% Mizar ND problem: t119_finseq_3,finseq_3,2788,24 fof(dh_c1_120__finseq_3,definition, ( ( ( v1_relat_1(c1_120__finseq_3) & v1_funct_1(c1_120__finseq_3) & v1_finseq_1(c1_120__finseq_3) ) => ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( k3_finseq_1(c1_120__finseq_3) = k1_nat_1(B,1) => ( r1_xreal_0(A,C) | k1_funct_1(k2_finseq_3(A,c1_120__finseq_3),C) = k1_funct_1(c1_120__finseq_3,C) ) ) ) ) ) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ! [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) => ( k3_finseq_1(D) = k1_nat_1(F,1) => ( r1_xreal_0(E,G) | k1_funct_1(k2_finseq_3(E,D),G) = k1_funct_1(D,G) ) ) ) ) ) ) ), introduced(definition,[new_symbol(c1_120__finseq_3),file(finseq_3,c1_120__finseq_3)]), [interesting(0.8),axiom,file(finseq_3,c1_120__finseq_3)]). fof(dh_c2_120__finseq_3,definition, ( ( m2_subset_1(c2_120__finseq_3,k1_numbers,k5_numbers) => ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( k3_finseq_1(c1_120__finseq_3) = k1_nat_1(A,1) => ( r1_xreal_0(c2_120__finseq_3,B) | k1_funct_1(k2_finseq_3(c2_120__finseq_3,c1_120__finseq_3),B) = k1_funct_1(c1_120__finseq_3,B) ) ) ) ) ) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ( k3_finseq_1(c1_120__finseq_3) = k1_nat_1(D,1) => ( r1_xreal_0(C,E) | k1_funct_1(k2_finseq_3(C,c1_120__finseq_3),E) = k1_funct_1(c1_120__finseq_3,E) ) ) ) ) ) ), introduced(definition,[new_symbol(c2_120__finseq_3),file(finseq_3,c2_120__finseq_3)]), [interesting(0.8),axiom,file(finseq_3,c2_120__finseq_3)]). fof(dh_c3_120__finseq_3,definition, ( ( m2_subset_1(c3_120__finseq_3,k1_numbers,k5_numbers) => ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ( k3_finseq_1(c1_120__finseq_3) = k1_nat_1(c3_120__finseq_3,1) => ( r1_xreal_0(c2_120__finseq_3,A) | k1_funct_1(k2_finseq_3(c2_120__finseq_3,c1_120__finseq_3),A) = k1_funct_1(c1_120__finseq_3,A) ) ) ) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( k3_finseq_1(c1_120__finseq_3) = k1_nat_1(B,1) => ( r1_xreal_0(c2_120__finseq_3,C) | k1_funct_1(k2_finseq_3(c2_120__finseq_3,c1_120__finseq_3),C) = k1_funct_1(c1_120__finseq_3,C) ) ) ) ) ), introduced(definition,[new_symbol(c3_120__finseq_3),file(finseq_3,c3_120__finseq_3)]), [interesting(0.8),axiom,file(finseq_3,c3_120__finseq_3)]). fof(dh_c4_120__finseq_3,definition, ( ( m2_subset_1(c4_120__finseq_3,k1_numbers,k5_numbers) => ( k3_finseq_1(c1_120__finseq_3) = k1_nat_1(c3_120__finseq_3,1) => ( r1_xreal_0(c2_120__finseq_3,c4_120__finseq_3) | k1_funct_1(k2_finseq_3(c2_120__finseq_3,c1_120__finseq_3),c4_120__finseq_3) = k1_funct_1(c1_120__finseq_3,c4_120__finseq_3) ) ) ) => ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ( k3_finseq_1(c1_120__finseq_3) = k1_nat_1(c3_120__finseq_3,1) => ( r1_xreal_0(c2_120__finseq_3,A) | k1_funct_1(k2_finseq_3(c2_120__finseq_3,c1_120__finseq_3),A) = k1_funct_1(c1_120__finseq_3,A) ) ) ) ), introduced(definition,[new_symbol(c4_120__finseq_3),file(finseq_3,c4_120__finseq_3)]), [interesting(0.8),axiom,file(finseq_3,c4_120__finseq_3)]). fof(e1_120__finseq_3,assumption, ( k3_finseq_1(c1_120__finseq_3) = k1_nat_1(c3_120__finseq_3,1) & ~ r1_xreal_0(c2_120__finseq_3,c4_120__finseq_3) ), introduced(assumption,[file(finseq_3,e1_120__finseq_3)]), [interesting(0.8),axiom,file(finseq_3,e1_120__finseq_3)]). fof(e1_120_1_1__finseq_3,assumption,( r2_hidden(c2_120__finseq_3,k4_finseq_1(c1_120__finseq_3)) ), introduced(assumption,[file(finseq_3,e1_120_1_1__finseq_3)]), [interesting(0.5),axiom,file(finseq_3,e1_120_1_1__finseq_3)]). 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(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_relset_1,theorem,( ! [A,B,C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => v1_relat_1(C) ) ), file(relset_1,cc1_relset_1), [interesting(0.9),axiom,file(relset_1,cc1_relset_1)]). fof(fc14_finset_1,theorem,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_zfmisc_1(A,B)) ) ), file(finset_1,fc14_finset_1), [interesting(0.9),axiom,file(finset_1,fc14_finset_1)]). fof(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(rc4_funct_1,theorem,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc4_funct_1), [interesting(0.9),axiom,file(funct_1,rc4_funct_1)]). fof(reflexivity_r1_tarski,theorem,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), [interesting(0.9),axiom,file(tarski,r1_tarski)]). fof(antisymmetry_r2_hidden,theorem,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), [interesting(0.9),axiom,file(hidden,r2_hidden)]). fof(existence_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(redefinition_m2_relset_1,definition,( ! [A,B,C] : ( m2_relset_1(C,A,B) <=> m1_relset_1(C,A,B) ) ), file(relset_1,m2_relset_1), [interesting(0.9),axiom,file(relset_1,m2_relset_1)]). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]). fof(dt_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_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_xreal_0,theorem,( ! [A] : ( ( v1_xreal_0(A) & v2_xreal_0(A) ) => ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(xreal_0,cc3_xreal_0), [interesting(0.9),axiom,file(xreal_0,cc3_xreal_0)]). fof(cc6_xreal_0,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & v3_xreal_0(A) ) ) ), file(xreal_0,cc6_xreal_0), [interesting(0.9),axiom,file(xreal_0,cc6_xreal_0)]). fof(cc8_xreal_0,theorem,( ! [A] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(xreal_0,cc8_xreal_0), [interesting(0.9),axiom,file(xreal_0,cc8_xreal_0)]). fof(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(rc2_finset_1,theorem,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_ordinal1(B) & v2_ordinal1(B) & v3_ordinal1(B) & v4_ordinal2(B) & v1_finset_1(B) ) ), file(finset_1,rc2_finset_1), [interesting(0.9),axiom,file(finset_1,rc2_finset_1)]). fof(rc2_nat_1,theorem,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(A) & v3_ordinal1(A) ) ), file(nat_1,rc2_nat_1), [interesting(0.9),axiom,file(nat_1,rc2_nat_1)]). fof(rc2_xreal_0,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc2_xreal_0), [interesting(0.9),axiom,file(xreal_0,rc2_xreal_0)]). fof(rc3_finseq_1,theorem,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc3_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc3_finseq_1)]). fof(rc3_funct_1,theorem,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ), file(funct_1,rc3_funct_1), [interesting(0.9),axiom,file(funct_1,rc3_funct_1)]). fof(rc3_nat_1,theorem,( ? [A] : ( m1_subset_1(A,k5_numbers) & ~ v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(nat_1,rc3_nat_1), [interesting(0.9),axiom,file(nat_1,rc3_nat_1)]). fof(rc3_xreal_0,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & v3_xreal_0(A) ) ), file(xreal_0,rc3_xreal_0), [interesting(0.9),axiom,file(xreal_0,rc3_xreal_0)]). fof(rc4_finseq_1,theorem,( ! [A] : ? [B] : ( m1_finseq_1(B,A) & v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc4_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc4_finseq_1)]). fof(rc4_xreal_0,theorem,( ? [A] : ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc4_xreal_0), [interesting(0.9),axiom,file(xreal_0,rc4_xreal_0)]). fof(rc6_finseq_1,theorem,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc6_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc6_finseq_1)]). fof(t1_subset,theorem,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), [interesting(0.9),axiom,file(subset,t1_subset)]). fof(t3_boole,theorem,( ! [A] : k4_xboole_0(A,k1_xboole_0) = A ), file(boole,t3_boole), [interesting(0.9),axiom,file(boole,t3_boole)]). fof(t4_boole,theorem,( ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ), file(boole,t4_boole), [interesting(0.9),axiom,file(boole,t4_boole)]). fof(t4_subset,theorem,( ! [A,B,C] : ( ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) ) => m1_subset_1(A,C) ) ), file(subset,t4_subset), [interesting(0.9),axiom,file(subset,t4_subset)]). fof(t5_subset,theorem,( ! [A,B,C] : ~ ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C) ) ), file(subset,t5_subset), [interesting(0.9),axiom,file(subset,t5_subset)]). fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), [interesting(0.9),axiom,file(subset_1,m1_subset_1)]). fof(existence_m2_finseq_1,axiom,( ! [A] : ? [B] : m2_finseq_1(B,A) ), file(finseq_1,m2_finseq_1), [interesting(0.9),axiom,file(finseq_1,m2_finseq_1)]). fof(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(dt_k1_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), [interesting(0.9),axiom,file(relat_1,k1_relat_1)]). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]). fof(dt_k5_ordinal2,axiom,( $true ), file(ordinal2,k5_ordinal2), [interesting(0.9),axiom,file(ordinal2,k5_ordinal2)]). 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(cc1_finset_1,theorem,( ! [A] : ( v1_xboole_0(A) => v1_finset_1(A) ) ), file(finset_1,cc1_finset_1), [interesting(0.9),axiom,file(finset_1,cc1_finset_1)]). fof(cc1_funct_1,theorem,( ! [A] : ( v1_xboole_0(A) => v1_funct_1(A) ) ), file(funct_1,cc1_funct_1), [interesting(0.9),axiom,file(funct_1,cc1_funct_1)]). fof(cc1_nat_1,theorem,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(nat_1,cc1_nat_1), [interesting(0.9),axiom,file(nat_1,cc1_nat_1)]). fof(cc2_finset_1,theorem,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_finset_1(B) ) ) ), file(finset_1,cc2_finset_1), [interesting(0.9),axiom,file(finset_1,cc2_finset_1)]). fof(cc2_funct_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ) ), file(funct_1,cc2_funct_1), [interesting(0.9),axiom,file(funct_1,cc2_funct_1)]). fof(cc2_int_1,theorem,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_int_1(A) ) ) ), file(int_1,cc2_int_1), [interesting(0.9),axiom,file(int_1,cc2_int_1)]). fof(cc2_nat_1,theorem,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(nat_1,cc2_nat_1), [interesting(0.9),axiom,file(nat_1,cc2_nat_1)]). fof(cc2_xreal_0,theorem,( ! [A] : ( v1_xreal_0(A) => v1_xcmplx_0(A) ) ), file(xreal_0,cc2_xreal_0), [interesting(0.9),axiom,file(xreal_0,cc2_xreal_0)]). fof(cc4_int_1,theorem,( ! [A] : ( v1_int_1(A) => ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(int_1,cc4_int_1), [interesting(0.9),axiom,file(int_1,cc4_int_1)]). fof(cc4_xreal_0,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A) ) ) ), file(xreal_0,cc4_xreal_0), [interesting(0.9),axiom,file(xreal_0,cc4_xreal_0)]). fof(cc5_xreal_0,theorem,( ! [A] : ( ( v1_xreal_0(A) & v3_xreal_0(A) ) => ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) ) ) ), file(xreal_0,cc5_xreal_0), [interesting(0.9),axiom,file(xreal_0,cc5_xreal_0)]). fof(cc7_xreal_0,theorem,( ! [A] : ( ( v1_xboole_0(A) & v1_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(xreal_0,cc7_xreal_0), [interesting(0.9),axiom,file(xreal_0,cc7_xreal_0)]). fof(fc12_finset_1,theorem,( ! [A,B] : ( v1_finset_1(A) => v1_finset_1(k4_xboole_0(A,B)) ) ), file(finset_1,fc12_finset_1), [interesting(0.9),axiom,file(finset_1,fc12_finset_1)]). fof(fc17_finseq_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) => v1_finset_1(k1_relat_1(A)) ) ), file(finseq_1,fc17_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc17_finseq_1)]). fof(fc1_ordinal2,theorem, ( v1_ordinal1(k5_ordinal2) & v2_ordinal1(k5_ordinal2) & v3_ordinal1(k5_ordinal2) & ~ v1_xboole_0(k5_ordinal2) ), file(ordinal2,fc1_ordinal2), [interesting(0.9),axiom,file(ordinal2,fc1_ordinal2)]). fof(rc1_finset_1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) ) ), file(finset_1,rc1_finset_1), [interesting(0.9),axiom,file(finset_1,rc1_finset_1)]). fof(rc1_int_1,theorem,( ? [A] : ( m1_subset_1(A,k1_numbers) & v1_xcmplx_0(A) & v1_xreal_0(A) & v1_int_1(A) ) ), file(int_1,rc1_int_1), [interesting(0.9),axiom,file(int_1,rc1_int_1)]). fof(rc1_nat_1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(nat_1,rc1_nat_1), [interesting(0.9),axiom,file(nat_1,rc1_nat_1)]). fof(rc1_xreal_0,theorem,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(xreal_0,rc1_xreal_0), [interesting(0.9),axiom,file(xreal_0,rc1_xreal_0)]). fof(rc2_funct_1,theorem,( ? [A] : ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) ), file(funct_1,rc2_funct_1), [interesting(0.9),axiom,file(funct_1,rc2_funct_1)]). fof(rc2_int_1,theorem,( ? [A] : v1_int_1(A) ), file(int_1,rc2_int_1), [interesting(0.9),axiom,file(int_1,rc2_int_1)]). fof(rc3_finset_1,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc3_finset_1), [interesting(0.9),axiom,file(finset_1,rc3_finset_1)]). fof(rc4_finset_1,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc4_finset_1), [interesting(0.9),axiom,file(finset_1,rc4_finset_1)]). fof(rc7_finseq_1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc7_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc7_finseq_1)]). fof(rc8_finseq_1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc8_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc8_finseq_1)]). fof(t2_subset,theorem,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), [interesting(0.9),axiom,file(subset,t2_subset)]). fof(t3_subset,theorem,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), [interesting(0.9),axiom,file(subset,t3_subset)]). fof(t6_boole,theorem,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), [interesting(0.9),axiom,file(boole,t6_boole)]). fof(t7_boole,theorem,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), [interesting(0.9),axiom,file(boole,t7_boole)]). fof(t8_boole,theorem,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), [interesting(0.9),axiom,file(boole,t8_boole)]). fof(existence_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ? [C] : m2_subset_1(C,A,B) ) ), file(subset_1,m2_subset_1), [interesting(0.9),axiom,file(subset_1,m2_subset_1)]). fof(redefinition_k4_finseq_1,definition,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k4_finseq_1(A) = k1_relat_1(A) ) ), file(finseq_1,k4_finseq_1), [interesting(0.9),axiom,file(finseq_1,k4_finseq_1)]). fof(redefinition_k5_numbers,definition,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), [interesting(0.9),axiom,file(numbers,k5_numbers)]). 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_k14_finseq_1,axiom,( ! [A] : m2_finseq_1(k14_finseq_1(A),k5_numbers) ), file(finseq_1,k14_finseq_1), [interesting(0.9),axiom,file(finseq_1,k14_finseq_1)]). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), [interesting(0.9),axiom,file(numbers,k1_numbers)]). fof(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), [interesting(0.9),axiom,file(tarski,k1_tarski)]). fof(dt_k4_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m1_subset_1(k4_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ), file(finseq_1,k4_finseq_1), [interesting(0.9),axiom,file(finseq_1,k4_finseq_1)]). fof(dt_k4_xboole_0,axiom,( $true ), file(xboole_0,k4_xboole_0), [interesting(0.9),axiom,file(xboole_0,k4_xboole_0)]). 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_k5_relat_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => v1_relat_1(k5_relat_1(A,B)) ) ), file(relat_1,k5_relat_1), [interesting(0.9),axiom,file(relat_1,k5_relat_1)]). fof(dt_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) => m1_subset_1(C,A) ) ) ), file(subset_1,m2_subset_1), [interesting(0.9),axiom,file(subset_1,m2_subset_1)]). fof(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_xreal_0,theorem,( ! [A] : ( v4_ordinal2(A) => v1_xreal_0(A) ) ), file(xreal_0,cc1_xreal_0), [interesting(0.9),axiom,file(xreal_0,cc1_xreal_0)]). fof(cc3_int_1,theorem,( ! [A] : ( v4_ordinal2(A) => v1_int_1(A) ) ), file(int_1,cc3_int_1), [interesting(0.9),axiom,file(int_1,cc3_int_1)]). fof(cc3_nat_1,theorem,( ! [A] : ( v4_ordinal2(A) => ( v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(nat_1,cc3_nat_1), [interesting(0.9),axiom,file(nat_1,cc3_nat_1)]). fof(fc1_finset_1,theorem,( ! [A] : ( ~ v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)) ) ), file(finset_1,fc1_finset_1), [interesting(0.9),axiom,file(finset_1,fc1_finset_1)]). fof(fc1_funct_1,theorem,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => ( v1_relat_1(k5_relat_1(A,B)) & v1_funct_1(k5_relat_1(A,B)) ) ) ), file(funct_1,fc1_funct_1), [interesting(0.9),axiom,file(funct_1,fc1_funct_1)]). fof(rc1_finseq_1,theorem,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc1_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc1_finseq_1)]). fof(rc1_funct_1,theorem,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc1_funct_1), [interesting(0.9),axiom,file(funct_1,rc1_funct_1)]). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), [interesting(0.9),axiom,file(funct_1,k1_funct_1)]). fof(dt_k2_finseq_3,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( v1_relat_1(k2_finseq_3(A,B)) & v1_funct_1(k2_finseq_3(A,B)) & v1_finseq_1(k2_finseq_3(A,B)) ) ) ), file(finseq_3,k2_finseq_3), [interesting(0.9),axiom,file(finseq_3,k2_finseq_3)]). fof(dt_c1_120__finseq_3,assumption, ( v1_relat_1(c1_120__finseq_3) & v1_funct_1(c1_120__finseq_3) & v1_finseq_1(c1_120__finseq_3) ), introduced(assumption,[file(finseq_3,c1_120__finseq_3)]), [interesting(0.8),axiom,file(finseq_3,c1_120__finseq_3)]). fof(dt_c2_120__finseq_3,assumption,( m2_subset_1(c2_120__finseq_3,k1_numbers,k5_numbers) ), introduced(assumption,[file(finseq_3,c2_120__finseq_3)]), [interesting(0.8),axiom,file(finseq_3,c2_120__finseq_3)]). fof(dt_c4_120__finseq_3,assumption,( m2_subset_1(c4_120__finseq_3,k1_numbers,k5_numbers) ), introduced(assumption,[file(finseq_3,c4_120__finseq_3)]), [interesting(0.8),axiom,file(finseq_3,c4_120__finseq_3)]). fof(d2_finseq_3,definition,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => k2_finseq_3(A,B) = k5_relat_1(k14_finseq_1(k4_xboole_0(k4_finseq_1(B),k1_tarski(A))),B) ) ) ), file(finseq_3,d2_finseq_3), [interesting(0.9),axiom,file(finseq_3,d2_finseq_3)]). fof(e1_120_1_1_1_1_1__finseq_3,assumption,( r1_xreal_0(1,c4_120__finseq_3) ), introduced(assumption,[file(finseq_3,e1_120_1_1_1_1_1__finseq_3)]), [interesting(0.05),axiom,file(finseq_3,e1_120_1_1_1_1_1__finseq_3)]). fof(fc10_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v2_xreal_0(k2_xcmplx_0(B,A)) & ~ v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc10_xreal_0), [interesting(0.9),axiom,file(xreal_0,fc10_xreal_0)]). fof(fc11_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v2_xreal_0(k2_xcmplx_0(A,B)) & v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc11_xreal_0), [interesting(0.9),axiom,file(xreal_0,fc11_xreal_0)]). fof(fc12_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & ~ v2_xreal_0(k2_xcmplx_0(B,A)) & v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc12_xreal_0), [interesting(0.9),axiom,file(xreal_0,fc12_xreal_0)]). fof(fc14_xreal_0,theorem,( ! [A] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & ~ v2_xreal_0(k4_xcmplx_0(A)) ) ) ), file(xreal_0,fc14_xreal_0), [interesting(0.9),axiom,file(xreal_0,fc14_xreal_0)]). fof(fc15_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & ~ v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc15_xreal_0), [interesting(0.9),axiom,file(xreal_0,fc15_xreal_0)]). fof(fc16_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & ~ v2_xreal_0(k6_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc16_xreal_0), [interesting(0.9),axiom,file(xreal_0,fc16_xreal_0)]). fof(fc19_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & ~ v2_xreal_0(k6_xcmplx_0(A,B)) & v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc19_xreal_0), [interesting(0.9),axiom,file(xreal_0,fc19_xreal_0)]). fof(fc1_int_1,theorem,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_int_1(k2_xcmplx_0(A,B)) ) ) ), file(int_1,fc1_int_1), [interesting(0.9),axiom,file(int_1,fc1_int_1)]). fof(fc20_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k6_xcmplx_0(B,A)) & v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & v2_xreal_0(k6_xcmplx_0(B,A)) & ~ v3_xreal_0(k6_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc20_xreal_0), [interesting(0.9),axiom,file(xreal_0,fc20_xreal_0)]). fof(fc3_int_1,theorem,( ! [A] : ( v1_int_1(A) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & v1_int_1(k4_xcmplx_0(A)) ) ) ), file(int_1,fc3_int_1), [interesting(0.9),axiom,file(int_1,fc3_int_1)]). fof(fc4_int_1,theorem,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_int_1(k6_xcmplx_0(A,B)) ) ) ), file(int_1,fc4_int_1), [interesting(0.9),axiom,file(int_1,fc4_int_1)]). fof(fc6_int_1,theorem,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & v1_int_1(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v1_int_1(k2_xcmplx_0(B,A)) ) ) ), file(int_1,fc6_int_1), [interesting(0.9),axiom,file(int_1,fc6_int_1)]). fof(fc7_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc7_xreal_0), [interesting(0.9),axiom,file(xreal_0,fc7_xreal_0)]). fof(fc8_int_1,theorem,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & v1_int_1(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & v1_int_1(k6_xcmplx_0(B,A)) ) ) ), file(int_1,fc8_int_1), [interesting(0.9),axiom,file(int_1,fc8_int_1)]). fof(fc9_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v2_xreal_0(k2_xcmplx_0(A,B)) & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc9_xreal_0), [interesting(0.9),axiom,file(xreal_0,fc9_xreal_0)]). fof(t2_real,theorem,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & v3_xreal_0(B) ) => v3_xreal_0(A) ) ) ) ), file(real,t2_real), [interesting(0.9),axiom,file(real,t2_real)]). fof(t3_real,theorem,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xreal_0(A,B) & ~ v3_xreal_0(A) & v3_xreal_0(B) ) ) ) ), file(real,t3_real), [interesting(0.9),axiom,file(real,t3_real)]). fof(t5_real,theorem,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) => ( v1_xboole_0(B) | v3_xreal_0(A) | v2_xreal_0(B) ) ) ) ) ), file(real,t5_real), [interesting(0.9),axiom,file(real,t5_real)]). fof(t6_real,theorem,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) => ( v1_xboole_0(A) | v2_xreal_0(B) | v3_xreal_0(A) ) ) ) ) ), file(real,t6_real), [interesting(0.9),axiom,file(real,t6_real)]). fof(t7_real,theorem,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v2_xreal_0(A) & ~ v3_xreal_0(B) ) ) ) ), file(real,t7_real), [interesting(0.9),axiom,file(real,t7_real)]). fof(t8_real,theorem,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v3_xreal_0(B) & ~ v2_xreal_0(A) ) ) ) ), file(real,t8_real), [interesting(0.9),axiom,file(real,t8_real)]). fof(commutativity_k2_xcmplx_0,theorem,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ), file(xcmplx_0,k2_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k2_xcmplx_0)]). fof(dt_k1_card_1,axiom,( ! [A] : v1_card_1(k1_card_1(A)) ), file(card_1,k1_card_1), [interesting(0.9),axiom,file(card_1,k1_card_1)]). fof(dt_k1_finseq_1,axiom,( $true ), file(finseq_1,k1_finseq_1), [interesting(0.9),axiom,file(finseq_1,k1_finseq_1)]). fof(dt_k2_xcmplx_0,axiom,( $true ), file(xcmplx_0,k2_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k2_xcmplx_0)]). fof(fc13_xreal_0,theorem,( ! [A] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) ) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & ~ v3_xreal_0(k4_xcmplx_0(A)) ) ) ), file(xreal_0,fc13_xreal_0), [interesting(0.9),axiom,file(xreal_0,fc13_xreal_0)]). fof(fc17_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v2_xreal_0(k6_xcmplx_0(A,B)) & ~ v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc17_xreal_0), [interesting(0.9),axiom,file(xreal_0,fc17_xreal_0)]). fof(fc18_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k6_xcmplx_0(B,A)) & v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & ~ v2_xreal_0(k6_xcmplx_0(B,A)) & v3_xreal_0(k6_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc18_xreal_0), [interesting(0.9),axiom,file(xreal_0,fc18_xreal_0)]). fof(fc1_finseq_1,theorem,( ! [A] : ( v4_ordinal2(A) => v1_finset_1(k1_finseq_1(A)) ) ), file(finseq_1,fc1_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc1_finseq_1)]). fof(fc1_nat_1,theorem,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => ( v4_ordinal2(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(nat_1,fc1_nat_1), [interesting(0.9),axiom,file(nat_1,fc1_nat_1)]). fof(fc1_xreal_0,theorem,( ! [A] : ( v1_xreal_0(A) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) ) ) ), file(xreal_0,fc1_xreal_0), [interesting(0.9),axiom,file(xreal_0,fc1_xreal_0)]). fof(fc3_nat_1,theorem,( ! [A,B] : ( ( v4_ordinal2(A) & ~ v1_xboole_0(B) & v4_ordinal2(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v4_ordinal2(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(nat_1,fc3_nat_1), [interesting(0.9),axiom,file(nat_1,fc3_nat_1)]). fof(fc3_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc3_xreal_0), [interesting(0.9),axiom,file(xreal_0,fc3_xreal_0)]). fof(fc4_nat_1,theorem,( ! [A,B] : ( ( v4_ordinal2(A) & ~ v1_xboole_0(B) & v4_ordinal2(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v4_ordinal2(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(nat_1,fc4_nat_1), [interesting(0.9),axiom,file(nat_1,fc4_nat_1)]). fof(fc5_int_1,theorem,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & ~ v2_xreal_0(k4_xcmplx_0(A)) & v1_int_1(k4_xcmplx_0(A)) ) ) ), file(int_1,fc5_int_1), [interesting(0.9),axiom,file(int_1,fc5_int_1)]). fof(fc5_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc5_xreal_0), [interesting(0.9),axiom,file(xreal_0,fc5_xreal_0)]). fof(fc8_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v2_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc8_xreal_0), [interesting(0.9),axiom,file(xreal_0,fc8_xreal_0)]). fof(fc9_int_1,theorem,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_int_1(k6_xcmplx_0(A,B)) ) ) ), file(int_1,fc9_int_1), [interesting(0.9),axiom,file(int_1,fc9_int_1)]). fof(rqRealAdd__k2_xcmplx_0__r0_r0_r0,theorem,( k2_xcmplx_0(0,0) = 0 ), file(arithm,rqRealAdd__k2_xcmplx_0__r0_r0_r0), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_r0_r0)]). fof(rqRealAdd__k2_xcmplx_0__r0_r1_r1,theorem,( k2_xcmplx_0(0,1) = 1 ), file(arithm,rqRealAdd__k2_xcmplx_0__r0_r1_r1), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_r1_r1)]). fof(rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,theorem,( k2_xcmplx_0(0,k4_xcmplx_0(1)) = k4_xcmplx_0(1) ), file(arithm,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1)]). fof(rqRealAdd__k2_xcmplx_0__r1_r0_r1,theorem,( k2_xcmplx_0(1,0) = 1 ), file(arithm,rqRealAdd__k2_xcmplx_0__r1_r0_r1), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_r0_r1)]). fof(rqRealAdd__k2_xcmplx_0__r1_rm1_r0,theorem,( k2_xcmplx_0(1,k4_xcmplx_0(1)) = 0 ), file(arithm,rqRealAdd__k2_xcmplx_0__r1_rm1_r0), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_rm1_r0)]). fof(rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,theorem,( k2_xcmplx_0(k4_xcmplx_0(1),0) = k4_xcmplx_0(1) ), file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1)]). fof(rqRealAdd__k2_xcmplx_0__rm1_r1_r0,theorem,( k2_xcmplx_0(k4_xcmplx_0(1),1) = 0 ), file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r1_r0), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r1_r0)]). fof(spc1_arithm,theorem,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k2_xcmplx_0(A,k4_xcmplx_0(B)) = k6_xcmplx_0(A,B) ) ), file(arithm,spc1_arithm), [interesting(0.9),axiom,file(arithm,spc1_arithm)]). fof(spc6_arithm,theorem,( ! [A,B,C] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) ) => k2_xcmplx_0(k2_xcmplx_0(A,B),C) = k2_xcmplx_0(A,k2_xcmplx_0(B,C)) ) ), file(arithm,spc6_arithm), [interesting(0.9),axiom,file(arithm,spc6_arithm)]). fof(spc8_arithm,theorem,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k2_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(B)) = k4_xcmplx_0(k2_xcmplx_0(A,B)) ) ), file(arithm,spc8_arithm), [interesting(0.9),axiom,file(arithm,spc8_arithm)]). fof(spc9_arithm,theorem,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k6_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(B)) = k6_xcmplx_0(B,A) ) ), file(arithm,spc9_arithm), [interesting(0.9),axiom,file(arithm,spc9_arithm)]). fof(t1_arithm,theorem,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(A,0) = A ) ), file(arithm,t1_arithm), [interesting(0.9),axiom,file(arithm,t1_arithm)]). fof(t1_numerals,theorem,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), [interesting(0.9),axiom,file(numerals,t1_numerals)]). fof(t1_real,theorem,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & v2_xreal_0(A) ) => v2_xreal_0(B) ) ) ) ), file(real,t1_real), [interesting(0.9),axiom,file(real,t1_real)]). fof(t4_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(t4_real,theorem,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xreal_0(A,B) & ~ v2_xreal_0(B) & v2_xreal_0(A) ) ) ) ), file(real,t4_real), [interesting(0.9),axiom,file(real,t4_real)]). fof(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(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(reflexivity_r1_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => r1_xreal_0(A,A) ) ), file(xreal_0,r1_xreal_0), [interesting(0.9),axiom,file(xreal_0,r1_xreal_0)]). fof(connectedness_r1_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( r1_xreal_0(A,B) | r1_xreal_0(B,A) ) ) ), file(xreal_0,r1_xreal_0), [interesting(0.9),axiom,file(xreal_0,r1_xreal_0)]). fof(redefinition_k1_nat_1,definition,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k1_nat_1(A,B) = k2_xcmplx_0(A,B) ) ), file(nat_1,k1_nat_1), [interesting(0.9),axiom,file(nat_1,k1_nat_1)]). fof(redefinition_k2_finseq_1,definition,( ! [A] : ( v4_ordinal2(A) => k2_finseq_1(A) = k1_finseq_1(A) ) ), file(finseq_1,k2_finseq_1), [interesting(0.9),axiom,file(finseq_1,k2_finseq_1)]). fof(redefinition_k3_finseq_1,definition,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k3_finseq_1(A) = k1_card_1(A) ) ), file(finseq_1,k3_finseq_1), [interesting(0.9),axiom,file(finseq_1,k3_finseq_1)]). fof(dt_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => m2_subset_1(k1_nat_1(A,B),k1_numbers,k5_numbers) ) ), file(nat_1,k1_nat_1), [interesting(0.9),axiom,file(nat_1,k1_nat_1)]). fof(dt_k2_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => m1_subset_1(k2_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ), file(finseq_1,k2_finseq_1), [interesting(0.9),axiom,file(finseq_1,k2_finseq_1)]). fof(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_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_c3_120__finseq_3,assumption,( m2_subset_1(c3_120__finseq_3,k1_numbers,k5_numbers) ), introduced(assumption,[file(finseq_3,c3_120__finseq_3)]), [interesting(0.8),axiom,file(finseq_3,c3_120__finseq_3)]). fof(rqLessOrEqual__r1_xreal_0__r0_r0,theorem,( r1_xreal_0(0,0) ), file(arithm,rqLessOrEqual__r1_xreal_0__r0_r0), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_r0)]). fof(rqLessOrEqual__r1_xreal_0__r0_r1,theorem,( r1_xreal_0(0,1) ), file(arithm,rqLessOrEqual__r1_xreal_0__r0_r1), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_r1)]). fof(rqLessOrEqual__r1_xreal_0__r0_rm1,theorem,( ~ r1_xreal_0(0,k4_xcmplx_0(1)) ), file(arithm,rqLessOrEqual__r1_xreal_0__r0_rm1), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_rm1)]). fof(rqLessOrEqual__r1_xreal_0__r1_r0,theorem,( ~ r1_xreal_0(1,0) ), file(arithm,rqLessOrEqual__r1_xreal_0__r1_r0), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_r0)]). fof(rqLessOrEqual__r1_xreal_0__r1_r1,theorem,( r1_xreal_0(1,1) ), file(arithm,rqLessOrEqual__r1_xreal_0__r1_r1), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_r1)]). fof(rqLessOrEqual__r1_xreal_0__r1_rm1,theorem,( ~ r1_xreal_0(1,k4_xcmplx_0(1)) ), file(arithm,rqLessOrEqual__r1_xreal_0__r1_rm1), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_rm1)]). fof(rqLessOrEqual__r1_xreal_0__rm1_r0,theorem,( r1_xreal_0(k4_xcmplx_0(1),0) ), file(arithm,rqLessOrEqual__r1_xreal_0__rm1_r0), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm1_r0)]). fof(rqLessOrEqual__r1_xreal_0__rm1_r1,theorem,( r1_xreal_0(k4_xcmplx_0(1),1) ), file(arithm,rqLessOrEqual__r1_xreal_0__rm1_r1), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm1_r1)]). fof(rqLessOrEqual__r1_xreal_0__rm1_rm1,theorem,( r1_xreal_0(k4_xcmplx_0(1),k4_xcmplx_0(1)) ), file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rm1), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rm1)]). fof(rqRealDiff__k6_xcmplx_0__r0_r0_r0,theorem,( k6_xcmplx_0(0,0) = 0 ), file(arithm,rqRealDiff__k6_xcmplx_0__r0_r0_r0), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_r0_r0)]). fof(rqRealDiff__k6_xcmplx_0__r0_r1_rm1,theorem,( k6_xcmplx_0(0,1) = k4_xcmplx_0(1) ), file(arithm,rqRealDiff__k6_xcmplx_0__r0_r1_rm1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_r1_rm1)]). fof(rqRealDiff__k6_xcmplx_0__r0_rm1_r1,theorem,( k6_xcmplx_0(0,k4_xcmplx_0(1)) = 1 ), file(arithm,rqRealDiff__k6_xcmplx_0__r0_rm1_r1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_rm1_r1)]). fof(rqRealDiff__k6_xcmplx_0__r1_r0_r1,theorem,( k6_xcmplx_0(1,0) = 1 ), file(arithm,rqRealDiff__k6_xcmplx_0__r1_r0_r1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_r0_r1)]). fof(rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,theorem,( k6_xcmplx_0(k4_xcmplx_0(1),0) = k4_xcmplx_0(1) ), file(arithm,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1)]). fof(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(spc0_numerals,theorem, ( v2_xreal_0(0) & m2_subset_1(0,k1_numbers,k5_numbers) & m1_subset_1(0,k5_numbers) & m1_subset_1(0,k1_numbers) ), file(numerals,spc0_numerals), [interesting(0.9),axiom,file(numerals,spc0_numerals)]). fof(spc1_numerals,theorem, ( v2_xreal_0(1) & m2_subset_1(1,k1_numbers,k5_numbers) & m1_subset_1(1,k5_numbers) & m1_subset_1(1,k1_numbers) ), file(numerals,spc1_numerals), [interesting(0.9),axiom,file(numerals,spc1_numerals)]). fof(spc0_boole,theorem,( v1_xboole_0(0) ), file(boole,spc0_boole), [interesting(0.9),axiom,file(boole,spc0_boole)]). fof(spc1_boole,theorem,( ~ v1_xboole_0(1) ), file(boole,spc1_boole), [interesting(0.9),axiom,file(boole,spc1_boole)]). fof(fc27_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) & ~ v2_xreal_0(k7_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc27_xreal_0), [interesting(0.9),axiom,file(xreal_0,fc27_xreal_0)]). fof(fc28_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k7_xcmplx_0(B,A)) & v1_xreal_0(k7_xcmplx_0(B,A)) & ~ v2_xreal_0(k7_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc28_xreal_0), [interesting(0.9),axiom,file(xreal_0,fc28_xreal_0)]). fof(fc29_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) & ~ v3_xreal_0(k7_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc29_xreal_0), [interesting(0.9),axiom,file(xreal_0,fc29_xreal_0)]). fof(fc30_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) & ~ v3_xreal_0(k7_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc30_xreal_0), [interesting(0.9),axiom,file(xreal_0,fc30_xreal_0)]). fof(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(fc6_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc6_xreal_0), [interesting(0.9),axiom,file(xreal_0,fc6_xreal_0)]). fof(rqRealDiv__k7_xcmplx_0__r0_r1_r0,theorem,( k7_xcmplx_0(0,1) = 0 ), file(arithm,rqRealDiv__k7_xcmplx_0__r0_r1_r0), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r0_r1_r0)]). fof(rqRealDiv__k7_xcmplx_0__r1_r1_r1,theorem,( k7_xcmplx_0(1,1) = 1 ), file(arithm,rqRealDiv__k7_xcmplx_0__r1_r1_r1), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_r1_r1)]). fof(rqRealDiv__k7_xcmplx_0__rm1_r1_rm1,theorem,( k7_xcmplx_0(k4_xcmplx_0(1),1) = k4_xcmplx_0(1) ), file(arithm,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1)]). fof(t27_finseq_3,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v4_ordinal2(B) => ( r2_hidden(B,k4_finseq_1(A)) <=> ( r1_xreal_0(1,B) & r1_xreal_0(B,k3_finseq_1(A)) ) ) ) ) ), file(finseq_3,t27_finseq_3), [interesting(0.9),axiom,file(finseq_3,t27_finseq_3)]). fof(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(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(rqRealNeg__k4_xcmplx_0__rm1_r1,theorem,( k4_xcmplx_0(k4_xcmplx_0(1)) = 1 ), file(arithm,rqRealNeg__k4_xcmplx_0__rm1_r1), [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rm1_r1)]). fof(rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,theorem,( k6_xcmplx_0(k4_xcmplx_0(1),k4_xcmplx_0(1)) = 0 ), file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0)]). fof(e2_120_1_1_1_1_1__finseq_3,plain,( r1_xreal_0(c2_120__finseq_3,k1_nat_1(c3_120__finseq_3,1)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_120__finseq_3,dt_c2_120__finseq_3,dt_c3_120__finseq_3,dt_c4_120__finseq_3,e1_120__finseq_3,e1_120_1_1__finseq_3])],[rc4_funct_1,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k5_ordinal2,fc1_ordinal2,fc2_finseq_1,rc2_finset_1,rc2_nat_1,rc3_finseq_1,rc3_funct_1,rc3_nat_1,rc6_finseq_1,commutativity_k2_xcmplx_0,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_xcmplx_0,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc2_finset_1,cc2_funct_1,cc2_int_1,cc2_nat_1,cc2_xreal_0,cc3_xreal_0,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc13_xreal_0,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc17_finseq_1,fc17_xreal_0,fc18_xreal_0,fc19_xreal_0,fc1_int_1,fc1_nat_1,fc1_xreal_0,fc20_xreal_0,fc3_int_1,fc3_nat_1,fc3_xreal_0,fc4_int_1,fc4_nat_1,fc5_int_1,fc5_xreal_0,fc6_int_1,fc7_xreal_0,fc8_int_1,fc8_xreal_0,fc9_int_1,fc9_xreal_0,rc1_finset_1,rc1_int_1,rc1_nat_1,rc1_xreal_0,rc2_funct_1,rc2_int_1,rc2_xreal_0,rc3_finset_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc7_finseq_1,rc8_finseq_1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_rm1_r0,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,rqRealAdd__k2_xcmplx_0__rm1_r1_r0,spc1_arithm,spc6_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_numerals,t1_real,t2_real,t2_subset,t3_real,t3_subset,t4_arithm,t4_real,t4_subset,t5_real,t5_subset,t6_boole,t6_real,t7_real,t8_boole,t8_real,commutativity_k1_nat_1,involutiveness_k4_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,redefinition_k1_nat_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,dt_k1_nat_1,dt_k3_finseq_1,dt_k4_finseq_1,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_c1_120__finseq_3,dt_c2_120__finseq_3,dt_c3_120__finseq_3,dt_c4_120__finseq_3,cc1_finseq_1,cc1_xreal_0,cc3_int_1,cc3_nat_1,rc1_finseq_1,rc1_funct_1,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r0_rm1,rqLessOrEqual__r1_xreal_0__r1_r0,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r1_rm1,rqLessOrEqual__r1_xreal_0__rm1_r0,rqLessOrEqual__r1_xreal_0__rm1_r1,rqLessOrEqual__r1_xreal_0__rm1_rm1,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealNeg__k4_xcmplx_0__r0_r0,t1_subset,t7_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e1_120__finseq_3,e1_120_1_1__finseq_3,t27_finseq_3,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0]), [interesting(0.05),file(finseq_3,e2_120_1_1_1_1_1__finseq_3),[file(finseq_3,e2_120_1_1_1_1_1__finseq_3)]]). fof(t2_xreal_1,theorem,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xreal_0(A,B) & r1_xreal_0(B,C) ) => r1_xreal_0(A,C) ) ) ) ) ), file(xreal_1,t2_xreal_1), [interesting(0.9),axiom,file(xreal_1,t2_xreal_1)]). fof(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(e3_120_1_1_1_1_1__finseq_3,plain,( ~ r1_xreal_0(k1_nat_1(c3_120__finseq_3,1),c4_120__finseq_3) ), inference(mizar_by,[status(thm),assumptions([dt_c1_120__finseq_3,dt_c2_120__finseq_3,dt_c3_120__finseq_3,dt_c4_120__finseq_3,e1_120_1_1__finseq_3,e1_120__finseq_3])],[reflexivity_r1_tarski,rc4_funct_1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc1_xreal_0,cc2_finset_1,cc3_int_1,cc3_nat_1,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc19_xreal_0,fc1_int_1,fc1_nat_1,fc1_ordinal2,fc20_xreal_0,fc27_xreal_0,fc28_xreal_0,fc29_xreal_0,fc2_finseq_1,fc3_int_1,fc3_nat_1,fc4_int_1,fc4_nat_1,fc6_int_1,fc7_xreal_0,fc8_int_1,fc9_xreal_0,rc1_finset_1,rc1_int_1,rc1_nat_1,rc2_finset_1,rc2_int_1,rc2_nat_1,rc2_xreal_0,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc3_nat_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,commutativity_k2_xcmplx_0,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_numbers,dt_k2_xcmplx_0,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc2_funct_1,cc2_int_1,cc2_nat_1,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc13_xreal_0,fc17_xreal_0,fc18_xreal_0,fc30_xreal_0,fc3_xreal_0,fc5_int_1,fc8_xreal_0,fc9_int_1,rc1_finseq_1,rc1_funct_1,rc1_xreal_0,rc2_funct_1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_rm1_r0,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,rqRealAdd__k2_xcmplx_0__rm1_r1_r0,spc1_arithm,spc6_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_numerals,t1_real,t2_subset,t4_arithm,t4_real,t5_arithm,t6_arithm,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,involutiveness_k4_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k1_nat_1,redefinition_k3_finseq_1,dt_k1_nat_1,dt_k3_finseq_1,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_k7_xcmplx_0,dt_c1_120__finseq_3,dt_c2_120__finseq_3,dt_c3_120__finseq_3,dt_c4_120__finseq_3,cc2_xreal_0,fc1_xreal_0,fc5_xreal_0,fc6_xreal_0,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r0_rm1,rqLessOrEqual__r1_xreal_0__r1_r0,rqLessOrEqual__r1_xreal_0__r1_rm1,rqLessOrEqual__r1_xreal_0__rm1_r0,rqLessOrEqual__r1_xreal_0__rm1_r1,rqLessOrEqual__r1_xreal_0__rm1_rm1,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealDiv__k7_xcmplx_0__r0_r1_r0,rqRealDiv__k7_xcmplx_0__r1_r1_r1,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1,rqRealNeg__k4_xcmplx_0__r0_r0,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e2_120_1_1_1_1_1__finseq_3,e1_120__finseq_3,t2_xreal_1,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqLessOrEqual__r1_xreal_0__r1_r1]), [interesting(0.05),file(finseq_3,e3_120_1_1_1_1_1__finseq_3),[file(finseq_3,e3_120_1_1_1_1_1__finseq_3)]]). fof(t38_nat_1,theorem,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ( ~ r1_xreal_0(k2_xcmplx_0(B,1),A) <=> r1_xreal_0(A,B) ) ) ) ), file(nat_1,t38_nat_1), [interesting(0.9),axiom,file(nat_1,t38_nat_1)]). fof(e4_120_1_1_1_1_1__finseq_3,plain,( r1_xreal_0(c4_120__finseq_3,c3_120__finseq_3) ), inference(mizar_by,[status(thm),assumptions([dt_c1_120__finseq_3,dt_c2_120__finseq_3,dt_c3_120__finseq_3,dt_c4_120__finseq_3,e1_120_1_1__finseq_3,e1_120__finseq_3])],[reflexivity_r1_tarski,cc1_finseq_1,cc2_funct_1,rc1_finseq_1,rc1_funct_1,rc2_finset_1,rc2_funct_1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc2_finset_1,fc1_ordinal2,fc2_finseq_1,rc1_finset_1,rc2_nat_1,rc3_finset_1,rc3_nat_1,rc4_finset_1,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc2_int_1,cc2_nat_1,cc2_xreal_0,cc3_xreal_0,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc1_int_1,fc3_nat_1,fc3_xreal_0,fc4_nat_1,fc6_int_1,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,rc1_int_1,rc1_nat_1,rc1_xreal_0,rc2_int_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,spc6_arithm,t1_real,t2_real,t2_subset,t3_real,t4_real,t5_real,t6_boole,t6_real,t7_boole,t7_real,t8_boole,t8_real,commutativity_k1_nat_1,commutativity_k2_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k1_nat_1,dt_k1_nat_1,dt_k2_xcmplx_0,dt_c3_120__finseq_3,dt_c4_120__finseq_3,cc1_xreal_0,cc3_int_1,cc3_nat_1,fc1_nat_1,rqLessOrEqual__r1_xreal_0__r1_r1,spc1_numerals,spc1_boole,e3_120_1_1_1_1_1__finseq_3,t38_nat_1]), [interesting(0.05),file(finseq_3,e4_120_1_1_1_1_1__finseq_3),[file(finseq_3,e4_120_1_1_1_1_1__finseq_3)]]). fof(t3_finseq_1,theorem,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ( r2_hidden(A,k2_finseq_1(B)) <=> ( r1_xreal_0(1,A) & r1_xreal_0(A,B) ) ) ) ) ), file(finseq_1,t3_finseq_1), [interesting(0.9),axiom,file(finseq_1,t3_finseq_1)]). fof(e5_120_1_1_1_1_1__finseq_3,plain,( r2_hidden(c4_120__finseq_3,k2_finseq_1(c3_120__finseq_3)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_120__finseq_3,dt_c2_120__finseq_3,dt_c3_120__finseq_3,dt_c4_120__finseq_3,e1_120_1_1__finseq_3,e1_120__finseq_3,e1_120_1_1_1_1_1__finseq_3])],[cc1_finseq_1,cc2_funct_1,rc1_finseq_1,rc1_funct_1,rc2_finset_1,rc2_funct_1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k5_ordinal2,cc2_finset_1,fc1_ordinal2,fc2_finseq_1,rc1_finset_1,rc2_nat_1,rc3_finset_1,rc3_nat_1,rc4_finset_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_finseq_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc2_int_1,cc2_nat_1,cc2_xreal_0,cc3_xreal_0,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc1_finseq_1,rc1_int_1,rc1_nat_1,rc1_xreal_0,rc2_int_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_real,t2_real,t2_subset,t3_real,t3_subset,t4_real,t4_subset,t5_real,t5_subset,t6_boole,t6_real,t7_real,t8_boole,t8_real,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,redefinition_k2_finseq_1,dt_k2_finseq_1,dt_c3_120__finseq_3,dt_c4_120__finseq_3,cc1_xreal_0,cc3_int_1,cc3_nat_1,t1_subset,t7_boole,spc1_numerals,spc1_boole,e4_120_1_1_1_1_1__finseq_3,e1_120_1_1_1_1_1__finseq_3,t3_finseq_1,rqLessOrEqual__r1_xreal_0__r1_r1]), [interesting(0.05),file(finseq_3,e5_120_1_1_1_1_1__finseq_3),[file(finseq_3,e5_120_1_1_1_1_1__finseq_3)]]). fof(d3_finseq_1,definition,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( B = k3_finseq_1(A) <=> k2_finseq_1(B) = k1_relat_1(A) ) ) ) ), file(finseq_1,d3_finseq_1), [interesting(0.9),axiom,file(finseq_1,d3_finseq_1)]). fof(e6_120_1_1_1_1_1__finseq_3,plain, ( k4_finseq_1(c1_120__finseq_3) = k2_finseq_1(k3_finseq_1(c1_120__finseq_3)) & k4_finseq_1(k14_finseq_1(k4_xboole_0(k4_finseq_1(c1_120__finseq_3),k1_tarski(c2_120__finseq_3)))) = k2_finseq_1(k3_finseq_1(k14_finseq_1(k4_xboole_0(k4_finseq_1(c1_120__finseq_3),k1_tarski(c2_120__finseq_3))))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_120__finseq_3,dt_c2_120__finseq_3])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,fc14_finset_1,rc2_finseq_1,rc2_xreal_0,rc3_xreal_0,rc4_funct_1,rc4_xreal_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_m1_finseq_1,dt_m2_relset_1,cc2_xreal_0,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc2_finseq_1,rc1_int_1,rc1_nat_1,rc1_xreal_0,rc2_finset_1,rc2_int_1,rc2_nat_1,rc3_finseq_1,rc3_funct_1,rc3_nat_1,rc4_finseq_1,rc6_finseq_1,t1_subset,t3_boole,t4_boole,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,dt_m2_finseq_1,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc1_xreal_0,cc2_finset_1,cc2_funct_1,cc2_int_1,cc2_nat_1,cc3_int_1,cc3_nat_1,fc12_finset_1,fc17_finseq_1,fc1_finseq_1,fc1_ordinal2,rc1_finset_1,rc2_funct_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,existence_m2_subset_1,redefinition_k2_finseq_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k14_finseq_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_tarski,dt_k2_finseq_1,dt_k3_finseq_1,dt_k4_finseq_1,dt_k4_xboole_0,dt_k5_numbers,dt_m2_subset_1,dt_c1_120__finseq_3,dt_c2_120__finseq_3,cc1_finseq_1,fc1_finset_1,rc1_finseq_1,rc1_funct_1,d3_finseq_1]), [interesting(0.05),file(finseq_3,e6_120_1_1_1_1_1__finseq_3),[file(finseq_3,e6_120_1_1_1_1_1__finseq_3)]]). fof(t117_finseq_3,theorem,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( ( D = k1_nat_1(C,1) & r2_hidden(B,k2_finseq_1(D)) & r2_hidden(A,k2_finseq_1(C)) ) => ( ( r1_xreal_0(1,A) => ( r1_xreal_0(B,A) | k1_funct_1(k14_finseq_1(k4_xboole_0(k2_finseq_1(D),k1_tarski(B))),A) = A ) ) & ( ( r1_xreal_0(B,A) & r1_xreal_0(A,C) ) => k1_funct_1(k14_finseq_1(k4_xboole_0(k2_finseq_1(D),k1_tarski(B))),A) = k1_nat_1(A,1) ) ) ) ) ) ) ) ), file(finseq_3,t117_finseq_3), [interesting(0.9),axiom,file(finseq_3,t117_finseq_3)]). fof(e10_120_1_1_1_1_1__finseq_3,plain, ( r1_xreal_0(1,c4_120__finseq_3) => ( r1_xreal_0(c2_120__finseq_3,c4_120__finseq_3) | k1_funct_1(k14_finseq_1(k4_xboole_0(k4_finseq_1(c1_120__finseq_3),k1_tarski(c2_120__finseq_3))),c4_120__finseq_3) = c4_120__finseq_3 ) ), inference(mizar_by,[status(thm),assumptions([dt_c3_120__finseq_3,dt_c4_120__finseq_3,e1_120_1_1__finseq_3,e1_120__finseq_3,e1_120_1_1_1_1_1__finseq_3,dt_c1_120__finseq_3,dt_c2_120__finseq_3])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,rc2_finseq_1,rc4_funct_1,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_m1_finseq_1,dt_m2_relset_1,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc19_xreal_0,fc1_int_1,fc20_xreal_0,fc2_finseq_1,fc3_int_1,fc4_int_1,fc6_int_1,fc7_xreal_0,fc8_int_1,fc9_xreal_0,rc1_int_1,rc2_finset_1,rc2_int_1,rc2_nat_1,rc2_xreal_0,rc3_finseq_1,rc3_funct_1,rc3_nat_1,rc3_xreal_0,rc4_finseq_1,rc4_xreal_0,rc6_finseq_1,t2_real,t3_boole,t3_real,t4_boole,t5_real,t6_real,t7_real,t8_real,commutativity_k2_xcmplx_0,existence_m1_subset_1,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_xcmplx_0,dt_k5_ordinal2,dt_m1_subset_1,dt_m2_finseq_1,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc1_xreal_0,cc2_finset_1,cc2_funct_1,cc2_int_1,cc2_nat_1,cc2_xreal_0,cc3_int_1,cc3_nat_1,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc12_finset_1,fc13_xreal_0,fc17_finseq_1,fc17_xreal_0,fc18_xreal_0,fc1_finseq_1,fc1_nat_1,fc1_ordinal2,fc1_xreal_0,fc3_nat_1,fc3_xreal_0,fc4_nat_1,fc5_int_1,fc5_xreal_0,fc8_xreal_0,fc9_int_1,rc1_finseq_1,rc1_finset_1,rc1_funct_1,rc1_nat_1,rc1_xreal_0,rc2_funct_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_rm1_r0,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,rqRealAdd__k2_xcmplx_0__rm1_r1_r0,spc1_arithm,spc6_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_numerals,t1_real,t2_subset,t3_subset,t4_arithm,t4_real,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k1_nat_1,involutiveness_k4_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m2_subset_1,redefinition_k1_nat_1,redefinition_k2_finseq_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k14_finseq_1,dt_k1_funct_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_tarski,dt_k2_finseq_1,dt_k3_finseq_1,dt_k4_finseq_1,dt_k4_xboole_0,dt_k4_xcmplx_0,dt_k5_numbers,dt_k6_xcmplx_0,dt_m2_subset_1,dt_c1_120__finseq_3,dt_c2_120__finseq_3,dt_c3_120__finseq_3,dt_c4_120__finseq_3,fc1_finset_1,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r0_rm1,rqLessOrEqual__r1_xreal_0__r1_r0,rqLessOrEqual__r1_xreal_0__r1_rm1,rqLessOrEqual__r1_xreal_0__rm1_r0,rqLessOrEqual__r1_xreal_0__rm1_r1,rqLessOrEqual__r1_xreal_0__rm1_rm1,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealNeg__k4_xcmplx_0__r0_r0,t1_subset,t7_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e1_120__finseq_3,e1_120_1_1__finseq_3,e5_120_1_1_1_1_1__finseq_3,e6_120_1_1_1_1_1__finseq_3,t117_finseq_3,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqLessOrEqual__r1_xreal_0__r1_r1]), [interesting(0.05),file(finseq_3,e10_120_1_1_1_1_1__finseq_3),[file(finseq_3,e10_120_1_1_1_1_1__finseq_3)]]). fof(fc11_finseq_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_finset_1(A) ) => v1_finset_1(k2_relat_1(A)) ) ), file(finseq_1,fc11_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc11_finseq_1)]). fof(dt_k2_relat_1,axiom,( $true ), file(relat_1,k2_relat_1), [interesting(0.9),axiom,file(relat_1,k2_relat_1)]). fof(t36_xboole_1,theorem,( ! [A,B] : r1_tarski(k4_xboole_0(A,B),A) ), file(xboole_1,t36_xboole_1), [interesting(0.9),axiom,file(xboole_1,t36_xboole_1)]). fof(e7_120_1_1_1_1_1__finseq_3,plain, ( k2_finseq_3(c2_120__finseq_3,c1_120__finseq_3) = k5_relat_1(k14_finseq_1(k4_xboole_0(k4_finseq_1(c1_120__finseq_3),k1_tarski(c2_120__finseq_3))),c1_120__finseq_3) & r1_tarski(k4_xboole_0(k4_finseq_1(c1_120__finseq_3),k1_tarski(c2_120__finseq_3)),k2_finseq_1(k3_finseq_1(c1_120__finseq_3))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_120__finseq_3,dt_c2_120__finseq_3])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,fc14_finset_1,rc2_finseq_1,rc2_xreal_0,rc3_xreal_0,rc4_funct_1,rc4_xreal_0,antisymmetry_r2_hidden,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,cc2_xreal_0,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc1_ordinal2,fc2_finseq_1,rc1_int_1,rc1_nat_1,rc1_xreal_0,rc2_finset_1,rc2_int_1,rc2_nat_1,rc3_finseq_1,rc3_funct_1,rc3_nat_1,rc4_finseq_1,rc6_finseq_1,t1_subset,t3_boole,t4_boole,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_subset_1,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc1_xreal_0,cc2_finset_1,cc2_funct_1,cc2_int_1,cc2_nat_1,cc3_int_1,cc3_nat_1,fc12_finset_1,fc17_finseq_1,fc1_finseq_1,fc1_funct_1,rc1_finseq_1,rc1_finset_1,rc1_funct_1,rc2_funct_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t6_boole,t7_boole,t8_boole,reflexivity_r1_tarski,redefinition_k2_finseq_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,dt_k14_finseq_1,dt_k1_tarski,dt_k2_finseq_1,dt_k2_finseq_3,dt_k3_finseq_1,dt_k4_finseq_1,dt_k4_xboole_0,dt_k5_relat_1,dt_c1_120__finseq_3,dt_c2_120__finseq_3,fc1_finset_1,t3_subset,d2_finseq_3,e6_120_1_1_1_1_1__finseq_3,t36_xboole_1]), [interesting(0.05),file(finseq_3,e7_120_1_1_1_1_1__finseq_3),[file(finseq_3,e7_120_1_1_1_1_1__finseq_3)]]). fof(d13_finseq_1,definition,( ! [A] : ( ? [B] : ( v4_ordinal2(B) & r1_tarski(A,k2_finseq_1(B)) ) => ! [B] : ( m2_finseq_1(B,k5_numbers) => ( B = k14_finseq_1(A) <=> ( k2_relat_1(B) = A & ! [C] : ( v4_ordinal2(C) => ! [D] : ( v4_ordinal2(D) => ! [E] : ( v4_ordinal2(E) => ! [F] : ( v4_ordinal2(F) => ~ ( r1_xreal_0(1,C) & ~ r1_xreal_0(D,C) & r1_xreal_0(D,k3_finseq_1(B)) & E = k1_funct_1(B,C) & F = k1_funct_1(B,D) & r1_xreal_0(F,E) ) ) ) ) ) ) ) ) ) ), file(finseq_1,d13_finseq_1), [interesting(0.9),axiom,file(finseq_1,d13_finseq_1)]). fof(e8_120_1_1_1_1_1__finseq_3,plain,( k2_relat_1(k14_finseq_1(k4_xboole_0(k4_finseq_1(c1_120__finseq_3),k1_tarski(c2_120__finseq_3)))) = k4_xboole_0(k4_finseq_1(c1_120__finseq_3),k1_tarski(c2_120__finseq_3)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_120__finseq_3,dt_c2_120__finseq_3])],[rc4_funct_1,antisymmetry_r2_hidden,existence_m1_relset_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,fc2_finseq_1,rc2_finseq_1,rc2_finset_1,rc2_nat_1,rc3_finseq_1,rc3_funct_1,rc3_nat_1,rc4_finseq_1,rc6_finseq_1,t1_subset,t3_boole,t4_boole,t4_subset,t5_subset,existence_m1_finseq_1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc2_finset_1,cc2_funct_1,cc2_int_1,cc2_nat_1,cc2_xreal_0,cc3_xreal_0,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc11_finseq_1,fc12_finset_1,fc17_finseq_1,fc1_finseq_1,fc1_funct_1,fc1_ordinal2,rc1_finseq_1,rc1_finset_1,rc1_funct_1,rc1_int_1,rc1_nat_1,rc1_xreal_0,rc2_funct_1,rc2_int_1,rc2_xreal_0,rc3_finset_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc7_finseq_1,rc8_finseq_1,t1_real,t2_real,t2_subset,t3_real,t4_real,t5_real,t6_boole,t6_real,t7_boole,t7_real,t8_boole,t8_real,reflexivity_r1_tarski,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m2_finseq_1,redefinition_k2_finseq_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k14_finseq_1,dt_k1_funct_1,dt_k1_tarski,dt_k2_finseq_1,dt_k2_finseq_3,dt_k2_relat_1,dt_k3_finseq_1,dt_k4_finseq_1,dt_k4_xboole_0,dt_k5_numbers,dt_k5_relat_1,dt_m2_finseq_1,dt_c1_120__finseq_3,dt_c2_120__finseq_3,cc1_xreal_0,cc3_int_1,cc3_nat_1,fc1_finset_1,rqLessOrEqual__r1_xreal_0__r1_r1,t3_subset,d2_finseq_3,spc1_numerals,spc1_boole,e7_120_1_1_1_1_1__finseq_3,d13_finseq_1]), [interesting(0.05),file(finseq_3,e8_120_1_1_1_1_1__finseq_3),[file(finseq_3,e8_120_1_1_1_1_1__finseq_3)]]). fof(t116_finseq_3,theorem,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ! [C] : ( v4_ordinal2(C) => ( ( A = k2_xcmplx_0(B,1) & r2_hidden(C,k2_finseq_1(A)) ) => k3_finseq_1(k14_finseq_1(k4_xboole_0(k2_finseq_1(A),k1_tarski(C)))) = B ) ) ) ) ), file(finseq_3,t116_finseq_3), [interesting(0.9),axiom,file(finseq_3,t116_finseq_3)]). fof(t46_relat_1,theorem,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( r1_tarski(k2_relat_1(A),k1_relat_1(B)) => k1_relat_1(k5_relat_1(A,B)) = k1_relat_1(A) ) ) ) ), file(relat_1,t46_relat_1), [interesting(0.9),axiom,file(relat_1,t46_relat_1)]). fof(e9_120_1_1_1_1_1__finseq_3,plain, ( k1_relat_1(k5_relat_1(k14_finseq_1(k4_xboole_0(k4_finseq_1(c1_120__finseq_3),k1_tarski(c2_120__finseq_3))),c1_120__finseq_3)) = k4_finseq_1(k14_finseq_1(k4_xboole_0(k4_finseq_1(c1_120__finseq_3),k1_tarski(c2_120__finseq_3)))) & k3_finseq_1(k14_finseq_1(k4_xboole_0(k4_finseq_1(c1_120__finseq_3),k1_tarski(c2_120__finseq_3)))) = c3_120__finseq_3 ), inference(mizar_by,[status(thm),assumptions([dt_c3_120__finseq_3,dt_c4_120__finseq_3,e1_120__finseq_3,e1_120_1_1__finseq_3,dt_c1_120__finseq_3,dt_c2_120__finseq_3])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,rc2_finseq_1,rc4_funct_1,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,fc1_ordinal2,fc2_finseq_1,rc2_finset_1,rc2_nat_1,rc3_finseq_1,rc3_funct_1,rc3_nat_1,rc4_finseq_1,rc6_finseq_1,t3_boole,t4_boole,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_subset_1,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc2_finset_1,cc2_funct_1,cc2_int_1,cc2_nat_1,cc2_xreal_0,cc3_xreal_0,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_finseq_1,fc11_xreal_0,fc12_finset_1,fc12_xreal_0,fc13_xreal_0,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc17_finseq_1,fc17_xreal_0,fc18_xreal_0,fc19_xreal_0,fc1_finseq_1,fc1_funct_1,fc1_int_1,fc1_xreal_0,fc20_xreal_0,fc3_int_1,fc3_nat_1,fc3_xreal_0,fc4_int_1,fc4_nat_1,fc5_int_1,fc5_xreal_0,fc6_int_1,fc7_xreal_0,fc8_int_1,fc8_xreal_0,fc9_int_1,fc9_xreal_0,rc1_finseq_1,rc1_finset_1,rc1_funct_1,rc1_int_1,rc1_nat_1,rc1_xreal_0,rc2_funct_1,rc2_int_1,rc2_xreal_0,rc3_finset_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc7_finseq_1,rc8_finseq_1,spc1_arithm,spc6_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_numerals,t1_real,t2_real,t2_subset,t3_real,t4_arithm,t4_real,t4_subset,t5_real,t5_subset,t6_boole,t6_real,t7_real,t8_boole,t8_real,commutativity_k1_nat_1,commutativity_k2_xcmplx_0,involutiveness_k4_xcmplx_0,reflexivity_r1_tarski,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,redefinition_k1_nat_1,redefinition_k2_finseq_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,dt_k14_finseq_1,dt_k1_nat_1,dt_k1_relat_1,dt_k1_tarski,dt_k2_finseq_1,dt_k2_finseq_3,dt_k2_relat_1,dt_k2_xcmplx_0,dt_k3_finseq_1,dt_k4_finseq_1,dt_k4_xboole_0,dt_k4_xcmplx_0,dt_k5_relat_1,dt_k6_xcmplx_0,dt_c1_120__finseq_3,dt_c2_120__finseq_3,dt_c3_120__finseq_3,dt_c4_120__finseq_3,cc1_xreal_0,cc3_int_1,cc3_nat_1,fc1_finset_1,fc1_nat_1,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r0_rm1,rqLessOrEqual__r1_xreal_0__r1_r0,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r1_rm1,rqLessOrEqual__r1_xreal_0__rm1_r0,rqLessOrEqual__r1_xreal_0__rm1_r1,rqLessOrEqual__r1_xreal_0__rm1_rm1,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,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealNeg__k4_xcmplx_0__r0_r0,t1_subset,t3_subset,t7_boole,d2_finseq_3,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e8_120_1_1_1_1_1__finseq_3,e1_120__finseq_3,e1_120_1_1__finseq_3,e6_120_1_1_1_1_1__finseq_3,e7_120_1_1_1_1_1__finseq_3,t116_finseq_3,t46_relat_1,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0]), [interesting(0.05),file(finseq_3,e9_120_1_1_1_1_1__finseq_3),[file(finseq_3,e9_120_1_1_1_1_1__finseq_3)]]). fof(t22_funct_1,theorem,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(A,k1_relat_1(k5_relat_1(C,B))) => k1_funct_1(k5_relat_1(C,B),A) = k1_funct_1(B,k1_funct_1(C,A)) ) ) ) ), file(funct_1,t22_funct_1), [interesting(0.9),axiom,file(funct_1,t22_funct_1)]). fof(e11_120_1_1_1_1_1__finseq_3,plain,( k1_funct_1(k2_finseq_3(c2_120__finseq_3,c1_120__finseq_3),c4_120__finseq_3) = k1_funct_1(c1_120__finseq_3,c4_120__finseq_3) ), inference(mizar_by,[status(thm),assumptions([e1_120_1_1_1_1_1__finseq_3,dt_c3_120__finseq_3,dt_c4_120__finseq_3,e1_120__finseq_3,e1_120_1_1__finseq_3,dt_c1_120__finseq_3,dt_c2_120__finseq_3])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,rc2_finseq_1,rc4_funct_1,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc19_xreal_0,fc1_int_1,fc1_ordinal2,fc20_xreal_0,fc2_finseq_1,fc3_int_1,fc4_int_1,fc6_int_1,fc7_xreal_0,fc8_int_1,fc9_xreal_0,rc1_int_1,rc2_finset_1,rc2_int_1,rc2_nat_1,rc2_xreal_0,rc3_finseq_1,rc3_funct_1,rc3_nat_1,rc3_xreal_0,rc4_finseq_1,rc4_xreal_0,rc6_finseq_1,t2_real,t3_boole,t3_real,t4_boole,t5_real,t6_real,t7_real,t8_real,commutativity_k2_xcmplx_0,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_xcmplx_0,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_subset_1,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc1_xreal_0,cc2_finset_1,cc2_funct_1,cc2_int_1,cc2_nat_1,cc2_xreal_0,cc3_int_1,cc3_nat_1,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc12_finset_1,fc13_xreal_0,fc17_finseq_1,fc17_xreal_0,fc18_xreal_0,fc1_finseq_1,fc1_nat_1,fc1_xreal_0,fc3_nat_1,fc3_xreal_0,fc4_nat_1,fc5_int_1,fc5_xreal_0,fc8_xreal_0,fc9_int_1,rc1_finseq_1,rc1_finset_1,rc1_nat_1,rc1_xreal_0,rc2_funct_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_rm1_r0,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,rqRealAdd__k2_xcmplx_0__rm1_r1_r0,spc1_arithm,spc6_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_numerals,t1_real,t2_subset,t3_subset,t4_arithm,t4_real,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k1_nat_1,involutiveness_k4_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,redefinition_k1_nat_1,redefinition_k2_finseq_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,dt_k14_finseq_1,dt_k1_funct_1,dt_k1_nat_1,dt_k1_relat_1,dt_k1_tarski,dt_k2_finseq_1,dt_k2_finseq_3,dt_k3_finseq_1,dt_k4_finseq_1,dt_k4_xboole_0,dt_k4_xcmplx_0,dt_k5_relat_1,dt_k6_xcmplx_0,dt_c1_120__finseq_3,dt_c2_120__finseq_3,dt_c3_120__finseq_3,dt_c4_120__finseq_3,fc1_finset_1,fc1_funct_1,rc1_funct_1,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r0_rm1,rqLessOrEqual__r1_xreal_0__r1_r0,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r1_rm1,rqLessOrEqual__r1_xreal_0__rm1_r0,rqLessOrEqual__r1_xreal_0__rm1_r1,rqLessOrEqual__r1_xreal_0__rm1_rm1,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealNeg__k4_xcmplx_0__r0_r0,t1_subset,t7_boole,d2_finseq_3,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e10_120_1_1_1_1_1__finseq_3,e1_120__finseq_3,e1_120_1_1_1_1_1__finseq_3,e5_120_1_1_1_1_1__finseq_3,e6_120_1_1_1_1_1__finseq_3,e9_120_1_1_1_1_1__finseq_3,t22_funct_1,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealDiff__k6_xcmplx_0__r1_r1_r0]), [interesting(0.05),file(finseq_3,e11_120_1_1_1_1_1__finseq_3),[file(finseq_3,e11_120_1_1_1_1_1__finseq_3)]]). fof(i2_120_1_1_1_1_1__finseq_3,theorem,( $true ), introduced(tautology,[file(finseq_3,i2_120_1_1_1_1_1__finseq_3)]), [interesting(0.05),trivial,file(finseq_3,i2_120_1_1_1_1_1__finseq_3)]). fof(i1_120_1_1_1_1_1__finseq_3,plain,( k1_funct_1(k2_finseq_3(c2_120__finseq_3,c1_120__finseq_3),c4_120__finseq_3) = k1_funct_1(c1_120__finseq_3,c4_120__finseq_3) ), inference(conclusion,[status(thm),assumptions([e1_120_1_1_1_1_1__finseq_3,dt_c3_120__finseq_3,dt_c4_120__finseq_3,e1_120__finseq_3,e1_120_1_1__finseq_3,dt_c1_120__finseq_3,dt_c2_120__finseq_3])],[e11_120_1_1_1_1_1__finseq_3,i2_120_1_1_1_1_1__finseq_3]), [interesting(0.05),file(finseq_3,i1_120_1_1_1_1_1__finseq_3),[file(finseq_3,i1_120_1_1_1_1_1__finseq_3)]]). fof(i1_120_1_1_1_1__finseq_3,plain, ( r1_xreal_0(1,c4_120__finseq_3) => k1_funct_1(k2_finseq_3(c2_120__finseq_3,c1_120__finseq_3),c4_120__finseq_3) = k1_funct_1(c1_120__finseq_3,c4_120__finseq_3) ), inference(discharge_asm,[status(thm),assumptions([dt_c3_120__finseq_3,dt_c4_120__finseq_3,e1_120__finseq_3,e1_120_1_1__finseq_3,dt_c1_120__finseq_3,dt_c2_120__finseq_3]),discharge_asm(discharge,[e1_120_1_1_1_1_1__finseq_3])],[e1_120_1_1_1_1_1__finseq_3,i1_120_1_1_1_1_1__finseq_3]), [interesting(0.2),file(finseq_3,i1_120_1_1_1_1__finseq_3),[file(finseq_3,i1_120_1_1_1_1__finseq_3)]]). fof(e1_120_1_1_1_1_2__finseq_3,assumption,( ~ r1_xreal_0(1,c4_120__finseq_3) ), introduced(assumption,[file(finseq_3,e1_120_1_1_1_1_2__finseq_3)]), [interesting(0.05),axiom,file(finseq_3,e1_120_1_1_1_1_2__finseq_3)]). 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(dt_k2_tarski,axiom,( $true ), file(tarski,k2_tarski), [interesting(0.9),axiom,file(tarski,k2_tarski)]). fof(fc2_finset_1,theorem,( ! [A,B] : ( ~ v1_xboole_0(k2_tarski(A,B)) & v1_finset_1(k2_tarski(A,B)) ) ), file(finset_1,fc2_finset_1), [interesting(0.9),axiom,file(finset_1,fc2_finset_1)]). fof(dt_k4_tarski,axiom,( $true ), file(tarski,k4_tarski), [interesting(0.9),axiom,file(tarski,k4_tarski)]). fof(d5_tarski,definition,( ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ), file(tarski,d5_tarski), [interesting(0.9),axiom,file(tarski,d5_tarski)]). fof(t118_finseq_3,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v4_ordinal2(B) => ! [C] : ( v4_ordinal2(C) => ( ( k3_finseq_1(A) = k2_xcmplx_0(C,1) & r2_hidden(B,k4_finseq_1(A)) ) => k3_finseq_1(k2_finseq_3(B,A)) = C ) ) ) ) ), file(finseq_3,t118_finseq_3), [interesting(0.9),axiom,file(finseq_3,t118_finseq_3)]). fof(e4_120_1_1_1_1_2__finseq_3,plain,( k2_finseq_1(k3_finseq_1(k2_finseq_3(c2_120__finseq_3,c1_120__finseq_3))) = k2_finseq_1(c3_120__finseq_3) ), inference(mizar_by,[status(thm),assumptions([dt_c1_120__finseq_3,dt_c2_120__finseq_3,dt_c3_120__finseq_3,dt_c4_120__finseq_3,e1_120__finseq_3,e1_120_1_1__finseq_3])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,rc2_finseq_1,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,rc4_finseq_1,rc4_funct_1,reflexivity_r1_tarski,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_xboole_0,dt_k5_ordinal2,dt_m2_finseq_1,fc1_ordinal2,fc2_finseq_1,rc2_finset_1,rc2_nat_1,rc3_finseq_1,rc3_funct_1,rc3_nat_1,rc6_finseq_1,t3_boole,t4_boole,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k14_finseq_1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k4_xboole_0,dt_k5_numbers,dt_k5_relat_1,dt_m1_subset_1,dt_m2_subset_1,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc2_finset_1,cc2_funct_1,cc2_int_1,cc2_nat_1,cc2_xreal_0,cc3_xreal_0,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_finset_1,fc12_xreal_0,fc13_xreal_0,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc17_finseq_1,fc17_xreal_0,fc18_xreal_0,fc19_xreal_0,fc1_finseq_1,fc1_finset_1,fc1_funct_1,fc1_int_1,fc1_xreal_0,fc20_xreal_0,fc3_int_1,fc3_nat_1,fc3_xreal_0,fc4_int_1,fc4_nat_1,fc5_int_1,fc5_xreal_0,fc6_int_1,fc7_xreal_0,fc8_int_1,fc8_xreal_0,fc9_int_1,fc9_xreal_0,rc1_finset_1,rc1_int_1,rc1_nat_1,rc1_xreal_0,rc2_funct_1,rc2_int_1,rc2_xreal_0,rc3_finset_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc7_finseq_1,rc8_finseq_1,spc1_arithm,spc6_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_numerals,t1_real,t2_real,t2_subset,t3_real,t3_subset,t4_arithm,t4_real,t4_subset,t5_real,t5_subset,t6_boole,t6_real,t7_real,t8_boole,t8_real,commutativity_k1_nat_1,commutativity_k2_xcmplx_0,involutiveness_k4_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,redefinition_k1_nat_1,redefinition_k2_finseq_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,dt_k1_nat_1,dt_k2_finseq_1,dt_k2_finseq_3,dt_k2_xcmplx_0,dt_k3_finseq_1,dt_k4_finseq_1,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_c1_120__finseq_3,dt_c2_120__finseq_3,dt_c3_120__finseq_3,dt_c4_120__finseq_3,cc1_finseq_1,cc1_xreal_0,cc3_int_1,cc3_nat_1,fc1_nat_1,rc1_finseq_1,rc1_funct_1,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r0_rm1,rqLessOrEqual__r1_xreal_0__r1_r0,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r1_rm1,rqLessOrEqual__r1_xreal_0__rm1_r0,rqLessOrEqual__r1_xreal_0__rm1_r1,rqLessOrEqual__r1_xreal_0__rm1_rm1,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,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealNeg__k4_xcmplx_0__r0_r0,t1_subset,t7_boole,d2_finseq_3,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e1_120__finseq_3,e1_120_1_1__finseq_3,t118_finseq_3,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0]), [interesting(0.05),file(finseq_3,e4_120_1_1_1_1_2__finseq_3),[file(finseq_3,e4_120_1_1_1_1_2__finseq_3)]]). fof(e5_120_1_1_1_1_2__finseq_3,plain,( k4_finseq_1(k2_finseq_3(c2_120__finseq_3,c1_120__finseq_3)) = k2_finseq_1(c3_120__finseq_3) ), inference(mizar_by,[status(thm),assumptions([dt_c1_120__finseq_3,dt_c2_120__finseq_3,dt_c3_120__finseq_3,dt_c4_120__finseq_3,e1_120__finseq_3,e1_120_1_1__finseq_3])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,rc2_finseq_1,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_finseq_1,rc4_funct_1,rc4_xreal_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_xboole_0,dt_m2_finseq_1,cc2_xreal_0,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc2_finseq_1,rc1_int_1,rc1_nat_1,rc1_xreal_0,rc2_finset_1,rc2_int_1,rc2_nat_1,rc3_finseq_1,rc3_funct_1,rc3_nat_1,rc6_finseq_1,t1_subset,t3_boole,t4_boole,t4_subset,t5_subset,existence_m1_subset_1,dt_k14_finseq_1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k4_xboole_0,dt_k5_ordinal2,dt_k5_relat_1,dt_m1_subset_1,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc1_xreal_0,cc2_finset_1,cc2_funct_1,cc2_int_1,cc2_nat_1,cc3_int_1,cc3_nat_1,fc12_finset_1,fc17_finseq_1,fc1_finseq_1,fc1_finset_1,fc1_funct_1,fc1_ordinal2,rc1_finset_1,rc2_funct_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,existence_m2_subset_1,redefinition_k2_finseq_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_relat_1,dt_k2_finseq_1,dt_k2_finseq_3,dt_k3_finseq_1,dt_k4_finseq_1,dt_k5_numbers,dt_m2_subset_1,dt_c1_120__finseq_3,dt_c2_120__finseq_3,dt_c3_120__finseq_3,cc1_finseq_1,rc1_finseq_1,rc1_funct_1,d2_finseq_3,e4_120_1_1_1_1_2__finseq_3,d3_finseq_1]), [interesting(0.05),file(finseq_3,e5_120_1_1_1_1_2__finseq_3),[file(finseq_3,e5_120_1_1_1_1_2__finseq_3)]]). fof(e6_120_1_1_1_1_2__finseq_3,plain,( ~ r2_hidden(c4_120__finseq_3,k4_finseq_1(k2_finseq_3(c2_120__finseq_3,c1_120__finseq_3))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_120__finseq_3,dt_c2_120__finseq_3,dt_c3_120__finseq_3,dt_c4_120__finseq_3,e1_120__finseq_3,e1_120_1_1__finseq_3,e1_120_1_1_1_1_2__finseq_3])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,rc2_finseq_1,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,rc4_finseq_1,rc4_funct_1,reflexivity_r1_tarski,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_xboole_0,dt_k5_ordinal2,dt_m2_finseq_1,cc2_finset_1,fc12_finset_1,fc17_finseq_1,fc1_ordinal2,fc2_finseq_1,rc1_finset_1,rc2_finset_1,rc2_nat_1,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc3_nat_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t3_boole,t4_boole,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k14_finseq_1,dt_k1_finseq_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k4_xboole_0,dt_k5_numbers,dt_k5_relat_1,dt_m1_subset_1,dt_m2_subset_1,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc2_funct_1,cc2_int_1,cc2_nat_1,cc2_xreal_0,cc3_xreal_0,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc1_finseq_1,fc1_finset_1,fc1_funct_1,rc1_finseq_1,rc1_funct_1,rc1_int_1,rc1_nat_1,rc1_xreal_0,rc2_funct_1,rc2_int_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_real,t2_real,t2_subset,t3_real,t3_subset,t4_real,t4_subset,t5_real,t5_subset,t6_boole,t6_real,t7_real,t8_boole,t8_real,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,redefinition_k2_finseq_1,redefinition_k4_finseq_1,dt_k2_finseq_1,dt_k2_finseq_3,dt_k4_finseq_1,dt_c1_120__finseq_3,dt_c2_120__finseq_3,dt_c3_120__finseq_3,dt_c4_120__finseq_3,cc1_xreal_0,cc3_int_1,cc3_nat_1,rqLessOrEqual__r1_xreal_0__r1_r1,t1_subset,t7_boole,d2_finseq_3,spc1_numerals,spc1_boole,e5_120_1_1_1_1_2__finseq_3,e1_120_1_1_1_1_2__finseq_3,t3_finseq_1]), [interesting(0.05),file(finseq_3,e6_120_1_1_1_1_2__finseq_3),[file(finseq_3,e6_120_1_1_1_1_2__finseq_3)]]). fof(e2_120_1_1_1_1_2__finseq_3,plain,( ~ r2_hidden(c4_120__finseq_3,k4_finseq_1(c1_120__finseq_3)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_120__finseq_3,dt_c4_120__finseq_3,e1_120_1_1_1_1_2__finseq_3])],[rc4_funct_1,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k5_ordinal2,fc1_ordinal2,fc2_finseq_1,rc2_finset_1,rc2_nat_1,rc3_finseq_1,rc3_funct_1,rc3_nat_1,rc6_finseq_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc2_finset_1,cc2_funct_1,cc2_int_1,cc2_nat_1,cc2_xreal_0,cc3_xreal_0,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc17_finseq_1,rc1_finset_1,rc1_int_1,rc1_nat_1,rc1_xreal_0,rc2_funct_1,rc2_int_1,rc2_xreal_0,rc3_finset_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc7_finseq_1,rc8_finseq_1,t1_real,t2_real,t2_subset,t3_real,t3_subset,t4_real,t4_subset,t5_real,t5_subset,t6_boole,t6_real,t7_real,t8_boole,t8_real,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,redefinition_k3_finseq_1,redefinition_k4_finseq_1,dt_k3_finseq_1,dt_k4_finseq_1,dt_c1_120__finseq_3,dt_c4_120__finseq_3,cc1_finseq_1,cc1_xreal_0,cc3_int_1,cc3_nat_1,rc1_finseq_1,rc1_funct_1,rqLessOrEqual__r1_xreal_0__r1_r1,t1_subset,t7_boole,spc1_numerals,spc1_boole,e1_120_1_1_1_1_2__finseq_3,t27_finseq_3]), [interesting(0.05),file(finseq_3,e2_120_1_1_1_1_2__finseq_3),[file(finseq_3,e2_120_1_1_1_1_2__finseq_3)]]). fof(d4_funct_1,definition,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B,C] : ( ( r2_hidden(B,k1_relat_1(A)) => ( C = k1_funct_1(A,B) <=> r2_hidden(k4_tarski(B,C),A) ) ) & ( ~ r2_hidden(B,k1_relat_1(A)) => ( C = k1_funct_1(A,B) <=> C = k1_xboole_0 ) ) ) ) ), file(funct_1,d4_funct_1), [interesting(0.9),axiom,file(funct_1,d4_funct_1)]). fof(e3_120_1_1_1_1_2__finseq_3,plain,( k1_funct_1(c1_120__finseq_3,c4_120__finseq_3) = k1_xboole_0 ), inference(mizar_by,[status(thm),assumptions([dt_c1_120__finseq_3,dt_c4_120__finseq_3,e1_120_1_1_1_1_2__finseq_3])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,reflexivity_r1_tarski,dt_k5_ordinal2,cc1_xreal_0,cc2_xreal_0,cc3_int_1,cc3_nat_1,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc1_ordinal2,rc1_int_1,rc1_nat_1,rc1_xreal_0,rc2_finset_1,rc2_int_1,rc2_nat_1,rc3_nat_1,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_tarski,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc2_finset_1,cc2_funct_1,cc2_int_1,cc2_nat_1,fc17_finseq_1,fc1_finset_1,fc2_finset_1,rc1_finseq_1,rc1_finset_1,rc2_funct_1,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc4_finset_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t3_subset,t4_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,redefinition_k4_finseq_1,dt_k1_funct_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k4_finseq_1,dt_k4_tarski,dt_c1_120__finseq_3,dt_c4_120__finseq_3,fc2_finseq_1,rc1_funct_1,t1_subset,t6_boole,t7_boole,d5_tarski,e2_120_1_1_1_1_2__finseq_3,d4_funct_1]), [interesting(0.05),file(finseq_3,e3_120_1_1_1_1_2__finseq_3),[file(finseq_3,e3_120_1_1_1_1_2__finseq_3)]]). fof(e7_120_1_1_1_1_2__finseq_3,plain,( k1_funct_1(k2_finseq_3(c2_120__finseq_3,c1_120__finseq_3),c4_120__finseq_3) = k1_funct_1(c1_120__finseq_3,c4_120__finseq_3) ), inference(mizar_by,[status(thm),assumptions([dt_c2_120__finseq_3,dt_c3_120__finseq_3,e1_120__finseq_3,e1_120_1_1__finseq_3,dt_c1_120__finseq_3,dt_c4_120__finseq_3,e1_120_1_1_1_1_2__finseq_3])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,rc2_finseq_1,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_finseq_1,rc4_xreal_0,reflexivity_r1_tarski,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k5_ordinal2,dt_m2_finseq_1,cc2_xreal_0,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc1_ordinal2,rc1_int_1,rc1_nat_1,rc1_xreal_0,rc2_finset_1,rc2_int_1,rc2_nat_1,rc3_nat_1,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k14_finseq_1,dt_k1_numbers,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_tarski,dt_k4_xboole_0,dt_k5_numbers,dt_k5_relat_1,dt_m1_subset_1,dt_m2_subset_1,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc1_xreal_0,cc2_finset_1,cc2_funct_1,cc2_int_1,cc2_nat_1,cc3_int_1,cc3_nat_1,fc12_finset_1,fc17_finseq_1,fc1_finset_1,fc1_funct_1,fc2_finset_1,rc1_finseq_1,rc1_finset_1,rc2_funct_1,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc4_finset_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t3_boole,t3_subset,t4_boole,t4_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,redefinition_k4_finseq_1,dt_k1_funct_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k2_finseq_3,dt_k4_finseq_1,dt_k4_tarski,dt_c1_120__finseq_3,dt_c2_120__finseq_3,dt_c4_120__finseq_3,fc2_finseq_1,rc1_funct_1,t1_subset,t6_boole,t7_boole,d2_finseq_3,d5_tarski,e6_120_1_1_1_1_2__finseq_3,e3_120_1_1_1_1_2__finseq_3,d4_funct_1]), [interesting(0.05),file(finseq_3,e7_120_1_1_1_1_2__finseq_3),[file(finseq_3,e7_120_1_1_1_1_2__finseq_3)]]). fof(i2_120_1_1_1_1_2__finseq_3,theorem,( $true ), introduced(tautology,[file(finseq_3,i2_120_1_1_1_1_2__finseq_3)]), [interesting(0.05),trivial,file(finseq_3,i2_120_1_1_1_1_2__finseq_3)]). fof(i1_120_1_1_1_1_2__finseq_3,plain,( k1_funct_1(k2_finseq_3(c2_120__finseq_3,c1_120__finseq_3),c4_120__finseq_3) = k1_funct_1(c1_120__finseq_3,c4_120__finseq_3) ), inference(conclusion,[status(thm),assumptions([dt_c2_120__finseq_3,dt_c3_120__finseq_3,e1_120__finseq_3,e1_120_1_1__finseq_3,dt_c1_120__finseq_3,dt_c4_120__finseq_3,e1_120_1_1_1_1_2__finseq_3])],[e7_120_1_1_1_1_2__finseq_3,i2_120_1_1_1_1_2__finseq_3]), [interesting(0.05),file(finseq_3,i1_120_1_1_1_1_2__finseq_3),[file(finseq_3,i1_120_1_1_1_1_2__finseq_3)]]). fof(i2_120_1_1_1_1__finseq_3,plain, ( ~ r1_xreal_0(1,c4_120__finseq_3) => k1_funct_1(k2_finseq_3(c2_120__finseq_3,c1_120__finseq_3),c4_120__finseq_3) = k1_funct_1(c1_120__finseq_3,c4_120__finseq_3) ), inference(discharge_asm,[status(thm),assumptions([dt_c2_120__finseq_3,dt_c3_120__finseq_3,e1_120__finseq_3,e1_120_1_1__finseq_3,dt_c1_120__finseq_3,dt_c4_120__finseq_3]),discharge_asm(discharge,[e1_120_1_1_1_1_2__finseq_3])],[e1_120_1_1_1_1_2__finseq_3,i1_120_1_1_1_1_2__finseq_3]), [interesting(0.2),file(finseq_3,i2_120_1_1_1_1__finseq_3),[file(finseq_3,i2_120_1_1_1_1__finseq_3)]]). fof(e1_120_1_1_1_1__finseq_3,plain,( ~ ( ~ r1_xreal_0(1,c4_120__finseq_3) & r1_xreal_0(1,c4_120__finseq_3) ) ), inference(mizar_by,[status(thm),assumptions([dt_c4_120__finseq_3])],[reflexivity_r1_tarski,cc1_finseq_1,cc2_funct_1,rc1_finseq_1,rc1_funct_1,rc2_finset_1,rc2_funct_1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc1_xreal_0,cc2_finset_1,cc3_int_1,cc3_nat_1,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,fc2_finseq_1,rc1_finset_1,rc1_int_1,rc1_nat_1,rc1_xreal_0,rc2_int_1,rc2_nat_1,rc2_xreal_0,rc3_finset_1,rc3_nat_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_boole,t8_real,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,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc2_int_1,cc2_nat_1,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,t1_real,t2_subset,t4_real,t6_boole,t7_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,dt_c4_120__finseq_3,rqLessOrEqual__r1_xreal_0__r1_r1,spc1_numerals,spc1_boole]), [interesting(0.2),file(finseq_3,e1_120_1_1_1_1__finseq_3),[file(finseq_3,e1_120_1_1_1_1__finseq_3)]]). fof(e2_120_1_1__finseq_3,plain,( k1_funct_1(k2_finseq_3(c2_120__finseq_3,c1_120__finseq_3),c4_120__finseq_3) = k1_funct_1(c1_120__finseq_3,c4_120__finseq_3) ), inference(percases,[status(thm),assumptions([dt_c2_120__finseq_3,dt_c3_120__finseq_3,e1_120__finseq_3,e1_120_1_1__finseq_3,dt_c1_120__finseq_3,dt_c4_120__finseq_3])],[i1_120_1_1_1_1__finseq_3,i2_120_1_1_1_1__finseq_3,e1_120_1_1_1_1__finseq_3]), [interesting(0.5),file(finseq_3,e2_120_1_1__finseq_3),[file(finseq_3,e2_120_1_1__finseq_3)]]). fof(e3_120_1_1__finseq_3,plain,( k1_funct_1(k2_finseq_3(c2_120__finseq_3,c1_120__finseq_3),c4_120__finseq_3) = k1_funct_1(c1_120__finseq_3,c4_120__finseq_3) ), inference(mizar_by,[status(thm),assumptions([dt_c2_120__finseq_3,dt_c3_120__finseq_3,e1_120__finseq_3,e1_120_1_1__finseq_3,dt_c1_120__finseq_3,dt_c4_120__finseq_3])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,rc2_finseq_1,rc4_funct_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_m1_finseq_1,dt_m2_relset_1,cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,fc2_finseq_1,rc2_finset_1,rc2_nat_1,rc2_xreal_0,rc3_finseq_1,rc3_funct_1,rc3_nat_1,rc3_xreal_0,rc4_finseq_1,rc4_xreal_0,rc6_finseq_1,t1_subset,t3_boole,t4_boole,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,dt_m2_finseq_1,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc2_finset_1,cc2_funct_1,cc2_int_1,cc2_nat_1,cc2_xreal_0,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc12_finset_1,fc17_finseq_1,fc1_ordinal2,rc1_finset_1,rc1_int_1,rc1_nat_1,rc1_xreal_0,rc2_funct_1,rc2_int_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,existence_m2_subset_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k14_finseq_1,dt_k1_numbers,dt_k1_tarski,dt_k4_finseq_1,dt_k4_xboole_0,dt_k5_numbers,dt_k5_relat_1,dt_m2_subset_1,cc1_finseq_1,cc1_xreal_0,cc3_int_1,cc3_nat_1,fc1_finset_1,fc1_funct_1,rc1_finseq_1,rc1_funct_1,dt_k1_funct_1,dt_k2_finseq_3,dt_c1_120__finseq_3,dt_c2_120__finseq_3,dt_c4_120__finseq_3,d2_finseq_3,e2_120_1_1__finseq_3]), [interesting(0.5),file(finseq_3,e3_120_1_1__finseq_3),[file(finseq_3,e3_120_1_1__finseq_3)]]). fof(i2_120_1_1__finseq_3,theorem,( $true ), introduced(tautology,[file(finseq_3,i2_120_1_1__finseq_3)]), [interesting(0.5),trivial,file(finseq_3,i2_120_1_1__finseq_3)]). fof(i1_120_1_1__finseq_3,plain,( k1_funct_1(k2_finseq_3(c2_120__finseq_3,c1_120__finseq_3),c4_120__finseq_3) = k1_funct_1(c1_120__finseq_3,c4_120__finseq_3) ), inference(conclusion,[status(thm),assumptions([dt_c2_120__finseq_3,dt_c3_120__finseq_3,e1_120__finseq_3,e1_120_1_1__finseq_3,dt_c1_120__finseq_3,dt_c4_120__finseq_3])],[e3_120_1_1__finseq_3,i2_120_1_1__finseq_3]), [interesting(0.5),file(finseq_3,i1_120_1_1__finseq_3),[file(finseq_3,i1_120_1_1__finseq_3)]]). fof(i1_120_1__finseq_3,plain, ( r2_hidden(c2_120__finseq_3,k4_finseq_1(c1_120__finseq_3)) => k1_funct_1(k2_finseq_3(c2_120__finseq_3,c1_120__finseq_3),c4_120__finseq_3) = k1_funct_1(c1_120__finseq_3,c4_120__finseq_3) ), inference(discharge_asm,[status(thm),assumptions([dt_c2_120__finseq_3,dt_c3_120__finseq_3,e1_120__finseq_3,dt_c1_120__finseq_3,dt_c4_120__finseq_3]),discharge_asm(discharge,[e1_120_1_1__finseq_3])],[e1_120_1_1__finseq_3,i1_120_1_1__finseq_3]), [interesting(0.65),file(finseq_3,i1_120_1__finseq_3),[file(finseq_3,i1_120_1__finseq_3)]]). fof(e1_120_1_2__finseq_3,assumption,( ~ r2_hidden(c2_120__finseq_3,k4_finseq_1(c1_120__finseq_3)) ), introduced(assumption,[file(finseq_3,e1_120_1_2__finseq_3)]), [interesting(0.5),axiom,file(finseq_3,e1_120_1_2__finseq_3)]). fof(t113_finseq_3,theorem,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ~ ( r2_hidden(A,k4_finseq_1(B)) & ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ~ ( k3_finseq_1(B) = k1_nat_1(C,1) & k3_finseq_1(k2_finseq_3(A,B)) = C ) ) ) & ( ~ r2_hidden(A,k4_finseq_1(B)) => k2_finseq_3(A,B) = B ) ) ) ) ), file(finseq_3,t113_finseq_3), [interesting(0.9),axiom,file(finseq_3,t113_finseq_3)]). fof(e2_120_1_2__finseq_3,plain,( k1_funct_1(k2_finseq_3(c2_120__finseq_3,c1_120__finseq_3),c4_120__finseq_3) = k1_funct_1(c1_120__finseq_3,c4_120__finseq_3) ), inference(mizar_by,[status(thm),assumptions([dt_c1_120__finseq_3,dt_c2_120__finseq_3,dt_c4_120__finseq_3,e1_120_1_2__finseq_3])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,rc2_finseq_1,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,rc4_finseq_1,rc4_funct_1,reflexivity_r1_tarski,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_xboole_0,dt_m2_finseq_1,fc2_finseq_1,rc2_finset_1,rc2_nat_1,rc3_finseq_1,rc3_funct_1,rc3_nat_1,rc6_finseq_1,t3_boole,t4_boole,commutativity_k2_xcmplx_0,existence_m1_subset_1,dt_k14_finseq_1,dt_k1_card_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_xcmplx_0,dt_k4_xboole_0,dt_k5_ordinal2,dt_k5_relat_1,dt_m1_subset_1,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc2_finset_1,cc2_funct_1,cc2_int_1,cc2_nat_1,cc2_xreal_0,cc3_xreal_0,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_finset_1,fc12_xreal_0,fc17_finseq_1,fc1_finset_1,fc1_funct_1,fc1_int_1,fc1_nat_1,fc1_ordinal2,fc3_nat_1,fc3_xreal_0,fc4_nat_1,fc6_int_1,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,rc1_finset_1,rc1_int_1,rc1_nat_1,rc1_xreal_0,rc2_funct_1,rc2_int_1,rc2_xreal_0,rc3_finset_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc7_finseq_1,rc8_finseq_1,spc6_arithm,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k1_nat_1,antisymmetry_r2_hidden,existence_m2_subset_1,redefinition_k1_nat_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_nat_1,dt_k1_numbers,dt_k2_finseq_3,dt_k3_finseq_1,dt_k4_finseq_1,dt_k5_numbers,dt_m2_subset_1,dt_c1_120__finseq_3,dt_c2_120__finseq_3,dt_c4_120__finseq_3,cc1_finseq_1,cc1_xreal_0,cc3_int_1,cc3_nat_1,rc1_finseq_1,rc1_funct_1,t1_subset,t7_boole,d2_finseq_3,spc1_numerals,spc1_boole,e1_120_1_2__finseq_3,t113_finseq_3]), [interesting(0.5),file(finseq_3,e2_120_1_2__finseq_3),[file(finseq_3,e2_120_1_2__finseq_3)]]). fof(i2_120_1_2__finseq_3,theorem,( $true ), introduced(tautology,[file(finseq_3,i2_120_1_2__finseq_3)]), [interesting(0.5),trivial,file(finseq_3,i2_120_1_2__finseq_3)]). fof(i1_120_1_2__finseq_3,plain,( k1_funct_1(k2_finseq_3(c2_120__finseq_3,c1_120__finseq_3),c4_120__finseq_3) = k1_funct_1(c1_120__finseq_3,c4_120__finseq_3) ), inference(conclusion,[status(thm),assumptions([dt_c1_120__finseq_3,dt_c2_120__finseq_3,dt_c4_120__finseq_3,e1_120_1_2__finseq_3])],[e2_120_1_2__finseq_3,i2_120_1_2__finseq_3]), [interesting(0.5),file(finseq_3,i1_120_1_2__finseq_3),[file(finseq_3,i1_120_1_2__finseq_3)]]). fof(i2_120_1__finseq_3,plain, ( ~ r2_hidden(c2_120__finseq_3,k4_finseq_1(c1_120__finseq_3)) => k1_funct_1(k2_finseq_3(c2_120__finseq_3,c1_120__finseq_3),c4_120__finseq_3) = k1_funct_1(c1_120__finseq_3,c4_120__finseq_3) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_120__finseq_3,dt_c2_120__finseq_3,dt_c4_120__finseq_3]),discharge_asm(discharge,[e1_120_1_2__finseq_3])],[e1_120_1_2__finseq_3,i1_120_1_2__finseq_3]), [interesting(0.65),file(finseq_3,i2_120_1__finseq_3),[file(finseq_3,i2_120_1__finseq_3)]]). fof(e1_120_1__finseq_3,plain,( ~ ( ~ r2_hidden(c2_120__finseq_3,k4_finseq_1(c1_120__finseq_3)) & r2_hidden(c2_120__finseq_3,k4_finseq_1(c1_120__finseq_3)) ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_120__finseq_3,dt_c2_120__finseq_3])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_funct_1,rc4_xreal_0,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k5_ordinal2,cc1_xreal_0,cc2_finset_1,cc2_xreal_0,cc3_int_1,cc3_nat_1,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc17_finseq_1,fc1_ordinal2,fc2_finseq_1,rc1_finset_1,rc1_int_1,rc1_nat_1,rc1_xreal_0,rc2_finset_1,rc2_int_1,rc2_nat_1,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc3_nat_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc2_funct_1,cc2_int_1,cc2_nat_1,rc1_finseq_1,rc1_funct_1,rc2_funct_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k4_finseq_1,dt_k4_finseq_1,dt_c1_120__finseq_3,dt_c2_120__finseq_3,t1_subset,t7_boole]), [interesting(0.65),file(finseq_3,e1_120_1__finseq_3),[file(finseq_3,e1_120_1__finseq_3)]]). fof(i3_120__finseq_3,plain,( k1_funct_1(k2_finseq_3(c2_120__finseq_3,c1_120__finseq_3),c4_120__finseq_3) = k1_funct_1(c1_120__finseq_3,c4_120__finseq_3) ), inference(percases,[status(thm),assumptions([dt_c3_120__finseq_3,e1_120__finseq_3,dt_c4_120__finseq_3,dt_c1_120__finseq_3,dt_c2_120__finseq_3])],[i1_120_1__finseq_3,i2_120_1__finseq_3,e1_120_1__finseq_3]), [interesting(0.8),file(finseq_3,i3_120__finseq_3),[file(finseq_3,i3_120__finseq_3)]]). fof(i2_120__finseq_3,plain, ( k3_finseq_1(c1_120__finseq_3) = k1_nat_1(c3_120__finseq_3,1) => ( r1_xreal_0(c2_120__finseq_3,c4_120__finseq_3) | k1_funct_1(k2_finseq_3(c2_120__finseq_3,c1_120__finseq_3),c4_120__finseq_3) = k1_funct_1(c1_120__finseq_3,c4_120__finseq_3) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c3_120__finseq_3,dt_c4_120__finseq_3,dt_c1_120__finseq_3,dt_c2_120__finseq_3]),discharge_asm(discharge,[e1_120__finseq_3])],[e1_120__finseq_3,i3_120__finseq_3]), [interesting(0.8),file(finseq_3,i2_120__finseq_3),[file(finseq_3,i2_120__finseq_3)]]). fof(i2_120_tmp__finseq_3,plain, ( ( m2_subset_1(c2_120__finseq_3,k1_numbers,k5_numbers) & m2_subset_1(c3_120__finseq_3,k1_numbers,k5_numbers) & m2_subset_1(c4_120__finseq_3,k1_numbers,k5_numbers) ) => ( k3_finseq_1(c1_120__finseq_3) = k1_nat_1(c3_120__finseq_3,1) => ( r1_xreal_0(c2_120__finseq_3,c4_120__finseq_3) | k1_funct_1(k2_finseq_3(c2_120__finseq_3,c1_120__finseq_3),c4_120__finseq_3) = k1_funct_1(c1_120__finseq_3,c4_120__finseq_3) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_120__finseq_3]),discharge_asm(discharge,[dt_c2_120__finseq_3,dt_c3_120__finseq_3,dt_c4_120__finseq_3])],[dt_c2_120__finseq_3,dt_c3_120__finseq_3,dt_c4_120__finseq_3,i2_120__finseq_3]), [interesting(0.8),i1_120__finseq_3]). fof(i1_120__finseq_3,plain,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( k3_finseq_1(c1_120__finseq_3) = k1_nat_1(B,1) => ( r1_xreal_0(A,C) | k1_funct_1(k2_finseq_3(A,c1_120__finseq_3),C) = k1_funct_1(c1_120__finseq_3,C) ) ) ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_120__finseq_3])],[i2_120_tmp__finseq_3,dh_c2_120__finseq_3,dh_c3_120__finseq_3,dh_c4_120__finseq_3]), [interesting(0.8),file(finseq_3,i1_120__finseq_3),[file(finseq_3,i1_120__finseq_3)]]). fof(i1_120_tmp__finseq_3,plain, ( ( v1_relat_1(c1_120__finseq_3) & v1_funct_1(c1_120__finseq_3) & v1_finseq_1(c1_120__finseq_3) ) => ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( k3_finseq_1(c1_120__finseq_3) = k1_nat_1(B,1) => ( r1_xreal_0(A,C) | k1_funct_1(k2_finseq_3(A,c1_120__finseq_3),C) = k1_funct_1(c1_120__finseq_3,C) ) ) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_120__finseq_3])],[dt_c1_120__finseq_3,i1_120__finseq_3]), [interesting(1),t119_finseq_3]). fof(t119_finseq_3,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( k3_finseq_1(A) = k1_nat_1(C,1) => ( r1_xreal_0(B,D) | k1_funct_1(k2_finseq_3(B,A),D) = k1_funct_1(A,D) ) ) ) ) ) ) ), inference(let,[status(thm),assumptions([])],[i1_120_tmp__finseq_3,dh_c1_120__finseq_3]), [interesting(1),file(finseq_3,t119_finseq_3),[file(finseq_3,t119_finseq_3)]]).