% Mizar ND problem: t5_alg_1,alg_1,102,25 fof(dh_c1_5__alg_1,definition, ( ( ( ~ v3_struct_0(c1_5__alg_1) & v6_unialg_1(c1_5__alg_1) & v7_unialg_1(c1_5__alg_1) & v8_unialg_1(c1_5__alg_1) & l1_unialg_1(c1_5__alg_1) ) => ! [A] : ( ( ~ v3_struct_0(A) & v6_unialg_1(A) & v7_unialg_1(A) & v8_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v6_unialg_1(B) & v7_unialg_1(B) & v8_unialg_1(B) & l1_unialg_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(c1_5__alg_1),u1_struct_0(A)) & m2_relset_1(C,u1_struct_0(c1_5__alg_1),u1_struct_0(A)) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) ) => ! [E] : ( m2_finseq_1(E,u1_struct_0(c1_5__alg_1)) => k5_finseqop(u1_struct_0(A),u1_struct_0(B),k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(A),E,C),D) = k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(B),E,k7_funct_2(u1_struct_0(c1_5__alg_1),u1_struct_0(A),u1_struct_0(B),C,D)) ) ) ) ) ) ) => ! [F] : ( ( ~ v3_struct_0(F) & v6_unialg_1(F) & v7_unialg_1(F) & v8_unialg_1(F) & l1_unialg_1(F) ) => ! [G] : ( ( ~ v3_struct_0(G) & v6_unialg_1(G) & v7_unialg_1(G) & v8_unialg_1(G) & l1_unialg_1(G) ) => ! [H] : ( ( ~ v3_struct_0(H) & v6_unialg_1(H) & v7_unialg_1(H) & v8_unialg_1(H) & l1_unialg_1(H) ) => ! [I] : ( ( v1_funct_1(I) & v1_funct_2(I,u1_struct_0(F),u1_struct_0(G)) & m2_relset_1(I,u1_struct_0(F),u1_struct_0(G)) ) => ! [J] : ( ( v1_funct_1(J) & v1_funct_2(J,u1_struct_0(G),u1_struct_0(H)) & m2_relset_1(J,u1_struct_0(G),u1_struct_0(H)) ) => ! [K] : ( m2_finseq_1(K,u1_struct_0(F)) => k5_finseqop(u1_struct_0(G),u1_struct_0(H),k5_finseqop(u1_struct_0(F),u1_struct_0(G),K,I),J) = k5_finseqop(u1_struct_0(F),u1_struct_0(H),K,k7_funct_2(u1_struct_0(F),u1_struct_0(G),u1_struct_0(H),I,J)) ) ) ) ) ) ) ), introduced(definition,[new_symbol(c1_5__alg_1),file(alg_1,c1_5__alg_1)]), [interesting(0.8),axiom,file(alg_1,c1_5__alg_1)]). fof(dh_c2_5__alg_1,definition, ( ( ( ~ v3_struct_0(c2_5__alg_1) & v6_unialg_1(c2_5__alg_1) & v7_unialg_1(c2_5__alg_1) & v8_unialg_1(c2_5__alg_1) & l1_unialg_1(c2_5__alg_1) ) => ! [A] : ( ( ~ v3_struct_0(A) & v6_unialg_1(A) & v7_unialg_1(A) & v8_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1)) & m2_relset_1(B,u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1)) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(c2_5__alg_1),u1_struct_0(A)) & m2_relset_1(C,u1_struct_0(c2_5__alg_1),u1_struct_0(A)) ) => ! [D] : ( m2_finseq_1(D,u1_struct_0(c1_5__alg_1)) => k5_finseqop(u1_struct_0(c2_5__alg_1),u1_struct_0(A),k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),D,B),C) = k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(A),D,k7_funct_2(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),u1_struct_0(A),B,C)) ) ) ) ) ) => ! [E] : ( ( ~ v3_struct_0(E) & v6_unialg_1(E) & v7_unialg_1(E) & v8_unialg_1(E) & l1_unialg_1(E) ) => ! [F] : ( ( ~ v3_struct_0(F) & v6_unialg_1(F) & v7_unialg_1(F) & v8_unialg_1(F) & l1_unialg_1(F) ) => ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,u1_struct_0(c1_5__alg_1),u1_struct_0(E)) & m2_relset_1(G,u1_struct_0(c1_5__alg_1),u1_struct_0(E)) ) => ! [H] : ( ( v1_funct_1(H) & v1_funct_2(H,u1_struct_0(E),u1_struct_0(F)) & m2_relset_1(H,u1_struct_0(E),u1_struct_0(F)) ) => ! [I] : ( m2_finseq_1(I,u1_struct_0(c1_5__alg_1)) => k5_finseqop(u1_struct_0(E),u1_struct_0(F),k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(E),I,G),H) = k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(F),I,k7_funct_2(u1_struct_0(c1_5__alg_1),u1_struct_0(E),u1_struct_0(F),G,H)) ) ) ) ) ) ), introduced(definition,[new_symbol(c2_5__alg_1),file(alg_1,c2_5__alg_1)]), [interesting(0.8),axiom,file(alg_1,c2_5__alg_1)]). fof(dh_c3_5__alg_1,definition, ( ( ( ~ v3_struct_0(c3_5__alg_1) & v6_unialg_1(c3_5__alg_1) & v7_unialg_1(c3_5__alg_1) & v8_unialg_1(c3_5__alg_1) & l1_unialg_1(c3_5__alg_1) ) => ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1)) & m2_relset_1(A,u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1)) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1)) & m2_relset_1(B,u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1)) ) => ! [C] : ( m2_finseq_1(C,u1_struct_0(c1_5__alg_1)) => k5_finseqop(u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),C,A),B) = k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c3_5__alg_1),C,k7_funct_2(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),A,B)) ) ) ) ) => ! [D] : ( ( ~ v3_struct_0(D) & v6_unialg_1(D) & v7_unialg_1(D) & v8_unialg_1(D) & l1_unialg_1(D) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1)) & m2_relset_1(E,u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1)) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,u1_struct_0(c2_5__alg_1),u1_struct_0(D)) & m2_relset_1(F,u1_struct_0(c2_5__alg_1),u1_struct_0(D)) ) => ! [G] : ( m2_finseq_1(G,u1_struct_0(c1_5__alg_1)) => k5_finseqop(u1_struct_0(c2_5__alg_1),u1_struct_0(D),k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),G,E),F) = k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(D),G,k7_funct_2(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),u1_struct_0(D),E,F)) ) ) ) ) ), introduced(definition,[new_symbol(c3_5__alg_1),file(alg_1,c3_5__alg_1)]), [interesting(0.8),axiom,file(alg_1,c3_5__alg_1)]). fof(dh_c4_5__alg_1,definition, ( ( ( v1_funct_1(c4_5__alg_1) & v1_funct_2(c4_5__alg_1,u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1)) & m2_relset_1(c4_5__alg_1,u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1)) ) => ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1)) & m2_relset_1(A,u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1)) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(c1_5__alg_1)) => k5_finseqop(u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),B,c4_5__alg_1),A) = k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c3_5__alg_1),B,k7_funct_2(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),c4_5__alg_1,A)) ) ) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1)) & m2_relset_1(C,u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1)) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1)) & m2_relset_1(D,u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1)) ) => ! [E] : ( m2_finseq_1(E,u1_struct_0(c1_5__alg_1)) => k5_finseqop(u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),E,C),D) = k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c3_5__alg_1),E,k7_funct_2(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),C,D)) ) ) ) ), introduced(definition,[new_symbol(c4_5__alg_1),file(alg_1,c4_5__alg_1)]), [interesting(0.8),axiom,file(alg_1,c4_5__alg_1)]). fof(dh_c5_5__alg_1,definition, ( ( ( v1_funct_1(c5_5__alg_1) & v1_funct_2(c5_5__alg_1,u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1)) & m2_relset_1(c5_5__alg_1,u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1)) ) => ! [A] : ( m2_finseq_1(A,u1_struct_0(c1_5__alg_1)) => k5_finseqop(u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),A,c4_5__alg_1),c5_5__alg_1) = k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c3_5__alg_1),A,k7_funct_2(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),c4_5__alg_1,c5_5__alg_1)) ) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1)) & m2_relset_1(B,u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1)) ) => ! [C] : ( m2_finseq_1(C,u1_struct_0(c1_5__alg_1)) => k5_finseqop(u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),C,c4_5__alg_1),B) = k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c3_5__alg_1),C,k7_funct_2(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),c4_5__alg_1,B)) ) ) ), introduced(definition,[new_symbol(c5_5__alg_1),file(alg_1,c5_5__alg_1)]), [interesting(0.8),axiom,file(alg_1,c5_5__alg_1)]). fof(dh_c6_5__alg_1,definition, ( ( m2_finseq_1(c6_5__alg_1,u1_struct_0(c1_5__alg_1)) => k5_finseqop(u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),c6_5__alg_1,c4_5__alg_1),c5_5__alg_1) = k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c3_5__alg_1),c6_5__alg_1,k7_funct_2(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),c4_5__alg_1,c5_5__alg_1)) ) => ! [A] : ( m2_finseq_1(A,u1_struct_0(c1_5__alg_1)) => k5_finseqop(u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),A,c4_5__alg_1),c5_5__alg_1) = k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c3_5__alg_1),A,k7_funct_2(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),c4_5__alg_1,c5_5__alg_1)) ) ), introduced(definition,[new_symbol(c6_5__alg_1),file(alg_1,c6_5__alg_1)]), [interesting(0.8),axiom,file(alg_1,c6_5__alg_1)]). fof(cc1_arytm_3,theorem,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_ordinal1(B) & v2_ordinal1(B) & v3_ordinal1(B) ) ) ) ), file(arytm_3,cc1_arytm_3), [interesting(0.9),axiom,file(arytm_3,cc1_arytm_3)]). fof(cc2_arytm_3,theorem,( ! [A] : ( ( v1_xboole_0(A) & v3_ordinal1(A) ) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ) ), file(arytm_3,cc2_arytm_3), [interesting(0.9),axiom,file(arytm_3,cc2_arytm_3)]). fof(rc1_arytm_3,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ), file(arytm_3,rc1_arytm_3), [interesting(0.9),axiom,file(arytm_3,rc1_arytm_3)]). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), [interesting(0.9),axiom,file(numbers,k1_numbers)]). fof(dt_k5_ordinal2,axiom,( $true ), file(ordinal2,k5_ordinal2), [interesting(0.9),axiom,file(ordinal2,k5_ordinal2)]). fof(cc3_arytm_3,theorem,( ! [A] : ( m1_subset_1(A,k5_ordinal2) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ) ), file(arytm_3,cc3_arytm_3), [interesting(0.9),axiom,file(arytm_3,cc3_arytm_3)]). fof(cc6_membered,theorem,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v1_membered(A) & v2_membered(A) ) ) ), file(membered,cc6_membered), [interesting(0.9),axiom,file(membered,cc6_membered)]). fof(fc2_membered,theorem, ( ~ v1_xboole_0(k1_numbers) & v1_membered(k1_numbers) & v2_membered(k1_numbers) ), file(membered,fc2_membered), [interesting(0.9),axiom,file(membered,fc2_membered)]). fof(fc5_membered,theorem, ( v1_membered(k5_ordinal2) & v2_membered(k5_ordinal2) & v3_membered(k5_ordinal2) & v4_membered(k5_ordinal2) & v5_membered(k5_ordinal2) ), file(membered,fc5_membered), [interesting(0.9),axiom,file(membered,fc5_membered)]). fof(redefinition_k5_numbers,definition,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), [interesting(0.9),axiom,file(numbers,k5_numbers)]). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), [interesting(0.9),axiom,file(zfmisc_1,k2_zfmisc_1)]). fof(dt_k5_numbers,axiom,( m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ), file(numbers,k5_numbers), [interesting(0.9),axiom,file(numbers,k5_numbers)]). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), [interesting(0.9),axiom,file(subset_1,m1_subset_1)]). fof(cc10_membered,theorem,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,A) => v1_xcmplx_0(B) ) ) ), file(membered,cc10_membered), [interesting(0.9),axiom,file(membered,cc10_membered)]). fof(cc11_membered,theorem,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) ) ) ) ), file(membered,cc11_membered), [interesting(0.9),axiom,file(membered,cc11_membered)]). fof(cc12_membered,theorem,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_rat_1(B) ) ) ) ), file(membered,cc12_membered), [interesting(0.9),axiom,file(membered,cc12_membered)]). fof(cc13_membered,theorem,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc13_membered), [interesting(0.9),axiom,file(membered,cc13_membered)]). fof(cc14_membered,theorem,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v4_ordinal2(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc14_membered), [interesting(0.9),axiom,file(membered,cc14_membered)]). fof(cc16_membered,theorem,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_membered(B) ) ) ), file(membered,cc16_membered), [interesting(0.9),axiom,file(membered,cc16_membered)]). fof(cc17_membered,theorem,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) ) ) ) ), file(membered,cc17_membered), [interesting(0.9),axiom,file(membered,cc17_membered)]). fof(cc18_membered,theorem,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) ) ) ) ), file(membered,cc18_membered), [interesting(0.9),axiom,file(membered,cc18_membered)]). fof(cc19_membered,theorem,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) ) ) ) ), file(membered,cc19_membered), [interesting(0.9),axiom,file(membered,cc19_membered)]). fof(cc1_funct_2,theorem,( ! [A,B,C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_partfun1(C,A,B) ) => ( v1_funct_1(C) & v1_funct_2(C,A,B) ) ) ) ), file(funct_2,cc1_funct_2), [interesting(0.9),axiom,file(funct_2,cc1_funct_2)]). fof(cc1_membered,theorem,( ! [A] : ( v5_membered(A) => v4_membered(A) ) ), file(membered,cc1_membered), [interesting(0.9),axiom,file(membered,cc1_membered)]). fof(cc1_relset_1,theorem,( ! [A,B,C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => v1_relat_1(C) ) ), file(relset_1,cc1_relset_1), [interesting(0.9),axiom,file(relset_1,cc1_relset_1)]). fof(cc20_membered,theorem,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) ) ) ) ), file(membered,cc20_membered), [interesting(0.9),axiom,file(membered,cc20_membered)]). fof(cc2_membered,theorem,( ! [A] : ( v4_membered(A) => v3_membered(A) ) ), file(membered,cc2_membered), [interesting(0.9),axiom,file(membered,cc2_membered)]). fof(cc3_membered,theorem,( ! [A] : ( v3_membered(A) => v2_membered(A) ) ), file(membered,cc3_membered), [interesting(0.9),axiom,file(membered,cc3_membered)]). fof(cc4_membered,theorem,( ! [A] : ( v2_membered(A) => v1_membered(A) ) ), file(membered,cc4_membered), [interesting(0.9),axiom,file(membered,cc4_membered)]). fof(cc9_membered,theorem,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k5_numbers)) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc9_membered), [interesting(0.9),axiom,file(membered,cc9_membered)]). fof(rc1_funct_2,theorem,( ! [A,B] : ? [C] : ( m1_relset_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C) & v1_funct_2(C,A,B) ) ), file(funct_2,rc1_funct_2), [interesting(0.9),axiom,file(funct_2,rc1_funct_2)]). fof(rc1_membered,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ), file(membered,rc1_membered), [interesting(0.9),axiom,file(membered,rc1_membered)]). fof(rc2_partfun1,theorem,( ! [A,B] : ? [C] : ( m1_relset_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C) ) ), file(partfun1,rc2_partfun1), [interesting(0.9),axiom,file(partfun1,rc2_partfun1)]). fof(rc5_struct_0,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) ) ) ), file(struct_0,rc5_struct_0), [interesting(0.9),axiom,file(struct_0,rc5_struct_0)]). fof(redefinition_m2_finseq_1,definition,( ! [A,B] : ( m2_finseq_1(B,A) <=> m1_finseq_1(B,A) ) ), file(finseq_1,m2_finseq_1), [interesting(0.9),axiom,file(finseq_1,m2_finseq_1)]). fof(redefinition_m2_relset_1,definition,( ! [A,B,C] : ( m2_relset_1(C,A,B) <=> m1_relset_1(C,A,B) ) ), file(relset_1,m2_relset_1), [interesting(0.9),axiom,file(relset_1,m2_relset_1)]). fof(dt_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_l1_struct_0,axiom,( $true ), file(struct_0,l1_struct_0), [interesting(0.9),axiom,file(struct_0,l1_struct_0)]). fof(dt_l1_unialg_1,axiom,( ! [A] : ( l1_unialg_1(A) => l1_struct_0(A) ) ), file(unialg_1,l1_unialg_1), [interesting(0.9),axiom,file(unialg_1,l1_unialg_1)]). fof(dt_m1_finseq_1,axiom,( ! [A,B] : ( m1_finseq_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) ) ), file(finseq_1,m1_finseq_1), [interesting(0.9),axiom,file(finseq_1,m1_finseq_1)]). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), [interesting(0.9),axiom,file(relset_1,m1_relset_1)]). fof(dt_m2_finseq_1,axiom,( ! [A,B] : ( m2_finseq_1(B,A) => ( v1_funct_1(B) & v1_finseq_1(B) & m2_relset_1(B,k5_numbers,A) ) ) ), file(finseq_1,m2_finseq_1), [interesting(0.9),axiom,file(finseq_1,m2_finseq_1)]). fof(dt_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ), file(relset_1,m2_relset_1), [interesting(0.9),axiom,file(relset_1,m2_relset_1)]). fof(cc15_membered,theorem,( ! [A] : ( v1_xboole_0(A) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc15_membered), [interesting(0.9),axiom,file(membered,cc15_membered)]). fof(cc5_funct_2,theorem,( ! [A,B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_funct_2(C,A,B) ) => ( v1_funct_1(C) & v1_partfun1(C,A,B) & v1_funct_2(C,A,B) ) ) ) ) ), file(funct_2,cc5_funct_2), [interesting(0.9),axiom,file(funct_2,cc5_funct_2)]). fof(cc6_funct_2,theorem,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ! [C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_funct_2(C,A,B) ) => ( v1_funct_1(C) & ~ v1_xboole_0(C) & v1_partfun1(C,A,B) & v1_funct_2(C,A,B) ) ) ) ) ), file(funct_2,cc6_funct_2), [interesting(0.9),axiom,file(funct_2,cc6_funct_2)]). fof(fc1_struct_0,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ~ v1_xboole_0(u1_struct_0(A)) ) ), file(struct_0,fc1_struct_0), [interesting(0.9),axiom,file(struct_0,fc1_struct_0)]). fof(rc3_struct_0,theorem,( ? [A] : ( l1_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc3_struct_0), [interesting(0.9),axiom,file(struct_0,rc3_struct_0)]). fof(redefinition_k5_finseqop,definition,( ! [A,B,C,D] : ( ( m1_finseq_1(C,A) & v1_funct_1(D) & v1_funct_2(D,A,B) & m1_relset_1(D,A,B) ) => k5_finseqop(A,B,C,D) = k5_relat_1(C,D) ) ), file(finseqop,k5_finseqop), [interesting(0.9),axiom,file(finseqop,k5_finseqop)]). fof(redefinition_k7_funct_2,definition,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(D,A,B) & m1_relset_1(D,A,B) & v1_funct_1(E) & v1_funct_2(E,B,C) & m1_relset_1(E,B,C) ) => k7_funct_2(A,B,C,D,E) = k5_relat_1(D,E) ) ), file(funct_2,k7_funct_2), [interesting(0.9),axiom,file(funct_2,k7_funct_2)]). fof(dt_k5_finseqop,axiom,( ! [A,B,C,D] : ( ( m1_finseq_1(C,A) & v1_funct_1(D) & v1_funct_2(D,A,B) & m1_relset_1(D,A,B) ) => m2_finseq_1(k5_finseqop(A,B,C,D),B) ) ), file(finseqop,k5_finseqop), [interesting(0.9),axiom,file(finseqop,k5_finseqop)]). fof(dt_k7_funct_2,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(D,A,B) & m1_relset_1(D,A,B) & v1_funct_1(E) & v1_funct_2(E,B,C) & m1_relset_1(E,B,C) ) => ( v1_funct_1(k7_funct_2(A,B,C,D,E)) & v1_funct_2(k7_funct_2(A,B,C,D,E),A,C) & m2_relset_1(k7_funct_2(A,B,C,D,E),A,C) ) ) ), file(funct_2,k7_funct_2), [interesting(0.9),axiom,file(funct_2,k7_funct_2)]). fof(dt_u1_struct_0,axiom,( $true ), file(struct_0,u1_struct_0), [interesting(0.9),axiom,file(struct_0,u1_struct_0)]). fof(dt_c1_5__alg_1,assumption, ( ~ v3_struct_0(c1_5__alg_1) & v6_unialg_1(c1_5__alg_1) & v7_unialg_1(c1_5__alg_1) & v8_unialg_1(c1_5__alg_1) & l1_unialg_1(c1_5__alg_1) ), introduced(assumption,[file(alg_1,c1_5__alg_1)]), [interesting(0.8),axiom,file(alg_1,c1_5__alg_1)]). fof(dt_c2_5__alg_1,assumption, ( ~ v3_struct_0(c2_5__alg_1) & v6_unialg_1(c2_5__alg_1) & v7_unialg_1(c2_5__alg_1) & v8_unialg_1(c2_5__alg_1) & l1_unialg_1(c2_5__alg_1) ), introduced(assumption,[file(alg_1,c2_5__alg_1)]), [interesting(0.8),axiom,file(alg_1,c2_5__alg_1)]). fof(dt_c3_5__alg_1,assumption, ( ~ v3_struct_0(c3_5__alg_1) & v6_unialg_1(c3_5__alg_1) & v7_unialg_1(c3_5__alg_1) & v8_unialg_1(c3_5__alg_1) & l1_unialg_1(c3_5__alg_1) ), introduced(assumption,[file(alg_1,c3_5__alg_1)]), [interesting(0.8),axiom,file(alg_1,c3_5__alg_1)]). fof(dt_c4_5__alg_1,assumption, ( v1_funct_1(c4_5__alg_1) & v1_funct_2(c4_5__alg_1,u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1)) & m2_relset_1(c4_5__alg_1,u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1)) ), introduced(assumption,[file(alg_1,c4_5__alg_1)]), [interesting(0.8),axiom,file(alg_1,c4_5__alg_1)]). fof(dt_c5_5__alg_1,assumption, ( v1_funct_1(c5_5__alg_1) & v1_funct_2(c5_5__alg_1,u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1)) & m2_relset_1(c5_5__alg_1,u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1)) ), introduced(assumption,[file(alg_1,c5_5__alg_1)]), [interesting(0.8),axiom,file(alg_1,c5_5__alg_1)]). fof(dt_c6_5__alg_1,assumption,( m2_finseq_1(c6_5__alg_1,u1_struct_0(c1_5__alg_1)) ), introduced(assumption,[file(alg_1,c6_5__alg_1)]), [interesting(0.8),axiom,file(alg_1,c6_5__alg_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(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]). fof(fc6_membered,theorem, ( v1_xboole_0(k1_xboole_0) & v1_membered(k1_xboole_0) & v2_membered(k1_xboole_0) & v3_membered(k1_xboole_0) & v4_membered(k1_xboole_0) & v5_membered(k1_xboole_0) ), file(membered,fc6_membered), [interesting(0.9),axiom,file(membered,fc6_membered)]). fof(existence_l1_struct_0,axiom,( ? [A] : l1_struct_0(A) ), file(struct_0,l1_struct_0), [interesting(0.9),axiom,file(struct_0,l1_struct_0)]). fof(existence_l1_unialg_1,axiom,( ? [A] : l1_unialg_1(A) ), file(unialg_1,l1_unialg_1), [interesting(0.9),axiom,file(unialg_1,l1_unialg_1)]). fof(existence_m1_finseq_1,axiom,( ! [A] : ? [B] : m1_finseq_1(B,A) ), file(finseq_1,m1_finseq_1), [interesting(0.9),axiom,file(finseq_1,m1_finseq_1)]). fof(existence_m1_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), [interesting(0.9),axiom,file(relset_1,m1_relset_1)]). fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), [interesting(0.9),axiom,file(subset_1,m1_subset_1)]). fof(existence_m2_finseq_1,axiom,( ! [A] : ? [B] : m2_finseq_1(B,A) ), file(finseq_1,m2_finseq_1), [interesting(0.9),axiom,file(finseq_1,m2_finseq_1)]). fof(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), [interesting(0.9),axiom,file(relset_1,m2_relset_1)]). fof(dt_k1_card_1,axiom,( ! [A] : v1_card_1(k1_card_1(A)) ), file(card_1,k1_card_1), [interesting(0.9),axiom,file(card_1,k1_card_1)]). fof(dt_k1_finseq_1,axiom,( $true ), file(finseq_1,k1_finseq_1), [interesting(0.9),axiom,file(finseq_1,k1_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(t2_subset,theorem,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), [interesting(0.9),axiom,file(subset,t2_subset)]). fof(t3_subset,theorem,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), [interesting(0.9),axiom,file(subset,t3_subset)]). fof(t4_subset,theorem,( ! [A,B,C] : ( ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) ) => m1_subset_1(A,C) ) ), file(subset,t4_subset), [interesting(0.9),axiom,file(subset,t4_subset)]). fof(t5_subset,theorem,( ! [A,B,C] : ~ ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C) ) ), file(subset,t5_subset), [interesting(0.9),axiom,file(subset,t5_subset)]). fof(t6_boole,theorem,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), [interesting(0.9),axiom,file(boole,t6_boole)]). fof(t8_boole,theorem,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), [interesting(0.9),axiom,file(boole,t8_boole)]). fof(antisymmetry_r2_hidden,theorem,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), [interesting(0.9),axiom,file(hidden,r2_hidden)]). fof(existence_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ? [C] : m2_subset_1(C,A,B) ) ), file(subset_1,m2_subset_1), [interesting(0.9),axiom,file(subset_1,m2_subset_1)]). fof(redefinition_k2_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(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_m2_subset_1,definition,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(subset_1,m2_subset_1), [interesting(0.9),axiom,file(subset_1,m2_subset_1)]). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), [interesting(0.9),axiom,file(funct_1,k1_funct_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_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_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(t1_subset,theorem,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), [interesting(0.9),axiom,file(subset,t1_subset)]). fof(t7_boole,theorem,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), [interesting(0.9),axiom,file(boole,t7_boole)]). fof(dh_c1_5_1__alg_1,definition, ( ( m2_subset_1(c1_5_1__alg_1,k1_numbers,k5_numbers) => ( r2_hidden(c1_5_1__alg_1,k4_finseq_1(c6_5__alg_1)) => k1_funct_1(k5_finseqop(u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),c6_5__alg_1,c4_5__alg_1),c5_5__alg_1),c1_5_1__alg_1) = k1_funct_1(k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c3_5__alg_1),c6_5__alg_1,k7_funct_2(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),c4_5__alg_1,c5_5__alg_1)),c1_5_1__alg_1) ) ) => ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ( r2_hidden(A,k4_finseq_1(c6_5__alg_1)) => k1_funct_1(k5_finseqop(u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),c6_5__alg_1,c4_5__alg_1),c5_5__alg_1),A) = k1_funct_1(k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c3_5__alg_1),c6_5__alg_1,k7_funct_2(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),c4_5__alg_1,c5_5__alg_1)),A) ) ) ), introduced(definition,[new_symbol(c1_5_1__alg_1),file(alg_1,c1_5_1__alg_1)]), [interesting(0.65),axiom,file(alg_1,c1_5_1__alg_1)]). fof(dt_c1_5_1__alg_1,assumption,( m2_subset_1(c1_5_1__alg_1,k1_numbers,k5_numbers) ), introduced(assumption,[file(alg_1,c1_5_1__alg_1)]), [interesting(0.65),axiom,file(alg_1,c1_5_1__alg_1)]). fof(e1_5_1__alg_1,assumption,( r2_hidden(c1_5_1__alg_1,k4_finseq_1(c6_5__alg_1)) ), introduced(assumption,[file(alg_1,e1_5_1__alg_1)]), [interesting(0.65),axiom,file(alg_1,e1_5_1__alg_1)]). fof(t1_alg_1,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) ) => ( k4_finseq_1(k5_finseqop(A,B,C,D)) = k4_finseq_1(C) & k3_finseq_1(k5_finseqop(A,B,C,D)) = k3_finseq_1(C) & ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ( r2_hidden(E,k4_finseq_1(k5_finseqop(A,B,C,D))) => k1_funct_1(k5_finseqop(A,B,C,D),E) = k1_funct_1(D,k1_funct_1(C,E)) ) ) ) ) ) ) ) ), file(alg_1,t1_alg_1), [interesting(0.9),axiom,file(alg_1,t1_alg_1)]). fof(e2_5__alg_1,plain,( k4_finseq_1(k5_finseqop(u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),c6_5__alg_1,c4_5__alg_1),c5_5__alg_1)) = k4_finseq_1(k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),c6_5__alg_1,c4_5__alg_1)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__alg_1,dt_c2_5__alg_1,dt_c3_5__alg_1,dt_c4_5__alg_1,dt_c5_5__alg_1,dt_c6_5__alg_1])],[reflexivity_r1_tarski,cc1_arytm_3,cc1_funct_2,cc2_arytm_3,rc1_arytm_3,existence_l1_struct_0,existence_l1_unialg_1,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,dt_k1_card_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_k5_relat_1,dt_l1_struct_0,dt_l1_unialg_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc5_funct_2,cc6_funct_2,cc6_membered,cc9_membered,fc1_struct_0,fc5_membered,fc6_membered,rc1_funct_2,rc1_membered,rc2_partfun1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,antisymmetry_r2_hidden,existence_m2_finseq_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k5_finseqop,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k3_finseq_1,dt_k4_finseq_1,dt_k5_finseqop,dt_k5_numbers,dt_m2_finseq_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_5__alg_1,dt_c2_5__alg_1,dt_c3_5__alg_1,dt_c4_5__alg_1,dt_c5_5__alg_1,dt_c6_5__alg_1,cc15_membered,fc2_membered,t1_subset,t6_boole,t7_boole,t8_boole,t1_alg_1]), [interesting(0.8),file(alg_1,e2_5__alg_1),[file(alg_1,e2_5__alg_1)]]). fof(e4_5__alg_1,plain,( k4_finseq_1(k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),c6_5__alg_1,c4_5__alg_1)) = k4_finseq_1(c6_5__alg_1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__alg_1,dt_c2_5__alg_1,dt_c4_5__alg_1,dt_c6_5__alg_1])],[reflexivity_r1_tarski,cc1_arytm_3,cc1_funct_2,cc2_arytm_3,rc1_arytm_3,existence_l1_struct_0,existence_l1_unialg_1,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,dt_k1_card_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_k5_relat_1,dt_l1_struct_0,dt_l1_unialg_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc5_funct_2,cc6_funct_2,cc6_membered,cc9_membered,fc1_struct_0,fc5_membered,fc6_membered,rc1_funct_2,rc1_membered,rc2_partfun1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,antisymmetry_r2_hidden,existence_m2_finseq_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k5_finseqop,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k3_finseq_1,dt_k4_finseq_1,dt_k5_finseqop,dt_k5_numbers,dt_m2_finseq_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_5__alg_1,dt_c2_5__alg_1,dt_c4_5__alg_1,dt_c6_5__alg_1,cc15_membered,fc2_membered,t1_subset,t6_boole,t7_boole,t8_boole,t1_alg_1]), [interesting(0.8),file(alg_1,e4_5__alg_1),[file(alg_1,e4_5__alg_1)]]). fof(e1_5_1_1__alg_1,plain,( k1_funct_1(k5_finseqop(u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),c6_5__alg_1,c4_5__alg_1),c5_5__alg_1),c1_5_1__alg_1) = k1_funct_1(c5_5__alg_1,k1_funct_1(k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),c6_5__alg_1,c4_5__alg_1),c1_5_1__alg_1)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5_1__alg_1,dt_c3_5__alg_1,dt_c5_5__alg_1,dt_c1_5__alg_1,dt_c2_5__alg_1,dt_c4_5__alg_1,dt_c6_5__alg_1,e1_5_1__alg_1])],[reflexivity_r1_tarski,cc1_arytm_3,cc1_funct_2,cc2_arytm_3,rc1_arytm_3,existence_l1_struct_0,existence_l1_unialg_1,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,dt_k1_card_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_k5_relat_1,dt_l1_struct_0,dt_l1_unialg_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc5_funct_2,cc6_funct_2,cc6_membered,cc9_membered,fc1_struct_0,fc5_membered,fc6_membered,rc1_funct_2,rc1_membered,rc2_partfun1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,antisymmetry_r2_hidden,existence_m2_finseq_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k5_finseqop,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k3_finseq_1,dt_k4_finseq_1,dt_k5_finseqop,dt_k5_numbers,dt_m2_finseq_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_5__alg_1,dt_c1_5_1__alg_1,dt_c2_5__alg_1,dt_c3_5__alg_1,dt_c4_5__alg_1,dt_c5_5__alg_1,dt_c6_5__alg_1,cc15_membered,fc2_membered,t1_subset,t6_boole,t7_boole,t8_boole,e2_5__alg_1,e4_5__alg_1,e1_5_1__alg_1,t1_alg_1]), [interesting(0.5),file(alg_1,e1_5_1_1__alg_1),[file(alg_1,e1_5_1_1__alg_1)]]). fof(e2_5_1_1__alg_1,plain,( k1_funct_1(c5_5__alg_1,k1_funct_1(k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),c6_5__alg_1,c4_5__alg_1),c1_5_1__alg_1)) = k1_funct_1(c5_5__alg_1,k1_funct_1(c4_5__alg_1,k1_funct_1(c6_5__alg_1,c1_5_1__alg_1))) ), inference(mizar_by,[status(thm),assumptions([dt_c3_5__alg_1,dt_c1_5_1__alg_1,dt_c5_5__alg_1,dt_c1_5__alg_1,dt_c2_5__alg_1,dt_c4_5__alg_1,dt_c6_5__alg_1,e1_5_1__alg_1])],[reflexivity_r1_tarski,cc1_arytm_3,cc1_funct_2,cc2_arytm_3,rc1_arytm_3,existence_l1_struct_0,existence_l1_unialg_1,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,dt_k1_card_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_k5_relat_1,dt_l1_struct_0,dt_l1_unialg_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,dt_c3_5__alg_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc5_funct_2,cc6_funct_2,cc6_membered,cc9_membered,fc1_struct_0,fc5_membered,fc6_membered,rc1_funct_2,rc1_membered,rc2_partfun1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,antisymmetry_r2_hidden,existence_m2_finseq_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k5_finseqop,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k3_finseq_1,dt_k4_finseq_1,dt_k5_finseqop,dt_k5_numbers,dt_m2_finseq_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_5__alg_1,dt_c1_5_1__alg_1,dt_c2_5__alg_1,dt_c4_5__alg_1,dt_c5_5__alg_1,dt_c6_5__alg_1,cc15_membered,fc2_membered,t1_subset,t6_boole,t7_boole,t8_boole,e4_5__alg_1,e1_5_1__alg_1,t1_alg_1]), [interesting(0.5),file(alg_1,e2_5_1_1__alg_1),[file(alg_1,e2_5_1_1__alg_1)]]). fof(t13_finseq_2,theorem,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B,C] : ( m2_finseq_1(C,B) => ( r2_hidden(A,k4_finseq_1(C)) => r2_hidden(k1_funct_1(C,A),B) ) ) ) ), file(finseq_2,t13_finseq_2), [interesting(0.9),axiom,file(finseq_2,t13_finseq_2)]). fof(e2_5_1__alg_1,plain,( r2_hidden(k1_funct_1(c6_5__alg_1,c1_5_1__alg_1),u1_struct_0(c1_5__alg_1)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__alg_1,dt_c1_5_1__alg_1,dt_c6_5__alg_1,e1_5_1__alg_1])],[reflexivity_r1_tarski,existence_m1_relset_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_relset_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_arytm_3,cc1_membered,cc1_relset_1,cc20_membered,cc2_arytm_3,cc2_membered,cc3_membered,fc6_membered,rc1_arytm_3,rc1_membered,rc2_partfun1,existence_l1_struct_0,existence_l1_unialg_1,existence_m1_finseq_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l1_struct_0,dt_l1_unialg_1,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc3_arytm_3,cc4_membered,cc6_membered,cc9_membered,fc1_struct_0,fc5_membered,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m2_finseq_1,existence_m2_subset_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k4_finseq_1,dt_k5_numbers,dt_m2_finseq_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_5__alg_1,dt_c1_5_1__alg_1,dt_c6_5__alg_1,fc2_membered,t1_subset,t7_boole,e1_5_1__alg_1,t13_finseq_2]), [interesting(0.65),file(alg_1,e2_5_1__alg_1),[file(alg_1,e2_5_1__alg_1)]]). fof(t21_funct_2,theorem,( ! [A,B,C,D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ( r2_hidden(C,A) => ( B = k1_xboole_0 | k1_funct_1(k5_relat_1(D,E),C) = k1_funct_1(E,k1_funct_1(D,C)) ) ) ) ) ), file(funct_2,t21_funct_2), [interesting(0.9),axiom,file(funct_2,t21_funct_2)]). fof(e3_5_1_1__alg_1,plain,( k1_funct_1(c5_5__alg_1,k1_funct_1(c4_5__alg_1,k1_funct_1(c6_5__alg_1,c1_5_1__alg_1))) = k1_funct_1(k7_funct_2(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),c4_5__alg_1,c5_5__alg_1),k1_funct_1(c6_5__alg_1,c1_5_1__alg_1)) ), inference(mizar_by,[status(thm),assumptions([dt_c2_5__alg_1,dt_c3_5__alg_1,dt_c4_5__alg_1,dt_c5_5__alg_1,dt_c1_5__alg_1,dt_c1_5_1__alg_1,dt_c6_5__alg_1,e1_5_1__alg_1])],[cc1_arytm_3,cc2_arytm_3,rc1_arytm_3,reflexivity_r1_tarski,existence_m1_finseq_1,dt_k5_ordinal2,dt_m1_finseq_1,cc1_funct_2,cc3_arytm_3,fc5_membered,existence_l1_struct_0,existence_l1_unialg_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_numbers,dt_l1_struct_0,dt_l1_unialg_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc5_funct_2,cc6_funct_2,cc6_membered,cc9_membered,fc1_struct_0,fc2_membered,rc1_funct_2,rc1_membered,rc2_partfun1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_k7_funct_2,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_xboole_0,dt_k5_relat_1,dt_k7_funct_2,dt_m2_relset_1,dt_u1_struct_0,dt_c1_5__alg_1,dt_c1_5_1__alg_1,dt_c2_5__alg_1,dt_c3_5__alg_1,dt_c4_5__alg_1,dt_c5_5__alg_1,dt_c6_5__alg_1,fc6_membered,t1_subset,t6_boole,t7_boole,e2_5_1__alg_1,t21_funct_2]), [interesting(0.5),file(alg_1,e3_5_1_1__alg_1),[file(alg_1,e3_5_1_1__alg_1)]]). fof(e6_5__alg_1,plain,( k4_finseq_1(c6_5__alg_1) = k4_finseq_1(k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c3_5__alg_1),c6_5__alg_1,k7_funct_2(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),c4_5__alg_1,c5_5__alg_1))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__alg_1,dt_c2_5__alg_1,dt_c3_5__alg_1,dt_c4_5__alg_1,dt_c5_5__alg_1,dt_c6_5__alg_1])],[reflexivity_r1_tarski,cc1_arytm_3,cc1_funct_2,cc2_arytm_3,rc1_arytm_3,existence_l1_struct_0,existence_l1_unialg_1,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,dt_k1_card_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_k5_relat_1,dt_l1_struct_0,dt_l1_unialg_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc5_funct_2,cc6_funct_2,cc6_membered,cc9_membered,fc1_struct_0,fc5_membered,fc6_membered,rc1_funct_2,rc1_membered,rc2_partfun1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,antisymmetry_r2_hidden,existence_m2_finseq_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k5_finseqop,redefinition_k5_numbers,redefinition_k7_funct_2,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k3_finseq_1,dt_k4_finseq_1,dt_k5_finseqop,dt_k5_numbers,dt_k7_funct_2,dt_m2_finseq_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_5__alg_1,dt_c2_5__alg_1,dt_c3_5__alg_1,dt_c4_5__alg_1,dt_c5_5__alg_1,dt_c6_5__alg_1,cc15_membered,fc2_membered,t1_subset,t6_boole,t7_boole,t8_boole,t1_alg_1]), [interesting(0.8),file(alg_1,e6_5__alg_1),[file(alg_1,e6_5__alg_1)]]). fof(e4_5_1_1__alg_1,plain,( k1_funct_1(k7_funct_2(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),c4_5__alg_1,c5_5__alg_1),k1_funct_1(c6_5__alg_1,c1_5_1__alg_1)) = k1_funct_1(k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c3_5__alg_1),c6_5__alg_1,k7_funct_2(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),c4_5__alg_1,c5_5__alg_1)),c1_5_1__alg_1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5_1__alg_1,dt_c1_5__alg_1,dt_c2_5__alg_1,dt_c3_5__alg_1,dt_c4_5__alg_1,dt_c5_5__alg_1,dt_c6_5__alg_1,e1_5_1__alg_1])],[reflexivity_r1_tarski,cc1_arytm_3,cc1_funct_2,cc2_arytm_3,rc1_arytm_3,existence_l1_struct_0,existence_l1_unialg_1,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,dt_k1_card_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_k5_relat_1,dt_l1_struct_0,dt_l1_unialg_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc5_funct_2,cc6_funct_2,cc6_membered,cc9_membered,fc1_struct_0,fc5_membered,fc6_membered,rc1_funct_2,rc1_membered,rc2_partfun1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,antisymmetry_r2_hidden,existence_m2_finseq_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k5_finseqop,redefinition_k5_numbers,redefinition_k7_funct_2,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k3_finseq_1,dt_k4_finseq_1,dt_k5_finseqop,dt_k5_numbers,dt_k7_funct_2,dt_m2_finseq_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_5__alg_1,dt_c1_5_1__alg_1,dt_c2_5__alg_1,dt_c3_5__alg_1,dt_c4_5__alg_1,dt_c5_5__alg_1,dt_c6_5__alg_1,cc15_membered,fc2_membered,t1_subset,t6_boole,t7_boole,t8_boole,e6_5__alg_1,e1_5_1__alg_1,t1_alg_1]), [interesting(0.5),file(alg_1,e4_5_1_1__alg_1),[file(alg_1,e4_5_1_1__alg_1)]]). fof(e3_5_1__alg_1,plain,( k1_funct_1(k5_finseqop(u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),c6_5__alg_1,c4_5__alg_1),c5_5__alg_1),c1_5_1__alg_1) = k1_funct_1(k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c3_5__alg_1),c6_5__alg_1,k7_funct_2(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),c4_5__alg_1,c5_5__alg_1)),c1_5_1__alg_1) ), inference(iterative_eq,[status(thm),assumptions([dt_c1_5_1__alg_1,dt_c1_5__alg_1,dt_c2_5__alg_1,dt_c3_5__alg_1,dt_c4_5__alg_1,dt_c5_5__alg_1,dt_c6_5__alg_1,e1_5_1__alg_1])],[cc1_arytm_3,cc2_arytm_3,rc1_arytm_3,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc5_membered,rc1_membered,rc5_struct_0,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_k5_relat_1,dt_l1_struct_0,dt_l1_unialg_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m2_finseq_1,dt_m2_relset_1,dt_m2_subset_1,cc15_membered,cc5_funct_2,cc6_funct_2,fc1_struct_0,fc2_membered,rc1_funct_2,rc2_partfun1,rc3_struct_0,redefinition_k5_finseqop,redefinition_k7_funct_2,dt_k1_funct_1,dt_k5_finseqop,dt_k7_funct_2,dt_u1_struct_0,dt_c1_5__alg_1,dt_c1_5_1__alg_1,dt_c2_5__alg_1,dt_c3_5__alg_1,dt_c4_5__alg_1,dt_c5_5__alg_1,dt_c6_5__alg_1,e1_5_1_1__alg_1,e2_5_1_1__alg_1,e3_5_1_1__alg_1,e4_5_1_1__alg_1]), [interesting(0.65),file(alg_1,e3_5_1__alg_1),[file(alg_1,e3_5_1__alg_1)]]). fof(i3_5_1__alg_1,theorem,( $true ), introduced(tautology,[file(alg_1,i3_5_1__alg_1)]), [interesting(0.65),trivial,file(alg_1,i3_5_1__alg_1)]). fof(i2_5_1__alg_1,plain,( k1_funct_1(k5_finseqop(u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),c6_5__alg_1,c4_5__alg_1),c5_5__alg_1),c1_5_1__alg_1) = k1_funct_1(k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c3_5__alg_1),c6_5__alg_1,k7_funct_2(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),c4_5__alg_1,c5_5__alg_1)),c1_5_1__alg_1) ), inference(conclusion,[status(thm),assumptions([dt_c1_5_1__alg_1,dt_c1_5__alg_1,dt_c2_5__alg_1,dt_c3_5__alg_1,dt_c4_5__alg_1,dt_c5_5__alg_1,dt_c6_5__alg_1,e1_5_1__alg_1])],[cc1_arytm_3,cc2_arytm_3,rc1_arytm_3,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc5_membered,rc1_membered,rc5_struct_0,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_k5_relat_1,dt_l1_struct_0,dt_l1_unialg_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m2_finseq_1,dt_m2_relset_1,dt_m2_subset_1,cc15_membered,cc5_funct_2,cc6_funct_2,fc1_struct_0,fc2_membered,rc1_funct_2,rc2_partfun1,rc3_struct_0,redefinition_k5_finseqop,redefinition_k7_funct_2,dt_k1_funct_1,dt_k5_finseqop,dt_k7_funct_2,dt_u1_struct_0,dt_c1_5__alg_1,dt_c1_5_1__alg_1,dt_c2_5__alg_1,dt_c3_5__alg_1,dt_c4_5__alg_1,dt_c5_5__alg_1,dt_c6_5__alg_1,e3_5_1__alg_1,i3_5_1__alg_1]), [interesting(0.65),file(alg_1,i2_5_1__alg_1),[file(alg_1,i2_5_1__alg_1)]]). fof(i2_5_1_tmp__alg_1,plain, ( r2_hidden(c1_5_1__alg_1,k4_finseq_1(c6_5__alg_1)) => k1_funct_1(k5_finseqop(u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),c6_5__alg_1,c4_5__alg_1),c5_5__alg_1),c1_5_1__alg_1) = k1_funct_1(k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c3_5__alg_1),c6_5__alg_1,k7_funct_2(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),c4_5__alg_1,c5_5__alg_1)),c1_5_1__alg_1) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_5_1__alg_1,dt_c1_5__alg_1,dt_c2_5__alg_1,dt_c3_5__alg_1,dt_c4_5__alg_1,dt_c5_5__alg_1,dt_c6_5__alg_1]),discharge_asm(discharge,[e1_5_1__alg_1])],[e1_5_1__alg_1,i2_5_1__alg_1]), [interesting(0.65),i1_5_1__alg_1]). fof(i1_5_1__alg_1,plain, ( r2_hidden(c1_5_1__alg_1,k4_finseq_1(c6_5__alg_1)) => k1_funct_1(k5_finseqop(u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),c6_5__alg_1,c4_5__alg_1),c5_5__alg_1),c1_5_1__alg_1) = k1_funct_1(k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c3_5__alg_1),c6_5__alg_1,k7_funct_2(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),c4_5__alg_1,c5_5__alg_1)),c1_5_1__alg_1) ), inference(mizar_def_expansion,[status(thm),assumptions([dt_c1_5_1__alg_1,dt_c1_5__alg_1,dt_c2_5__alg_1,dt_c3_5__alg_1,dt_c4_5__alg_1,dt_c5_5__alg_1,dt_c6_5__alg_1])],[i2_5_1_tmp__alg_1,cc1_arytm_3,cc2_arytm_3,rc1_arytm_3,dt_k2_zfmisc_1,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,fc5_membered,rc1_membered,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k5_numbers,dt_k5_relat_1,dt_l1_struct_0,dt_l1_unialg_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_relset_1,dt_m2_subset_1,cc15_membered,cc5_funct_2,cc6_funct_2,cc6_membered,cc9_membered,fc1_struct_0,fc2_membered,rc1_funct_2,rc2_partfun1,rc3_struct_0,rc5_struct_0,antisymmetry_r2_hidden,redefinition_k4_finseq_1,redefinition_k5_finseqop,redefinition_k7_funct_2,dt_k1_funct_1,dt_k4_finseq_1,dt_k5_finseqop,dt_k7_funct_2,dt_u1_struct_0,dt_c1_5__alg_1,dt_c1_5_1__alg_1,dt_c2_5__alg_1,dt_c3_5__alg_1,dt_c4_5__alg_1,dt_c5_5__alg_1,dt_c6_5__alg_1]), [interesting(0.65),file(alg_1,i1_5_1__alg_1),[file(alg_1,i1_5_1__alg_1)]]). fof(i1_5_1_tmp__alg_1,plain, ( m2_subset_1(c1_5_1__alg_1,k1_numbers,k5_numbers) => ( r2_hidden(c1_5_1__alg_1,k4_finseq_1(c6_5__alg_1)) => k1_funct_1(k5_finseqop(u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),c6_5__alg_1,c4_5__alg_1),c5_5__alg_1),c1_5_1__alg_1) = k1_funct_1(k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c3_5__alg_1),c6_5__alg_1,k7_funct_2(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),c4_5__alg_1,c5_5__alg_1)),c1_5_1__alg_1) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_5__alg_1,dt_c2_5__alg_1,dt_c3_5__alg_1,dt_c4_5__alg_1,dt_c5_5__alg_1,dt_c6_5__alg_1]),discharge_asm(discharge,[dt_c1_5_1__alg_1])],[dt_c1_5_1__alg_1,i1_5_1__alg_1]), [interesting(0.8),e8_5__alg_1]). fof(e8_5__alg_1,plain,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ( r2_hidden(A,k4_finseq_1(c6_5__alg_1)) => k1_funct_1(k5_finseqop(u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),c6_5__alg_1,c4_5__alg_1),c5_5__alg_1),A) = k1_funct_1(k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c3_5__alg_1),c6_5__alg_1,k7_funct_2(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),c4_5__alg_1,c5_5__alg_1)),A) ) ) ), inference(let,[status(thm),assumptions([dt_c1_5__alg_1,dt_c2_5__alg_1,dt_c3_5__alg_1,dt_c4_5__alg_1,dt_c5_5__alg_1,dt_c6_5__alg_1])],[i1_5_1_tmp__alg_1,dh_c1_5_1__alg_1]), [interesting(0.8),file(alg_1,e8_5__alg_1),[file(alg_1,e8_5__alg_1)]]). fof(e1_5__alg_1,plain,( k3_finseq_1(k5_finseqop(u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),c6_5__alg_1,c4_5__alg_1),c5_5__alg_1)) = k3_finseq_1(k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),c6_5__alg_1,c4_5__alg_1)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__alg_1,dt_c2_5__alg_1,dt_c3_5__alg_1,dt_c4_5__alg_1,dt_c5_5__alg_1,dt_c6_5__alg_1])],[reflexivity_r1_tarski,cc1_arytm_3,cc1_funct_2,cc2_arytm_3,rc1_arytm_3,existence_l1_struct_0,existence_l1_unialg_1,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,dt_k1_card_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_k5_relat_1,dt_l1_struct_0,dt_l1_unialg_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc5_funct_2,cc6_funct_2,cc6_membered,cc9_membered,fc1_struct_0,fc5_membered,fc6_membered,rc1_funct_2,rc1_membered,rc2_partfun1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,antisymmetry_r2_hidden,existence_m2_finseq_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k5_finseqop,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k3_finseq_1,dt_k4_finseq_1,dt_k5_finseqop,dt_k5_numbers,dt_m2_finseq_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_5__alg_1,dt_c2_5__alg_1,dt_c3_5__alg_1,dt_c4_5__alg_1,dt_c5_5__alg_1,dt_c6_5__alg_1,cc15_membered,fc2_membered,t1_subset,t6_boole,t7_boole,t8_boole,t1_alg_1]), [interesting(0.8),file(alg_1,e1_5__alg_1),[file(alg_1,e1_5__alg_1)]]). fof(e3_5__alg_1,plain,( k3_finseq_1(k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),c6_5__alg_1,c4_5__alg_1)) = k3_finseq_1(c6_5__alg_1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__alg_1,dt_c2_5__alg_1,dt_c4_5__alg_1,dt_c6_5__alg_1])],[reflexivity_r1_tarski,cc1_arytm_3,cc1_funct_2,cc2_arytm_3,rc1_arytm_3,existence_l1_struct_0,existence_l1_unialg_1,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,dt_k1_card_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_k5_relat_1,dt_l1_struct_0,dt_l1_unialg_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc5_funct_2,cc6_funct_2,cc6_membered,cc9_membered,fc1_struct_0,fc5_membered,fc6_membered,rc1_funct_2,rc1_membered,rc2_partfun1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,antisymmetry_r2_hidden,existence_m2_finseq_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k5_finseqop,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k3_finseq_1,dt_k4_finseq_1,dt_k5_finseqop,dt_k5_numbers,dt_m2_finseq_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_5__alg_1,dt_c2_5__alg_1,dt_c4_5__alg_1,dt_c6_5__alg_1,cc15_membered,fc2_membered,t1_subset,t6_boole,t7_boole,t8_boole,t1_alg_1]), [interesting(0.8),file(alg_1,e3_5__alg_1),[file(alg_1,e3_5__alg_1)]]). fof(e5_5__alg_1,plain,( k3_finseq_1(c6_5__alg_1) = k3_finseq_1(k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c3_5__alg_1),c6_5__alg_1,k7_funct_2(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),c4_5__alg_1,c5_5__alg_1))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__alg_1,dt_c2_5__alg_1,dt_c3_5__alg_1,dt_c4_5__alg_1,dt_c5_5__alg_1,dt_c6_5__alg_1])],[reflexivity_r1_tarski,cc1_arytm_3,cc1_funct_2,cc2_arytm_3,rc1_arytm_3,existence_l1_struct_0,existence_l1_unialg_1,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,dt_k1_card_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_k5_relat_1,dt_l1_struct_0,dt_l1_unialg_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc5_funct_2,cc6_funct_2,cc6_membered,cc9_membered,fc1_struct_0,fc5_membered,fc6_membered,rc1_funct_2,rc1_membered,rc2_partfun1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,antisymmetry_r2_hidden,existence_m2_finseq_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k5_finseqop,redefinition_k5_numbers,redefinition_k7_funct_2,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k3_finseq_1,dt_k4_finseq_1,dt_k5_finseqop,dt_k5_numbers,dt_k7_funct_2,dt_m2_finseq_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_5__alg_1,dt_c2_5__alg_1,dt_c3_5__alg_1,dt_c4_5__alg_1,dt_c5_5__alg_1,dt_c6_5__alg_1,cc15_membered,fc2_membered,t1_subset,t6_boole,t7_boole,t8_boole,t1_alg_1]), [interesting(0.8),file(alg_1,e5_5__alg_1),[file(alg_1,e5_5__alg_1)]]). 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(e7_5__alg_1,plain, ( k4_finseq_1(c6_5__alg_1) = k2_finseq_1(k3_finseq_1(c6_5__alg_1)) & k4_finseq_1(k5_finseqop(u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),c6_5__alg_1,c4_5__alg_1),c5_5__alg_1)) = k2_finseq_1(k3_finseq_1(c6_5__alg_1)) & k4_finseq_1(k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),c6_5__alg_1,c4_5__alg_1)) = k2_finseq_1(k3_finseq_1(c6_5__alg_1)) & k4_finseq_1(k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c3_5__alg_1),c6_5__alg_1,k7_funct_2(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),c4_5__alg_1,c5_5__alg_1))) = k2_finseq_1(k3_finseq_1(c6_5__alg_1)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__alg_1,dt_c2_5__alg_1,dt_c3_5__alg_1,dt_c4_5__alg_1,dt_c5_5__alg_1,dt_c6_5__alg_1])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_arytm_3,cc1_funct_2,cc1_membered,cc1_relset_1,cc20_membered,cc2_arytm_3,cc2_membered,cc3_membered,fc6_membered,rc1_arytm_3,rc1_membered,t1_subset,t4_subset,t5_subset,existence_l1_struct_0,existence_l1_unialg_1,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_relset_1,redefinition_m2_finseq_1,redefinition_m2_relset_1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_k5_relat_1,dt_l1_struct_0,dt_l1_unialg_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc3_arytm_3,cc4_membered,cc5_funct_2,cc6_funct_2,cc6_membered,cc9_membered,fc1_struct_0,fc5_membered,rc1_funct_2,rc2_partfun1,rc3_struct_0,rc5_struct_0,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_finseqop,redefinition_k5_numbers,redefinition_k7_funct_2,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_relat_1,dt_k2_finseq_1,dt_k3_finseq_1,dt_k4_finseq_1,dt_k5_finseqop,dt_k5_numbers,dt_k7_funct_2,dt_m2_subset_1,dt_u1_struct_0,dt_c1_5__alg_1,dt_c2_5__alg_1,dt_c3_5__alg_1,dt_c4_5__alg_1,dt_c5_5__alg_1,dt_c6_5__alg_1,fc2_membered,e2_5__alg_1,e4_5__alg_1,e5_5__alg_1,d3_finseq_1]), [interesting(0.8),file(alg_1,e7_5__alg_1),[file(alg_1,e7_5__alg_1)]]). fof(t10_finseq_2,theorem,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( ( k3_finseq_1(B) = A & k3_finseq_1(C) = A & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( r2_hidden(D,k2_finseq_1(A)) => k1_funct_1(B,D) = k1_funct_1(C,D) ) ) ) => B = C ) ) ) ) ), file(finseq_2,t10_finseq_2), [interesting(0.9),axiom,file(finseq_2,t10_finseq_2)]). fof(e9_5__alg_1,plain,( k5_finseqop(u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),c6_5__alg_1,c4_5__alg_1),c5_5__alg_1) = k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c3_5__alg_1),c6_5__alg_1,k7_funct_2(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),c4_5__alg_1,c5_5__alg_1)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__alg_1,dt_c2_5__alg_1,dt_c3_5__alg_1,dt_c4_5__alg_1,dt_c5_5__alg_1,dt_c6_5__alg_1])],[reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_arytm_3,cc1_funct_2,cc1_membered,cc1_relset_1,cc20_membered,cc2_arytm_3,cc2_membered,cc3_membered,fc6_membered,rc1_arytm_3,rc1_membered,existence_l1_struct_0,existence_l1_unialg_1,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_relset_1,redefinition_m2_finseq_1,redefinition_m2_relset_1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_k5_relat_1,dt_l1_struct_0,dt_l1_unialg_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc3_arytm_3,cc4_membered,cc5_funct_2,cc6_funct_2,cc6_membered,cc9_membered,fc1_struct_0,fc5_membered,rc1_funct_2,rc2_partfun1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m2_subset_1,redefinition_k2_finseq_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k5_finseqop,redefinition_k5_numbers,redefinition_k7_funct_2,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_finseq_1,dt_k3_finseq_1,dt_k4_finseq_1,dt_k5_finseqop,dt_k5_numbers,dt_k7_funct_2,dt_m2_subset_1,dt_u1_struct_0,dt_c1_5__alg_1,dt_c2_5__alg_1,dt_c3_5__alg_1,dt_c4_5__alg_1,dt_c5_5__alg_1,dt_c6_5__alg_1,fc2_membered,t1_subset,t7_boole,e8_5__alg_1,e1_5__alg_1,e3_5__alg_1,e5_5__alg_1,e7_5__alg_1,t10_finseq_2]), [interesting(0.8),file(alg_1,e9_5__alg_1),[file(alg_1,e9_5__alg_1)]]). fof(i7_5__alg_1,theorem,( $true ), introduced(tautology,[file(alg_1,i7_5__alg_1)]), [interesting(0.8),trivial,file(alg_1,i7_5__alg_1)]). fof(i6_5__alg_1,plain,( k5_finseqop(u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),c6_5__alg_1,c4_5__alg_1),c5_5__alg_1) = k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c3_5__alg_1),c6_5__alg_1,k7_funct_2(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),c4_5__alg_1,c5_5__alg_1)) ), inference(conclusion,[status(thm),assumptions([dt_c1_5__alg_1,dt_c2_5__alg_1,dt_c3_5__alg_1,dt_c4_5__alg_1,dt_c5_5__alg_1,dt_c6_5__alg_1])],[cc1_arytm_3,cc2_arytm_3,rc1_arytm_3,dt_k1_numbers,dt_k5_ordinal2,cc3_arytm_3,cc6_membered,fc2_membered,fc5_membered,redefinition_k5_numbers,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc9_membered,rc1_funct_2,rc1_membered,rc2_partfun1,rc5_struct_0,redefinition_m2_finseq_1,redefinition_m2_relset_1,dt_k5_relat_1,dt_l1_struct_0,dt_l1_unialg_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m2_finseq_1,dt_m2_relset_1,cc15_membered,cc5_funct_2,cc6_funct_2,fc1_struct_0,rc3_struct_0,redefinition_k5_finseqop,redefinition_k7_funct_2,dt_k5_finseqop,dt_k7_funct_2,dt_u1_struct_0,dt_c1_5__alg_1,dt_c2_5__alg_1,dt_c3_5__alg_1,dt_c4_5__alg_1,dt_c5_5__alg_1,dt_c6_5__alg_1,e9_5__alg_1,i7_5__alg_1]), [interesting(0.8),file(alg_1,i6_5__alg_1),[file(alg_1,i6_5__alg_1)]]). fof(i6_5_tmp__alg_1,plain, ( m2_finseq_1(c6_5__alg_1,u1_struct_0(c1_5__alg_1)) => k5_finseqop(u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),c6_5__alg_1,c4_5__alg_1),c5_5__alg_1) = k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c3_5__alg_1),c6_5__alg_1,k7_funct_2(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),c4_5__alg_1,c5_5__alg_1)) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_5__alg_1,dt_c2_5__alg_1,dt_c3_5__alg_1,dt_c4_5__alg_1,dt_c5_5__alg_1]),discharge_asm(discharge,[dt_c6_5__alg_1])],[dt_c6_5__alg_1,i6_5__alg_1]), [interesting(0.8),i5_5__alg_1]). fof(i5_5__alg_1,plain,( ! [A] : ( m2_finseq_1(A,u1_struct_0(c1_5__alg_1)) => k5_finseqop(u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),A,c4_5__alg_1),c5_5__alg_1) = k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c3_5__alg_1),A,k7_funct_2(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),c4_5__alg_1,c5_5__alg_1)) ) ), inference(let,[status(thm),assumptions([dt_c1_5__alg_1,dt_c2_5__alg_1,dt_c3_5__alg_1,dt_c4_5__alg_1,dt_c5_5__alg_1])],[i6_5_tmp__alg_1,dh_c6_5__alg_1]), [interesting(0.8),file(alg_1,i5_5__alg_1),[file(alg_1,i5_5__alg_1)]]). fof(i5_5_tmp__alg_1,plain, ( ( v1_funct_1(c5_5__alg_1) & v1_funct_2(c5_5__alg_1,u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1)) & m2_relset_1(c5_5__alg_1,u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1)) ) => ! [A] : ( m2_finseq_1(A,u1_struct_0(c1_5__alg_1)) => k5_finseqop(u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),A,c4_5__alg_1),c5_5__alg_1) = k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c3_5__alg_1),A,k7_funct_2(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),c4_5__alg_1,c5_5__alg_1)) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_5__alg_1,dt_c2_5__alg_1,dt_c3_5__alg_1,dt_c4_5__alg_1]),discharge_asm(discharge,[dt_c5_5__alg_1])],[dt_c5_5__alg_1,i5_5__alg_1]), [interesting(0.8),i4_5__alg_1]). fof(i4_5__alg_1,plain,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1)) & m2_relset_1(A,u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1)) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(c1_5__alg_1)) => k5_finseqop(u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),B,c4_5__alg_1),A) = k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c3_5__alg_1),B,k7_funct_2(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),c4_5__alg_1,A)) ) ) ), inference(let,[status(thm),assumptions([dt_c1_5__alg_1,dt_c2_5__alg_1,dt_c3_5__alg_1,dt_c4_5__alg_1])],[i5_5_tmp__alg_1,dh_c5_5__alg_1]), [interesting(0.8),file(alg_1,i4_5__alg_1),[file(alg_1,i4_5__alg_1)]]). fof(i4_5_tmp__alg_1,plain, ( ( v1_funct_1(c4_5__alg_1) & v1_funct_2(c4_5__alg_1,u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1)) & m2_relset_1(c4_5__alg_1,u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1)) ) => ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1)) & m2_relset_1(A,u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1)) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(c1_5__alg_1)) => k5_finseqop(u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),B,c4_5__alg_1),A) = k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c3_5__alg_1),B,k7_funct_2(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),c4_5__alg_1,A)) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_5__alg_1,dt_c2_5__alg_1,dt_c3_5__alg_1]),discharge_asm(discharge,[dt_c4_5__alg_1])],[dt_c4_5__alg_1,i4_5__alg_1]), [interesting(0.8),i3_5__alg_1]). fof(i3_5__alg_1,plain,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1)) & m2_relset_1(A,u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1)) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1)) & m2_relset_1(B,u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1)) ) => ! [C] : ( m2_finseq_1(C,u1_struct_0(c1_5__alg_1)) => k5_finseqop(u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),C,A),B) = k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c3_5__alg_1),C,k7_funct_2(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),A,B)) ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_5__alg_1,dt_c2_5__alg_1,dt_c3_5__alg_1])],[i4_5_tmp__alg_1,dh_c4_5__alg_1]), [interesting(0.8),file(alg_1,i3_5__alg_1),[file(alg_1,i3_5__alg_1)]]). fof(i3_5_tmp__alg_1,plain, ( ( ~ v3_struct_0(c3_5__alg_1) & v6_unialg_1(c3_5__alg_1) & v7_unialg_1(c3_5__alg_1) & v8_unialg_1(c3_5__alg_1) & l1_unialg_1(c3_5__alg_1) ) => ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1)) & m2_relset_1(A,u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1)) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1)) & m2_relset_1(B,u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1)) ) => ! [C] : ( m2_finseq_1(C,u1_struct_0(c1_5__alg_1)) => k5_finseqop(u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),C,A),B) = k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c3_5__alg_1),C,k7_funct_2(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),u1_struct_0(c3_5__alg_1),A,B)) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_5__alg_1,dt_c2_5__alg_1]),discharge_asm(discharge,[dt_c3_5__alg_1])],[dt_c3_5__alg_1,i3_5__alg_1]), [interesting(0.8),i2_5__alg_1]). fof(i2_5__alg_1,plain,( ! [A] : ( ( ~ v3_struct_0(A) & v6_unialg_1(A) & v7_unialg_1(A) & v8_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1)) & m2_relset_1(B,u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1)) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(c2_5__alg_1),u1_struct_0(A)) & m2_relset_1(C,u1_struct_0(c2_5__alg_1),u1_struct_0(A)) ) => ! [D] : ( m2_finseq_1(D,u1_struct_0(c1_5__alg_1)) => k5_finseqop(u1_struct_0(c2_5__alg_1),u1_struct_0(A),k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),D,B),C) = k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(A),D,k7_funct_2(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),u1_struct_0(A),B,C)) ) ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_5__alg_1,dt_c2_5__alg_1])],[i3_5_tmp__alg_1,dh_c3_5__alg_1]), [interesting(0.8),file(alg_1,i2_5__alg_1),[file(alg_1,i2_5__alg_1)]]). fof(i2_5_tmp__alg_1,plain, ( ( ~ v3_struct_0(c2_5__alg_1) & v6_unialg_1(c2_5__alg_1) & v7_unialg_1(c2_5__alg_1) & v8_unialg_1(c2_5__alg_1) & l1_unialg_1(c2_5__alg_1) ) => ! [A] : ( ( ~ v3_struct_0(A) & v6_unialg_1(A) & v7_unialg_1(A) & v8_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1)) & m2_relset_1(B,u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1)) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(c2_5__alg_1),u1_struct_0(A)) & m2_relset_1(C,u1_struct_0(c2_5__alg_1),u1_struct_0(A)) ) => ! [D] : ( m2_finseq_1(D,u1_struct_0(c1_5__alg_1)) => k5_finseqop(u1_struct_0(c2_5__alg_1),u1_struct_0(A),k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),D,B),C) = k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(A),D,k7_funct_2(u1_struct_0(c1_5__alg_1),u1_struct_0(c2_5__alg_1),u1_struct_0(A),B,C)) ) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_5__alg_1]),discharge_asm(discharge,[dt_c2_5__alg_1])],[dt_c2_5__alg_1,i2_5__alg_1]), [interesting(0.8),i1_5__alg_1]). fof(i1_5__alg_1,plain,( ! [A] : ( ( ~ v3_struct_0(A) & v6_unialg_1(A) & v7_unialg_1(A) & v8_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v6_unialg_1(B) & v7_unialg_1(B) & v8_unialg_1(B) & l1_unialg_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(c1_5__alg_1),u1_struct_0(A)) & m2_relset_1(C,u1_struct_0(c1_5__alg_1),u1_struct_0(A)) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) ) => ! [E] : ( m2_finseq_1(E,u1_struct_0(c1_5__alg_1)) => k5_finseqop(u1_struct_0(A),u1_struct_0(B),k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(A),E,C),D) = k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(B),E,k7_funct_2(u1_struct_0(c1_5__alg_1),u1_struct_0(A),u1_struct_0(B),C,D)) ) ) ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_5__alg_1])],[i2_5_tmp__alg_1,dh_c2_5__alg_1]), [interesting(0.8),file(alg_1,i1_5__alg_1),[file(alg_1,i1_5__alg_1)]]). fof(i1_5_tmp__alg_1,plain, ( ( ~ v3_struct_0(c1_5__alg_1) & v6_unialg_1(c1_5__alg_1) & v7_unialg_1(c1_5__alg_1) & v8_unialg_1(c1_5__alg_1) & l1_unialg_1(c1_5__alg_1) ) => ! [A] : ( ( ~ v3_struct_0(A) & v6_unialg_1(A) & v7_unialg_1(A) & v8_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v6_unialg_1(B) & v7_unialg_1(B) & v8_unialg_1(B) & l1_unialg_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(c1_5__alg_1),u1_struct_0(A)) & m2_relset_1(C,u1_struct_0(c1_5__alg_1),u1_struct_0(A)) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) ) => ! [E] : ( m2_finseq_1(E,u1_struct_0(c1_5__alg_1)) => k5_finseqop(u1_struct_0(A),u1_struct_0(B),k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(A),E,C),D) = k5_finseqop(u1_struct_0(c1_5__alg_1),u1_struct_0(B),E,k7_funct_2(u1_struct_0(c1_5__alg_1),u1_struct_0(A),u1_struct_0(B),C,D)) ) ) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_5__alg_1])],[dt_c1_5__alg_1,i1_5__alg_1]), [interesting(1),t5_alg_1]). fof(t5_alg_1,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & v6_unialg_1(A) & v7_unialg_1(A) & v8_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v6_unialg_1(B) & v7_unialg_1(B) & v8_unialg_1(B) & l1_unialg_1(B) ) => ! [C] : ( ( ~ v3_struct_0(C) & v6_unialg_1(C) & v7_unialg_1(C) & v8_unialg_1(C) & l1_unialg_1(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C)) & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) ) => ! [F] : ( m2_finseq_1(F,u1_struct_0(A)) => k5_finseqop(u1_struct_0(B),u1_struct_0(C),k5_finseqop(u1_struct_0(A),u1_struct_0(B),F,D),E) = k5_finseqop(u1_struct_0(A),u1_struct_0(C),F,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E)) ) ) ) ) ) ) ), inference(let,[status(thm),assumptions([])],[i1_5_tmp__alg_1,dh_c1_5__alg_1]), [interesting(1),file(alg_1,t5_alg_1),[file(alg_1,t5_alg_1)]]).