0__r3_r0_r3,theorem,( k6_xcmplx_0(3,0) = 3 ), file(arithm,rqRealDiff__k6_xcmplx_0__r3_r0_r3), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r3_r0_r3)]). fof(rqRealDiff__k6_xcmplx_0__r3_r1_r2,theorem,( k6_xcmplx_0(3,1) = 2 ), file(arithm,rqRealDiff__k6_xcmplx_0__r3_r1_r2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r3_r1_r2)]). fof(rqRealDiff__k6_xcmplx_0__r3_r2_r1,theorem,( k6_xcmplx_0(3,2) = 1 ), file(arithm,rqRealDiff__k6_xcmplx_0__r3_r2_r1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r3_r2_r1)]). fof(rqRealDiff__k6_xcmplx_0__r3_r3_r0,theorem,( k6_xcmplx_0(3,3) = 0 ), file(arithm,rqRealDiff__k6_xcmplx_0__r3_r3_r0), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r3_r3_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_r2_rm3,theorem,( k6_xcmplx_0(k4_xcmplx_0(1),2) = k4_xcmplx_0(3) ), file(arithm,rqRealDiff__k6_xcmplx_0__rm1_r2_rm3), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_r2_rm3)]). 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_rm3_r2,theorem,( k6_xcmplx_0(k4_xcmplx_0(1),k4_xcmplx_0(3)) = 2 ), file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm3_r2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm3_r2)]). 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_r1_rm3,theorem,( k6_xcmplx_0(k4_xcmplx_0(2),1) = k4_xcmplx_0(3) ), file(arithm,rqRealDiff__k6_xcmplx_0__rm2_r1_rm3), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm2_r1_rm3)]). 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__rm2_rm3_r1,theorem,( k6_xcmplx_0(k4_xcmplx_0(2),k4_xcmplx_0(3)) = 1 ), file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rm3_r1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rm3_r1)]). fof(rqRealDiff__k6_xcmplx_0__rm3_r0_rm3,theorem,( k6_xcmplx_0(k4_xcmplx_0(3),0) = k4_xcmplx_0(3) ), file(arithm,rqRealDiff__k6_xcmplx_0__rm3_r0_rm3), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm3_r0_rm3)]). fof(rqRealDiff__k6_xcmplx_0__rm3_rm1_rm2,theorem,( k6_xcmplx_0(k4_xcmplx_0(3),k4_xcmplx_0(1)) = k4_xcmplx_0(2) ), file(arithm,rqRealDiff__k6_xcmplx_0__rm3_rm1_rm2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm3_rm1_rm2)]). fof(rqRealDiff__k6_xcmplx_0__rm3_rm2_rm1,theorem,( k6_xcmplx_0(k4_xcmplx_0(3),k4_xcmplx_0(2)) = k4_xcmplx_0(1) ), file(arithm,rqRealDiff__k6_xcmplx_0__rm3_rm2_rm1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm3_rm2_rm1)]). fof(rqRealDiff__k6_xcmplx_0__rm3_rm3_r0,theorem,( k6_xcmplx_0(k4_xcmplx_0(3),k4_xcmplx_0(3)) = 0 ), file(arithm,rqRealDiff__k6_xcmplx_0__rm3_rm3_r0), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm3_rm3_r0)]). fof(rqRealMult__k3_xcmplx_0__r0_r3_r0,theorem,( k3_xcmplx_0(0,3) = 0 ), file(arithm,rqRealMult__k3_xcmplx_0__r0_r3_r0), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r0_r3_r0)]). fof(rqRealMult__k3_xcmplx_0__r0_rm2_r0,theorem,( k3_xcmplx_0(0,k4_xcmplx_0(2)) = 0 ), file(arithm,rqRealMult__k3_xcmplx_0__r0_rm2_r0), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r0_rm2_r0)]). fof(rqRealMult__k3_xcmplx_0__r0_rm3_r0,theorem,( k3_xcmplx_0(0,k4_xcmplx_0(3)) = 0 ), file(arithm,rqRealMult__k3_xcmplx_0__r0_rm3_r0), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r0_rm3_r0)]). fof(rqRealMult__k3_xcmplx_0__r1_r3_r3,theorem,( k3_xcmplx_0(1,3) = 3 ), file(arithm,rqRealMult__k3_xcmplx_0__r1_r3_r3), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_r3_r3)]). fof(rqRealMult__k3_xcmplx_0__r1_rm2_rm2,theorem,( k3_xcmplx_0(1,k4_xcmplx_0(2)) = k4_xcmplx_0(2) ), file(arithm,rqRealMult__k3_xcmplx_0__r1_rm2_rm2), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_rm2_rm2)]). fof(rqRealMult__k3_xcmplx_0__r1_rm3_rm3,theorem,( k3_xcmplx_0(1,k4_xcmplx_0(3)) = k4_xcmplx_0(3) ), file(arithm,rqRealMult__k3_xcmplx_0__r1_rm3_rm3), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_rm3_rm3)]). fof(rqRealMult__k3_xcmplx_0__r3_r0_r0,theorem,( k3_xcmplx_0(3,0) = 0 ), file(arithm,rqRealMult__k3_xcmplx_0__r3_r0_r0), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r3_r0_r0)]). fof(rqRealMult__k3_xcmplx_0__r3_r1_r3,theorem,( k3_xcmplx_0(3,1) = 3 ), file(arithm,rqRealMult__k3_xcmplx_0__r3_r1_r3), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r3_r1_r3)]). fof(rqRealMult__k3_xcmplx_0__rm2_r0_r0,theorem,( k3_xcmplx_0(k4_xcmplx_0(2),0) = 0 ), file(arithm,rqRealMult__k3_xcmplx_0__rm2_r0_r0), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm2_r0_r0)]). fof(rqRealMult__k3_xcmplx_0__rm2_r1_rm2,theorem,( k3_xcmplx_0(k4_xcmplx_0(2),1) = k4_xcmplx_0(2) ), file(arithm,rqRealMult__k3_xcmplx_0__rm2_r1_rm2), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm2_r1_rm2)]). fof(rqRealMult__k3_xcmplx_0__rm3_r0_r0,theorem,( k3_xcmplx_0(k4_xcmplx_0(3),0) = 0 ), file(arithm,rqRealMult__k3_xcmplx_0__rm3_r0_r0), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm3_r0_r0)]). fof(rqRealMult__k3_xcmplx_0__rm3_r1_rm3,theorem,( k3_xcmplx_0(k4_xcmplx_0(3),1) = k4_xcmplx_0(3) ), file(arithm,rqRealMult__k3_xcmplx_0__rm3_r1_rm3), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm3_r1_rm3)]). 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(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__r3_rm3,theorem,( k4_xcmplx_0(3) = k4_xcmplx_0(3) ), file(arithm,rqRealNeg__k4_xcmplx_0__r3_rm3), [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__r3_rm3)]). 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__rm3_r3,theorem,( k4_xcmplx_0(k4_xcmplx_0(3)) = 3 ), file(arithm,rqRealNeg__k4_xcmplx_0__rm3_r3), [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rm3_r3)]). fof(spc3_numerals,theorem, ( v2_xreal_0(3) & m2_subset_1(3,k1_numbers,k5_numbers) & m1_subset_1(3,k5_numbers) & m1_subset_1(3,k1_numbers) ), file(numerals,spc3_numerals), [interesting(0.9),axiom,file(numerals,spc3_numerals)]). fof(spc3_boole,theorem,( ~ v1_xboole_0(3) ), file(boole,spc3_boole), [interesting(0.9),axiom,file(boole,spc3_boole)]). fof(spc4_arithm,theorem,( ! [A,B,C] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) ) => k3_xcmplx_0(A,k7_xcmplx_0(B,C)) = k7_xcmplx_0(k3_xcmplx_0(A,B),C) ) ), file(arithm,spc4_arithm), [interesting(0.9),axiom,file(arithm,spc4_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(dt_k7_xcmplx_0,axiom,( $true ), file(xcmplx_0,k7_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k7_xcmplx_0)]). 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_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__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__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(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_r0_r1,theorem,( k6_xcmplx_0(1,0) = 1 ), file(arithm,rqRealDiff__k6_xcmplx_0__r1_r0_r1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_r0_r1)]). fof(rqRealDiff__k6_xcmplx_0__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__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(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__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__r0_rn1d2_r0,theorem,( k7_xcmplx_0(0,k7_xcmplx_0(1,2)) = 0 ), file(arithm,rqRealDiv__k7_xcmplx_0__r0_rn1d2_r0), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r0_rn1d2_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_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(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(rqRealDiv__k7_xcmplx_0__rnm1d2_rn1d2_rm1,theorem,( k7_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(1,2)) = k4_xcmplx_0(1) ), file(arithm,rqRealDiv__k7_xcmplx_0__rnm1d2_rn1d2_rm1), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__rnm1d2_rn1d2_rm1)]). fof(rqRealMult__k3_xcmplx_0__r0_rn1d2_r0,theorem,( k3_xcmplx_0(0,k7_xcmplx_0(1,2)) = 0 ), file(arithm,rqRealMult__k3_xcmplx_0__r0_rn1d2_r0), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r0_rn1d2_r0)]). fof(rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2,theorem,( k3_xcmplx_0(1,k7_xcmplx_0(1,2)) = k7_xcmplx_0(1,2) ), file(arithm,rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2)]). fof(rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2,theorem,( k3_xcmplx_0(1,k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ), file(arithm,rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2)]). fof(rqRealMult__k3_xcmplx_0__r2_rn1d2_r1,theorem,( k3_xcmplx_0(2,k7_xcmplx_0(1,2)) = 1 ), file(arithm,rqRealMult__k3_xcmplx_0__r2_rn1d2_r1), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r2_rn1d2_r1)]). fof(rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1,theorem,( k3_xcmplx_0(2,k7_xcmplx_0(k4_xcmplx_0(1),2)) = k4_xcmplx_0(1) ), file(arithm,rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1)]). fof(rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1,theorem,( k3_xcmplx_0(k4_xcmplx_0(2),k7_xcmplx_0(1,2)) = k4_xcmplx_0(1) ), file(arithm,rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1)]). fof(rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1,theorem,( k3_xcmplx_0(k4_xcmplx_0(2),k7_xcmplx_0(k4_xcmplx_0(1),2)) = 1 ), file(arithm,rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1)]). fof(rqRealMult__k3_xcmplx_0__rn1d2_r0_r0,theorem,( k3_xcmplx_0(k7_xcmplx_0(1,2),0) = 0 ), file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_r0_r0), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_r0_r0)]). fof(rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2,theorem,( k3_xcmplx_0(k7_xcmplx_0(1,2),1) = k7_xcmplx_0(1,2) ), file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2)]). fof(rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1,theorem,( k3_xcmplx_0(k7_xcmplx_0(1,2),k4_xcmplx_0(2)) = k4_xcmplx_0(1) ), file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1)]). fof(rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2,theorem,( k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),1) = k7_xcmplx_0(k4_xcmplx_0(1),2) ), file(arithm,rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2)]). fof(rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1,theorem,( k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),2) = k4_xcmplx_0(1) ), file(arithm,rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1)]). fof(rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1,theorem,( k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k4_xcmplx_0(2)) = 1 ), file(arithm,rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1)]). 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(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(e2_5_1_2_1_1_1__bintree1,plain,( k3_finseq_1(k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0))) = 0 ), inference(mizar_by,[status(thm),assumptions([dt_c2_5__bintree1,e1_5_1_2_1_1_1__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc4_subset_1,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_arytm_3,cc1_fraenkel,cc2_arytm_3,cc7_trees_3,fc7_trees_3,fc8_trees_3,rc1_arytm_3,rc1_fraenkel,rc4_finseq_1,rc5_trees_3,rc7_trees_3,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_2,dt_m2_finseq_1,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc20_membered,cc3_arytm_3,cc6_membered,cc9_membered,fc10_trees_3,fc13_trees_3,fc16_finseq_1,fc1_subset_1,fc5_membered,fc9_finseq_1,rc1_subset_1,rc2_subset_1,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m1_trees_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_card_1,dt_k2_trees_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc1_dtconstr,cc1_finseq_1,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc3_finseq_1,fc4_finseq_1,rc1_finseq_1,rc1_membered,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,spc2_boole,spc2_numerals,t1_numerals,t2_subset,t7_boole,t8_boole,spc2_numerals,spc2_boole,redefinition_k3_finseq_1,redefinition_k3_lang1,dt_k1_numbers,dt_k1_xboole_0,dt_k3_finseq_1,dt_k3_lang1,dt_k7_finseq_1,dt_c2_5__bintree1,fc2_finseq_1,fc2_membered,fc6_membered,t6_boole,spc0_numerals,spc0_boole,e1_5_1_2_1_1_1__bintree1]), [interesting(0.05),file(bintree1,e2_5_1_2_1_1_1__bintree1),[file(bintree1,e2_5_1_2_1_1_1__bintree1)]]). fof(t35_finseq_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => k3_finseq_1(k7_finseq_1(A,B)) = k1_nat_1(k3_finseq_1(A),k3_finseq_1(B)) ) ) ), file(finseq_1,t35_finseq_1), [interesting(0.9),axiom,file(finseq_1,t35_finseq_1)]). fof(e3_5_1_2_1_1_1__bintree1,plain,( k1_nat_1(k3_finseq_1(c2_5__bintree1),k3_finseq_1(k3_lang1(k1_numbers,0))) = 0 ), inference(mizar_by,[status(thm),assumptions([dt_c2_5__bintree1,e1_5_1_2_1_1_1__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc4_subset_1,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_arytm_3,cc1_fraenkel,cc2_arytm_3,cc7_trees_3,fc7_trees_3,fc8_trees_3,rc1_arytm_3,rc1_fraenkel,rc3_finseq_1,rc4_finseq_1,rc5_trees_3,rc6_finseq_1,rc7_trees_3,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_2,dt_m2_finseq_1,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc6_membered,cc9_membered,fc10_trees_3,fc13_trees_3,fc16_finseq_1,fc1_subset_1,fc2_finseq_1,fc5_membered,fc6_membered,fc9_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,spc6_arithm,t1_arithm,t1_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m1_trees_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_card_1,dt_k2_trees_1,dt_k2_xcmplx_0,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_dtconstr,cc4_membered,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc3_finseq_1,fc4_finseq_1,rc7_finseq_1,rc8_finseq_1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r2_r2,rqRealAdd__k2_xcmplx_0__r2_r0_r2,spc2_boole,spc2_numerals,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,spc2_numerals,spc2_boole,commutativity_k1_nat_1,redefinition_k1_nat_1,redefinition_k3_finseq_1,redefinition_k3_lang1,dt_k1_nat_1,dt_k1_numbers,dt_k3_finseq_1,dt_k3_lang1,dt_k7_finseq_1,dt_c2_5__bintree1,cc1_finseq_1,fc2_membered,rc1_finseq_1,spc0_numerals,spc0_boole,e2_5_1_2_1_1_1__bintree1,t35_finseq_1]), [interesting(0.05),file(bintree1,e3_5_1_2_1_1_1__bintree1),[file(bintree1,e3_5_1_2_1_1_1__bintree1)]]). fof(t56_finseq_1,theorem,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( B = k9_finseq_1(A) <=> ( k3_finseq_1(B) = 1 & k2_relat_1(B) = k1_tarski(A) ) ) ) ), file(finseq_1,t56_finseq_1), [interesting(0.9),axiom,file(finseq_1,t56_finseq_1)]). fof(rqRealAdd__k2_xcmplx_0__r1_r1_r2,theorem,( k2_xcmplx_0(1,1) = 2 ), file(arithm,rqRealAdd__k2_xcmplx_0__r1_r1_r2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_r1_r2)]). fof(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(rqRealMult__k3_xcmplx_0__rn1d2_r2_r1,theorem,( k3_xcmplx_0(k7_xcmplx_0(1,2),2) = 1 ), file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_r2_r1), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_r2_r1)]). 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(rqRealMult__k3_xcmplx_0__r2_r1_r2,theorem,( k3_xcmplx_0(2,1) = 2 ), file(arithm,rqRealMult__k3_xcmplx_0__r2_r1_r2), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r2_r1_r2)]). 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__r0_r1_rm1,theorem,( k6_xcmplx_0(0,1) = k4_xcmplx_0(1) ), file(arithm,rqRealDiff__k6_xcmplx_0__r0_r1_rm1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_r1_rm1)]). fof(rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,theorem,( k6_xcmplx_0(k4_xcmplx_0(1),k4_xcmplx_0(1)) = 0 ), file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0)]). fof(rqRealDiff__k6_xcmplx_0__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__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(e4_5_1_2_1_1_1__bintree1,plain,( k1_nat_1(1,k3_finseq_1(k3_lang1(k1_numbers,0))) = 0 ), inference(mizar_by,[status(thm),assumptions([dt_c2_5__bintree1,e1_5_1_2_1_1_1__bintree1,e1_5_1_2__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc4_subset_1,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_arytm_3,cc1_fraenkel,cc2_arytm_3,cc7_trees_3,fc10_membered,fc11_membered,fc9_membered,rc1_arytm_3,rc1_fraenkel,rc3_finseq_1,rc4_finseq_1,rc5_trees_3,rc6_finseq_1,rc7_trees_3,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_2,dt_m2_finseq_1,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc6_membered,cc9_membered,fc10_trees_3,fc13_trees_3,fc16_finseq_1,fc1_subset_1,fc2_finseq_1,fc5_membered,fc6_membered,fc8_membered,fc9_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m1_trees_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_card_1,dt_k2_trees_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_dtconstr,cc4_membered,fc11_finseq_1,fc12_finseq_1,fc3_finseq_1,fc4_finseq_1,fc7_membered,rc7_finseq_1,rc8_finseq_1,spc1_arithm,spc2_arithm,spc4_arithm,spc5_arithm,spc6_arithm,spc7_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_numerals,t2_arithm,t2_subset,t3_arithm,t4_arithm,t5_arithm,t6_arithm,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,commutativity_k2_xcmplx_0,commutativity_k3_xcmplx_0,involutiveness_k4_xcmplx_0,redefinition_k1_nat_1,redefinition_k3_finseq_1,redefinition_k3_lang1,redefinition_k9_finseq_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_tarski,dt_k2_relat_1,dt_k2_xcmplx_0,dt_k3_finseq_1,dt_k3_lang1,dt_k3_xcmplx_0,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_k7_xcmplx_0,dt_k9_finseq_1,dt_c2_5__bintree1,cc1_finseq_1,fc2_membered,fc2_subset_1,rc1_finseq_1,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_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,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r0_rm2_r2,rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2,rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__r1_rm1_r2,rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2,rqRealDiff__k6_xcmplx_0__r2_r0_r2,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealDiff__k6_xcmplx_0__rm1_r1_rm2,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__r0_rn1d2_r0,rqRealDiv__k7_xcmplx_0__r1_r1_r1,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1,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,rqRealDiv__k7_xcmplx_0__rnm1d2_rn1d2_rm1,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r0_r2_r0,rqRealMult__k3_xcmplx_0__r0_rm2_r0,rqRealMult__k3_xcmplx_0__r0_rn1d2_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealMult__k3_xcmplx_0__r1_r2_r2,rqRealMult__k3_xcmplx_0__r1_rm2_rm2,rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2,rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2,rqRealMult__k3_xcmplx_0__r2_r0_r0,rqRealMult__k3_xcmplx_0__r2_rn1d2_r1,rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1,rqRealMult__k3_xcmplx_0__rm2_r0_r0,rqRealMult__k3_xcmplx_0__rm2_r1_rm2,rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1,rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1,rqRealMult__k3_xcmplx_0__rn1d2_r0_r0,rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2,rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1,rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2,rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1,rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1,rqRealNeg__k4_xcmplx_0__rm1_r1,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,e3_5_1_2_1_1_1__bintree1,e1_5_1_2__bintree1,t56_finseq_1,rqRealAdd__k2_xcmplx_0__r1_r1_r2,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2,rqRealMult__k3_xcmplx_0__rn1d2_r2_r1,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealMult__k3_xcmplx_0__r2_r1_r2,rqRealDiff__k6_xcmplx_0__r2_r2_r0,rqRealDiff__k6_xcmplx_0__r2_r1_r1,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqRealNeg__k4_xcmplx_0__r2_rm2,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealDiff__k6_xcmplx_0__r0_r2_rm2,rqRealDiff__k6_xcmplx_0__r1_r2_rm1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r0_r1_r1]), [interesting(0.05),file(bintree1,e4_5_1_2_1_1_1__bintree1),[file(bintree1,e4_5_1_2_1_1_1__bintree1)]]). fof(rqRealDiff__k6_xcmplx_0__r2_rm1_r3,theorem,( k6_xcmplx_0(2,k4_xcmplx_0(1)) = 3 ), file(arithm,rqRealDiff__k6_xcmplx_0__r2_rm1_r3), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r2_rm1_r3)]). fof(e5_5_1_2_1_1_1__bintree1,plain,( k1_nat_1(1,1) = 0 ), inference(mizar_by,[status(thm),assumptions([dt_c2_5__bintree1,e1_5_1_2_1_1_1__bintree1,e1_5_1_2__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc4_subset_1,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_arytm_3,cc1_fraenkel,cc2_arytm_3,fc10_membered,fc11_membered,fc9_membered,rc1_arytm_3,rc1_fraenkel,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_2,dt_m2_finseq_1,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc6_membered,cc9_membered,fc16_finseq_1,fc1_subset_1,fc2_finseq_1,fc5_membered,fc6_membered,fc8_membered,fc9_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_card_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_dtconstr,cc4_membered,fc11_finseq_1,fc12_finseq_1,fc3_finseq_1,fc4_finseq_1,fc7_membered,rc7_finseq_1,rc8_finseq_1,spc1_arithm,spc2_arithm,spc5_arithm,spc6_arithm,spc7_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_numerals,t2_arithm,t2_subset,t3_arithm,t4_arithm,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,commutativity_k2_xcmplx_0,commutativity_k3_xcmplx_0,involutiveness_k4_xcmplx_0,redefinition_k1_nat_1,redefinition_k3_finseq_1,redefinition_k3_lang1,redefinition_k9_finseq_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_tarski,dt_k2_relat_1,dt_k2_xcmplx_0,dt_k3_finseq_1,dt_k3_lang1,dt_k3_xcmplx_0,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_k9_finseq_1,cc1_finseq_1,fc2_membered,fc2_subset_1,rc1_finseq_1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_r2_r2,rqRealAdd__k2_xcmplx_0__r0_r3_r3,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r0_rm2_rm2,rqRealAdd__k2_xcmplx_0__r0_rm3_rm3,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_r2_r3,rqRealAdd__k2_xcmplx_0__r1_rm1_r0,rqRealAdd__k2_xcmplx_0__r1_rm2_rm1,rqRealAdd__k2_xcmplx_0__r1_rm3_rm2,rqRealAdd__k2_xcmplx_0__r2_r0_r2,rqRealAdd__k2_xcmplx_0__r2_r1_r3,rqRealAdd__k2_xcmplx_0__r2_rm1_r1,rqRealAdd__k2_xcmplx_0__r2_rm2_r0,rqRealAdd__k2_xcmplx_0__r2_rm3_rm1,rqRealAdd__k2_xcmplx_0__r3_r0_r3,rqRealAdd__k2_xcmplx_0__r3_rm1_r2,rqRealAdd__k2_xcmplx_0__r3_rm2_r1,rqRealAdd__k2_xcmplx_0__r3_rm3_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_r3_r2,rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2,rqRealAdd__k2_xcmplx_0__rm1_rm2_rm3,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__rm2_r3_r1,rqRealAdd__k2_xcmplx_0__rm2_rm1_rm3,rqRealAdd__k2_xcmplx_0__rm3_r1_rm2,rqRealAdd__k2_xcmplx_0__rm3_r2_rm1,rqRealAdd__k2_xcmplx_0__rm3_r3_r0,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_r3_rm3,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r0_rm2_r2,rqRealDiff__k6_xcmplx_0__r0_rm3_r3,rqRealDiff__k6_xcmplx_0__r1_r3_rm2,rqRealDiff__k6_xcmplx_0__r1_rm2_r3,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__r2_r3_rm1,rqRealDiff__k6_xcmplx_0__r3_r0_r3,rqRealDiff__k6_xcmplx_0__r3_r1_r2,rqRealDiff__k6_xcmplx_0__r3_r2_r1,rqRealDiff__k6_xcmplx_0__r3_r3_r0,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealDiff__k6_xcmplx_0__rm1_r2_rm3,rqRealDiff__k6_xcmplx_0__rm1_rm2_r1,rqRealDiff__k6_xcmplx_0__rm1_rm3_r2,rqRealDiff__k6_xcmplx_0__rm2_r0_rm2,rqRealDiff__k6_xcmplx_0__rm2_r1_rm3,rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1,rqRealDiff__k6_xcmplx_0__rm2_rm2_r0,rqRealDiff__k6_xcmplx_0__rm2_rm3_r1,rqRealDiff__k6_xcmplx_0__rm3_r0_rm3,rqRealDiff__k6_xcmplx_0__rm3_rm1_rm2,rqRealDiff__k6_xcmplx_0__rm3_rm2_rm1,rqRealDiff__k6_xcmplx_0__rm3_rm3_r0,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r0_r2_r0,rqRealMult__k3_xcmplx_0__r0_r3_r0,rqRealMult__k3_xcmplx_0__r0_rm2_r0,rqRealMult__k3_xcmplx_0__r0_rm3_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealMult__k3_xcmplx_0__r1_r2_r2,rqRealMult__k3_xcmplx_0__r1_r3_r3,rqRealMult__k3_xcmplx_0__r1_rm2_rm2,rqRealMult__k3_xcmplx_0__r1_rm3_rm3,rqRealMult__k3_xcmplx_0__r2_r0_r0,rqRealMult__k3_xcmplx_0__r3_r0_r0,rqRealMult__k3_xcmplx_0__r3_r1_r3,rqRealMult__k3_xcmplx_0__rm2_r0_r0,rqRealMult__k3_xcmplx_0__rm2_r1_rm2,rqRealMult__k3_xcmplx_0__rm3_r0_r0,rqRealMult__k3_xcmplx_0__rm3_r1_rm3,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealNeg__k4_xcmplx_0__r2_rm2,rqRealNeg__k4_xcmplx_0__r3_rm3,rqRealNeg__k4_xcmplx_0__rm2_r2,rqRealNeg__k4_xcmplx_0__rm3_r3,spc0_numerals,spc1_numerals,spc2_numerals,spc3_numerals,spc0_boole,spc1_boole,spc2_boole,spc3_boole,e4_5_1_2_1_1_1__bintree1,t56_finseq_1,rqRealAdd__k2_xcmplx_0__r1_r1_r2,rqRealMult__k3_xcmplx_0__r2_r1_r2,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealDiff__k6_xcmplx_0__r1_r2_rm1,rqRealDiff__k6_xcmplx_0__rm1_r1_rm2,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__r0_r2_rm2,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__r1_rm1_r2,rqRealDiff__k6_xcmplx_0__r2_rm1_r3]), [interesting(0.05),file(bintree1,e5_5_1_2_1_1_1__bintree1),[file(bintree1,e5_5_1_2_1_1_1__bintree1)]]). fof(e6_5_1_2_1_1_1__bintree1,plain,( ~ $true ), inference(mizar_by,[status(thm),assumptions([dt_c2_5__bintree1,e1_5_1_2_1_1_1__bintree1,e1_5_1_2__bintree1])],[reflexivity_r1_tarski,cc1_arytm_3,cc1_finseq_1,cc2_arytm_3,rc1_arytm_3,rc1_finseq_1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc1_subset_1,fc2_finseq_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,fc2_membered,spc5_arithm,spc6_arithm,spc7_arithm,t1_arithm,t1_numerals,t2_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,commutativity_k2_xcmplx_0,commutativity_k3_xcmplx_0,redefinition_k1_nat_1,dt_k1_nat_1,dt_k2_xcmplx_0,dt_k3_xcmplx_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__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r2_r0_r2,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r0_r2_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealMult__k3_xcmplx_0__r1_r2_r2,rqRealMult__k3_xcmplx_0__r2_r0_r0,spc0_numerals,spc1_numerals,spc2_numerals,spc0_boole,spc1_boole,spc2_boole,e5_5_1_2_1_1_1__bintree1,rqRealAdd__k2_xcmplx_0__r1_r1_r2,rqRealMult__k3_xcmplx_0__r2_r1_r2]), [interesting(0.05),file(bintree1,e6_5_1_2_1_1_1__bintree1),[file(bintree1,e6_5_1_2_1_1_1__bintree1)]]). fof(i2_5_1_2_1_1_1__bintree1,theorem,( $true ), introduced(tautology,[file(bintree1,i2_5_1_2_1_1_1__bintree1)]), [interesting(0.05),trivial,file(bintree1,i2_5_1_2_1_1_1__bintree1)]). fof(i1_5_1_2_1_1_1__bintree1,plain,( ~ $true ), inference(conclusion,[status(thm),assumptions([dt_c2_5__bintree1,e1_5_1_2_1_1_1__bintree1,e1_5_1_2__bintree1])],[e6_5_1_2_1_1_1__bintree1,i2_5_1_2_1_1_1__bintree1]), [interesting(0.05),file(bintree1,i1_5_1_2_1_1_1__bintree1),[file(bintree1,i1_5_1_2_1_1_1__bintree1)]]). fof(i1_5_1_2_1_1__bintree1,plain,( k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)) != k1_xboole_0 ), inference(discharge_asm,[status(thm),assumptions([dt_c2_5__bintree1,e1_5_1_2__bintree1]),discharge_asm(discharge,[e1_5_1_2_1_1_1__bintree1])],[e1_5_1_2_1_1_1__bintree1,i1_5_1_2_1_1_1__bintree1]), [interesting(0.2),file(bintree1,i1_5_1_2_1_1__bintree1),[file(bintree1,i1_5_1_2_1_1__bintree1)]]). fof(e1_5_1_2_1_1_2__bintree1,assumption,( k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)) = k3_lang1(k1_numbers,0) ), introduced(assumption,[file(bintree1,e1_5_1_2_1_1_2__bintree1)]), [interesting(0.05),axiom,file(bintree1,e1_5_1_2_1_1_2__bintree1)]). fof(e2_5_1_2_1_1_2__bintree1,plain,( k1_nat_1(k3_finseq_1(k3_lang1(k1_numbers,0)),k3_finseq_1(k3_lang1(k1_numbers,0))) = k3_finseq_1(k3_lang1(k1_numbers,0)) ), inference(mizar_by,[status(thm),assumptions([dt_c2_5__bintree1,e1_5_1_2_1_1_2__bintree1,e1_5_1_2__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc4_subset_1,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_arytm_3,cc1_fraenkel,cc2_arytm_3,cc7_trees_3,fc7_trees_3,fc8_trees_3,rc1_arytm_3,rc1_fraenkel,rc3_finseq_1,rc4_finseq_1,rc5_trees_3,rc6_finseq_1,rc7_trees_3,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_2,dt_m2_finseq_1,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc6_membered,cc9_membered,fc10_trees_3,fc13_trees_3,fc16_finseq_1,fc1_subset_1,fc2_finseq_1,fc5_membered,fc6_membered,fc9_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m1_trees_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_card_1,dt_k2_trees_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_dtconstr,cc4_membered,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc3_finseq_1,fc4_finseq_1,rc7_finseq_1,rc8_finseq_1,spc6_arithm,t1_arithm,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,commutativity_k2_xcmplx_0,redefinition_k1_nat_1,redefinition_k3_finseq_1,redefinition_k3_lang1,dt_k1_nat_1,dt_k1_numbers,dt_k2_xcmplx_0,dt_k3_finseq_1,dt_k3_lang1,dt_k7_finseq_1,dt_c2_5__bintree1,cc1_finseq_1,fc2_membered,rc1_finseq_1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_r2_r2,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r2_r0_r2,spc0_numerals,spc1_numerals,spc2_numerals,spc0_boole,spc1_boole,spc2_boole,e1_5_1_2_1_1_2__bintree1,e1_5_1_2__bintree1,t35_finseq_1,rqRealAdd__k2_xcmplx_0__r1_r1_r2]), [interesting(0.05),file(bintree1,e2_5_1_2_1_1_2__bintree1),[file(bintree1,e2_5_1_2_1_1_2__bintree1)]]). fof(e3_5_1_2_1_1_2__bintree1,plain,( k1_nat_1(1,k3_finseq_1(k3_lang1(k1_numbers,0))) = k3_finseq_1(k3_lang1(k1_numbers,0)) ), inference(mizar_by,[status(thm),assumptions([dt_c2_5__bintree1,e1_5_1_2_1_1_2__bintree1,e1_5_1_2__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc4_subset_1,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_arytm_3,cc1_fraenkel,cc2_arytm_3,fc10_membered,fc11_membered,fc9_membered,rc1_arytm_3,rc1_fraenkel,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_2,dt_m2_finseq_1,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc6_membered,cc9_membered,fc16_finseq_1,fc1_subset_1,fc2_finseq_1,fc5_membered,fc6_membered,fc8_membered,fc9_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_card_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_dtconstr,cc4_membered,fc11_finseq_1,fc12_finseq_1,fc3_finseq_1,fc4_finseq_1,fc7_membered,rc7_finseq_1,rc8_finseq_1,spc1_arithm,spc2_arithm,spc5_arithm,spc6_arithm,spc7_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_numerals,t2_arithm,t2_subset,t3_arithm,t4_arithm,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,commutativity_k2_xcmplx_0,commutativity_k3_xcmplx_0,involutiveness_k4_xcmplx_0,redefinition_k1_nat_1,redefinition_k3_finseq_1,redefinition_k3_lang1,redefinition_k9_finseq_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_tarski,dt_k2_relat_1,dt_k2_xcmplx_0,dt_k3_finseq_1,dt_k3_lang1,dt_k3_xcmplx_0,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_k9_finseq_1,cc1_finseq_1,fc2_membered,fc2_subset_1,rc1_finseq_1,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__r1_rm1_r0,rqRealAdd__k2_xcmplx_0__r1_rm2_rm1,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__rm2_r0_rm2,rqRealAdd__k2_xcmplx_0__rm2_r1_rm1,rqRealAdd__k2_xcmplx_0__rm2_r2_r0,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__r1_r2_rm1,rqRealDiff__k6_xcmplx_0__r1_rm1_r2,rqRealDiff__k6_xcmplx_0__r2_r0_r2,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealDiff__k6_xcmplx_0__rm1_r1_rm2,rqRealDiff__k6_xcmplx_0__rm1_rm2_r1,rqRealDiff__k6_xcmplx_0__rm2_r0_rm2,rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1,rqRealDiff__k6_xcmplx_0__rm2_rm2_r0,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r0_r2_r0,rqRealMult__k3_xcmplx_0__r0_rm2_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealMult__k3_xcmplx_0__r1_r2_r2,rqRealMult__k3_xcmplx_0__r1_rm2_rm2,rqRealMult__k3_xcmplx_0__r2_r0_r0,rqRealMult__k3_xcmplx_0__rm2_r0_r0,rqRealMult__k3_xcmplx_0__rm2_r1_rm2,rqRealNeg__k4_xcmplx_0__r2_rm2,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealNeg__k4_xcmplx_0__rm2_r2,spc0_numerals,spc1_numerals,spc2_numerals,spc0_boole,spc1_boole,spc2_boole,e2_5_1_2_1_1_2__bintree1,t56_finseq_1,rqRealAdd__k2_xcmplx_0__r1_r1_r2,rqRealDiff__k6_xcmplx_0__r2_r1_r1,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealMult__k3_xcmplx_0__r2_r1_r2,rqRealDiff__k6_xcmplx_0__r2_r2_r0,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r0_r1_r1]), [interesting(0.05),file(bintree1,e3_5_1_2_1_1_2__bintree1),[file(bintree1,e3_5_1_2_1_1_2__bintree1)]]). fof(e4_5_1_2_1_1_2__bintree1,plain,( k1_nat_1(1,1) = k3_finseq_1(k3_lang1(k1_numbers,0)) ), inference(mizar_by,[status(thm),assumptions([dt_c2_5__bintree1,e1_5_1_2_1_1_2__bintree1,e1_5_1_2__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc4_subset_1,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_arytm_3,cc1_fraenkel,cc2_arytm_3,rc1_arytm_3,rc1_fraenkel,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_2,dt_m2_finseq_1,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc6_membered,cc9_membered,fc16_finseq_1,fc1_subset_1,fc2_finseq_1,fc5_membered,fc6_membered,fc9_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,rc7_finseq_1,rc8_finseq_1,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_card_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_dtconstr,cc1_finseq_1,cc4_membered,fc12_finseq_1,fc3_finseq_1,fc4_finseq_1,rc1_finseq_1,spc5_arithm,spc6_arithm,spc7_arithm,t1_arithm,t1_numerals,t2_arithm,t2_subset,t3_arithm,t4_arithm,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,commutativity_k2_xcmplx_0,commutativity_k3_xcmplx_0,redefinition_k1_nat_1,redefinition_k3_finseq_1,redefinition_k3_lang1,dt_k1_nat_1,dt_k1_numbers,dt_k2_xcmplx_0,dt_k3_finseq_1,dt_k3_lang1,dt_k3_xcmplx_0,dt_k6_xcmplx_0,fc2_membered,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__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r2_r0_r2,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__r2_r0_r2,rqRealDiff__k6_xcmplx_0__r2_r1_r1,rqRealDiff__k6_xcmplx_0__r2_r2_r0,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r0_r2_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealMult__k3_xcmplx_0__r1_r2_r2,rqRealMult__k3_xcmplx_0__r2_r0_r0,spc0_numerals,spc1_numerals,spc2_numerals,spc0_boole,spc1_boole,spc2_boole,e3_5_1_2_1_1_2__bintree1,rqRealAdd__k2_xcmplx_0__r1_r1_r2,rqRealMult__k3_xcmplx_0__r2_r1_r2,rqRealDiff__k6_xcmplx_0__r1_r1_r0]), [interesting(0.05),file(bintree1,e4_5_1_2_1_1_2__bintree1),[file(bintree1,e4_5_1_2_1_1_2__bintree1)]]). fof(e5_5_1_2_1_1_2__bintree1,plain,( ~ $true ), inference(mizar_by,[status(thm),assumptions([dt_c2_5__bintree1,e1_5_1_2_1_1_2__bintree1,e1_5_1_2__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc4_subset_1,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_arytm_3,cc1_fraenkel,cc2_arytm_3,fc10_membered,fc11_membered,fc9_membered,rc1_arytm_3,rc1_fraenkel,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_2,dt_m2_finseq_1,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc6_membered,cc9_membered,fc16_finseq_1,fc1_subset_1,fc2_finseq_1,fc5_membered,fc6_membered,fc8_membered,fc9_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_card_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_dtconstr,cc4_membered,fc11_finseq_1,fc12_finseq_1,fc3_finseq_1,fc4_finseq_1,fc7_membered,rc7_finseq_1,rc8_finseq_1,spc5_arithm,spc6_arithm,spc7_arithm,t1_arithm,t1_numerals,t2_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,commutativity_k2_xcmplx_0,commutativity_k3_xcmplx_0,redefinition_k1_nat_1,redefinition_k3_finseq_1,redefinition_k3_lang1,redefinition_k9_finseq_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_tarski,dt_k2_relat_1,dt_k2_xcmplx_0,dt_k3_finseq_1,dt_k3_lang1,dt_k3_xcmplx_0,dt_k9_finseq_1,cc1_finseq_1,fc2_membered,fc2_subset_1,rc1_finseq_1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_r2_r2,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r2_r0_r2,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r0_r2_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealMult__k3_xcmplx_0__r1_r2_r2,rqRealMult__k3_xcmplx_0__r2_r0_r0,spc0_numerals,spc1_numerals,spc2_numerals,spc0_boole,spc1_boole,spc2_boole,e4_5_1_2_1_1_2__bintree1,t56_finseq_1,rqRealAdd__k2_xcmplx_0__r1_r1_r2,rqRealMult__k3_xcmplx_0__r2_r1_r2]), [interesting(0.05),file(bintree1,e5_5_1_2_1_1_2__bintree1),[file(bintree1,e5_5_1_2_1_1_2__bintree1)]]). fof(i2_5_1_2_1_1_2__bintree1,theorem,( $true ), introduced(tautology,[file(bintree1,i2_5_1_2_1_1_2__bintree1)]), [interesting(0.05),trivial,file(bintree1,i2_5_1_2_1_1_2__bintree1)]). fof(i1_5_1_2_1_1_2__bintree1,plain,( ~ $true ), inference(conclusion,[status(thm),assumptions([dt_c2_5__bintree1,e1_5_1_2_1_1_2__bintree1,e1_5_1_2__bintree1])],[e5_5_1_2_1_1_2__bintree1,i2_5_1_2_1_1_2__bintree1]), [interesting(0.05),file(bintree1,i1_5_1_2_1_1_2__bintree1),[file(bintree1,i1_5_1_2_1_1_2__bintree1)]]). fof(i2_5_1_2_1_1__bintree1,plain,( k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)) != k3_lang1(k1_numbers,0) ), inference(discharge_asm,[status(thm),assumptions([dt_c2_5__bintree1,e1_5_1_2__bintree1]),discharge_asm(discharge,[e1_5_1_2_1_1_2__bintree1])],[e1_5_1_2_1_1_2__bintree1,i1_5_1_2_1_1_2__bintree1]), [interesting(0.2),file(bintree1,i2_5_1_2_1_1__bintree1),[file(bintree1,i2_5_1_2_1_1__bintree1)]]). fof(e1_5_1_2_1_1_3__bintree1,assumption,( k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)) = k3_lang1(k1_numbers,1) ), introduced(assumption,[file(bintree1,e1_5_1_2_1_1_3__bintree1)]), [interesting(0.05),axiom,file(bintree1,e1_5_1_2_1_1_3__bintree1)]). fof(e2_5_1_2_1_1_3__bintree1,plain,( k1_nat_1(k3_finseq_1(k3_lang1(k1_numbers,0)),k3_finseq_1(k3_lang1(k1_numbers,0))) = k3_finseq_1(k3_lang1(k1_numbers,1)) ), inference(mizar_by,[status(thm),assumptions([dt_c2_5__bintree1,e1_5_1_2_1_1_3__bintree1,e1_5_1_2__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc4_subset_1,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_arytm_3,cc1_fraenkel,cc2_arytm_3,cc7_trees_3,fc7_trees_3,fc8_trees_3,rc1_arytm_3,rc1_fraenkel,rc3_finseq_1,rc4_finseq_1,rc5_trees_3,rc6_finseq_1,rc7_trees_3,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_2,dt_m2_finseq_1,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc6_membered,cc9_membered,fc10_trees_3,fc13_trees_3,fc16_finseq_1,fc1_subset_1,fc2_finseq_1,fc5_membered,fc6_membered,fc9_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m1_trees_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_card_1,dt_k2_trees_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_dtconstr,cc4_membered,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc3_finseq_1,fc4_finseq_1,rc7_finseq_1,rc8_finseq_1,spc6_arithm,t1_arithm,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,commutativity_k2_xcmplx_0,redefinition_k1_nat_1,redefinition_k3_finseq_1,redefinition_k3_lang1,dt_k1_nat_1,dt_k1_numbers,dt_k2_xcmplx_0,dt_k3_finseq_1,dt_k3_lang1,dt_k7_finseq_1,dt_c2_5__bintree1,cc1_finseq_1,fc2_membered,rc1_finseq_1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_r2_r2,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r2_r0_r2,spc0_numerals,spc1_numerals,spc2_numerals,spc0_boole,spc1_boole,spc2_boole,e1_5_1_2_1_1_3__bintree1,e1_5_1_2__bintree1,t35_finseq_1,rqRealAdd__k2_xcmplx_0__r1_r1_r2]), [interesting(0.05),file(bintree1,e2_5_1_2_1_1_3__bintree1),[file(bintree1,e2_5_1_2_1_1_3__bintree1)]]). fof(e3_5_1_2_1_1_3__bintree1,plain,( k1_nat_1(1,k3_finseq_1(k3_lang1(k1_numbers,0))) = k3_finseq_1(k3_lang1(k1_numbers,1)) ), inference(mizar_by,[status(thm),assumptions([dt_c2_5__bintree1,e1_5_1_2_1_1_3__bintree1,e1_5_1_2__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc4_subset_1,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_arytm_3,cc1_fraenkel,cc2_arytm_3,fc10_membered,fc11_membered,fc9_membered,rc1_arytm_3,rc1_fraenkel,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_2,dt_m2_finseq_1,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc6_membered,cc9_membered,fc16_finseq_1,fc1_subset_1,fc2_finseq_1,fc5_membered,fc6_membered,fc8_membered,fc9_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_card_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_dtconstr,cc4_membered,fc11_finseq_1,fc12_finseq_1,fc3_finseq_1,fc4_finseq_1,fc7_membered,rc7_finseq_1,rc8_finseq_1,spc1_arithm,spc6_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_numerals,t2_subset,t4_arithm,t5_arithm,t6_arithm,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,commutativity_k2_xcmplx_0,involutiveness_k4_xcmplx_0,redefinition_k1_nat_1,redefinition_k3_finseq_1,redefinition_k3_lang1,redefinition_k9_finseq_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_tarski,dt_k2_relat_1,dt_k2_xcmplx_0,dt_k3_finseq_1,dt_k3_lang1,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_k7_xcmplx_0,dt_k9_finseq_1,cc1_finseq_1,fc2_membered,fc2_subset_1,rc1_finseq_1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_r2_r2,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r0_rm2_rm2,rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2,rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_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,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_r2_r0,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealDiff__k6_xcmplx_0__rm1_r1_rm2,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,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__r0_rn1d2_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,rqRealDiv__k7_xcmplx_0__rnm1d2_rn1d2_rm1,rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2,rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2,spc0_numerals,spc1_numerals,spc2_numerals,spc0_boole,spc1_boole,spc2_boole,e2_5_1_2_1_1_3__bintree1,t56_finseq_1,rqRealAdd__k2_xcmplx_0__r1_r1_r2,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealNeg__k4_xcmplx_0__r2_rm2,rqRealDiff__k6_xcmplx_0__r2_r1_r1,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqRealNeg__k4_xcmplx_0__rm2_r2,rqRealDiff__k6_xcmplx_0__rm1_rm2_r1,rqRealDiff__k6_xcmplx_0__r1_r0_r1]), [interesting(0.05),file(bintree1,e3_5_1_2_1_1_3__bintree1),[file(bintree1,e3_5_1_2_1_1_3__bintree1)]]). fof(e4_5_1_2_1_1_3__bintree1,plain,( k1_nat_1(1,1) = k3_finseq_1(k3_lang1(k1_numbers,1)) ), inference(mizar_by,[status(thm),assumptions([dt_c2_5__bintree1,e1_5_1_2_1_1_3__bintree1,e1_5_1_2__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc4_subset_1,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_arytm_3,cc1_fraenkel,cc2_arytm_3,fc10_membered,fc11_membered,fc9_membered,rc1_arytm_3,rc1_fraenkel,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_2,dt_m2_finseq_1,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc6_membered,cc9_membered,fc16_finseq_1,fc1_subset_1,fc2_finseq_1,fc5_membered,fc6_membered,fc8_membered,fc9_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_card_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_dtconstr,cc4_membered,fc11_finseq_1,fc12_finseq_1,fc3_finseq_1,fc4_finseq_1,fc7_membered,rc7_finseq_1,rc8_finseq_1,spc1_arithm,spc2_arithm,spc4_arithm,spc5_arithm,spc6_arithm,spc7_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_numerals,t2_arithm,t2_subset,t3_arithm,t4_arithm,t5_arithm,t6_arithm,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,commutativity_k2_xcmplx_0,commutativity_k3_xcmplx_0,involutiveness_k4_xcmplx_0,redefinition_k1_nat_1,redefinition_k3_finseq_1,redefinition_k3_lang1,redefinition_k9_finseq_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_tarski,dt_k2_relat_1,dt_k2_xcmplx_0,dt_k3_finseq_1,dt_k3_lang1,dt_k3_xcmplx_0,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_k7_xcmplx_0,dt_k9_finseq_1,cc1_finseq_1,fc2_membered,fc2_subset_1,rc1_finseq_1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_r2_r2,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r0_rm2_rm2,rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2,rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_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,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_rm1_r2,rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2,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_r1_rm2,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_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__r0_rn1d2_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,rqRealDiv__k7_xcmplx_0__rnm1d2_rn1d2_rm1,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r0_r2_r0,rqRealMult__k3_xcmplx_0__r0_rm2_r0,rqRealMult__k3_xcmplx_0__r0_rn1d2_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealMult__k3_xcmplx_0__r1_r2_r2,rqRealMult__k3_xcmplx_0__r1_rm2_rm2,rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2,rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2,rqRealMult__k3_xcmplx_0__r2_r0_r0,rqRealMult__k3_xcmplx_0__r2_rn1d2_r1,rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1,rqRealMult__k3_xcmplx_0__rm2_r0_r0,rqRealMult__k3_xcmplx_0__rm2_r1_rm2,rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1,rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1,rqRealMult__k3_xcmplx_0__rn1d2_r0_r0,rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2,rqRealMult__k3_xcmplx_0__rn1d2_r2_r1,rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1,rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2,rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1,rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1,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,e3_5_1_2_1_1_3__bintree1,t56_finseq_1,rqRealAdd__k2_xcmplx_0__r1_r1_r2,rqRealMult__k3_xcmplx_0__r2_r1_r2,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqRealDiff__k6_xcmplx_0__r1_r2_rm1,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealNeg__k4_xcmplx_0__r2_rm2,rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealDiff__k6_xcmplx_0__r2_r0_r2]), [interesting(0.05),file(bintree1,e4_5_1_2_1_1_3__bintree1),[file(bintree1,e4_5_1_2_1_1_3__bintree1)]]). fof(e5_5_1_2_1_1_3__bintree1,plain,( ~ $true ), inference(mizar_by,[status(thm),assumptions([dt_c2_5__bintree1,e1_5_1_2_1_1_3__bintree1,e1_5_1_2__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc4_subset_1,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_arytm_3,cc1_fraenkel,cc2_arytm_3,fc10_membered,fc11_membered,fc9_membered,rc1_arytm_3,rc1_fraenkel,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_2,dt_m2_finseq_1,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc6_membered,cc9_membered,fc16_finseq_1,fc1_subset_1,fc2_finseq_1,fc5_membered,fc6_membered,fc8_membered,fc9_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_card_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_dtconstr,cc4_membered,fc11_finseq_1,fc12_finseq_1,fc3_finseq_1,fc4_finseq_1,fc7_membered,rc7_finseq_1,rc8_finseq_1,spc5_arithm,spc6_arithm,spc7_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,commutativity_k2_xcmplx_0,commutativity_k3_xcmplx_0,redefinition_k1_nat_1,redefinition_k3_finseq_1,redefinition_k3_lang1,redefinition_k9_finseq_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_tarski,dt_k2_relat_1,dt_k2_xcmplx_0,dt_k3_finseq_1,dt_k3_lang1,dt_k3_xcmplx_0,dt_k9_finseq_1,cc1_finseq_1,fc2_membered,fc2_subset_1,rc1_finseq_1,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealMult__k3_xcmplx_0__r1_r2_r2,spc1_numerals,spc2_numerals,spc1_boole,spc2_boole,e4_5_1_2_1_1_3__bintree1,t56_finseq_1,rqRealAdd__k2_xcmplx_0__r1_r1_r2,rqRealMult__k3_xcmplx_0__r2_r1_r2]), [interesting(0.05),file(bintree1,e5_5_1_2_1_1_3__bintree1),[file(bintree1,e5_5_1_2_1_1_3__bintree1)]]). fof(i2_5_1_2_1_1_3__bintree1,theorem,( $true ), introduced(tautology,[file(bintree1,i2_5_1_2_1_1_3__bintree1)]), [interesting(0.05),trivial,file(bintree1,i2_5_1_2_1_1_3__bintree1)]). fof(i1_5_1_2_1_1_3__bintree1,plain,( ~ $true ), inference(conclusion,[status(thm),assumptions([dt_c2_5__bintree1,e1_5_1_2_1_1_3__bintree1,e1_5_1_2__bintree1])],[e5_5_1_2_1_1_3__bintree1,i2_5_1_2_1_1_3__bintree1]), [interesting(0.05),file(bintree1,i1_5_1_2_1_1_3__bintree1),[file(bintree1,i1_5_1_2_1_1_3__bintree1)]]). fof(i3_5_1_2_1_1__bintree1,plain,( k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)) != k3_lang1(k1_numbers,1) ), inference(discharge_asm,[status(thm),assumptions([dt_c2_5__bintree1,e1_5_1_2__bintree1]),discharge_asm(discharge,[e1_5_1_2_1_1_3__bintree1])],[e1_5_1_2_1_1_3__bintree1,i1_5_1_2_1_1_3__bintree1]), [interesting(0.2),file(bintree1,i3_5_1_2_1_1__bintree1),[file(bintree1,i3_5_1_2_1_1__bintree1)]]). fof(e1_5_1_2_1_1__bintree1,plain,( ~ ( k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)) != k1_xboole_0 & k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)) != k3_lang1(k1_numbers,0) & k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)) != k3_lang1(k1_numbers,1) ) ), inference(mizar_by,[status(thm),assumptions([dt_c2_5__bintree1,e1_5_1_2_1__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_fraenkel,cc1_relset_1,fc4_subset_1,rc1_fraenkel,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m1_finseq_2,existence_m2_relset_1,redefinition_m2_relset_1,dt_k13_finseq_1,dt_m1_finseq_1,dt_m1_finseq_2,dt_m2_relset_1,cc1_arytm_3,cc2_arytm_3,cc7_trees_3,fc16_finseq_1,fc17_membered,fc18_membered,fc19_membered,fc20_membered,fc21_membered,fc7_trees_3,fc8_trees_3,fc9_finseq_1,rc1_arytm_3,rc4_finseq_1,rc5_trees_3,rc7_trees_3,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_m1_trees_1,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_zfmisc_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_1,dt_m2_finseq_2,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_dtconstr,cc1_finseq_1,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc10_trees_3,fc12_finseq_1,fc13_finseq_1,fc13_trees_3,fc14_finseq_1,fc1_subset_1,fc3_finseq_1,fc4_finseq_1,fc5_membered,rc1_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,redefinition_k12_finseq_1,redefinition_k3_lang1,redefinition_k5_numbers,dt_k12_finseq_1,dt_k1_enumset1,dt_k1_numbers,dt_k1_xboole_0,dt_k2_trees_1,dt_k3_lang1,dt_k5_numbers,dt_k7_finseq_1,dt_c2_5__bintree1,fc2_finseq_1,fc2_membered,fc6_membered,t1_subset,t6_boole,t7_boole,spc0_numerals,spc1_numerals,spc2_numerals,spc0_boole,spc1_boole,spc2_boole,e1_5_1_2_1__bintree1,d1_enumset1,t10_modal_1]), [interesting(0.2),file(bintree1,e1_5_1_2_1_1__bintree1),[file(bintree1,e1_5_1_2_1_1__bintree1)]]). fof(i1_5_1_2_1__bintree1,plain,( ~ $true ), inference(percases,[status(thm),assumptions([e1_5_1_2__bintree1,dt_c2_5__bintree1,e1_5_1_2_1__bintree1])],[i1_5_1_2_1_1__bintree1,i2_5_1_2_1_1__bintree1,i3_5_1_2_1_1__bintree1,e1_5_1_2_1_1__bintree1]), [interesting(0.35),file(bintree1,i1_5_1_2_1__bintree1),[file(bintree1,i1_5_1_2_1__bintree1)]]). fof(e2_5_1_2__bintree1,plain,( ~ r2_hidden(k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)),k2_trees_1(2)) ), inference(discharge_asm,[status(thm),assumptions([e1_5_1_2__bintree1,dt_c2_5__bintree1]),discharge_asm(discharge,[e1_5_1_2_1__bintree1])],[e1_5_1_2_1__bintree1,i1_5_1_2_1__bintree1]), [interesting(0.5),file(bintree1,e2_5_1_2__bintree1),[file(bintree1,e2_5_1_2__bintree1)]]). fof(t53_modal_1,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m1_trees_1(B,A) => ( r2_hidden(B,k3_trees_1(A)) <=> ~ r2_hidden(k8_finseq_1(k5_numbers,B,k12_finseq_1(k5_numbers,0)),A) ) ) ) ), file(modal_1,t53_modal_1), [interesting(0.9),axiom,file(modal_1,t53_modal_1)]). fof(e3_5_1_2__bintree1,plain,( k1_trees_2(k2_trees_1(2),c2_5__bintree1) = k2_tarski(k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)),k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,1))) ), inference(mizar_by,[status(thm),assumptions([e1_5_1_2__bintree1,dt_c2_5__bintree1,e1_5__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_fraenkel,cc1_relset_1,fc4_subset_1,rc1_fraenkel,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_2,existence_m2_relset_1,redefinition_m2_relset_1,dt_k13_finseq_1,dt_m1_finseq_2,dt_m2_relset_1,cc1_arytm_3,cc2_arytm_3,cc7_trees_3,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_finseq_1,fc16_membered,fc7_trees_3,fc8_trees_3,fc9_finseq_1,rc1_arytm_3,rc3_finseq_1,rc4_finseq_1,rc5_trees_3,rc6_finseq_1,rc7_trees_3,existence_m1_finseq_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_dtconstr,cc1_finseq_1,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc10_trees_3,fc12_finseq_1,fc13_finseq_1,fc13_trees_3,fc14_finseq_1,fc1_subset_1,fc21_trees_3,fc2_finseq_1,fc3_finseq_1,fc4_finseq_1,fc4_trees_2,fc5_membered,fc6_membered,rc1_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,rc7_finseq_1,rc8_finseq_1,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,antisymmetry_r2_hidden,existence_m1_trees_1,redefinition_k12_finseq_1,redefinition_k3_lang1,redefinition_k5_numbers,redefinition_k8_finseq_1,redefinition_m1_trees_1,dt_k12_finseq_1,dt_k1_numbers,dt_k1_trees_2,dt_k2_tarski,dt_k2_trees_1,dt_k3_lang1,dt_k3_trees_1,dt_k5_numbers,dt_k7_finseq_1,dt_k8_finseq_1,dt_m1_trees_1,dt_c2_5__bintree1,cc15_membered,fc2_membered,fc3_subset_1,spc0_boole,spc1_boole,spc2_boole,t1_subset,t6_boole,t7_boole,t8_boole,spc0_numerals,spc1_numerals,spc2_numerals,spc0_boole,spc1_boole,spc2_boole,e2_5_1_2__bintree1,e1_5__bintree1,t53_modal_1]), [interesting(0.5),file(bintree1,e3_5_1_2__bintree1),[file(bintree1,e3_5_1_2__bintree1)]]). fof(i2_5_1_2__bintree1,theorem,( $true ), introduced(tautology,[file(bintree1,i2_5_1_2__bintree1)]), [interesting(0.5),trivial,file(bintree1,i2_5_1_2__bintree1)]). fof(i1_5_1_2__bintree1,plain,( k1_trees_2(k2_trees_1(2),c2_5__bintree1) = k2_tarski(k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)),k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,1))) ), inference(conclusion,[status(thm),assumptions([e1_5_1_2__bintree1,dt_c2_5__bintree1,e1_5__bintree1])],[e3_5_1_2__bintree1,i2_5_1_2__bintree1]), [interesting(0.5),file(bintree1,i1_5_1_2__bintree1),[file(bintree1,i1_5_1_2__bintree1)]]). fof(i2_5_1__bintree1,plain, ( c2_5__bintree1 = k3_lang1(k1_numbers,0) => k1_trees_2(k2_trees_1(2),c2_5__bintree1) = k2_tarski(k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)),k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,1))) ), inference(discharge_asm,[status(thm),assumptions([dt_c2_5__bintree1,e1_5__bintree1]),discharge_asm(discharge,[e1_5_1_2__bintree1])],[e1_5_1_2__bintree1,i1_5_1_2__bintree1]), [interesting(0.65),file(bintree1,i2_5_1__bintree1),[file(bintree1,i2_5_1__bintree1)]]). fof(e1_5_1_3__bintree1,assumption,( c2_5__bintree1 = k3_lang1(k1_numbers,1) ), introduced(assumption,[file(bintree1,e1_5_1_3__bintree1)]), [interesting(0.5),axiom,file(bintree1,e1_5_1_3__bintree1)]). fof(e1_5_1_3_1__bintree1,assumption,( r2_hidden(k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)),k2_trees_1(2)) ), introduced(assumption,[file(bintree1,e1_5_1_3_1__bintree1)]), [interesting(0.35),axiom,file(bintree1,e1_5_1_3_1__bintree1)]). fof(e1_5_1_3_1_1_1__bintree1,assumption,( k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)) = k1_xboole_0 ), introduced(assumption,[file(bintree1,e1_5_1_3_1_1_1__bintree1)]), [interesting(0.05),axiom,file(bintree1,e1_5_1_3_1_1_1__bintree1)]). fof(e2_5_1_3_1_1_1__bintree1,plain,( k3_finseq_1(k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0))) = 0 ), inference(mizar_by,[status(thm),assumptions([dt_c2_5__bintree1,e1_5_1_3_1_1_1__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc4_subset_1,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_arytm_3,cc1_fraenkel,cc2_arytm_3,cc7_trees_3,fc7_trees_3,fc8_trees_3,rc1_arytm_3,rc1_fraenkel,rc4_finseq_1,rc5_trees_3,rc7_trees_3,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_2,dt_m2_finseq_1,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc20_membered,cc3_arytm_3,cc6_membered,cc9_membered,fc10_trees_3,fc13_trees_3,fc16_finseq_1,fc1_subset_1,fc5_membered,fc9_finseq_1,rc1_subset_1,rc2_subset_1,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m1_trees_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_card_1,dt_k2_trees_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc1_dtconstr,cc1_finseq_1,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc3_finseq_1,fc4_finseq_1,rc1_finseq_1,rc1_membered,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,spc2_boole,spc2_numerals,t1_numerals,t2_subset,t7_boole,t8_boole,spc2_numerals,spc2_boole,redefinition_k3_finseq_1,redefinition_k3_lang1,dt_k1_numbers,dt_k1_xboole_0,dt_k3_finseq_1,dt_k3_lang1,dt_k7_finseq_1,dt_c2_5__bintree1,fc2_finseq_1,fc2_membered,fc6_membered,t6_boole,spc0_numerals,spc0_boole,e1_5_1_3_1_1_1__bintree1]), [interesting(0.05),file(bintree1,e2_5_1_3_1_1_1__bintree1),[file(bintree1,e2_5_1_3_1_1_1__bintree1)]]). fof(e3_5_1_3_1_1_1__bintree1,plain,( k1_nat_1(k3_finseq_1(c2_5__bintree1),k3_finseq_1(k3_lang1(k1_numbers,0))) = 0 ), inference(mizar_by,[status(thm),assumptions([dt_c2_5__bintree1,e1_5_1_3_1_1_1__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc4_subset_1,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_arytm_3,cc1_fraenkel,cc2_arytm_3,cc7_trees_3,fc7_trees_3,fc8_trees_3,rc1_arytm_3,rc1_fraenkel,rc3_finseq_1,rc4_finseq_1,rc5_trees_3,rc6_finseq_1,rc7_trees_3,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_2,dt_m2_finseq_1,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc6_membered,cc9_membered,fc10_trees_3,fc13_trees_3,fc16_finseq_1,fc1_subset_1,fc2_finseq_1,fc5_membered,fc6_membered,fc9_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,spc6_arithm,t1_arithm,t1_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m1_trees_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_card_1,dt_k2_trees_1,dt_k2_xcmplx_0,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_dtconstr,cc4_membered,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc3_finseq_1,fc4_finseq_1,rc7_finseq_1,rc8_finseq_1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r2_r2,rqRealAdd__k2_xcmplx_0__r2_r0_r2,spc2_boole,spc2_numerals,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,spc2_numerals,spc2_boole,commutativity_k1_nat_1,redefinition_k1_nat_1,redefinition_k3_finseq_1,redefinition_k3_lang1,dt_k1_nat_1,dt_k1_numbers,dt_k3_finseq_1,dt_k3_lang1,dt_k7_finseq_1,dt_c2_5__bintree1,cc1_finseq_1,fc2_membered,rc1_finseq_1,spc0_numerals,spc0_boole,e2_5_1_3_1_1_1__bintree1,t35_finseq_1]), [interesting(0.05),file(bintree1,e3_5_1_3_1_1_1__bintree1),[file(bintree1,e3_5_1_3_1_1_1__bintree1)]]). fof(e4_5_1_3_1_1_1__bintree1,plain,( k1_nat_1(1,k3_finseq_1(k3_lang1(k1_numbers,0))) = 0 ), inference(mizar_by,[status(thm),assumptions([dt_c2_5__bintree1,e1_5_1_3_1_1_1__bintree1,e1_5_1_3__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc4_subset_1,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_arytm_3,cc1_fraenkel,cc2_arytm_3,cc7_trees_3,fc10_membered,fc11_membered,fc9_membered,rc1_arytm_3,rc1_fraenkel,rc3_finseq_1,rc4_finseq_1,rc5_trees_3,rc6_finseq_1,rc7_trees_3,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_2,dt_m2_finseq_1,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc6_membered,cc9_membered,fc10_trees_3,fc13_trees_3,fc16_finseq_1,fc1_subset_1,fc2_finseq_1,fc5_membered,fc6_membered,fc8_membered,fc9_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,t1_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m1_trees_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_card_1,dt_k2_trees_1,dt_k2_xcmplx_0,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_dtconstr,cc4_membered,fc11_finseq_1,fc12_finseq_1,fc3_finseq_1,fc4_finseq_1,fc7_membered,rc7_finseq_1,rc8_finseq_1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_r2_r2,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r0_rm2_rm2,rqRealAdd__k2_xcmplx_0__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__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__rm2_r0_rm2,rqRealAdd__k2_xcmplx_0__rm2_r1_rm1,rqRealAdd__k2_xcmplx_0__rm2_r2_r0,spc1_arithm,spc6_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_numerals,t2_subset,t4_arithm,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,involutiveness_k4_xcmplx_0,redefinition_k1_nat_1,redefinition_k3_finseq_1,redefinition_k3_lang1,redefinition_k9_finseq_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_tarski,dt_k2_relat_1,dt_k3_finseq_1,dt_k3_lang1,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_k9_finseq_1,dt_c2_5__bintree1,cc1_finseq_1,fc2_membered,fc2_subset_1,rc1_finseq_1,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r0_rm2_r2,rqRealDiff__k6_xcmplx_0__r1_r0_r1,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__rm2_r0_rm2,rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1,rqRealDiff__k6_xcmplx_0__rm2_rm2_r0,rqRealNeg__k4_xcmplx_0__rm2_r2,spc0_numerals,spc1_numerals,spc2_numerals,spc0_boole,spc1_boole,spc2_boole,e3_5_1_3_1_1_1__bintree1,e1_5_1_3__bintree1,t56_finseq_1,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqRealNeg__k4_xcmplx_0__r2_rm2,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__r0_r2_rm2,rqRealDiff__k6_xcmplx_0__r1_r2_rm1,rqRealDiff__k6_xcmplx_0__r1_rm1_r2,rqRealDiff__k6_xcmplx_0__rm1_r1_rm2]), [interesting(0.05),file(bintree1,e4_5_1_3_1_1_1__bintree1),[file(bintree1,e4_5_1_3_1_1_1__bintree1)]]). fof(e5_5_1_3_1_1_1__bintree1,plain,( k1_nat_1(1,1) = 0 ), inference(mizar_by,[status(thm),assumptions([dt_c2_5__bintree1,e1_5_1_3_1_1_1__bintree1,e1_5_1_3__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc4_subset_1,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_arytm_3,cc1_fraenkel,cc2_arytm_3,fc10_membered,fc11_membered,fc9_membered,rc1_arytm_3,rc1_fraenkel,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_2,dt_m2_finseq_1,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc6_membered,cc9_membered,fc16_finseq_1,fc1_subset_1,fc2_finseq_1,fc5_membered,fc6_membered,fc8_membered,fc9_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_card_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_dtconstr,cc4_membered,fc11_finseq_1,fc12_finseq_1,fc3_finseq_1,fc4_finseq_1,fc7_membered,rc7_finseq_1,rc8_finseq_1,spc1_arithm,spc2_arithm,spc5_arithm,spc6_arithm,spc7_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_numerals,t2_arithm,t2_subset,t3_arithm,t4_arithm,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,commutativity_k2_xcmplx_0,commutativity_k3_xcmplx_0,involutiveness_k4_xcmplx_0,redefinition_k1_nat_1,redefinition_k3_finseq_1,redefinition_k3_lang1,redefinition_k9_finseq_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_tarski,dt_k2_relat_1,dt_k2_xcmplx_0,dt_k3_finseq_1,dt_k3_lang1,dt_k3_xcmplx_0,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_k9_finseq_1,cc1_finseq_1,fc2_membered,fc2_subset_1,rc1_finseq_1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_r2_r2,rqRealAdd__k2_xcmplx_0__r0_r3_r3,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r0_rm2_rm2,rqRealAdd__k2_xcmplx_0__r0_rm3_rm3,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_r2_r3,rqRealAdd__k2_xcmplx_0__r1_rm1_r0,rqRealAdd__k2_xcmplx_0__r1_rm2_rm1,rqRealAdd__k2_xcmplx_0__r1_rm3_rm2,rqRealAdd__k2_xcmplx_0__r2_r0_r2,rqRealAdd__k2_xcmplx_0__r2_r1_r3,rqRealAdd__k2_xcmplx_0__r2_rm1_r1,rqRealAdd__k2_xcmplx_0__r2_rm2_r0,rqRealAdd__k2_xcmplx_0__r2_rm3_rm1,rqRealAdd__k2_xcmplx_0__r3_r0_r3,rqRealAdd__k2_xcmplx_0__r3_rm1_r2,rqRealAdd__k2_xcmplx_0__r3_rm2_r1,rqRealAdd__k2_xcmplx_0__r3_rm3_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_r3_r2,rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2,rqRealAdd__k2_xcmplx_0__rm1_rm2_rm3,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__rm2_r3_r1,rqRealAdd__k2_xcmplx_0__rm2_rm1_rm3,rqRealAdd__k2_xcmplx_0__rm3_r1_rm2,rqRealAdd__k2_xcmplx_0__rm3_r2_rm1,rqRealAdd__k2_xcmplx_0__rm3_r3_r0,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_r3_rm3,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r0_rm2_r2,rqRealDiff__k6_xcmplx_0__r0_rm3_r3,rqRealDiff__k6_xcmplx_0__r1_r3_rm2,rqRealDiff__k6_xcmplx_0__r1_rm2_r3,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__r2_r3_rm1,rqRealDiff__k6_xcmplx_0__r3_r0_r3,rqRealDiff__k6_xcmplx_0__r3_r1_r2,rqRealDiff__k6_xcmplx_0__r3_r2_r1,rqRealDiff__k6_xcmplx_0__r3_r3_r0,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealDiff__k6_xcmplx_0__rm1_r2_rm3,rqRealDiff__k6_xcmplx_0__rm1_rm2_r1,rqRealDiff__k6_xcmplx_0__rm1_rm3_r2,rqRealDiff__k6_xcmplx_0__rm2_r0_rm2,rqRealDiff__k6_xcmplx_0__rm2_r1_rm3,rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1,rqRealDiff__k6_xcmplx_0__rm2_rm2_r0,rqRealDiff__k6_xcmplx_0__rm2_rm3_r1,rqRealDiff__k6_xcmplx_0__rm3_r0_rm3,rqRealDiff__k6_xcmplx_0__rm3_rm1_rm2,rqRealDiff__k6_xcmplx_0__rm3_rm2_rm1,rqRealDiff__k6_xcmplx_0__rm3_rm3_r0,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r0_r2_r0,rqRealMult__k3_xcmplx_0__r0_r3_r0,rqRealMult__k3_xcmplx_0__r0_rm2_r0,rqRealMult__k3_xcmplx_0__r0_rm3_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealMult__k3_xcmplx_0__r1_r2_r2,rqRealMult__k3_xcmplx_0__r1_r3_r3,rqRealMult__k3_xcmplx_0__r1_rm2_rm2,rqRealMult__k3_xcmplx_0__r1_rm3_rm3,rqRealMult__k3_xcmplx_0__r2_r0_r0,rqRealMult__k3_xcmplx_0__r3_r0_r0,rqRealMult__k3_xcmplx_0__r3_r1_r3,rqRealMult__k3_xcmplx_0__rm2_r0_r0,rqRealMult__k3_xcmplx_0__rm2_r1_rm2,rqRealMult__k3_xcmplx_0__rm3_r0_r0,rqRealMult__k3_xcmplx_0__rm3_r1_rm3,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealNeg__k4_xcmplx_0__r2_rm2,rqRealNeg__k4_xcmplx_0__r3_rm3,rqRealNeg__k4_xcmplx_0__rm2_r2,rqRealNeg__k4_xcmplx_0__rm3_r3,spc0_numerals,spc1_numerals,spc2_numerals,spc3_numerals,spc0_boole,spc1_boole,spc2_boole,spc3_boole,e4_5_1_3_1_1_1__bintree1,t56_finseq_1,rqRealAdd__k2_xcmplx_0__r1_r1_r2,rqRealMult__k3_xcmplx_0__r2_r1_r2,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealDiff__k6_xcmplx_0__r1_r2_rm1,rqRealDiff__k6_xcmplx_0__rm1_r1_rm2,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__r0_r2_rm2,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__r1_rm1_r2,rqRealDiff__k6_xcmplx_0__r2_rm1_r3]), [interesting(0.05),file(bintree1,e5_5_1_3_1_1_1__bintree1),[file(bintree1,e5_5_1_3_1_1_1__bintree1)]]). fof(e6_5_1_3_1_1_1__bintree1,plain,( ~ $true ), inference(mizar_by,[status(thm),assumptions([dt_c2_5__bintree1,e1_5_1_3_1_1_1__bintree1,e1_5_1_3__bintree1])],[reflexivity_r1_tarski,cc1_arytm_3,cc1_finseq_1,cc2_arytm_3,rc1_arytm_3,rc1_finseq_1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc1_subset_1,fc2_finseq_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,fc2_membered,spc5_arithm,spc6_arithm,spc7_arithm,t1_arithm,t1_numerals,t2_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,commutativity_k2_xcmplx_0,commutativity_k3_xcmplx_0,redefinition_k1_nat_1,dt_k1_nat_1,dt_k2_xcmplx_0,dt_k3_xcmplx_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__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r2_r0_r2,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r0_r2_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealMult__k3_xcmplx_0__r1_r2_r2,rqRealMult__k3_xcmplx_0__r2_r0_r0,spc0_numerals,spc1_numerals,spc2_numerals,spc0_boole,spc1_boole,spc2_boole,e5_5_1_3_1_1_1__bintree1,rqRealAdd__k2_xcmplx_0__r1_r1_r2,rqRealMult__k3_xcmplx_0__r2_r1_r2]), [interesting(0.05),file(bintree1,e6_5_1_3_1_1_1__bintree1),[file(bintree1,e6_5_1_3_1_1_1__bintree1)]]). fof(i2_5_1_3_1_1_1__bintree1,theorem,( $true ), introduced(tautology,[file(bintree1,i2_5_1_3_1_1_1__bintree1)]), [interesting(0.05),trivial,file(bintree1,i2_5_1_3_1_1_1__bintree1)]). fof(i1_5_1_3_1_1_1__bintree1,plain,( ~ $true ), inference(conclusion,[status(thm),assumptions([dt_c2_5__bintree1,e1_5_1_3_1_1_1__bintree1,e1_5_1_3__bintree1])],[e6_5_1_3_1_1_1__bintree1,i2_5_1_3_1_1_1__bintree1]), [interesting(0.05),file(bintree1,i1_5_1_3_1_1_1__bintree1),[file(bintree1,i1_5_1_3_1_1_1__bintree1)]]). fof(i1_5_1_3_1_1__bintree1,plain,( k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)) != k1_xboole_0 ), inference(discharge_asm,[status(thm),assumptions([dt_c2_5__bintree1,e1_5_1_3__bintree1]),discharge_asm(discharge,[e1_5_1_3_1_1_1__bintree1])],[e1_5_1_3_1_1_1__bintree1,i1_5_1_3_1_1_1__bintree1]), [interesting(0.2),file(bintree1,i1_5_1_3_1_1__bintree1),[file(bintree1,i1_5_1_3_1_1__bintree1)]]). fof(e1_5_1_3_1_1_2__bintree1,assumption,( k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)) = k3_lang1(k1_numbers,0) ), introduced(assumption,[file(bintree1,e1_5_1_3_1_1_2__bintree1)]), [interesting(0.05),axiom,file(bintree1,e1_5_1_3_1_1_2__bintree1)]). fof(e2_5_1_3_1_1_2__bintree1,plain,( k1_nat_1(k3_finseq_1(k3_lang1(k1_numbers,1)),k3_finseq_1(k3_lang1(k1_numbers,0))) = k3_finseq_1(k3_lang1(k1_numbers,0)) ), inference(mizar_by,[status(thm),assumptions([dt_c2_5__bintree1,e1_5_1_3_1_1_2__bintree1,e1_5_1_3__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc4_subset_1,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_arytm_3,cc1_fraenkel,cc2_arytm_3,cc7_trees_3,fc7_trees_3,fc8_trees_3,rc1_arytm_3,rc1_fraenkel,rc3_finseq_1,rc4_finseq_1,rc5_trees_3,rc6_finseq_1,rc7_trees_3,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_2,dt_m2_finseq_1,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc6_membered,cc9_membered,fc10_trees_3,fc13_trees_3,fc16_finseq_1,fc1_subset_1,fc2_finseq_1,fc5_membered,fc6_membered,fc9_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,spc6_arithm,t1_arithm,t1_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m1_trees_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_card_1,dt_k2_trees_1,dt_k2_xcmplx_0,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_dtconstr,cc4_membered,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc3_finseq_1,fc4_finseq_1,rc7_finseq_1,rc8_finseq_1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_r2_r2,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_r1_r2,rqRealAdd__k2_xcmplx_0__r2_r0_r2,spc2_boole,spc2_numerals,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,spc2_numerals,spc2_boole,commutativity_k1_nat_1,redefinition_k1_nat_1,redefinition_k3_finseq_1,redefinition_k3_lang1,dt_k1_nat_1,dt_k1_numbers,dt_k3_finseq_1,dt_k3_lang1,dt_k7_finseq_1,dt_c2_5__bintree1,cc1_finseq_1,fc2_membered,rc1_finseq_1,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e1_5_1_3_1_1_2__bintree1,e1_5_1_3__bintree1,t35_finseq_1]), [interesting(0.05),file(bintree1,e2_5_1_3_1_1_2__bintree1),[file(bintree1,e2_5_1_3_1_1_2__bintree1)]]). fof(e3_5_1_3_1_1_2__bintree1,plain,( k1_nat_1(1,k3_finseq_1(k3_lang1(k1_numbers,0))) = k3_finseq_1(k3_lang1(k1_numbers,0)) ), inference(mizar_by,[status(thm),assumptions([dt_c2_5__bintree1,e1_5_1_3_1_1_2__bintree1,e1_5_1_3__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc4_subset_1,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_arytm_3,cc1_fraenkel,cc2_arytm_3,fc10_membered,fc11_membered,fc9_membered,rc1_arytm_3,rc1_fraenkel,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_2,dt_m2_finseq_1,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc6_membered,cc9_membered,fc16_finseq_1,fc1_subset_1,fc2_finseq_1,fc5_membered,fc6_membered,fc8_membered,fc9_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,t1_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_m1_subset_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_card_1,dt_k2_xcmplx_0,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_dtconstr,cc4_membered,fc11_finseq_1,fc12_finseq_1,fc3_finseq_1,fc4_finseq_1,fc7_membered,rc7_finseq_1,rc8_finseq_1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_rm1_r0,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,rqRealAdd__k2_xcmplx_0__rm1_r1_r0,spc1_arithm,spc6_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_numerals,t2_subset,t4_arithm,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,involutiveness_k4_xcmplx_0,redefinition_k1_nat_1,redefinition_k3_finseq_1,redefinition_k3_lang1,redefinition_k9_finseq_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_tarski,dt_k2_relat_1,dt_k3_finseq_1,dt_k3_lang1,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_k9_finseq_1,cc1_finseq_1,fc2_membered,fc2_subset_1,rc1_finseq_1,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealNeg__k4_xcmplx_0__rm1_r1,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e2_5_1_3_1_1_2__bintree1,t56_finseq_1,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealDiff__k6_xcmplx_0__r1_r0_r1]), [interesting(0.05),file(bintree1,e3_5_1_3_1_1_2__bintree1),[file(bintree1,e3_5_1_3_1_1_2__bintree1)]]). fof(e4_5_1_3_1_1_2__bintree1,plain,( k1_nat_1(1,1) = k3_finseq_1(k3_lang1(k1_numbers,0)) ), inference(mizar_by,[status(thm),assumptions([dt_c2_5__bintree1,e1_5_1_3_1_1_2__bintree1,e1_5_1_3__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc4_subset_1,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_arytm_3,cc1_fraenkel,cc2_arytm_3,rc1_arytm_3,rc1_fraenkel,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_2,dt_m2_finseq_1,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc6_membered,cc9_membered,fc16_finseq_1,fc1_subset_1,fc2_finseq_1,fc5_membered,fc6_membered,fc9_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,rc7_finseq_1,rc8_finseq_1,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_card_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_dtconstr,cc1_finseq_1,cc4_membered,fc12_finseq_1,fc3_finseq_1,fc4_finseq_1,rc1_finseq_1,spc5_arithm,spc6_arithm,spc7_arithm,t1_arithm,t1_numerals,t2_arithm,t2_subset,t3_arithm,t4_arithm,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,commutativity_k2_xcmplx_0,commutativity_k3_xcmplx_0,redefinition_k1_nat_1,redefinition_k3_finseq_1,redefinition_k3_lang1,dt_k1_nat_1,dt_k1_numbers,dt_k2_xcmplx_0,dt_k3_finseq_1,dt_k3_lang1,dt_k3_xcmplx_0,dt_k6_xcmplx_0,fc2_membered,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__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r2_r0_r2,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__r2_r0_r2,rqRealDiff__k6_xcmplx_0__r2_r1_r1,rqRealDiff__k6_xcmplx_0__r2_r2_r0,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r0_r2_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealMult__k3_xcmplx_0__r1_r2_r2,rqRealMult__k3_xcmplx_0__r2_r0_r0,spc0_numerals,spc1_numerals,spc2_numerals,spc0_boole,spc1_boole,spc2_boole,e3_5_1_3_1_1_2__bintree1,rqRealAdd__k2_xcmplx_0__r1_r1_r2,rqRealMult__k3_xcmplx_0__r2_r1_r2,rqRealDiff__k6_xcmplx_0__r1_r1_r0]), [interesting(0.05),file(bintree1,e4_5_1_3_1_1_2__bintree1),[file(bintree1,e4_5_1_3_1_1_2__bintree1)]]). fof(e5_5_1_3_1_1_2__bintree1,plain,( ~ $true ), inference(mizar_by,[status(thm),assumptions([dt_c2_5__bintree1,e1_5_1_3_1_1_2__bintree1,e1_5_1_3__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc4_subset_1,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_arytm_3,cc1_fraenkel,cc2_arytm_3,fc10_membered,fc11_membered,fc9_membered,rc1_arytm_3,rc1_fraenkel,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_2,dt_m2_finseq_1,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc6_membered,cc9_membered,fc16_finseq_1,fc1_subset_1,fc2_finseq_1,fc5_membered,fc6_membered,fc8_membered,fc9_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_card_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_dtconstr,cc4_membered,fc11_finseq_1,fc12_finseq_1,fc3_finseq_1,fc4_finseq_1,fc7_membered,rc7_finseq_1,rc8_finseq_1,spc5_arithm,spc6_arithm,spc7_arithm,t1_arithm,t1_numerals,t2_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,commutativity_k2_xcmplx_0,commutativity_k3_xcmplx_0,redefinition_k1_nat_1,redefinition_k3_finseq_1,redefinition_k3_lang1,redefinition_k9_finseq_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_tarski,dt_k2_relat_1,dt_k2_xcmplx_0,dt_k3_finseq_1,dt_k3_lang1,dt_k3_xcmplx_0,dt_k9_finseq_1,cc1_finseq_1,fc2_membered,fc2_subset_1,rc1_finseq_1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_r2_r2,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r2_r0_r2,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r0_r2_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealMult__k3_xcmplx_0__r1_r2_r2,rqRealMult__k3_xcmplx_0__r2_r0_r0,spc0_numerals,spc1_numerals,spc2_numerals,spc0_boole,spc1_boole,spc2_boole,e4_5_1_3_1_1_2__bintree1,t56_finseq_1,rqRealAdd__k2_xcmplx_0__r1_r1_r2,rqRealMult__k3_xcmplx_0__r2_r1_r2]), [interesting(0.05),file(bintree1,e5_5_1_3_1_1_2__bintree1),[file(bintree1,e5_5_1_3_1_1_2__bintree1)]]). fof(i2_5_1_3_1_1_2__bintree1,theorem,( $true ), introduced(tautology,[file(bintree1,i2_5_1_3_1_1_2__bintree1)]), [interesting(0.05),trivial,file(bintree1,i2_5_1_3_1_1_2__bintree1)]). fof(i1_5_1_3_1_1_2__bintree1,plain,( ~ $true ), inference(conclusion,[status(thm),assumptions([dt_c2_5__bintree1,e1_5_1_3_1_1_2__bintree1,e1_5_1_3__bintree1])],[e5_5_1_3_1_1_2__bintree1,i2_5_1_3_1_1_2__bintree1]), [interesting(0.05),file(bintree1,i1_5_1_3_1_1_2__bintree1),[file(bintree1,i1_5_1_3_1_1_2__bintree1)]]). fof(i2_5_1_3_1_1__bintree1,plain,( k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)) != k3_lang1(k1_numbers,0) ), inference(discharge_asm,[status(thm),assumptions([dt_c2_5__bintree1,e1_5_1_3__bintree1]),discharge_asm(discharge,[e1_5_1_3_1_1_2__bintree1])],[e1_5_1_3_1_1_2__bintree1,i1_5_1_3_1_1_2__bintree1]), [interesting(0.2),file(bintree1,i2_5_1_3_1_1__bintree1),[file(bintree1,i2_5_1_3_1_1__bintree1)]]). fof(e1_5_1_3_1_1_3__bintree1,assumption,( k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)) = k3_lang1(k1_numbers,1) ), introduced(assumption,[file(bintree1,e1_5_1_3_1_1_3__bintree1)]), [interesting(0.05),axiom,file(bintree1,e1_5_1_3_1_1_3__bintree1)]). fof(e2_5_1_3_1_1_3__bintree1,plain,( k1_nat_1(k3_finseq_1(k3_lang1(k1_numbers,1)),k3_finseq_1(k3_lang1(k1_numbers,0))) = k3_finseq_1(k3_lang1(k1_numbers,1)) ), inference(mizar_by,[status(thm),assumptions([dt_c2_5__bintree1,e1_5_1_3_1_1_3__bintree1,e1_5_1_3__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc4_subset_1,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_arytm_3,cc1_fraenkel,cc2_arytm_3,cc7_trees_3,fc7_trees_3,fc8_trees_3,rc1_arytm_3,rc1_fraenkel,rc3_finseq_1,rc4_finseq_1,rc5_trees_3,rc6_finseq_1,rc7_trees_3,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_2,dt_m2_finseq_1,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc6_membered,cc9_membered,fc10_trees_3,fc13_trees_3,fc16_finseq_1,fc1_subset_1,fc2_finseq_1,fc5_membered,fc6_membered,fc9_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,spc6_arithm,t1_arithm,t1_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m1_trees_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_card_1,dt_k2_trees_1,dt_k2_xcmplx_0,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_dtconstr,cc4_membered,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc3_finseq_1,fc4_finseq_1,rc7_finseq_1,rc8_finseq_1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_r2_r2,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_r1_r2,rqRealAdd__k2_xcmplx_0__r2_r0_r2,spc2_boole,spc2_numerals,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,spc2_numerals,spc2_boole,commutativity_k1_nat_1,redefinition_k1_nat_1,redefinition_k3_finseq_1,redefinition_k3_lang1,dt_k1_nat_1,dt_k1_numbers,dt_k3_finseq_1,dt_k3_lang1,dt_k7_finseq_1,dt_c2_5__bintree1,cc1_finseq_1,fc2_membered,rc1_finseq_1,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e1_5_1_3_1_1_3__bintree1,e1_5_1_3__bintree1,t35_finseq_1]), [interesting(0.05),file(bintree1,e2_5_1_3_1_1_3__bintree1),[file(bintree1,e2_5_1_3_1_1_3__bintree1)]]). fof(e3_5_1_3_1_1_3__bintree1,plain,( k1_nat_1(1,k3_finseq_1(k3_lang1(k1_numbers,0))) = k3_finseq_1(k3_lang1(k1_numbers,1)) ), inference(mizar_by,[status(thm),assumptions([dt_c2_5__bintree1,e1_5_1_3_1_1_3__bintree1,e1_5_1_3__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc4_subset_1,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_arytm_3,cc1_fraenkel,cc2_arytm_3,fc10_membered,fc11_membered,fc9_membered,rc1_arytm_3,rc1_fraenkel,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_2,dt_m2_finseq_1,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc6_membered,cc9_membered,fc16_finseq_1,fc1_subset_1,fc2_finseq_1,fc5_membered,fc6_membered,fc8_membered,fc9_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_card_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_dtconstr,cc4_membered,fc11_finseq_1,fc12_finseq_1,fc3_finseq_1,fc4_finseq_1,fc7_membered,rc7_finseq_1,rc8_finseq_1,spc1_arithm,spc6_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_numerals,t2_subset,t4_arithm,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,commutativity_k2_xcmplx_0,involutiveness_k4_xcmplx_0,redefinition_k1_nat_1,redefinition_k3_finseq_1,redefinition_k3_lang1,redefinition_k9_finseq_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_tarski,dt_k2_relat_1,dt_k2_xcmplx_0,dt_k3_finseq_1,dt_k3_lang1,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_k9_finseq_1,cc1_finseq_1,fc2_membered,fc2_subset_1,rc1_finseq_1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r1_rm1_r0,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,rqRealAdd__k2_xcmplx_0__rm1_r1_r0,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealNeg__k4_xcmplx_0__rm1_r1,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e2_5_1_3_1_1_3__bintree1,t56_finseq_1,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r0_r1_r1]), [interesting(0.05),file(bintree1,e3_5_1_3_1_1_3__bintree1),[file(bintree1,e3_5_1_3_1_1_3__bintree1)]]). fof(e4_5_1_3_1_1_3__bintree1,plain,( k1_nat_1(1,1) = k3_finseq_1(k3_lang1(k1_numbers,1)) ), inference(mizar_by,[status(thm),assumptions([dt_c2_5__bintree1,e1_5_1_3_1_1_3__bintree1,e1_5_1_3__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc4_subset_1,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_arytm_3,cc1_fraenkel,cc2_arytm_3,fc10_membered,fc11_membered,fc9_membered,rc1_arytm_3,rc1_fraenkel,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_2,dt_m2_finseq_1,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc6_membered,cc9_membered,fc16_finseq_1,fc1_subset_1,fc2_finseq_1,fc5_membered,fc6_membered,fc8_membered,fc9_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_card_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_dtconstr,cc4_membered,fc11_finseq_1,fc12_finseq_1,fc3_finseq_1,fc4_finseq_1,fc7_membered,rc7_finseq_1,rc8_finseq_1,spc1_arithm,spc2_arithm,spc4_arithm,spc5_arithm,spc6_arithm,spc7_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_numerals,t2_arithm,t2_subset,t3_arithm,t4_arithm,t5_arithm,t6_arithm,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,commutativity_k2_xcmplx_0,commutativity_k3_xcmplx_0,involutiveness_k4_xcmplx_0,redefinition_k1_nat_1,redefinition_k3_finseq_1,redefinition_k3_lang1,redefinition_k9_finseq_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_tarski,dt_k2_relat_1,dt_k2_xcmplx_0,dt_k3_finseq_1,dt_k3_lang1,dt_k3_xcmplx_0,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_k7_xcmplx_0,dt_k9_finseq_1,cc1_finseq_1,fc2_membered,fc2_subset_1,rc1_finseq_1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_r2_r2,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r0_rm2_rm2,rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2,rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_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,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_rm1_r2,rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2,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_r1_rm2,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_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__r0_rn1d2_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,rqRealDiv__k7_xcmplx_0__rnm1d2_rn1d2_rm1,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r0_r2_r0,rqRealMult__k3_xcmplx_0__r0_rm2_r0,rqRealMult__k3_xcmplx_0__r0_rn1d2_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealMult__k3_xcmplx_0__r1_r2_r2,rqRealMult__k3_xcmplx_0__r1_rm2_rm2,rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2,rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2,rqRealMult__k3_xcmplx_0__r2_r0_r0,rqRealMult__k3_xcmplx_0__r2_rn1d2_r1,rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1,rqRealMult__k3_xcmplx_0__rm2_r0_r0,rqRealMult__k3_xcmplx_0__rm2_r1_rm2,rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1,rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1,rqRealMult__k3_xcmplx_0__rn1d2_r0_r0,rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2,rqRealMult__k3_xcmplx_0__rn1d2_r2_r1,rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1,rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2,rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1,rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1,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,e3_5_1_3_1_1_3__bintree1,t56_finseq_1,rqRealAdd__k2_xcmplx_0__r1_r1_r2,rqRealMult__k3_xcmplx_0__r2_r1_r2,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqRealDiff__k6_xcmplx_0__r1_r2_rm1,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealNeg__k4_xcmplx_0__r2_rm2,rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealDiff__k6_xcmplx_0__r2_r0_r2]), [interesting(0.05),file(bintree1,e4_5_1_3_1_1_3__bintree1),[file(bintree1,e4_5_1_3_1_1_3__bintree1)]]). fof(e5_5_1_3_1_1_3__bintree1,plain,( ~ $true ), inference(mizar_by,[status(thm),assumptions([dt_c2_5__bintree1,e1_5_1_3_1_1_3__bintree1,e1_5_1_3__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc4_subset_1,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_arytm_3,cc1_fraenkel,cc2_arytm_3,fc10_membered,fc11_membered,fc9_membered,rc1_arytm_3,rc1_fraenkel,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_2,dt_m2_finseq_1,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc6_membered,cc9_membered,fc16_finseq_1,fc1_subset_1,fc2_finseq_1,fc5_membered,fc6_membered,fc8_membered,fc9_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_card_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_dtconstr,cc4_membered,fc11_finseq_1,fc12_finseq_1,fc3_finseq_1,fc4_finseq_1,fc7_membered,rc7_finseq_1,rc8_finseq_1,spc5_arithm,spc6_arithm,spc7_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,commutativity_k2_xcmplx_0,commutativity_k3_xcmplx_0,redefinition_k1_nat_1,redefinition_k3_finseq_1,redefinition_k3_lang1,redefinition_k9_finseq_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_tarski,dt_k2_relat_1,dt_k2_xcmplx_0,dt_k3_finseq_1,dt_k3_lang1,dt_k3_xcmplx_0,dt_k9_finseq_1,cc1_finseq_1,fc2_membered,fc2_subset_1,rc1_finseq_1,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealMult__k3_xcmplx_0__r1_r2_r2,spc1_numerals,spc2_numerals,spc1_boole,spc2_boole,e4_5_1_3_1_1_3__bintree1,t56_finseq_1,rqRealAdd__k2_xcmplx_0__r1_r1_r2,rqRealMult__k3_xcmplx_0__r2_r1_r2]), [interesting(0.05),file(bintree1,e5_5_1_3_1_1_3__bintree1),[file(bintree1,e5_5_1_3_1_1_3__bintree1)]]). fof(i2_5_1_3_1_1_3__bintree1,theorem,( $true ), introduced(tautology,[file(bintree1,i2_5_1_3_1_1_3__bintree1)]), [interesting(0.05),trivial,file(bintree1,i2_5_1_3_1_1_3__bintree1)]). fof(i1_5_1_3_1_1_3__bintree1,plain,( ~ $true ), inference(conclusion,[status(thm),assumptions([dt_c2_5__bintree1,e1_5_1_3_1_1_3__bintree1,e1_5_1_3__bintree1])],[e5_5_1_3_1_1_3__bintree1,i2_5_1_3_1_1_3__bintree1]), [interesting(0.05),file(bintree1,i1_5_1_3_1_1_3__bintree1),[file(bintree1,i1_5_1_3_1_1_3__bintree1)]]). fof(i3_5_1_3_1_1__bintree1,plain,( k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)) != k3_lang1(k1_numbers,1) ), inference(discharge_asm,[status(thm),assumptions([dt_c2_5__bintree1,e1_5_1_3__bintree1]),discharge_asm(discharge,[e1_5_1_3_1_1_3__bintree1])],[e1_5_1_3_1_1_3__bintree1,i1_5_1_3_1_1_3__bintree1]), [interesting(0.2),file(bintree1,i3_5_1_3_1_1__bintree1),[file(bintree1,i3_5_1_3_1_1__bintree1)]]). fof(e1_5_1_3_1_1__bintree1,plain,( ~ ( k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)) != k1_xboole_0 & k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)) != k3_lang1(k1_numbers,0) & k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)) != k3_lang1(k1_numbers,1) ) ), inference(mizar_by,[status(thm),assumptions([dt_c2_5__bintree1,e1_5_1_3_1__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_fraenkel,cc1_relset_1,fc4_subset_1,rc1_fraenkel,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m1_finseq_2,existence_m2_relset_1,redefinition_m2_relset_1,dt_k13_finseq_1,dt_m1_finseq_1,dt_m1_finseq_2,dt_m2_relset_1,cc1_arytm_3,cc2_arytm_3,cc7_trees_3,fc16_finseq_1,fc17_membered,fc18_membered,fc19_membered,fc20_membered,fc21_membered,fc7_trees_3,fc8_trees_3,fc9_finseq_1,rc1_arytm_3,rc4_finseq_1,rc5_trees_3,rc7_trees_3,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_m1_trees_1,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_zfmisc_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_1,dt_m2_finseq_2,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_dtconstr,cc1_finseq_1,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc10_trees_3,fc12_finseq_1,fc13_finseq_1,fc13_trees_3,fc14_finseq_1,fc1_subset_1,fc3_finseq_1,fc4_finseq_1,fc5_membered,rc1_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,redefinition_k12_finseq_1,redefinition_k3_lang1,redefinition_k5_numbers,dt_k12_finseq_1,dt_k1_enumset1,dt_k1_numbers,dt_k1_xboole_0,dt_k2_trees_1,dt_k3_lang1,dt_k5_numbers,dt_k7_finseq_1,dt_c2_5__bintree1,fc2_finseq_1,fc2_membered,fc6_membered,t1_subset,t6_boole,t7_boole,spc0_numerals,spc1_numerals,spc2_numerals,spc0_boole,spc1_boole,spc2_boole,e1_5_1_3_1__bintree1,d1_enumset1,t10_modal_1]), [interesting(0.2),file(bintree1,e1_5_1_3_1_1__bintree1),[file(bintree1,e1_5_1_3_1_1__bintree1)]]). fof(i1_5_1_3_1__bintree1,plain,( ~ $true ), inference(percases,[status(thm),assumptions([e1_5_1_3__bintree1,dt_c2_5__bintree1,e1_5_1_3_1__bintree1])],[i1_5_1_3_1_1__bintree1,i2_5_1_3_1_1__bintree1,i3_5_1_3_1_1__bintree1,e1_5_1_3_1_1__bintree1]), [interesting(0.35),file(bintree1,i1_5_1_3_1__bintree1),[file(bintree1,i1_5_1_3_1__bintree1)]]). fof(e2_5_1_3__bintree1,plain,( ~ r2_hidden(k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)),k2_trees_1(2)) ), inference(discharge_asm,[status(thm),assumptions([e1_5_1_3__bintree1,dt_c2_5__bintree1]),discharge_asm(discharge,[e1_5_1_3_1__bintree1])],[e1_5_1_3_1__bintree1,i1_5_1_3_1__bintree1]), [interesting(0.5),file(bintree1,e2_5_1_3__bintree1),[file(bintree1,e2_5_1_3__bintree1)]]). fof(e3_5_1_3__bintree1,plain,( k1_trees_2(k2_trees_1(2),c2_5__bintree1) = k2_tarski(k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)),k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,1))) ), inference(mizar_by,[status(thm),assumptions([e1_5_1_3__bintree1,dt_c2_5__bintree1,e1_5__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_fraenkel,cc1_relset_1,fc4_subset_1,rc1_fraenkel,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_2,existence_m2_relset_1,redefinition_m2_relset_1,dt_k13_finseq_1,dt_m1_finseq_2,dt_m2_relset_1,cc1_arytm_3,cc2_arytm_3,cc7_trees_3,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_finseq_1,fc16_membered,fc7_trees_3,fc8_trees_3,fc9_finseq_1,rc1_arytm_3,rc3_finseq_1,rc4_finseq_1,rc5_trees_3,rc6_finseq_1,rc7_trees_3,existence_m1_finseq_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_dtconstr,cc1_finseq_1,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc10_trees_3,fc12_finseq_1,fc13_finseq_1,fc13_trees_3,fc14_finseq_1,fc1_subset_1,fc21_trees_3,fc2_finseq_1,fc3_finseq_1,fc4_finseq_1,fc4_trees_2,fc5_membered,fc6_membered,rc1_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,rc7_finseq_1,rc8_finseq_1,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,antisymmetry_r2_hidden,existence_m1_trees_1,redefinition_k12_finseq_1,redefinition_k3_lang1,redefinition_k5_numbers,redefinition_k8_finseq_1,redefinition_m1_trees_1,dt_k12_finseq_1,dt_k1_numbers,dt_k1_trees_2,dt_k2_tarski,dt_k2_trees_1,dt_k3_lang1,dt_k3_trees_1,dt_k5_numbers,dt_k7_finseq_1,dt_k8_finseq_1,dt_m1_trees_1,dt_c2_5__bintree1,cc15_membered,fc2_membered,fc3_subset_1,spc0_boole,spc1_boole,spc2_boole,t1_subset,t6_boole,t7_boole,t8_boole,spc0_numerals,spc1_numerals,spc2_numerals,spc0_boole,spc1_boole,spc2_boole,e2_5_1_3__bintree1,e1_5__bintree1,t53_modal_1]), [interesting(0.5),file(bintree1,e3_5_1_3__bintree1),[file(bintree1,e3_5_1_3__bintree1)]]). fof(i2_5_1_3__bintree1,theorem,( $true ), introduced(tautology,[file(bintree1,i2_5_1_3__bintree1)]), [interesting(0.5),trivial,file(bintree1,i2_5_1_3__bintree1)]). fof(i1_5_1_3__bintree1,plain,( k1_trees_2(k2_trees_1(2),c2_5__bintree1) = k2_tarski(k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)),k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,1))) ), inference(conclusion,[status(thm),assumptions([e1_5_1_3__bintree1,dt_c2_5__bintree1,e1_5__bintree1])],[e3_5_1_3__bintree1,i2_5_1_3__bintree1]), [interesting(0.5),file(bintree1,i1_5_1_3__bintree1),[file(bintree1,i1_5_1_3__bintree1)]]). fof(i3_5_1__bintree1,plain, ( c2_5__bintree1 = k3_lang1(k1_numbers,1) => k1_trees_2(k2_trees_1(2),c2_5__bintree1) = k2_tarski(k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)),k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,1))) ), inference(discharge_asm,[status(thm),assumptions([dt_c2_5__bintree1,e1_5__bintree1]),discharge_asm(discharge,[e1_5_1_3__bintree1])],[e1_5_1_3__bintree1,i1_5_1_3__bintree1]), [interesting(0.65),file(bintree1,i3_5_1__bintree1),[file(bintree1,i3_5_1__bintree1)]]). fof(e1_5_1__bintree1,plain,( ~ ( c2_5__bintree1 != k1_xboole_0 & c2_5__bintree1 != k3_lang1(k1_numbers,0) & c2_5__bintree1 != k3_lang1(k1_numbers,1) ) ), inference(mizar_by,[status(thm),assumptions([dt_c2_5__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_fraenkel,cc1_relset_1,fc4_subset_1,rc1_fraenkel,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m1_finseq_2,existence_m2_relset_1,redefinition_m2_relset_1,dt_k13_finseq_1,dt_m1_finseq_1,dt_m1_finseq_2,dt_m2_relset_1,cc1_arytm_3,cc2_arytm_3,cc7_trees_3,fc16_finseq_1,fc17_membered,fc18_membered,fc19_membered,fc20_membered,fc21_membered,fc9_finseq_1,rc1_arytm_3,rc4_finseq_1,rc5_trees_3,rc7_trees_3,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_m1_trees_1,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_zfmisc_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_1,dt_m2_finseq_2,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_dtconstr,cc1_finseq_1,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc10_trees_3,fc12_finseq_1,fc13_trees_3,fc1_subset_1,fc3_finseq_1,fc4_finseq_1,fc5_membered,rc1_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,redefinition_k12_finseq_1,redefinition_k3_lang1,redefinition_k5_numbers,dt_k12_finseq_1,dt_k1_enumset1,dt_k1_numbers,dt_k1_xboole_0,dt_k2_trees_1,dt_k3_lang1,dt_k5_numbers,dt_c2_5__bintree1,fc2_finseq_1,fc2_membered,fc6_membered,t1_subset,t6_boole,t7_boole,spc0_numerals,spc1_numerals,spc2_numerals,spc0_boole,spc1_boole,spc2_boole,d1_enumset1,t10_modal_1]), [interesting(0.65),file(bintree1,e1_5_1__bintree1),[file(bintree1,e1_5_1__bintree1)]]). fof(i2_5__bintree1,plain,( k1_trees_2(k2_trees_1(2),c2_5__bintree1) = k2_tarski(k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)),k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,1))) ), inference(percases,[status(thm),assumptions([e1_5__bintree1,dt_c2_5__bintree1])],[i1_5_1__bintree1,i2_5_1__bintree1,i3_5_1__bintree1,e1_5_1__bintree1]), [interesting(0.8),file(bintree1,i2_5__bintree1),[file(bintree1,i2_5__bintree1)]]). fof(i1_5__bintree1,plain, ( ~ r2_hidden(c2_5__bintree1,k3_trees_1(k2_trees_1(2))) => k1_trees_2(k2_trees_1(2),c2_5__bintree1) = k2_tarski(k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)),k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,1))) ), inference(discharge_asm,[status(thm),assumptions([dt_c2_5__bintree1]),discharge_asm(discharge,[e1_5__bintree1])],[e1_5__bintree1,i2_5__bintree1]), [interesting(0.8),file(bintree1,i1_5__bintree1),[file(bintree1,i1_5__bintree1)]]). fof(i1_5_tmp__bintree1,plain, ( m1_trees_1(c2_5__bintree1,k2_trees_1(2)) => ( ~ r2_hidden(c2_5__bintree1,k3_trees_1(k2_trees_1(2))) => k1_trees_2(k2_trees_1(2),c2_5__bintree1) = k2_tarski(k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,0)),k7_finseq_1(c2_5__bintree1,k3_lang1(k1_numbers,1))) ) ), inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c2_5__bintree1])],[dt_c2_5__bintree1,i1_5__bintree1]), [interesting(1),t7_bintree1]). fof(t7_bintree1,theorem,( v1_bintree1(k2_trees_1(2)) ), inference(let,[status(thm),assumptions([])],[i1_5_tmp__bintree1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_arytm_3,cc1_fraenkel,cc1_relset_1,cc2_arytm_3,fc4_subset_1,rc1_arytm_3,rc1_fraenkel,rc2_finseq_1,rc9_trees_2,redefinition_m2_relset_1,dt_k13_finseq_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_finseq_2,dt_m2_relset_1,cc3_arytm_3,cc7_trees_3,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_finseq_1,fc16_membered,fc5_membered,fc7_trees_3,fc8_trees_3,fc9_finseq_1,rc5_trees_3,rc7_trees_3,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_zfmisc_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_dtconstr,cc1_finseq_1,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc10_trees_3,fc12_finseq_1,fc13_finseq_1,fc13_trees_3,fc14_finseq_1,fc1_subset_1,fc21_trees_3,fc3_finseq_1,fc4_finseq_1,fc4_trees_2,rc1_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,rc7_finseq_1,rc8_finseq_1,commutativity_k2_tarski,antisymmetry_r2_hidden,redefinition_k3_lang1,redefinition_m1_trees_1,dt_k1_numbers,dt_k1_trees_2,dt_k2_tarski,dt_k2_trees_1,dt_k3_lang1,dt_k3_trees_1,dt_k7_finseq_1,dt_m1_trees_1,cc15_membered,fc2_membered,fc3_subset_1,spc0_numerals,spc1_numerals,spc2_numerals,spc0_boole,spc1_boole,spc2_boole,d2_bintree1,dh_c2_5__bintree1]), [interesting(1),file(bintree1,t7_bintree1),[file(bintree1,t7_bintree1)]]).