% Mizar ND problem: t32_trees_4,trees_4,1256,31 fof(dh_c1_54__trees_4,definition, ( ( ~ v1_xboole_0(c1_54__trees_4) => ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,c1_54__trees_4) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m2_finseq_1(D,k5_trees_3(k2_zfmisc_1(c1_54__trees_4,A))) => ? [E] : ( m2_finseq_1(E,k5_trees_3(A)) & k4_finseq_1(E) = k4_finseq_1(D) & ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ~ ( r2_hidden(F,k4_finseq_1(D)) & ! [G] : ( m5_trees_3(G,k2_zfmisc_1(c1_54__trees_4,A),k5_trees_3(k2_zfmisc_1(c1_54__trees_4,A))) => ~ ( G = k1_funct_1(D,F) & k1_funct_1(E,F) = k11_trees_3(c1_54__trees_4,A,G) ) ) ) ) & k11_trees_3(c1_54__trees_4,A,k12_trees_4(k2_zfmisc_1(c1_54__trees_4,A),k1_domain_1(c1_54__trees_4,A,B,C),D)) = k12_trees_4(A,C,E) ) ) ) ) ) ) => ! [H] : ( ~ v1_xboole_0(H) => ! [I] : ( ~ v1_xboole_0(I) => ! [J] : ( m1_subset_1(J,H) => ! [K] : ( m1_subset_1(K,I) => ! [L] : ( m2_finseq_1(L,k5_trees_3(k2_zfmisc_1(H,I))) => ? [M] : ( m2_finseq_1(M,k5_trees_3(I)) & k4_finseq_1(M) = k4_finseq_1(L) & ! [N] : ( m2_subset_1(N,k1_numbers,k5_numbers) => ~ ( r2_hidden(N,k4_finseq_1(L)) & ! [O] : ( m5_trees_3(O,k2_zfmisc_1(H,I),k5_trees_3(k2_zfmisc_1(H,I))) => ~ ( O = k1_funct_1(L,N) & k1_funct_1(M,N) = k11_trees_3(H,I,O) ) ) ) ) & k11_trees_3(H,I,k12_trees_4(k2_zfmisc_1(H,I),k1_domain_1(H,I,J,K),L)) = k12_trees_4(I,K,M) ) ) ) ) ) ) ), introduced(definition,[new_symbol(c1_54__trees_4),file(trees_4,c1_54__trees_4)]), [interesting(0.8),axiom,file(trees_4,c1_54__trees_4)]). fof(dh_c2_54__trees_4,definition, ( ( ~ v1_xboole_0(c2_54__trees_4) => ! [A] : ( m1_subset_1(A,c1_54__trees_4) => ! [B] : ( m1_subset_1(B,c2_54__trees_4) => ! [C] : ( m2_finseq_1(C,k5_trees_3(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4))) => ? [D] : ( m2_finseq_1(D,k5_trees_3(c2_54__trees_4)) & k4_finseq_1(D) = k4_finseq_1(C) & ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ~ ( r2_hidden(E,k4_finseq_1(C)) & ! [F] : ( m5_trees_3(F,k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k5_trees_3(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4))) => ~ ( F = k1_funct_1(C,E) & k1_funct_1(D,E) = k11_trees_3(c1_54__trees_4,c2_54__trees_4,F) ) ) ) ) & k11_trees_3(c1_54__trees_4,c2_54__trees_4,k12_trees_4(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k1_domain_1(c1_54__trees_4,c2_54__trees_4,A,B),C)) = k12_trees_4(c2_54__trees_4,B,D) ) ) ) ) ) => ! [G] : ( ~ v1_xboole_0(G) => ! [H] : ( m1_subset_1(H,c1_54__trees_4) => ! [I] : ( m1_subset_1(I,G) => ! [J] : ( m2_finseq_1(J,k5_trees_3(k2_zfmisc_1(c1_54__trees_4,G))) => ? [K] : ( m2_finseq_1(K,k5_trees_3(G)) & k4_finseq_1(K) = k4_finseq_1(J) & ! [L] : ( m2_subset_1(L,k1_numbers,k5_numbers) => ~ ( r2_hidden(L,k4_finseq_1(J)) & ! [M] : ( m5_trees_3(M,k2_zfmisc_1(c1_54__trees_4,G),k5_trees_3(k2_zfmisc_1(c1_54__trees_4,G))) => ~ ( M = k1_funct_1(J,L) & k1_funct_1(K,L) = k11_trees_3(c1_54__trees_4,G,M) ) ) ) ) & k11_trees_3(c1_54__trees_4,G,k12_trees_4(k2_zfmisc_1(c1_54__trees_4,G),k1_domain_1(c1_54__trees_4,G,H,I),J)) = k12_trees_4(G,I,K) ) ) ) ) ) ), introduced(definition,[new_symbol(c2_54__trees_4),file(trees_4,c2_54__trees_4)]), [interesting(0.8),axiom,file(trees_4,c2_54__trees_4)]). fof(dh_c3_54__trees_4,definition, ( ( m1_subset_1(c3_54__trees_4,c1_54__trees_4) => ! [A] : ( m1_subset_1(A,c2_54__trees_4) => ! [B] : ( m2_finseq_1(B,k5_trees_3(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4))) => ? [C] : ( m2_finseq_1(C,k5_trees_3(c2_54__trees_4)) & k4_finseq_1(C) = k4_finseq_1(B) & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ~ ( r2_hidden(D,k4_finseq_1(B)) & ! [E] : ( m5_trees_3(E,k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k5_trees_3(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4))) => ~ ( E = k1_funct_1(B,D) & k1_funct_1(C,D) = k11_trees_3(c1_54__trees_4,c2_54__trees_4,E) ) ) ) ) & k11_trees_3(c1_54__trees_4,c2_54__trees_4,k12_trees_4(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k1_domain_1(c1_54__trees_4,c2_54__trees_4,c3_54__trees_4,A),B)) = k12_trees_4(c2_54__trees_4,A,C) ) ) ) ) => ! [F] : ( m1_subset_1(F,c1_54__trees_4) => ! [G] : ( m1_subset_1(G,c2_54__trees_4) => ! [H] : ( m2_finseq_1(H,k5_trees_3(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4))) => ? [I] : ( m2_finseq_1(I,k5_trees_3(c2_54__trees_4)) & k4_finseq_1(I) = k4_finseq_1(H) & ! [J] : ( m2_subset_1(J,k1_numbers,k5_numbers) => ~ ( r2_hidden(J,k4_finseq_1(H)) & ! [K] : ( m5_trees_3(K,k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k5_trees_3(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4))) => ~ ( K = k1_funct_1(H,J) & k1_funct_1(I,J) = k11_trees_3(c1_54__trees_4,c2_54__trees_4,K) ) ) ) ) & k11_trees_3(c1_54__trees_4,c2_54__trees_4,k12_trees_4(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k1_domain_1(c1_54__trees_4,c2_54__trees_4,F,G),H)) = k12_trees_4(c2_54__trees_4,G,I) ) ) ) ) ), introduced(definition,[new_symbol(c3_54__trees_4),file(trees_4,c3_54__trees_4)]), [interesting(0.8),axiom,file(trees_4,c3_54__trees_4)]). fof(dh_c4_54__trees_4,definition, ( ( m1_subset_1(c4_54__trees_4,c2_54__trees_4) => ! [A] : ( m2_finseq_1(A,k5_trees_3(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4))) => ? [B] : ( m2_finseq_1(B,k5_trees_3(c2_54__trees_4)) & k4_finseq_1(B) = k4_finseq_1(A) & ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ~ ( r2_hidden(C,k4_finseq_1(A)) & ! [D] : ( m5_trees_3(D,k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k5_trees_3(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4))) => ~ ( D = k1_funct_1(A,C) & k1_funct_1(B,C) = k11_trees_3(c1_54__trees_4,c2_54__trees_4,D) ) ) ) ) & k11_trees_3(c1_54__trees_4,c2_54__trees_4,k12_trees_4(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k1_domain_1(c1_54__trees_4,c2_54__trees_4,c3_54__trees_4,c4_54__trees_4),A)) = k12_trees_4(c2_54__trees_4,c4_54__trees_4,B) ) ) ) => ! [E] : ( m1_subset_1(E,c2_54__trees_4) => ! [F] : ( m2_finseq_1(F,k5_trees_3(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4))) => ? [G] : ( m2_finseq_1(G,k5_trees_3(c2_54__trees_4)) & k4_finseq_1(G) = k4_finseq_1(F) & ! [H] : ( m2_subset_1(H,k1_numbers,k5_numbers) => ~ ( r2_hidden(H,k4_finseq_1(F)) & ! [I] : ( m5_trees_3(I,k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k5_trees_3(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4))) => ~ ( I = k1_funct_1(F,H) & k1_funct_1(G,H) = k11_trees_3(c1_54__trees_4,c2_54__trees_4,I) ) ) ) ) & k11_trees_3(c1_54__trees_4,c2_54__trees_4,k12_trees_4(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k1_domain_1(c1_54__trees_4,c2_54__trees_4,c3_54__trees_4,E),F)) = k12_trees_4(c2_54__trees_4,E,G) ) ) ) ), introduced(definition,[new_symbol(c4_54__trees_4),file(trees_4,c4_54__trees_4)]), [interesting(0.8),axiom,file(trees_4,c4_54__trees_4)]). fof(dh_c5_54__trees_4,definition, ( ( m2_finseq_1(c5_54__trees_4,k5_trees_3(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4))) => ? [A] : ( m2_finseq_1(A,k5_trees_3(c2_54__trees_4)) & k4_finseq_1(A) = k4_finseq_1(c5_54__trees_4) & ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ~ ( r2_hidden(B,k4_finseq_1(c5_54__trees_4)) & ! [C] : ( m5_trees_3(C,k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k5_trees_3(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4))) => ~ ( C = k1_funct_1(c5_54__trees_4,B) & k1_funct_1(A,B) = k11_trees_3(c1_54__trees_4,c2_54__trees_4,C) ) ) ) ) & k11_trees_3(c1_54__trees_4,c2_54__trees_4,k12_trees_4(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k1_domain_1(c1_54__trees_4,c2_54__trees_4,c3_54__trees_4,c4_54__trees_4),c5_54__trees_4)) = k12_trees_4(c2_54__trees_4,c4_54__trees_4,A) ) ) => ! [D] : ( m2_finseq_1(D,k5_trees_3(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4))) => ? [E] : ( m2_finseq_1(E,k5_trees_3(c2_54__trees_4)) & k4_finseq_1(E) = k4_finseq_1(D) & ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ~ ( r2_hidden(F,k4_finseq_1(D)) & ! [G] : ( m5_trees_3(G,k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k5_trees_3(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4))) => ~ ( G = k1_funct_1(D,F) & k1_funct_1(E,F) = k11_trees_3(c1_54__trees_4,c2_54__trees_4,G) ) ) ) ) & k11_trees_3(c1_54__trees_4,c2_54__trees_4,k12_trees_4(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k1_domain_1(c1_54__trees_4,c2_54__trees_4,c3_54__trees_4,c4_54__trees_4),D)) = k12_trees_4(c2_54__trees_4,c4_54__trees_4,E) ) ) ), introduced(definition,[new_symbol(c5_54__trees_4),file(trees_4,c5_54__trees_4)]), [interesting(0.8),axiom,file(trees_4,c5_54__trees_4)]). fof(rc6_trees_3,theorem,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finset_1(A) & v1_finseq_1(A) & v6_trees_3(A) ) ), file(trees_3,rc6_trees_3), [interesting(0.9),axiom,file(trees_3,rc6_trees_3)]). fof(rc8_trees_3,theorem,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v6_trees_3(A) ) ), file(trees_3,rc8_trees_3), [interesting(0.9),axiom,file(trees_3,rc8_trees_3)]). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), [interesting(0.9),axiom,file(relset_1,m1_relset_1)]). fof(cc10_trees_3,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_trees_3(A) ) => ! [B] : ( m1_finseq_1(B,A) => v6_trees_3(B) ) ) ), file(trees_3,cc10_trees_3), [interesting(0.9),axiom,file(trees_3,cc10_trees_3)]). 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(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_arytm_3,theorem,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_ordinal1(B) & v2_ordinal1(B) & v3_ordinal1(B) ) ) ) ), file(arytm_3,cc1_arytm_3), [interesting(0.9),axiom,file(arytm_3,cc1_arytm_3)]). fof(cc1_membered,theorem,( ! [A] : ( v5_membered(A) => v4_membered(A) ) ), file(membered,cc1_membered), [interesting(0.9),axiom,file(membered,cc1_membered)]). fof(cc1_trees_4,theorem,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v3_trees_3(A) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m1_finseq_1(C,B) => v6_trees_3(C) ) ) ), file(trees_4,cc1_trees_4), [interesting(0.9),axiom,file(trees_4,cc1_trees_4)]). 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_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(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_trees_3,theorem,( ! [A] : ( v3_trees_3(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v3_trees_3(B) ) ) ), file(trees_3,cc4_trees_3), [interesting(0.9),axiom,file(trees_3,cc4_trees_3)]). fof(fc17_finseq_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) => v1_finset_1(k1_relat_1(A)) ) ), file(finseq_1,fc17_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc17_finseq_1)]). fof(fc5_trees_2,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_finset_1(A) ) => v1_finset_1(k1_relat_1(A)) ) ), file(trees_2,fc5_trees_2), [interesting(0.9),axiom,file(trees_2,fc5_trees_2)]). fof(rc1_arytm_3,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ), file(arytm_3,rc1_arytm_3), [interesting(0.9),axiom,file(arytm_3,rc1_arytm_3)]). fof(rc1_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_finseq_1,theorem,( ! [A] : ? [B] : ( m1_relset_1(B,k5_numbers,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc2_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc2_finseq_1)]). fof(rc2_trees_3,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) & v3_trees_3(A) ) ), file(trees_3,rc2_trees_3), [interesting(0.9),axiom,file(trees_3,rc2_trees_3)]). fof(rc4_trees_3,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m4_trees_3(B,A) & ~ v1_xboole_0(B) & v1_finset_1(B) & v3_trees_3(B) ) ) ), file(trees_3,rc4_trees_3), [interesting(0.9),axiom,file(trees_3,rc4_trees_3)]). 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(rc7_trees_2,theorem,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v3_trees_2(A) ) ), file(trees_2,rc7_trees_2), [interesting(0.9),axiom,file(trees_2,rc7_trees_2)]). 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(rc8_trees_2,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m3_trees_2(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v3_trees_2(B) ) ) ), file(trees_2,rc8_trees_2), [interesting(0.9),axiom,file(trees_2,rc8_trees_2)]). fof(rc9_trees_2,theorem,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ? [C] : ( m1_relset_1(C,A,B) & v1_relat_1(C) & ~ v1_xboole_0(C) ) ) ), file(trees_2,rc9_trees_2), [interesting(0.9),axiom,file(trees_2,rc9_trees_2)]). fof(redefinition_m2_relset_1,definition,( ! [A,B,C] : ( m2_relset_1(C,A,B) <=> m1_relset_1(C,A,B) ) ), file(relset_1,m2_relset_1), [interesting(0.9),axiom,file(relset_1,m2_relset_1)]). fof(dt_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_k4_tarski,axiom,( $true ), file(tarski,k4_tarski), [interesting(0.9),axiom,file(tarski,k4_tarski)]). fof(dt_k4_trees_4,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( v1_relat_1(k4_trees_4(A,B)) & v1_funct_1(k4_trees_4(A,B)) & v3_trees_2(k4_trees_4(A,B)) ) ) ), file(trees_4,k4_trees_4), [interesting(0.9),axiom,file(trees_4,k4_trees_4)]). fof(dt_k5_ordinal2,axiom,( $true ), file(ordinal2,k5_ordinal2), [interesting(0.9),axiom,file(ordinal2,k5_ordinal2)]). fof(dt_m1_finseq_1,axiom,( ! [A,B] : ( m1_finseq_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) ) ), file(finseq_1,m1_finseq_1), [interesting(0.9),axiom,file(finseq_1,m1_finseq_1)]). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), [interesting(0.9),axiom,file(subset_1,m1_subset_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(dt_m3_trees_2,axiom,( ! [A,B] : ( m3_trees_2(B,A) => v1_relat_1(B) ) ), file(trees_2,m3_trees_2), [interesting(0.9),axiom,file(trees_2,m3_trees_2)]). fof(dt_m4_trees_3,axiom,( $true ), file(trees_3,m4_trees_3), [interesting(0.9),axiom,file(trees_3,m4_trees_3)]). 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(cc15_membered,theorem,( ! [A] : ( v1_xboole_0(A) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc15_membered), [interesting(0.9),axiom,file(membered,cc15_membered)]). fof(cc16_membered,theorem,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_membered(B) ) ) ), file(membered,cc16_membered), [interesting(0.9),axiom,file(membered,cc16_membered)]). fof(cc17_membered,theorem,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) ) ) ) ), file(membered,cc17_membered), [interesting(0.9),axiom,file(membered,cc17_membered)]). fof(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_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(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(cc4_membered,theorem,( ! [A] : ( v2_membered(A) => v1_membered(A) ) ), file(membered,cc4_membered), [interesting(0.9),axiom,file(membered,cc4_membered)]). fof(cc5_trees_3,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m4_trees_3(B,A) => v3_trees_3(B) ) ) ), file(trees_3,cc5_trees_3), [interesting(0.9),axiom,file(trees_3,cc5_trees_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(cc9_membered,theorem,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k5_numbers)) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc9_membered), [interesting(0.9),axiom,file(membered,cc9_membered)]). fof(fc1_ordinal2,theorem, ( v1_ordinal1(k5_ordinal2) & v2_ordinal1(k5_ordinal2) & v3_ordinal1(k5_ordinal2) & ~ v1_xboole_0(k5_ordinal2) ), file(ordinal2,fc1_ordinal2), [interesting(0.9),axiom,file(ordinal2,fc1_ordinal2)]). fof(fc1_subset_1,theorem,( ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ), file(subset_1,fc1_subset_1), [interesting(0.9),axiom,file(subset_1,fc1_subset_1)]). fof(fc26_trees_3,theorem,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k5_trees_3(A)) ) => ( ~ v1_xboole_0(k1_relat_1(B)) & v1_finset_1(k1_relat_1(B)) & v1_trees_1(k1_relat_1(B)) ) ) ), file(trees_3,fc26_trees_3), [interesting(0.9),axiom,file(trees_3,fc26_trees_3)]). fof(fc2_trees_2,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ( ~ v1_xboole_0(k1_relat_1(A)) & v1_trees_1(k1_relat_1(A)) ) ) ), file(trees_2,fc2_trees_2), [interesting(0.9),axiom,file(trees_2,fc2_trees_2)]). fof(fc4_subset_1,theorem,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ), file(subset_1,fc4_subset_1), [interesting(0.9),axiom,file(subset_1,fc4_subset_1)]). fof(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(fc6_trees_3,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ v1_xboole_0(k5_trees_3(A)) & v3_trees_3(k5_trees_3(A)) ) ) ), file(trees_3,fc6_trees_3), [interesting(0.9),axiom,file(trees_3,fc6_trees_3)]). 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_subset_1,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) ) ) ), file(subset_1,rc1_subset_1), [interesting(0.9),axiom,file(subset_1,rc1_subset_1)]). fof(rc2_subset_1,theorem,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) ) ), file(subset_1,rc2_subset_1), [interesting(0.9),axiom,file(subset_1,rc2_subset_1)]). fof(rc5_trees_2,theorem,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) ), file(trees_2,rc5_trees_2), [interesting(0.9),axiom,file(trees_2,rc5_trees_2)]). fof(rc6_trees_2,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m3_trees_2(B,A) & v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) ) ) ), file(trees_2,rc6_trees_2), [interesting(0.9),axiom,file(trees_2,rc6_trees_2)]). fof(antisymmetry_r2_hidden,theorem,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), [interesting(0.9),axiom,file(hidden,r2_hidden)]). fof(redefinition_k12_trees_4,definition,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & m1_finseq_1(C,k5_trees_3(A)) ) => k12_trees_4(A,B,C) = k4_trees_4(B,C) ) ), file(trees_4,k12_trees_4), [interesting(0.9),axiom,file(trees_4,k12_trees_4)]). fof(redefinition_k1_domain_1,definition,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(C,A) & m1_subset_1(D,B) ) => k1_domain_1(A,B,C,D) = k4_tarski(C,D) ) ), file(domain_1,k1_domain_1), [interesting(0.9),axiom,file(domain_1,k1_domain_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_finseq_1,definition,( ! [A,B] : ( m2_finseq_1(B,A) <=> m1_finseq_1(B,A) ) ), file(finseq_1,m2_finseq_1), [interesting(0.9),axiom,file(finseq_1,m2_finseq_1)]). fof(redefinition_m2_subset_1,definition,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(subset_1,m2_subset_1), [interesting(0.9),axiom,file(subset_1,m2_subset_1)]). fof(redefinition_m5_trees_3,definition,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m4_trees_3(B,A) ) => ! [C] : ( m5_trees_3(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(trees_3,m5_trees_3), [interesting(0.9),axiom,file(trees_3,m5_trees_3)]). fof(dt_k11_trees_3,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & v1_funct_1(C) & v3_trees_2(C) & m3_trees_2(C,k2_zfmisc_1(A,B)) ) => ( v1_funct_1(k11_trees_3(A,B,C)) & v3_trees_2(k11_trees_3(A,B,C)) & m3_trees_2(k11_trees_3(A,B,C),B) ) ) ), file(trees_3,k11_trees_3), [interesting(0.9),axiom,file(trees_3,k11_trees_3)]). fof(dt_k12_trees_4,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & m1_finseq_1(C,k5_trees_3(A)) ) => m5_trees_3(k12_trees_4(A,B,C),A,k5_trees_3(A)) ) ), file(trees_4,k12_trees_4), [interesting(0.9),axiom,file(trees_4,k12_trees_4)]). fof(dt_k1_domain_1,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(C,A) & m1_subset_1(D,B) ) => m1_subset_1(k1_domain_1(A,B,C,D),k2_zfmisc_1(A,B)) ) ), file(domain_1,k1_domain_1), [interesting(0.9),axiom,file(domain_1,k1_domain_1)]). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), [interesting(0.9),axiom,file(funct_1,k1_funct_1)]). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), [interesting(0.9),axiom,file(numbers,k1_numbers)]). 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_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_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_trees_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m4_trees_3(k5_trees_3(A),A) ) ), file(trees_3,k5_trees_3), [interesting(0.9),axiom,file(trees_3,k5_trees_3)]). fof(dt_m2_finseq_1,axiom,( ! [A,B] : ( m2_finseq_1(B,A) => ( v1_funct_1(B) & v1_finseq_1(B) & m2_relset_1(B,k5_numbers,A) ) ) ), file(finseq_1,m2_finseq_1), [interesting(0.9),axiom,file(finseq_1,m2_finseq_1)]). fof(dt_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) => m1_subset_1(C,A) ) ) ), file(subset_1,m2_subset_1), [interesting(0.9),axiom,file(subset_1,m2_subset_1)]). fof(dt_m5_trees_3,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m4_trees_3(B,A) ) => ! [C] : ( m5_trees_3(C,A,B) => ( v1_funct_1(C) & v3_trees_2(C) & m3_trees_2(C,A) ) ) ) ), file(trees_3,m5_trees_3), [interesting(0.9),axiom,file(trees_3,m5_trees_3)]). fof(dt_c1_54__trees_4,assumption,( ~ v1_xboole_0(c1_54__trees_4) ), introduced(assumption,[file(trees_4,c1_54__trees_4)]), [interesting(0.8),axiom,file(trees_4,c1_54__trees_4)]). fof(dt_c2_54__trees_4,assumption,( ~ v1_xboole_0(c2_54__trees_4) ), introduced(assumption,[file(trees_4,c2_54__trees_4)]), [interesting(0.8),axiom,file(trees_4,c2_54__trees_4)]). fof(dt_c3_54__trees_4,assumption,( m1_subset_1(c3_54__trees_4,c1_54__trees_4) ), introduced(assumption,[file(trees_4,c3_54__trees_4)]), [interesting(0.8),axiom,file(trees_4,c3_54__trees_4)]). fof(dt_c4_54__trees_4,assumption,( m1_subset_1(c4_54__trees_4,c2_54__trees_4) ), introduced(assumption,[file(trees_4,c4_54__trees_4)]), [interesting(0.8),axiom,file(trees_4,c4_54__trees_4)]). fof(dt_c5_54__trees_4,assumption,( m2_finseq_1(c5_54__trees_4,k5_trees_3(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4))) ), introduced(assumption,[file(trees_4,c5_54__trees_4)]), [interesting(0.8),axiom,file(trees_4,c5_54__trees_4)]). 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(fc10_membered,theorem,( ! [A] : ( v1_int_1(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) ) ) ), file(membered,fc10_membered), [interesting(0.9),axiom,file(membered,fc10_membered)]). fof(fc14_membered,theorem,( ! [A,B] : ( ( v1_rat_1(A) & v1_rat_1(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) ) ) ), file(membered,fc14_membered), [interesting(0.9),axiom,file(membered,fc14_membered)]). fof(fc15_membered,theorem,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) ) ) ), file(membered,fc15_membered), [interesting(0.9),axiom,file(membered,fc15_membered)]). fof(fc9_membered,theorem,( ! [A] : ( v1_rat_1(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) ) ) ), file(membered,fc9_membered), [interesting(0.9),axiom,file(membered,fc9_membered)]). fof(rc3_finseq_1,theorem,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc3_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc3_finseq_1)]). fof(rc4_finseq_1,theorem,( ! [A] : ? [B] : ( m1_finseq_1(B,A) & v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc4_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc4_finseq_1)]). fof(rc6_finseq_1,theorem,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc6_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc6_finseq_1)]). fof(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(reflexivity_r1_tarski,theorem,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), [interesting(0.9),axiom,file(tarski,r1_tarski)]). fof(existence_m1_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_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), [interesting(0.9),axiom,file(tarski,k1_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(dt_k2_tarski,axiom,( $true ), file(tarski,k2_tarski), [interesting(0.9),axiom,file(tarski,k2_tarski)]). fof(fc11_membered,theorem,( ! [A] : ( v4_ordinal2(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) & v5_membered(k1_tarski(A)) ) ) ), file(membered,fc11_membered), [interesting(0.9),axiom,file(membered,fc11_membered)]). fof(fc12_membered,theorem,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => v1_membered(k2_tarski(A,B)) ) ), file(membered,fc12_membered), [interesting(0.9),axiom,file(membered,fc12_membered)]). fof(fc13_membered,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) ) ) ), file(membered,fc13_membered), [interesting(0.9),axiom,file(membered,fc13_membered)]). fof(fc16_membered,theorem,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) & v5_membered(k2_tarski(A,B)) ) ) ), file(membered,fc16_membered), [interesting(0.9),axiom,file(membered,fc16_membered)]). fof(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(fc2_subset_1,theorem,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) ), file(subset_1,fc2_subset_1), [interesting(0.9),axiom,file(subset_1,fc2_subset_1)]). fof(fc3_subset_1,theorem,( ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ), file(subset_1,fc3_subset_1), [interesting(0.9),axiom,file(subset_1,fc3_subset_1)]). fof(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(fc7_membered,theorem,( ! [A] : ( v1_xcmplx_0(A) => v1_membered(k1_tarski(A)) ) ), file(membered,fc7_membered), [interesting(0.9),axiom,file(membered,fc7_membered)]). fof(fc8_membered,theorem,( ! [A] : ( v1_xreal_0(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) ) ) ), file(membered,fc8_membered), [interesting(0.9),axiom,file(membered,fc8_membered)]). fof(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_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_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(existence_m3_trees_2,axiom,( ! [A] : ? [B] : m3_trees_2(B,A) ), file(trees_2,m3_trees_2), [interesting(0.9),axiom,file(trees_2,m3_trees_2)]). fof(existence_m4_trees_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : m4_trees_3(B,A) ) ), file(trees_3,m4_trees_3), [interesting(0.9),axiom,file(trees_3,m4_trees_3)]). fof(fc5_trees_3,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ v1_xboole_0(k4_trees_3(A)) & v3_trees_3(k4_trees_3(A)) ) ) ), file(trees_3,fc5_trees_3), [interesting(0.9),axiom,file(trees_3,fc5_trees_3)]). 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(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(existence_m2_finseq_1,axiom,( ! [A] : ? [B] : m2_finseq_1(B,A) ), file(finseq_1,m2_finseq_1), [interesting(0.9),axiom,file(finseq_1,m2_finseq_1)]). fof(existence_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ? [C] : m2_subset_1(C,A,B) ) ), file(subset_1,m2_subset_1), [interesting(0.9),axiom,file(subset_1,m2_subset_1)]). fof(existence_m5_trees_3,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m4_trees_3(B,A) ) => ? [C] : m5_trees_3(C,A,B) ) ), file(trees_3,m5_trees_3), [interesting(0.9),axiom,file(trees_3,m5_trees_3)]). fof(redefinition_k8_trees_4,definition,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m4_trees_3(B,A) & m1_subset_1(C,A) & m1_finseq_1(D,B) ) => k8_trees_4(A,B,C,D) = k4_trees_4(C,D) ) ), file(trees_4,k8_trees_4), [interesting(0.9),axiom,file(trees_4,k8_trees_4)]). fof(dt_k4_trees_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m4_trees_3(k4_trees_3(A),A) ) ), file(trees_3,k4_trees_3), [interesting(0.9),axiom,file(trees_3,k4_trees_3)]). fof(dt_k8_trees_4,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m4_trees_3(B,A) & m1_subset_1(C,A) & m1_finseq_1(D,B) ) => ( v1_funct_1(k8_trees_4(A,B,C,D)) & v3_trees_2(k8_trees_4(A,B,C,D)) & m3_trees_2(k8_trees_4(A,B,C,D),A) ) ) ), file(trees_4,k8_trees_4), [interesting(0.9),axiom,file(trees_4,k8_trees_4)]). fof(dh_c6_54__trees_4,definition, ( ? [A] : ( m2_finseq_1(A,k4_trees_3(c2_54__trees_4)) & k4_finseq_1(A) = k4_finseq_1(c5_54__trees_4) & ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ~ ( r2_hidden(B,k4_finseq_1(c5_54__trees_4)) & ! [C] : ( m5_trees_3(C,k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k5_trees_3(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4))) => ~ ( C = k1_funct_1(c5_54__trees_4,B) & k1_funct_1(A,B) = k11_trees_3(c1_54__trees_4,c2_54__trees_4,C) ) ) ) ) & k11_trees_3(c1_54__trees_4,c2_54__trees_4,k12_trees_4(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k1_domain_1(c1_54__trees_4,c2_54__trees_4,c3_54__trees_4,c4_54__trees_4),c5_54__trees_4)) = k8_trees_4(c2_54__trees_4,k4_trees_3(c2_54__trees_4),c4_54__trees_4,A) ) => ( m2_finseq_1(c6_54__trees_4,k4_trees_3(c2_54__trees_4)) & k4_finseq_1(c6_54__trees_4) = k4_finseq_1(c5_54__trees_4) & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ~ ( r2_hidden(D,k4_finseq_1(c5_54__trees_4)) & ! [E] : ( m5_trees_3(E,k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k5_trees_3(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4))) => ~ ( E = k1_funct_1(c5_54__trees_4,D) & k1_funct_1(c6_54__trees_4,D) = k11_trees_3(c1_54__trees_4,c2_54__trees_4,E) ) ) ) ) & k11_trees_3(c1_54__trees_4,c2_54__trees_4,k12_trees_4(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k1_domain_1(c1_54__trees_4,c2_54__trees_4,c3_54__trees_4,c4_54__trees_4),c5_54__trees_4)) = k8_trees_4(c2_54__trees_4,k4_trees_3(c2_54__trees_4),c4_54__trees_4,c6_54__trees_4) ) ), introduced(definition,[new_symbol(c6_54__trees_4),file(trees_4,c6_54__trees_4)]), [interesting(0.8),axiom,file(trees_4,c6_54__trees_4)]). 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(t30_trees_4,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( ~ v1_xboole_0(E) & m4_trees_3(E,k2_zfmisc_1(A,B)) ) => ! [F] : ( m2_finseq_1(F,E) => ? [G] : ( m2_finseq_1(G,k4_trees_3(B)) & k4_finseq_1(G) = k4_finseq_1(F) & ! [H] : ( m2_subset_1(H,k1_numbers,k5_numbers) => ~ ( r2_hidden(H,k4_finseq_1(F)) & ! [I] : ( m5_trees_3(I,k2_zfmisc_1(A,B),E) => ~ ( I = k1_funct_1(F,H) & k1_funct_1(G,H) = k11_trees_3(A,B,I) ) ) ) ) & k11_trees_3(A,B,k8_trees_4(k2_zfmisc_1(A,B),E,k1_domain_1(A,B,C,D),F)) = k8_trees_4(B,k4_trees_3(B),D,G) ) ) ) ) ) ) ) ), file(trees_4,t30_trees_4), [interesting(0.9),axiom,file(trees_4,t30_trees_4)]). fof(e1_54__trees_4,plain,( ? [A] : ( m2_finseq_1(A,k4_trees_3(c2_54__trees_4)) & k4_finseq_1(A) = k4_finseq_1(c5_54__trees_4) & ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ~ ( r2_hidden(B,k4_finseq_1(c5_54__trees_4)) & ! [C] : ( m5_trees_3(C,k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k5_trees_3(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4))) => ~ ( C = k1_funct_1(c5_54__trees_4,B) & k1_funct_1(A,B) = k11_trees_3(c1_54__trees_4,c2_54__trees_4,C) ) ) ) ) & k11_trees_3(c1_54__trees_4,c2_54__trees_4,k12_trees_4(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k1_domain_1(c1_54__trees_4,c2_54__trees_4,c3_54__trees_4,c4_54__trees_4),c5_54__trees_4)) = k8_trees_4(c2_54__trees_4,k4_trees_3(c2_54__trees_4),c4_54__trees_4,A) ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_54__trees_4,dt_c2_54__trees_4,dt_c3_54__trees_4,dt_c4_54__trees_4,dt_c5_54__trees_4])],[commutativity_k2_tarski,reflexivity_r1_tarski,existence_m1_relset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_relset_1,cc1_arytm_3,cc2_arytm_3,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc17_finseq_1,fc2_subset_1,fc3_subset_1,fc5_trees_2,fc7_membered,fc8_membered,fc9_membered,rc1_arytm_3,rc2_finseq_1,rc2_trees_3,rc3_finseq_1,rc4_finseq_1,rc4_trees_3,rc6_finseq_1,rc6_trees_3,rc7_finseq_1,rc7_trees_2,rc8_finseq_1,rc8_trees_2,rc8_trees_3,rc9_trees_2,existence_m1_finseq_1,existence_m2_relset_1,existence_m3_trees_2,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k4_tarski,dt_k4_trees_4,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,dt_m3_trees_2,cc10_membered,cc10_trees_3,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finseq_1,cc1_membered,cc1_relset_1,cc1_trees_4,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc4_trees_3,cc6_membered,cc9_membered,fc1_ordinal2,fc1_subset_1,fc26_trees_3,fc2_finseq_1,fc2_trees_2,fc5_membered,fc6_membered,rc1_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,rc5_trees_2,rc6_trees_2,t3_subset,t4_subset,t5_subset,d5_tarski,antisymmetry_r2_hidden,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_subset_1,existence_m4_trees_3,existence_m5_trees_3,redefinition_k12_trees_4,redefinition_k1_domain_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_k8_trees_4,redefinition_m2_finseq_1,redefinition_m2_subset_1,redefinition_m5_trees_3,dt_k11_trees_3,dt_k12_trees_4,dt_k1_domain_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_zfmisc_1,dt_k4_finseq_1,dt_k4_trees_3,dt_k5_numbers,dt_k5_trees_3,dt_k8_trees_4,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_subset_1,dt_m4_trees_3,dt_m5_trees_3,dt_c1_54__trees_4,dt_c2_54__trees_4,dt_c3_54__trees_4,dt_c4_54__trees_4,dt_c5_54__trees_4,cc15_membered,cc5_trees_3,fc2_membered,fc4_subset_1,fc5_trees_3,fc6_trees_3,t1_subset,t2_subset,t6_boole,t7_boole,t8_boole,t30_trees_4]), [interesting(0.8),file(trees_4,e1_54__trees_4),[file(trees_4,e1_54__trees_4)]]). fof(dt_c6_54__trees_4,plain,( m2_finseq_1(c6_54__trees_4,k4_trees_3(c2_54__trees_4)) ), inference(consider,[status(thm),assumptions([dt_c1_54__trees_4,dt_c2_54__trees_4,dt_c3_54__trees_4,dt_c4_54__trees_4,dt_c5_54__trees_4])],[dh_c6_54__trees_4,e1_54__trees_4]), [interesting(0.8),file(trees_4,c6_54__trees_4),[file(trees_4,c6_54__trees_4)]]). 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(dt_c1_54_1__trees_4,assumption,( $true ), introduced(assumption,[file(trees_4,c1_54_1__trees_4)]), [interesting(0.65),axiom,file(trees_4,c1_54_1__trees_4)]). fof(d3_tarski,definition,( ! [A,B] : ( r1_tarski(A,B) <=> ! [C] : ( r2_hidden(C,A) => r2_hidden(C,B) ) ) ), file(tarski,d3_tarski), [interesting(0.9),axiom,file(tarski,d3_tarski)]). fof(dh_c1_54_1__trees_4,definition, ( ~ ( r2_hidden(c1_54_1__trees_4,k2_relat_1(c6_54__trees_4)) & ~ r2_hidden(c1_54_1__trees_4,k5_trees_3(c2_54__trees_4)) ) => ! [A] : ~ ( r2_hidden(A,k2_relat_1(c6_54__trees_4)) & ~ r2_hidden(A,k5_trees_3(c2_54__trees_4)) ) ), introduced(definition,[new_symbol(c1_54_1__trees_4),file(trees_4,c1_54_1__trees_4)]), [interesting(0.65),axiom,file(trees_4,c1_54_1__trees_4)]). fof(e1_54_1__trees_4,assumption,( r2_hidden(c1_54_1__trees_4,k2_relat_1(c6_54__trees_4)) ), introduced(assumption,[file(trees_4,e1_54_1__trees_4)]), [interesting(0.65),axiom,file(trees_4,e1_54_1__trees_4)]). fof(dh_c2_54_1__trees_4,definition, ( ? [A] : ( r2_hidden(A,k4_finseq_1(c6_54__trees_4)) & c1_54_1__trees_4 = k1_funct_1(c6_54__trees_4,A) ) => ( r2_hidden(c2_54_1__trees_4,k4_finseq_1(c6_54__trees_4)) & c1_54_1__trees_4 = k1_funct_1(c6_54__trees_4,c2_54_1__trees_4) ) ), introduced(definition,[new_symbol(c2_54_1__trees_4),file(trees_4,c2_54_1__trees_4)]), [interesting(0.65),axiom,file(trees_4,c2_54_1__trees_4)]). fof(d5_funct_1,definition,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( B = k2_relat_1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( r2_hidden(D,k1_relat_1(A)) & C = k1_funct_1(A,D) ) ) ) ) ), file(funct_1,d5_funct_1), [interesting(0.9),axiom,file(funct_1,d5_funct_1)]). fof(e2_54_1__trees_4,plain,( ? [A] : ( r2_hidden(A,k4_finseq_1(c6_54__trees_4)) & c1_54_1__trees_4 = k1_funct_1(c6_54__trees_4,A) ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_54_1__trees_4,dt_c1_54__trees_4,dt_c2_54__trees_4,dt_c3_54__trees_4,dt_c4_54__trees_4,dt_c5_54__trees_4,e1_54_1__trees_4])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_arytm_3,cc1_relset_1,cc2_arytm_3,fc4_subset_1,rc1_arytm_3,rc2_finseq_1,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,rc6_trees_3,rc8_trees_3,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,existence_m4_trees_3,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,dt_m4_trees_3,cc10_membered,cc10_trees_3,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_trees_4,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc4_trees_3,cc5_trees_3,cc6_membered,fc11_finseq_1,fc17_finseq_1,fc1_ordinal2,fc2_finseq_1,fc2_membered,fc5_membered,fc5_trees_2,fc6_membered,rc1_membered,rc2_trees_3,rc4_trees_3,rc7_finseq_1,rc8_finseq_1,existence_m1_subset_1,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k1_zfmisc_1,dt_k4_trees_3,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,dt_c2_54__trees_4,cc15_membered,cc1_finseq_1,cc9_membered,fc1_subset_1,fc5_trees_3,rc1_finseq_1,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k4_finseq_1,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_k4_finseq_1,dt_c1_54_1__trees_4,dt_c6_54__trees_4,t1_subset,t7_boole,e1_54_1__trees_4,d5_funct_1]), [interesting(0.65),file(trees_4,e2_54_1__trees_4),[file(trees_4,e2_54_1__trees_4)]]). fof(dt_c2_54_1__trees_4,plain,( $true ), inference(consider,[status(thm),assumptions([dt_c1_54_1__trees_4,dt_c1_54__trees_4,dt_c2_54__trees_4,dt_c3_54__trees_4,dt_c4_54__trees_4,dt_c5_54__trees_4,e1_54_1__trees_4])],[dh_c2_54_1__trees_4,e2_54_1__trees_4]), [interesting(0.65),file(trees_4,c2_54_1__trees_4),[file(trees_4,c2_54_1__trees_4)]]). fof(de_c3_54_1__trees_4,definition,( c3_54_1__trees_4 = c2_54_1__trees_4 ), introduced(definition,[new_symbol(c3_54_1__trees_4),file(trees_4,c3_54_1__trees_4)]), [interesting(0.65),axiom,file(trees_4,c3_54_1__trees_4)]). fof(e3_54_1__trees_4,plain, ( r2_hidden(c2_54_1__trees_4,k4_finseq_1(c6_54__trees_4)) & c1_54_1__trees_4 = k1_funct_1(c6_54__trees_4,c2_54_1__trees_4) ), inference(consider,[status(thm),assumptions([dt_c1_54_1__trees_4,dt_c1_54__trees_4,dt_c2_54__trees_4,dt_c3_54__trees_4,dt_c4_54__trees_4,dt_c5_54__trees_4,e1_54_1__trees_4])],[dh_c2_54_1__trees_4,e2_54_1__trees_4]), [interesting(0.65),file(trees_4,e3_54_1__trees_4),[file(trees_4,e3_54_1__trees_4)]]). fof(e4_54_1__trees_4,plain,( m2_subset_1(c2_54_1__trees_4,k1_numbers,k5_numbers) ), inference(mizar_by,[status(thm),assumptions([dt_c1_54_1__trees_4,dt_c1_54__trees_4,dt_c2_54__trees_4,dt_c3_54__trees_4,dt_c4_54__trees_4,dt_c5_54__trees_4,e1_54_1__trees_4])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc4_subset_1,rc2_finseq_1,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,rc6_trees_3,rc8_trees_3,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,existence_m4_trees_3,redefinition_m2_relset_1,dt_k1_xboole_0,dt_m1_finseq_1,dt_m2_relset_1,dt_m4_trees_3,cc10_trees_3,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_arytm_3,cc1_membered,cc1_trees_4,cc20_membered,cc2_arytm_3,cc2_membered,cc3_membered,cc4_trees_3,cc5_trees_3,fc17_finseq_1,fc2_finseq_1,fc5_trees_2,fc6_membered,rc1_arytm_3,rc1_membered,rc2_trees_3,rc4_trees_3,rc7_finseq_1,rc8_finseq_1,existence_m1_subset_1,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k4_trees_3,dt_k5_ordinal2,dt_m1_subset_1,dt_m2_finseq_1,dt_c2_54__trees_4,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finseq_1,cc3_arytm_3,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc1_subset_1,fc5_membered,fc5_trees_3,rc1_finseq_1,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m2_subset_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k4_finseq_1,dt_k5_numbers,dt_m2_subset_1,dt_c1_54_1__trees_4,dt_c2_54_1__trees_4,dt_c6_54__trees_4,fc2_membered,t1_subset,t7_boole,e3_54_1__trees_4]), [interesting(0.65),file(trees_4,e4_54_1__trees_4),[file(trees_4,e4_54_1__trees_4)]]). fof(dt_c3_54_1__trees_4,plain,( m2_subset_1(c3_54_1__trees_4,k1_numbers,k5_numbers) ), inference(mizar_by,[status(thm),assumptions([dt_c1_54_1__trees_4,dt_c1_54__trees_4,dt_c2_54__trees_4,dt_c3_54__trees_4,dt_c4_54__trees_4,dt_c5_54__trees_4,e1_54_1__trees_4])],[cc1_finseq_1,rc1_finseq_1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_arytm_3,cc1_membered,cc20_membered,cc2_arytm_3,cc2_membered,cc3_membered,fc2_finseq_1,fc6_membered,rc1_arytm_3,rc1_membered,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc3_arytm_3,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc1_subset_1,fc5_membered,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m2_subset_1,dt_c2_54_1__trees_4,fc2_membered,de_c3_54_1__trees_4,e4_54_1__trees_4]), [interesting(0.65),file(trees_4,c3_54_1__trees_4),[file(trees_4,c3_54_1__trees_4)]]). fof(dh_c4_54_1__trees_4,definition, ( ? [A] : ( m5_trees_3(A,k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k5_trees_3(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4))) & A = k1_funct_1(c5_54__trees_4,c3_54_1__trees_4) & k1_funct_1(c6_54__trees_4,c3_54_1__trees_4) = k11_trees_3(c1_54__trees_4,c2_54__trees_4,A) ) => ( m5_trees_3(c4_54_1__trees_4,k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k5_trees_3(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4))) & c4_54_1__trees_4 = k1_funct_1(c5_54__trees_4,c3_54_1__trees_4) & k1_funct_1(c6_54__trees_4,c3_54_1__trees_4) = k11_trees_3(c1_54__trees_4,c2_54__trees_4,c4_54_1__trees_4) ) ), introduced(definition,[new_symbol(c4_54_1__trees_4),file(trees_4,c4_54_1__trees_4)]), [interesting(0.65),axiom,file(trees_4,c4_54_1__trees_4)]). fof(e2_54__trees_4,plain,( k4_finseq_1(c6_54__trees_4) = k4_finseq_1(c5_54__trees_4) ), inference(consider,[status(thm),assumptions([dt_c1_54__trees_4,dt_c2_54__trees_4,dt_c3_54__trees_4,dt_c4_54__trees_4,dt_c5_54__trees_4])],[dh_c6_54__trees_4,e1_54__trees_4]), [interesting(0.8),file(trees_4,e2_54__trees_4),[file(trees_4,e2_54__trees_4)]]). fof(e3_54__trees_4,plain,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ~ ( r2_hidden(A,k4_finseq_1(c5_54__trees_4)) & ! [B] : ( m5_trees_3(B,k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k5_trees_3(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4))) => ~ ( B = k1_funct_1(c5_54__trees_4,A) & k1_funct_1(c6_54__trees_4,A) = k11_trees_3(c1_54__trees_4,c2_54__trees_4,B) ) ) ) ) ), inference(consider,[status(thm),assumptions([dt_c1_54__trees_4,dt_c2_54__trees_4,dt_c3_54__trees_4,dt_c4_54__trees_4,dt_c5_54__trees_4])],[rc6_trees_3,rc8_trees_3,dt_m1_relset_1,cc10_trees_3,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_arytm_3,cc1_membered,cc1_trees_4,cc20_membered,cc2_arytm_3,cc2_membered,cc3_membered,cc4_trees_3,fc17_finseq_1,fc5_trees_2,rc1_arytm_3,rc1_membered,rc2_finseq_1,rc2_trees_3,rc4_trees_3,rc7_finseq_1,rc7_trees_2,rc8_finseq_1,rc8_trees_2,rc9_trees_2,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k4_tarski,dt_k4_trees_4,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_relset_1,dt_m3_trees_2,dt_m4_trees_3,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finseq_1,cc1_relset_1,cc3_arytm_3,cc4_membered,cc5_trees_3,cc6_membered,cc9_membered,fc1_ordinal2,fc1_subset_1,fc26_trees_3,fc2_trees_2,fc4_subset_1,fc5_membered,fc5_trees_3,fc6_trees_3,rc1_finseq_1,rc1_subset_1,rc2_subset_1,rc5_trees_2,rc6_trees_2,antisymmetry_r2_hidden,redefinition_k12_trees_4,redefinition_k1_domain_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_k8_trees_4,redefinition_m2_finseq_1,redefinition_m2_subset_1,redefinition_m5_trees_3,dt_k11_trees_3,dt_k12_trees_4,dt_k1_domain_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_zfmisc_1,dt_k4_finseq_1,dt_k4_trees_3,dt_k5_numbers,dt_k5_trees_3,dt_k8_trees_4,dt_m2_finseq_1,dt_m2_subset_1,dt_m5_trees_3,dt_c1_54__trees_4,dt_c2_54__trees_4,dt_c3_54__trees_4,dt_c4_54__trees_4,dt_c5_54__trees_4,dt_c6_54__trees_4,fc2_membered,dh_c6_54__trees_4,e1_54__trees_4]), [interesting(0.8),file(trees_4,e3_54__trees_4),[file(trees_4,e3_54__trees_4)]]). fof(e5_54_1__trees_4,plain,( ? [A] : ( m5_trees_3(A,k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k5_trees_3(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4))) & A = k1_funct_1(c5_54__trees_4,c3_54_1__trees_4) & k1_funct_1(c6_54__trees_4,c3_54_1__trees_4) = k11_trees_3(c1_54__trees_4,c2_54__trees_4,A) ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_54_1__trees_4,dt_c1_54__trees_4,dt_c2_54__trees_4,dt_c3_54__trees_4,dt_c4_54__trees_4,dt_c5_54__trees_4,e1_54_1__trees_4])],[existence_m1_relset_1,dt_m1_relset_1,rc2_finseq_1,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,rc6_trees_3,rc8_trees_3,rc9_trees_2,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,cc10_trees_3,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_arytm_3,cc1_membered,cc1_trees_4,cc20_membered,cc2_arytm_3,cc2_membered,cc3_membered,cc4_trees_3,fc17_finseq_1,fc2_finseq_1,fc5_trees_2,fc6_membered,rc1_arytm_3,rc1_membered,rc2_trees_3,rc4_trees_3,rc7_finseq_1,rc7_trees_2,rc8_finseq_1,rc8_trees_2,existence_m1_subset_1,existence_m2_finseq_1,existence_m3_trees_2,existence_m4_trees_3,redefinition_m2_finseq_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k4_trees_3,dt_k5_ordinal2,dt_m1_subset_1,dt_m2_finseq_1,dt_m3_trees_2,dt_m4_trees_3,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finseq_1,cc1_relset_1,cc3_arytm_3,cc4_membered,cc5_trees_3,cc6_membered,cc9_membered,fc1_ordinal2,fc1_subset_1,fc26_trees_3,fc2_trees_2,fc4_subset_1,fc5_membered,fc5_trees_3,fc6_trees_3,rc1_finseq_1,rc1_subset_1,rc2_subset_1,rc5_trees_2,rc6_trees_2,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m2_subset_1,existence_m5_trees_3,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_m2_subset_1,redefinition_m5_trees_3,dt_k11_trees_3,dt_k1_funct_1,dt_k1_numbers,dt_k2_zfmisc_1,dt_k4_finseq_1,dt_k5_numbers,dt_k5_trees_3,dt_m2_subset_1,dt_m5_trees_3,dt_c1_54__trees_4,dt_c1_54_1__trees_4,dt_c2_54__trees_4,dt_c2_54_1__trees_4,dt_c3_54_1__trees_4,dt_c5_54__trees_4,dt_c6_54__trees_4,de_c3_54_1__trees_4,fc2_membered,t1_subset,t7_boole,e2_54__trees_4,e3_54__trees_4,e3_54_1__trees_4]), [interesting(0.65),file(trees_4,e5_54_1__trees_4),[file(trees_4,e5_54_1__trees_4)]]). fof(dt_c4_54_1__trees_4,plain,( m5_trees_3(c4_54_1__trees_4,k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k5_trees_3(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4))) ), inference(consider,[status(thm),assumptions([dt_c1_54_1__trees_4,dt_c1_54__trees_4,dt_c2_54__trees_4,dt_c3_54__trees_4,dt_c4_54__trees_4,dt_c5_54__trees_4,e1_54_1__trees_4])],[dh_c4_54_1__trees_4,e5_54_1__trees_4]), [interesting(0.65),file(trees_4,c4_54_1__trees_4),[file(trees_4,c4_54_1__trees_4)]]). fof(dt_k10_trees_3,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & v1_funct_1(C) & v3_trees_2(C) & m3_trees_2(C,k2_zfmisc_1(A,B)) ) => ( v1_funct_1(k10_trees_3(A,B,C)) & v3_trees_2(k10_trees_3(A,B,C)) & m3_trees_2(k10_trees_3(A,B,C),A) ) ) ), file(trees_3,k10_trees_3), [interesting(0.9),axiom,file(trees_3,k10_trees_3)]). fof(t24_trees_4,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v3_trees_2(C) & m3_trees_2(C,k2_zfmisc_1(A,B)) ) => ( k1_relat_1(k10_trees_3(A,B,C)) = k1_relat_1(C) & k1_relat_1(k11_trees_3(A,B,C)) = k1_relat_1(C) ) ) ) ) ), file(trees_4,t24_trees_4), [interesting(0.9),axiom,file(trees_4,t24_trees_4)]). fof(e7_54_1__trees_4,plain, ( v1_finset_1(k1_relat_1(c4_54_1__trees_4)) & k1_relat_1(k11_trees_3(c1_54__trees_4,c2_54__trees_4,c4_54_1__trees_4)) = k1_relat_1(c4_54_1__trees_4) ), inference(mizar_by,[status(thm),assumptions([dt_c1_54_1__trees_4,dt_c1_54__trees_4,dt_c2_54__trees_4,dt_c3_54__trees_4,dt_c4_54__trees_4,dt_c5_54__trees_4,e1_54_1__trees_4])],[existence_m1_subset_1,existence_m4_trees_3,dt_m1_subset_1,dt_m4_trees_3,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_finseq_1,cc5_trees_3,fc26_trees_3,rc1_finseq_1,rc2_trees_3,rc3_finseq_1,rc4_trees_3,rc6_finseq_1,rc8_finseq_1,t2_subset,antisymmetry_r2_hidden,existence_m5_trees_3,redefinition_m5_trees_3,dt_k1_xboole_0,dt_k5_trees_3,dt_m5_trees_3,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc17_finseq_1,fc2_finseq_1,fc2_trees_2,fc5_trees_2,fc6_membered,fc6_trees_3,rc1_membered,rc5_trees_2,rc6_trees_2,rc7_finseq_1,rc7_trees_2,rc8_trees_2,t1_subset,existence_m3_trees_2,dt_k10_trees_3,dt_k11_trees_3,dt_k1_relat_1,dt_k2_zfmisc_1,dt_m3_trees_2,dt_c1_54__trees_4,dt_c2_54__trees_4,dt_c4_54_1__trees_4,cc15_membered,fc4_subset_1,t6_boole,t7_boole,t8_boole,t24_trees_4]), [interesting(0.65),file(trees_4,e7_54_1__trees_4),[file(trees_4,e7_54_1__trees_4)]]). fof(e6_54_1__trees_4,plain, ( c4_54_1__trees_4 = k1_funct_1(c5_54__trees_4,c3_54_1__trees_4) & k1_funct_1(c6_54__trees_4,c3_54_1__trees_4) = k11_trees_3(c1_54__trees_4,c2_54__trees_4,c4_54_1__trees_4) ), inference(consider,[status(thm),assumptions([dt_c1_54_1__trees_4,dt_c1_54__trees_4,dt_c2_54__trees_4,dt_c3_54__trees_4,dt_c4_54__trees_4,dt_c5_54__trees_4,e1_54_1__trees_4])],[dh_c4_54_1__trees_4,e5_54_1__trees_4]), [interesting(0.65),file(trees_4,e6_54_1__trees_4),[file(trees_4,e6_54_1__trees_4)]]). fof(d8_trees_3,definition,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m4_trees_3(B,A) => ( B = k5_trees_3(A) <=> ! [C] : ( ( v1_funct_1(C) & v3_trees_2(C) & m3_trees_2(C,A) ) => ( v1_finset_1(k1_relat_1(C)) <=> r2_hidden(C,B) ) ) ) ) ) ), file(trees_3,d8_trees_3), [interesting(0.9),axiom,file(trees_3,d8_trees_3)]). fof(e8_54_1__trees_4,plain,( r2_hidden(c1_54_1__trees_4,k5_trees_3(c2_54__trees_4)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_54_1__trees_4,dt_c1_54__trees_4,dt_c2_54__trees_4,dt_c3_54__trees_4,dt_c4_54__trees_4,dt_c5_54__trees_4,e1_54_1__trees_4])],[existence_m1_relset_1,dt_m1_relset_1,cc1_arytm_3,cc2_arytm_3,rc1_arytm_3,rc2_finseq_1,rc6_trees_3,rc8_trees_3,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,cc10_trees_3,cc1_trees_4,cc3_arytm_3,fc1_ordinal2,fc5_membered,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_subset_1,existence_m5_trees_3,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_subset_1,redefinition_m5_trees_3,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k4_trees_3,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_subset_1,dt_m5_trees_3,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finseq_1,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc4_trees_3,cc6_membered,cc9_membered,fc17_finseq_1,fc1_subset_1,fc26_trees_3,fc2_finseq_1,fc2_membered,fc2_trees_2,fc4_subset_1,fc5_trees_2,fc5_trees_3,fc6_membered,rc1_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,rc2_trees_3,rc4_trees_3,rc5_trees_2,rc6_trees_2,rc7_finseq_1,rc7_trees_2,rc8_finseq_1,rc8_trees_2,t2_subset,t3_subset,t4_subset,t5_subset,antisymmetry_r2_hidden,existence_m3_trees_2,existence_m4_trees_3,redefinition_k4_finseq_1,dt_k11_trees_3,dt_k1_funct_1,dt_k1_relat_1,dt_k4_finseq_1,dt_k5_trees_3,dt_m3_trees_2,dt_m4_trees_3,dt_c1_54__trees_4,dt_c1_54_1__trees_4,dt_c2_54__trees_4,dt_c2_54_1__trees_4,dt_c3_54_1__trees_4,dt_c4_54_1__trees_4,dt_c5_54__trees_4,dt_c6_54__trees_4,de_c3_54_1__trees_4,cc15_membered,cc5_trees_3,fc6_trees_3,t1_subset,t6_boole,t7_boole,t8_boole,e7_54_1__trees_4,e3_54_1__trees_4,e6_54_1__trees_4,d8_trees_3]), [interesting(0.65),file(trees_4,e8_54_1__trees_4),[file(trees_4,e8_54_1__trees_4)]]). fof(i3_54_1__trees_4,theorem,( $true ), introduced(tautology,[file(trees_4,i3_54_1__trees_4)]), [interesting(0.65),trivial,file(trees_4,i3_54_1__trees_4)]). fof(i2_54_1__trees_4,plain,( r2_hidden(c1_54_1__trees_4,k5_trees_3(c2_54__trees_4)) ), inference(conclusion,[status(thm),assumptions([dt_c1_54_1__trees_4,dt_c1_54__trees_4,dt_c2_54__trees_4,dt_c3_54__trees_4,dt_c4_54__trees_4,dt_c5_54__trees_4,e1_54_1__trees_4])],[e8_54_1__trees_4,i3_54_1__trees_4]), [interesting(0.65),file(trees_4,i2_54_1__trees_4),[file(trees_4,i2_54_1__trees_4)]]). fof(i1_54_1__trees_4,plain,( ~ ( r2_hidden(c1_54_1__trees_4,k2_relat_1(c6_54__trees_4)) & ~ r2_hidden(c1_54_1__trees_4,k5_trees_3(c2_54__trees_4)) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_54_1__trees_4,dt_c1_54__trees_4,dt_c2_54__trees_4,dt_c3_54__trees_4,dt_c4_54__trees_4,dt_c5_54__trees_4]),discharge_asm(discharge,[e1_54_1__trees_4])],[e1_54_1__trees_4,i2_54_1__trees_4]), [interesting(0.65),file(trees_4,i1_54_1__trees_4),[file(trees_4,i1_54_1__trees_4)]]). fof(i1_54_1_tmp__trees_4,plain,( ~ ( r2_hidden(c1_54_1__trees_4,k2_relat_1(c6_54__trees_4)) & ~ r2_hidden(c1_54_1__trees_4,k5_trees_3(c2_54__trees_4)) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_54__trees_4,dt_c2_54__trees_4,dt_c3_54__trees_4,dt_c4_54__trees_4,dt_c5_54__trees_4]),discharge_asm(discharge,[dt_c1_54_1__trees_4])],[dt_c1_54_1__trees_4,i1_54_1__trees_4]), [interesting(0.8),e5_54__trees_4]). fof(e5_54__trees_4,plain,( r1_tarski(k2_relat_1(c6_54__trees_4),k5_trees_3(c2_54__trees_4)) ), inference(let,[status(thm),assumptions([dt_c1_54__trees_4,dt_c2_54__trees_4,dt_c3_54__trees_4,dt_c4_54__trees_4,dt_c5_54__trees_4])],[i1_54_1_tmp__trees_4,cc1_arytm_3,cc2_arytm_3,rc1_arytm_3,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_m1_relset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_relset_1,cc1_trees_4,cc20_membered,cc3_arytm_3,cc4_trees_3,cc6_membered,cc9_membered,fc11_finseq_1,fc1_ordinal2,fc1_subset_1,fc2_membered,fc4_subset_1,fc5_membered,rc1_subset_1,rc2_finseq_1,rc2_subset_1,rc2_trees_3,rc4_trees_3,rc6_trees_3,rc7_finseq_1,rc8_finseq_1,rc8_trees_3,rc9_trees_2,redefinition_k5_numbers,redefinition_m2_relset_1,dt_k5_numbers,dt_m1_finseq_1,dt_m2_relset_1,cc10_trees_3,cc1_finseq_1,cc1_membered,cc2_membered,cc3_membered,cc4_membered,rc1_finseq_1,rc1_membered,redefinition_m2_finseq_1,dt_k4_trees_3,dt_m2_finseq_1,dt_m4_trees_3,cc15_membered,cc5_trees_3,fc5_trees_3,fc6_trees_3,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k2_relat_1,dt_k5_trees_3,dt_c2_54__trees_4,dt_c6_54__trees_4,d3_tarski,dh_c1_54_1__trees_4]), [interesting(0.8),file(trees_4,e5_54__trees_4),[file(trees_4,e5_54__trees_4)]]). fof(d4_finseq_1,definition,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( m1_finseq_1(B,A) <=> r1_tarski(k2_relat_1(B),A) ) ) ), file(finseq_1,d4_finseq_1), [interesting(0.9),axiom,file(finseq_1,d4_finseq_1)]). fof(e6_54__trees_4,plain,( m2_finseq_1(c6_54__trees_4,k5_trees_3(c2_54__trees_4)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_54__trees_4,dt_c2_54__trees_4,dt_c3_54__trees_4,dt_c4_54__trees_4,dt_c5_54__trees_4])],[cc1_arytm_3,cc2_arytm_3,rc1_arytm_3,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,rc6_trees_3,rc8_trees_3,antisymmetry_r2_hidden,existence_m1_relset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_m1_relset_1,cc10_membered,cc10_trees_3,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc1_trees_4,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc4_trees_3,cc6_membered,fc1_ordinal2,fc2_finseq_1,fc2_membered,fc4_subset_1,fc5_membered,fc6_membered,rc1_membered,rc2_finseq_1,rc2_trees_3,rc4_trees_3,rc9_trees_2,t1_subset,t4_subset,t5_subset,t8_boole,existence_m1_subset_1,existence_m2_relset_1,existence_m4_trees_3,redefinition_k5_numbers,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k4_trees_3,dt_k5_numbers,dt_m1_subset_1,dt_m2_relset_1,dt_m4_trees_3,cc15_membered,cc5_trees_3,cc9_membered,fc11_finseq_1,fc1_subset_1,fc5_trees_3,fc6_trees_3,rc1_subset_1,rc2_subset_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t6_boole,t7_boole,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k2_relat_1,dt_k5_trees_3,dt_m1_finseq_1,dt_m2_finseq_1,dt_c2_54__trees_4,dt_c6_54__trees_4,cc1_finseq_1,rc1_finseq_1,t3_subset,e5_54__trees_4,d4_finseq_1]), [interesting(0.8),file(trees_4,e6_54__trees_4),[file(trees_4,e6_54__trees_4)]]). fof(e4_54__trees_4,plain,( k11_trees_3(c1_54__trees_4,c2_54__trees_4,k12_trees_4(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k1_domain_1(c1_54__trees_4,c2_54__trees_4,c3_54__trees_4,c4_54__trees_4),c5_54__trees_4)) = k8_trees_4(c2_54__trees_4,k4_trees_3(c2_54__trees_4),c4_54__trees_4,c6_54__trees_4) ), inference(consider,[status(thm),assumptions([dt_c1_54__trees_4,dt_c2_54__trees_4,dt_c3_54__trees_4,dt_c4_54__trees_4,dt_c5_54__trees_4])],[rc6_trees_3,rc8_trees_3,dt_m1_relset_1,cc10_trees_3,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_arytm_3,cc1_membered,cc1_trees_4,cc20_membered,cc2_arytm_3,cc2_membered,cc3_membered,cc4_trees_3,fc17_finseq_1,fc5_trees_2,rc1_arytm_3,rc1_membered,rc2_finseq_1,rc2_trees_3,rc4_trees_3,rc7_finseq_1,rc7_trees_2,rc8_finseq_1,rc8_trees_2,rc9_trees_2,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k4_tarski,dt_k4_trees_4,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_relset_1,dt_m3_trees_2,dt_m4_trees_3,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finseq_1,cc1_relset_1,cc3_arytm_3,cc4_membered,cc5_trees_3,cc6_membered,cc9_membered,fc1_ordinal2,fc1_subset_1,fc26_trees_3,fc2_trees_2,fc4_subset_1,fc5_membered,fc5_trees_3,fc6_trees_3,rc1_finseq_1,rc1_subset_1,rc2_subset_1,rc5_trees_2,rc6_trees_2,antisymmetry_r2_hidden,redefinition_k12_trees_4,redefinition_k1_domain_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_k8_trees_4,redefinition_m2_finseq_1,redefinition_m2_subset_1,redefinition_m5_trees_3,dt_k11_trees_3,dt_k12_trees_4,dt_k1_domain_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_zfmisc_1,dt_k4_finseq_1,dt_k4_trees_3,dt_k5_numbers,dt_k5_trees_3,dt_k8_trees_4,dt_m2_finseq_1,dt_m2_subset_1,dt_m5_trees_3,dt_c1_54__trees_4,dt_c2_54__trees_4,dt_c3_54__trees_4,dt_c4_54__trees_4,dt_c5_54__trees_4,dt_c6_54__trees_4,fc2_membered,dh_c6_54__trees_4,e1_54__trees_4]), [interesting(0.8),file(trees_4,e4_54__trees_4),[file(trees_4,e4_54__trees_4)]]). fof(e7_54__trees_4,plain,( ? [A] : ( m2_finseq_1(A,k5_trees_3(c2_54__trees_4)) & k4_finseq_1(A) = k4_finseq_1(c5_54__trees_4) & ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ~ ( r2_hidden(B,k4_finseq_1(c5_54__trees_4)) & ! [C] : ( m5_trees_3(C,k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k5_trees_3(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4))) => ~ ( C = k1_funct_1(c5_54__trees_4,B) & k1_funct_1(A,B) = k11_trees_3(c1_54__trees_4,c2_54__trees_4,C) ) ) ) ) & k11_trees_3(c1_54__trees_4,c2_54__trees_4,k12_trees_4(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k1_domain_1(c1_54__trees_4,c2_54__trees_4,c3_54__trees_4,c4_54__trees_4),c5_54__trees_4)) = k12_trees_4(c2_54__trees_4,c4_54__trees_4,A) ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_54__trees_4,dt_c2_54__trees_4,dt_c3_54__trees_4,dt_c4_54__trees_4,dt_c5_54__trees_4])],[fc10_membered,fc14_membered,fc15_membered,fc9_membered,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,rc6_trees_3,rc8_trees_3,commutativity_k2_tarski,reflexivity_r1_tarski,existence_m1_relset_1,dt_k1_tarski,dt_k1_xboole_0,dt_k2_tarski,dt_m1_relset_1,cc10_trees_3,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_arytm_3,cc1_membered,cc1_trees_4,cc20_membered,cc2_arytm_3,cc2_membered,cc3_membered,cc4_trees_3,fc11_membered,fc12_membered,fc13_membered,fc16_membered,fc17_finseq_1,fc2_finseq_1,fc2_subset_1,fc3_subset_1,fc5_trees_2,fc6_membered,fc7_membered,fc8_membered,rc1_arytm_3,rc1_membered,rc2_finseq_1,rc2_trees_3,rc4_trees_3,rc7_finseq_1,rc7_trees_2,rc8_finseq_1,rc8_trees_2,rc9_trees_2,existence_m1_finseq_1,existence_m1_subset_1,existence_m2_relset_1,existence_m3_trees_2,existence_m4_trees_3,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k4_tarski,dt_k4_trees_4,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_relset_1,dt_m3_trees_2,dt_m4_trees_3,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finseq_1,cc1_relset_1,cc3_arytm_3,cc4_membered,cc5_trees_3,cc6_membered,cc9_membered,fc1_ordinal2,fc1_subset_1,fc26_trees_3,fc2_trees_2,fc4_subset_1,fc5_membered,fc5_trees_3,fc6_trees_3,rc1_finseq_1,rc1_subset_1,rc2_subset_1,rc5_trees_2,rc6_trees_2,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,d5_tarski,antisymmetry_r2_hidden,existence_m2_finseq_1,existence_m2_subset_1,existence_m5_trees_3,redefinition_k12_trees_4,redefinition_k1_domain_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_k8_trees_4,redefinition_m2_finseq_1,redefinition_m2_subset_1,redefinition_m5_trees_3,dt_k11_trees_3,dt_k12_trees_4,dt_k1_domain_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_zfmisc_1,dt_k4_finseq_1,dt_k4_trees_3,dt_k5_numbers,dt_k5_trees_3,dt_k8_trees_4,dt_m2_finseq_1,dt_m2_subset_1,dt_m5_trees_3,dt_c1_54__trees_4,dt_c2_54__trees_4,dt_c3_54__trees_4,dt_c4_54__trees_4,dt_c5_54__trees_4,dt_c6_54__trees_4,fc2_membered,t1_subset,t7_boole,e6_54__trees_4,e2_54__trees_4,e3_54__trees_4,e4_54__trees_4]), [interesting(0.8),file(trees_4,e7_54__trees_4),[file(trees_4,e7_54__trees_4)]]). fof(i6_54__trees_4,theorem,( $true ), introduced(tautology,[file(trees_4,i6_54__trees_4)]), [interesting(0.8),trivial,file(trees_4,i6_54__trees_4)]). fof(i5_54__trees_4,plain,( ? [A] : ( m2_finseq_1(A,k5_trees_3(c2_54__trees_4)) & k4_finseq_1(A) = k4_finseq_1(c5_54__trees_4) & ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ~ ( r2_hidden(B,k4_finseq_1(c5_54__trees_4)) & ! [C] : ( m5_trees_3(C,k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k5_trees_3(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4))) => ~ ( C = k1_funct_1(c5_54__trees_4,B) & k1_funct_1(A,B) = k11_trees_3(c1_54__trees_4,c2_54__trees_4,C) ) ) ) ) & k11_trees_3(c1_54__trees_4,c2_54__trees_4,k12_trees_4(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k1_domain_1(c1_54__trees_4,c2_54__trees_4,c3_54__trees_4,c4_54__trees_4),c5_54__trees_4)) = k12_trees_4(c2_54__trees_4,c4_54__trees_4,A) ) ), inference(conclusion,[status(thm),assumptions([dt_c1_54__trees_4,dt_c2_54__trees_4,dt_c3_54__trees_4,dt_c4_54__trees_4,dt_c5_54__trees_4])],[rc6_trees_3,rc8_trees_3,dt_m1_relset_1,cc10_trees_3,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_arytm_3,cc1_membered,cc1_trees_4,cc20_membered,cc2_arytm_3,cc2_membered,cc3_membered,cc4_trees_3,fc17_finseq_1,fc5_trees_2,rc1_arytm_3,rc1_membered,rc2_finseq_1,rc2_trees_3,rc4_trees_3,rc7_finseq_1,rc7_trees_2,rc8_finseq_1,rc8_trees_2,rc9_trees_2,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k4_tarski,dt_k4_trees_4,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_relset_1,dt_m3_trees_2,dt_m4_trees_3,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finseq_1,cc1_relset_1,cc3_arytm_3,cc4_membered,cc5_trees_3,cc6_membered,cc9_membered,fc1_ordinal2,fc1_subset_1,fc26_trees_3,fc2_trees_2,fc4_subset_1,fc5_membered,fc6_trees_3,rc1_finseq_1,rc1_subset_1,rc2_subset_1,rc5_trees_2,rc6_trees_2,antisymmetry_r2_hidden,redefinition_k12_trees_4,redefinition_k1_domain_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_subset_1,redefinition_m5_trees_3,dt_k11_trees_3,dt_k12_trees_4,dt_k1_domain_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_zfmisc_1,dt_k4_finseq_1,dt_k5_numbers,dt_k5_trees_3,dt_m2_finseq_1,dt_m2_subset_1,dt_m5_trees_3,dt_c1_54__trees_4,dt_c2_54__trees_4,dt_c3_54__trees_4,dt_c4_54__trees_4,dt_c5_54__trees_4,fc2_membered,e7_54__trees_4,i6_54__trees_4]), [interesting(0.8),file(trees_4,i5_54__trees_4),[file(trees_4,i5_54__trees_4)]]). fof(i5_54_tmp__trees_4,plain, ( m2_finseq_1(c5_54__trees_4,k5_trees_3(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4))) => ? [A] : ( m2_finseq_1(A,k5_trees_3(c2_54__trees_4)) & k4_finseq_1(A) = k4_finseq_1(c5_54__trees_4) & ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ~ ( r2_hidden(B,k4_finseq_1(c5_54__trees_4)) & ! [C] : ( m5_trees_3(C,k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k5_trees_3(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4))) => ~ ( C = k1_funct_1(c5_54__trees_4,B) & k1_funct_1(A,B) = k11_trees_3(c1_54__trees_4,c2_54__trees_4,C) ) ) ) ) & k11_trees_3(c1_54__trees_4,c2_54__trees_4,k12_trees_4(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k1_domain_1(c1_54__trees_4,c2_54__trees_4,c3_54__trees_4,c4_54__trees_4),c5_54__trees_4)) = k12_trees_4(c2_54__trees_4,c4_54__trees_4,A) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_54__trees_4,dt_c2_54__trees_4,dt_c3_54__trees_4,dt_c4_54__trees_4]),discharge_asm(discharge,[dt_c5_54__trees_4])],[dt_c5_54__trees_4,i5_54__trees_4]), [interesting(0.8),i4_54__trees_4]). fof(i4_54__trees_4,plain,( ! [A] : ( m2_finseq_1(A,k5_trees_3(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4))) => ? [B] : ( m2_finseq_1(B,k5_trees_3(c2_54__trees_4)) & k4_finseq_1(B) = k4_finseq_1(A) & ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ~ ( r2_hidden(C,k4_finseq_1(A)) & ! [D] : ( m5_trees_3(D,k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k5_trees_3(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4))) => ~ ( D = k1_funct_1(A,C) & k1_funct_1(B,C) = k11_trees_3(c1_54__trees_4,c2_54__trees_4,D) ) ) ) ) & k11_trees_3(c1_54__trees_4,c2_54__trees_4,k12_trees_4(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k1_domain_1(c1_54__trees_4,c2_54__trees_4,c3_54__trees_4,c4_54__trees_4),A)) = k12_trees_4(c2_54__trees_4,c4_54__trees_4,B) ) ) ), inference(let,[status(thm),assumptions([dt_c1_54__trees_4,dt_c2_54__trees_4,dt_c3_54__trees_4,dt_c4_54__trees_4])],[i5_54_tmp__trees_4,dh_c5_54__trees_4]), [interesting(0.8),file(trees_4,i4_54__trees_4),[file(trees_4,i4_54__trees_4)]]). fof(i4_54_tmp__trees_4,plain, ( m1_subset_1(c4_54__trees_4,c2_54__trees_4) => ! [A] : ( m2_finseq_1(A,k5_trees_3(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4))) => ? [B] : ( m2_finseq_1(B,k5_trees_3(c2_54__trees_4)) & k4_finseq_1(B) = k4_finseq_1(A) & ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ~ ( r2_hidden(C,k4_finseq_1(A)) & ! [D] : ( m5_trees_3(D,k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k5_trees_3(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4))) => ~ ( D = k1_funct_1(A,C) & k1_funct_1(B,C) = k11_trees_3(c1_54__trees_4,c2_54__trees_4,D) ) ) ) ) & k11_trees_3(c1_54__trees_4,c2_54__trees_4,k12_trees_4(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k1_domain_1(c1_54__trees_4,c2_54__trees_4,c3_54__trees_4,c4_54__trees_4),A)) = k12_trees_4(c2_54__trees_4,c4_54__trees_4,B) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_54__trees_4,dt_c2_54__trees_4,dt_c3_54__trees_4]),discharge_asm(discharge,[dt_c4_54__trees_4])],[dt_c4_54__trees_4,i4_54__trees_4]), [interesting(0.8),i3_54__trees_4]). fof(i3_54__trees_4,plain,( ! [A] : ( m1_subset_1(A,c2_54__trees_4) => ! [B] : ( m2_finseq_1(B,k5_trees_3(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4))) => ? [C] : ( m2_finseq_1(C,k5_trees_3(c2_54__trees_4)) & k4_finseq_1(C) = k4_finseq_1(B) & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ~ ( r2_hidden(D,k4_finseq_1(B)) & ! [E] : ( m5_trees_3(E,k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k5_trees_3(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4))) => ~ ( E = k1_funct_1(B,D) & k1_funct_1(C,D) = k11_trees_3(c1_54__trees_4,c2_54__trees_4,E) ) ) ) ) & k11_trees_3(c1_54__trees_4,c2_54__trees_4,k12_trees_4(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k1_domain_1(c1_54__trees_4,c2_54__trees_4,c3_54__trees_4,A),B)) = k12_trees_4(c2_54__trees_4,A,C) ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_54__trees_4,dt_c2_54__trees_4,dt_c3_54__trees_4])],[i4_54_tmp__trees_4,dh_c4_54__trees_4]), [interesting(0.8),file(trees_4,i3_54__trees_4),[file(trees_4,i3_54__trees_4)]]). fof(i3_54_tmp__trees_4,plain, ( m1_subset_1(c3_54__trees_4,c1_54__trees_4) => ! [A] : ( m1_subset_1(A,c2_54__trees_4) => ! [B] : ( m2_finseq_1(B,k5_trees_3(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4))) => ? [C] : ( m2_finseq_1(C,k5_trees_3(c2_54__trees_4)) & k4_finseq_1(C) = k4_finseq_1(B) & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ~ ( r2_hidden(D,k4_finseq_1(B)) & ! [E] : ( m5_trees_3(E,k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k5_trees_3(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4))) => ~ ( E = k1_funct_1(B,D) & k1_funct_1(C,D) = k11_trees_3(c1_54__trees_4,c2_54__trees_4,E) ) ) ) ) & k11_trees_3(c1_54__trees_4,c2_54__trees_4,k12_trees_4(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k1_domain_1(c1_54__trees_4,c2_54__trees_4,c3_54__trees_4,A),B)) = k12_trees_4(c2_54__trees_4,A,C) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_54__trees_4,dt_c2_54__trees_4]),discharge_asm(discharge,[dt_c3_54__trees_4])],[dt_c3_54__trees_4,i3_54__trees_4]), [interesting(0.8),i2_54__trees_4]). fof(i2_54__trees_4,plain,( ! [A] : ( m1_subset_1(A,c1_54__trees_4) => ! [B] : ( m1_subset_1(B,c2_54__trees_4) => ! [C] : ( m2_finseq_1(C,k5_trees_3(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4))) => ? [D] : ( m2_finseq_1(D,k5_trees_3(c2_54__trees_4)) & k4_finseq_1(D) = k4_finseq_1(C) & ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ~ ( r2_hidden(E,k4_finseq_1(C)) & ! [F] : ( m5_trees_3(F,k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k5_trees_3(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4))) => ~ ( F = k1_funct_1(C,E) & k1_funct_1(D,E) = k11_trees_3(c1_54__trees_4,c2_54__trees_4,F) ) ) ) ) & k11_trees_3(c1_54__trees_4,c2_54__trees_4,k12_trees_4(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k1_domain_1(c1_54__trees_4,c2_54__trees_4,A,B),C)) = k12_trees_4(c2_54__trees_4,B,D) ) ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_54__trees_4,dt_c2_54__trees_4])],[i3_54_tmp__trees_4,dh_c3_54__trees_4]), [interesting(0.8),file(trees_4,i2_54__trees_4),[file(trees_4,i2_54__trees_4)]]). fof(i2_54_tmp__trees_4,plain, ( ~ v1_xboole_0(c2_54__trees_4) => ! [A] : ( m1_subset_1(A,c1_54__trees_4) => ! [B] : ( m1_subset_1(B,c2_54__trees_4) => ! [C] : ( m2_finseq_1(C,k5_trees_3(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4))) => ? [D] : ( m2_finseq_1(D,k5_trees_3(c2_54__trees_4)) & k4_finseq_1(D) = k4_finseq_1(C) & ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ~ ( r2_hidden(E,k4_finseq_1(C)) & ! [F] : ( m5_trees_3(F,k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k5_trees_3(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4))) => ~ ( F = k1_funct_1(C,E) & k1_funct_1(D,E) = k11_trees_3(c1_54__trees_4,c2_54__trees_4,F) ) ) ) ) & k11_trees_3(c1_54__trees_4,c2_54__trees_4,k12_trees_4(k2_zfmisc_1(c1_54__trees_4,c2_54__trees_4),k1_domain_1(c1_54__trees_4,c2_54__trees_4,A,B),C)) = k12_trees_4(c2_54__trees_4,B,D) ) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_54__trees_4]),discharge_asm(discharge,[dt_c2_54__trees_4])],[dt_c2_54__trees_4,i2_54__trees_4]), [interesting(0.8),i1_54__trees_4]). fof(i1_54__trees_4,plain,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,c1_54__trees_4) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m2_finseq_1(D,k5_trees_3(k2_zfmisc_1(c1_54__trees_4,A))) => ? [E] : ( m2_finseq_1(E,k5_trees_3(A)) & k4_finseq_1(E) = k4_finseq_1(D) & ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ~ ( r2_hidden(F,k4_finseq_1(D)) & ! [G] : ( m5_trees_3(G,k2_zfmisc_1(c1_54__trees_4,A),k5_trees_3(k2_zfmisc_1(c1_54__trees_4,A))) => ~ ( G = k1_funct_1(D,F) & k1_funct_1(E,F) = k11_trees_3(c1_54__trees_4,A,G) ) ) ) ) & k11_trees_3(c1_54__trees_4,A,k12_trees_4(k2_zfmisc_1(c1_54__trees_4,A),k1_domain_1(c1_54__trees_4,A,B,C),D)) = k12_trees_4(A,C,E) ) ) ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_54__trees_4])],[i2_54_tmp__trees_4,dh_c2_54__trees_4]), [interesting(0.8),file(trees_4,i1_54__trees_4),[file(trees_4,i1_54__trees_4)]]). fof(i1_54_tmp__trees_4,plain, ( ~ v1_xboole_0(c1_54__trees_4) => ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,c1_54__trees_4) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m2_finseq_1(D,k5_trees_3(k2_zfmisc_1(c1_54__trees_4,A))) => ? [E] : ( m2_finseq_1(E,k5_trees_3(A)) & k4_finseq_1(E) = k4_finseq_1(D) & ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ~ ( r2_hidden(F,k4_finseq_1(D)) & ! [G] : ( m5_trees_3(G,k2_zfmisc_1(c1_54__trees_4,A),k5_trees_3(k2_zfmisc_1(c1_54__trees_4,A))) => ~ ( G = k1_funct_1(D,F) & k1_funct_1(E,F) = k11_trees_3(c1_54__trees_4,A,G) ) ) ) ) & k11_trees_3(c1_54__trees_4,A,k12_trees_4(k2_zfmisc_1(c1_54__trees_4,A),k1_domain_1(c1_54__trees_4,A,B,C),D)) = k12_trees_4(A,C,E) ) ) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_54__trees_4])],[dt_c1_54__trees_4,i1_54__trees_4]), [interesting(1),t32_trees_4]). fof(t32_trees_4,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( m2_finseq_1(E,k5_trees_3(k2_zfmisc_1(A,B))) => ? [F] : ( m2_finseq_1(F,k5_trees_3(B)) & k4_finseq_1(F) = k4_finseq_1(E) & ! [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) => ~ ( r2_hidden(G,k4_finseq_1(E)) & ! [H] : ( m5_trees_3(H,k2_zfmisc_1(A,B),k5_trees_3(k2_zfmisc_1(A,B))) => ~ ( H = k1_funct_1(E,G) & k1_funct_1(F,G) = k11_trees_3(A,B,H) ) ) ) ) & k11_trees_3(A,B,k12_trees_4(k2_zfmisc_1(A,B),k1_domain_1(A,B,C,D),E)) = k12_trees_4(B,D,F) ) ) ) ) ) ) ), inference(let,[status(thm),assumptions([])],[i1_54_tmp__trees_4,dh_c1_54__trees_4]), [interesting(1),file(trees_4,t32_trees_4),[file(trees_4,t32_trees_4)]]).