% Mizar problem: t17_msafree3,msafree3,714,17 fof(t17_msafree3,conjecture,( ! [A,B] : ( ( ~ v2_msualg_1(B) & v1_instalg1(B) & l1_msualg_1(B) ) => ! [C] : ( ( v2_relat_1(C) & m1_pboole(C,u1_struct_0(B)) ) => ! [D] : ( m1_pboole(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( r2_hidden(A,k1_funct_1(k5_msafree3(B,C,D),E)) => m1_dtconstr(A,u1_struct_0(k5_msafree(B,C)),k5_trees_3(u1_struct_0(k5_msafree(B,C))),k1_msaterm(B,C)) ) ) ) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v1_lang1,abstractness_v4_msualg_1,antisymmetry_r2_hidden,cc1_catalg_1,cc1_finseq_1,cc1_funct_1,cc1_index_1,cc1_msaterm,cc1_msualg_6,cc1_pboole,cc1_relat_1,cc1_relset_1,cc2_funct_1,cc2_index_1,cc2_instalg1,cc2_pboole,cc3_instalg1,cc3_pboole,cc4_instalg1,cc4_msafree3,cc4_trees_3,cc4_trees_9,cc5_instalg1,cc5_trees_3,cc5_trees_9,cc6_trees_9,d5_msafree3,d6_msafree3,dt_g1_lang1,dt_g3_msualg_1,dt_k11_msafree,dt_k13_finseq_1,dt_k1_funct_1,dt_k1_msaterm,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_msafree3,dt_k2_zfmisc_1,dt_k3_finseq_2,dt_k4_msafree3,dt_k5_msafree,dt_k5_msafree3,dt_k5_relat_1,dt_k5_trees_3,dt_k6_pboole,dt_k7_msaterm,dt_k7_pboole,dt_l1_lang1,dt_l1_msualg_1,dt_l1_struct_0,dt_l2_msualg_1,dt_l3_msualg_1,dt_m1_dtconstr,dt_m1_finseq_2,dt_m1_pboole,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m3_pboole,dt_m3_trees_2,dt_m4_pboole,dt_m4_trees_3,dt_m5_trees_3,dt_u1_lang1,dt_u1_msualg_1,dt_u1_struct_0,dt_u2_msualg_1,dt_u3_msualg_1,dt_u4_msualg_1,dt_u5_msualg_1,existence_l1_lang1,existence_l1_msualg_1,existence_l1_struct_0,existence_l2_msualg_1,existence_l3_msualg_1,existence_m1_dtconstr,existence_m1_finseq_2,existence_m1_pboole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m3_pboole,existence_m3_trees_2,existence_m4_pboole,existence_m4_trees_3,existence_m5_trees_3,fc10_relat_1,fc12_relat_1,fc16_finseq_1,fc1_catalg_1,fc1_funct_1,fc1_instalg1,fc1_msaterm,fc1_msualg_1,fc1_pboole,fc1_struct_0,fc1_subset_1,fc2_catalg_1,fc2_finseq_1,fc2_msaterm,fc2_msualg_9,fc2_pboole,fc3_msafree,fc4_msafree,fc4_relat_1,fc4_subset_1,fc5_msafree,fc6_msualg_2,fc6_trees_3,fc7_funcop_1,fc8_funcop_1,fc8_msafree,fc9_finseq_1,fc9_relat_1,fraenkel_a_4_0_msafree3,free_g1_lang1,free_g3_msualg_1,rc1_catalg_1,rc1_finseq_1,rc1_funcop_1,rc1_funct_1,rc1_index_1,rc1_instalg1,rc1_msafree,rc1_msualg_6,rc1_pboole,rc1_relat_1,rc1_subset_1,rc2_catalg_1,rc2_funct_1,rc2_pboole,rc2_relat_1,rc2_subset_1,rc2_trees_3,rc3_finseq_1,rc3_funct_1,rc3_pboole,rc3_relat_1,rc3_struct_0,rc4_funct_1,rc4_pboole,rc4_trees_3,rc4_trees_9,rc5_funct_1,rc5_msualg_1,rc5_pboole,rc5_struct_0,rc5_trees_2,rc6_finseq_1,rc6_msualg_1,rc6_trees_2,rc7_finseq_1,rc7_trees_2,rc8_finseq_1,rc8_trees_2,rc9_trees_2,redefinition_k3_finseq_2,redefinition_k7_pboole,redefinition_m1_dtconstr,redefinition_m2_relset_1,redefinition_m5_trees_3,reflexivity_r1_tarski,reflexivity_r2_pboole,t1_subset,t2_subset,t2_tarski,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]), [file(msafree3,t17_msafree3)]). fof(abstractness_v1_lang1,axiom,( ! [A] : ( l1_lang1(A) => ( v1_lang1(A) => A = g1_lang1(u1_struct_0(A),u1_lang1(A)) ) ) ), file(lang1,v1_lang1), []). fof(abstractness_v4_msualg_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) & l3_msualg_1(B,A) ) => ( v4_msualg_1(B,A) => B = g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)) ) ) ), file(msualg_1,v4_msualg_1), []). fof(antisymmetry_r2_hidden,axiom,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), []). fof(cc1_catalg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ( v5_msualg_1(B,A) => ~ v1_catalg_1(B,A) ) ) ) ), file(catalg_1,cc1_catalg_1), []). fof(cc1_finseq_1,axiom,( ! [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), []). fof(cc1_funct_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_funct_1(A) ) ), file(funct_1,cc1_funct_1), []). fof(cc1_index_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_pboole(B,A) => ( v2_relat_1(B) => ~ v3_relat_1(B) ) ) ) ), file(index_1,cc1_index_1), []). fof(cc1_msaterm,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( m1_subset_1(C,k1_msaterm(A,B)) => v1_finset_1(C) ) ) ), file(msaterm,cc1_msaterm), []). fof(cc1_msualg_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ( v5_msualg_1(B,A) => v1_msualg_6(B,A) ) ) ) ), file(msualg_6,cc1_msualg_6), []). fof(cc1_pboole,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_pboole(B,A) => ( v2_relat_1(B) => ~ v3_relat_1(B) ) ) ) ), file(pboole,cc1_pboole), []). fof(cc1_relat_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_relat_1(A) ) ), file(relat_1,cc1_relat_1), []). fof(cc1_relset_1,axiom,( ! [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), []). fof(cc2_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ) ), file(funct_1,cc2_funct_1), []). fof(cc2_index_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_pboole(B,A) => ~ v1_xboole_0(B) ) ) ), file(index_1,cc2_index_1), []). fof(cc2_instalg1,axiom,( ! [A] : ( l1_msualg_1(A) => ( ~ v3_struct_0(A) => v1_instalg1(A) ) ) ), file(instalg1,cc2_instalg1), []). fof(cc2_pboole,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_pboole(B,A) => ( v3_relat_1(B) => ~ v2_relat_1(B) ) ) ) ), file(pboole,cc2_pboole), []). fof(cc3_instalg1,axiom,( ! [A] : ( l1_msualg_1(A) => ( v2_msualg_1(A) => v1_instalg1(A) ) ) ), file(instalg1,cc3_instalg1), []). fof(cc3_pboole,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => ! [D] : ( m3_pboole(D,A,B,C) => v1_funcop_1(D) ) ) ), file(pboole,cc3_pboole), []). fof(cc4_instalg1,axiom,( ! [A] : ( l1_msualg_1(A) => ( ( v3_struct_0(A) & v1_instalg1(A) ) => v2_msualg_1(A) ) ) ), file(instalg1,cc4_instalg1), []). fof(cc4_msafree3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) ) ), file(msafree3,cc4_msafree3), []). fof(cc4_trees_3,axiom,( ! [A] : ( v3_trees_3(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v3_trees_3(B) ) ) ), file(trees_3,cc4_trees_3), []). fof(cc4_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v3_trees_2(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) & v3_trees_9(A) ) ) ), file(trees_9,cc4_trees_9), []). fof(cc5_instalg1,axiom,( ! [A] : ( l1_msualg_1(A) => ( ( ~ v2_msualg_1(A) & v1_instalg1(A) ) => ~ v3_struct_0(A) ) ) ), file(instalg1,cc5_instalg1), []). fof(cc5_trees_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m4_trees_3(B,A) => v3_trees_3(B) ) ) ), file(trees_3,cc5_trees_3), []). fof(cc5_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) & v3_trees_9(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) & v4_trees_9(A) ) ) ), file(trees_9,cc5_trees_9), []). fof(cc6_trees_9,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k5_trees_3(A))) ) => ! [C] : ( m1_subset_1(C,B) => v1_finset_1(C) ) ) ), file(trees_9,cc6_trees_9), []). fof(d5_msafree3,axiom,( ! [A] : ( ( ~ v2_msualg_1(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( m1_dtconstr(C,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B)) => k4_msafree3(A,B,C) = k2_msafree3(A,C) ) ) ) ), file(msafree3,d5_msafree3), []). fof(d6_msafree3,axiom,( ! [A] : ( ( ~ v2_msualg_1(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( m1_pboole(C,u1_struct_0(A)) => ! [D] : ( m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,k11_msafree(A,B))) => ( D = k5_msafree3(A,B,C) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k1_funct_1(D,E) = a_4_0_msafree3(A,B,C,E) ) ) ) ) ) ) ), file(msafree3,d6_msafree3), []). fof(dt_g1_lang1,axiom,( ! [A,B] : ( m1_relset_1(B,A,k3_finseq_2(A)) => ( v1_lang1(g1_lang1(A,B)) & l1_lang1(g1_lang1(A,B)) ) ) ), file(lang1,g1_lang1), []). fof(dt_g3_msualg_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) & m1_pboole(B,u1_struct_0(A)) & m3_pboole(C,u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),B)),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),B)) ) => ( v4_msualg_1(g3_msualg_1(A,B,C),A) & l3_msualg_1(g3_msualg_1(A,B,C),A) ) ) ), file(msualg_1,g3_msualg_1), []). fof(dt_k11_msafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => l3_msualg_1(k11_msafree(A,B),A) ) ), file(msafree,k11_msafree), []). fof(dt_k13_finseq_1,axiom,( $true ), file(finseq_1,k13_finseq_1), []). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). fof(dt_k1_msaterm,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & m1_pboole(B,u1_struct_0(A)) ) => m1_subset_1(k1_msaterm(A,B),k1_zfmisc_1(k5_trees_3(u1_struct_0(k5_msafree(A,B))))) ) ), file(msaterm,k1_msaterm), []). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), []). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), []). fof(dt_k2_msafree3,axiom,( ! [A,B] : ( ( l1_msualg_1(A) & ~ v1_xboole_0(B) & v1_relat_1(B) ) => m1_pboole(k2_msafree3(A,B),u1_struct_0(A)) ) ), file(msafree3,k2_msafree3), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). fof(dt_k3_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(k3_finseq_2(A)) & m1_finseq_2(k3_finseq_2(A),A) ) ), file(finseq_2,k3_finseq_2), []). fof(dt_k4_msafree3,axiom,( ! [A,B,C] : ( ( ~ v2_msualg_1(A) & v1_instalg1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m1_subset_1(C,k1_msaterm(A,B)) ) => m4_pboole(k4_msafree3(A,B,C),u1_struct_0(A),B) ) ), file(msafree3,k4_msafree3), []). fof(dt_k5_msafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & m1_pboole(B,u1_struct_0(A)) ) => l1_lang1(k5_msafree(A,B)) ) ), file(msafree,k5_msafree), []). fof(dt_k5_msafree3,axiom,( ! [A,B,C] : ( ( ~ v2_msualg_1(A) & v1_instalg1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m1_pboole(C,u1_struct_0(A)) ) => m4_pboole(k5_msafree3(A,B,C),u1_struct_0(A),u4_msualg_1(A,k11_msafree(A,B))) ) ), file(msafree3,k5_msafree3), []). 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), []). 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), []). fof(dt_k6_pboole,axiom,( ! [A,B] : ( m1_pboole(B,A) => m1_pboole(k6_pboole(A,B),k3_finseq_2(A)) ) ), file(pboole,k6_pboole), []). fof(dt_k7_msaterm,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m1_subset_1(C,k1_msaterm(A,B)) ) => m1_subset_1(k7_msaterm(A,B,C),u1_struct_0(A)) ) ), file(msaterm,k7_msaterm), []). fof(dt_k7_pboole,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_pboole(D,B) ) => m1_pboole(k7_pboole(A,B,C,D),A) ) ), file(pboole,k7_pboole), []). fof(dt_l1_lang1,axiom,( ! [A] : ( l1_lang1(A) => l1_struct_0(A) ) ), file(lang1,l1_lang1), []). fof(dt_l1_msualg_1,axiom,( ! [A] : ( l1_msualg_1(A) => l1_struct_0(A) ) ), file(msualg_1,l1_msualg_1), []). fof(dt_l1_struct_0,axiom,( $true ), file(struct_0,l1_struct_0), []). fof(dt_l2_msualg_1,axiom,( $true ), file(msualg_1,l2_msualg_1), []). fof(dt_l3_msualg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => l2_msualg_1(B,A) ) ) ), file(msualg_1,l3_msualg_1), []). fof(dt_m1_dtconstr,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m4_trees_3(B,A) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(B)) ) => ! [D] : ( m1_dtconstr(D,A,B,C) => m5_trees_3(D,A,B) ) ) ), file(dtconstr,m1_dtconstr), []). fof(dt_m1_finseq_2,axiom,( $true ), file(finseq_2,m1_finseq_2), []). fof(dt_m1_pboole,axiom,( ! [A,B] : ( m1_pboole(B,A) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ), file(pboole,m1_pboole), []). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), []). fof(dt_m1_subset_1,axiom,( $true ), 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), []). fof(dt_m3_pboole,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => ! [D] : ( m3_pboole(D,A,B,C) => m1_pboole(D,A) ) ) ), file(pboole,m3_pboole), []). fof(dt_m3_trees_2,axiom,( ! [A,B] : ( m3_trees_2(B,A) => v1_relat_1(B) ) ), file(trees_2,m3_trees_2), []). fof(dt_m4_pboole,axiom,( ! [A,B] : ( m1_pboole(B,A) => ! [C] : ( m4_pboole(C,A,B) => m1_pboole(C,A) ) ) ), file(pboole,m4_pboole), []). fof(dt_m4_trees_3,axiom,( $true ), file(trees_3,m4_trees_3), []). 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), []). fof(dt_u1_lang1,axiom,( ! [A] : ( l1_lang1(A) => m2_relset_1(u1_lang1(A),u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) ) ), file(lang1,u1_lang1), []). fof(dt_u1_msualg_1,axiom,( $true ), file(msualg_1,u1_msualg_1), []). fof(dt_u1_struct_0,axiom,( $true ), file(struct_0,u1_struct_0), []). fof(dt_u2_msualg_1,axiom,( ! [A] : ( l1_msualg_1(A) => ( v1_funct_1(u2_msualg_1(A)) & v1_funct_2(u2_msualg_1(A),u1_msualg_1(A),k3_finseq_2(u1_struct_0(A))) & m2_relset_1(u2_msualg_1(A),u1_msualg_1(A),k3_finseq_2(u1_struct_0(A))) ) ) ), file(msualg_1,u2_msualg_1), []). fof(dt_u3_msualg_1,axiom,( ! [A] : ( l1_msualg_1(A) => ( v1_funct_1(u3_msualg_1(A)) & v1_funct_2(u3_msualg_1(A),u1_msualg_1(A),u1_struct_0(A)) & m2_relset_1(u3_msualg_1(A),u1_msualg_1(A),u1_struct_0(A)) ) ) ), file(msualg_1,u3_msualg_1), []). fof(dt_u4_msualg_1,axiom,( ! [A,B] : ( ( l1_struct_0(A) & l2_msualg_1(B,A) ) => m1_pboole(u4_msualg_1(A,B),u1_struct_0(A)) ) ), file(msualg_1,u4_msualg_1), []). fof(dt_u5_msualg_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) & l3_msualg_1(B,A) ) => m3_pboole(u5_msualg_1(A,B),u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),u4_msualg_1(A,B))),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,B))) ) ), file(msualg_1,u5_msualg_1), []). fof(existence_l1_lang1,axiom,( ? [A] : l1_lang1(A) ), file(lang1,l1_lang1), []). fof(existence_l1_msualg_1,axiom,( ? [A] : l1_msualg_1(A) ), file(msualg_1,l1_msualg_1), []). fof(existence_l1_struct_0,axiom,( ? [A] : l1_struct_0(A) ), file(struct_0,l1_struct_0), []). fof(existence_l2_msualg_1,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : l2_msualg_1(B,A) ) ), file(msualg_1,l2_msualg_1), []). fof(existence_l3_msualg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) ) => ? [B] : l3_msualg_1(B,A) ) ), file(msualg_1,l3_msualg_1), []). fof(existence_m1_dtconstr,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m4_trees_3(B,A) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(B)) ) => ? [D] : m1_dtconstr(D,A,B,C) ) ), file(dtconstr,m1_dtconstr), []). fof(existence_m1_finseq_2,axiom,( ! [A] : ? [B] : m1_finseq_2(B,A) ), file(finseq_2,m1_finseq_2), []). fof(existence_m1_pboole,axiom,( ! [A] : ? [B] : m1_pboole(B,A) ), file(pboole,m1_pboole), []). fof(existence_m1_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), 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), []). fof(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), []). fof(existence_m3_pboole,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => ? [D] : m3_pboole(D,A,B,C) ) ), file(pboole,m3_pboole), []). fof(existence_m3_trees_2,axiom,( ! [A] : ? [B] : m3_trees_2(B,A) ), file(trees_2,m3_trees_2), []). fof(existence_m4_pboole,axiom,( ! [A,B] : ( m1_pboole(B,A) => ? [C] : m4_pboole(C,A,B) ) ), file(pboole,m4_pboole), []). fof(existence_m4_trees_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : m4_trees_3(B,A) ) ), file(trees_3,m4_trees_3), []). 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), []). fof(fc10_relat_1,axiom,( ! [A,B] : ( ( v1_xboole_0(A) & v1_relat_1(B) ) => ( v1_xboole_0(k5_relat_1(B,A)) & v1_relat_1(k5_relat_1(B,A)) ) ) ), file(relat_1,fc10_relat_1), []). fof(fc12_relat_1,axiom, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) ), file(relat_1,fc12_relat_1), []). fof(fc16_finseq_1,axiom,( ! [A] : ( ~ v1_xboole_0(k13_finseq_1(A)) & v1_fraenkel(k13_finseq_1(A)) ) ), file(finseq_1,fc16_finseq_1), []). fof(fc1_catalg_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ( v4_msualg_1(k11_msafree(A,B),A) & v5_msualg_1(k11_msafree(A,B),A) & v1_msafree1(k11_msafree(A,B),A) & ~ v1_catalg_1(k11_msafree(A,B),A) ) ) ), file(catalg_1,fc1_catalg_1), []). fof(fc1_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => ( v1_relat_1(k5_relat_1(A,B)) & v1_funct_1(k5_relat_1(A,B)) ) ) ), file(funct_1,fc1_funct_1), []). fof(fc1_instalg1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) ) => ( v4_msualg_1(g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)),A) & v5_msualg_1(g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)),A) ) ) ), file(instalg1,fc1_instalg1), []). fof(fc1_msaterm,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v2_relat_1(B) & m1_pboole(B,A) & m1_subset_1(C,A) ) => ~ v1_xboole_0(k1_funct_1(B,C)) ) ), file(msaterm,fc1_msaterm), []). fof(fc1_msualg_1,axiom,( ! [A,B] : ( ( l1_struct_0(A) & v5_msualg_1(B,A) & l2_msualg_1(B,A) ) => ( v1_relat_1(u4_msualg_1(A,B)) & v2_relat_1(u4_msualg_1(A,B)) & v1_funct_1(u4_msualg_1(A,B)) ) ) ), file(msualg_1,fc1_msualg_1), []). fof(fc1_pboole,axiom,( ! [A,B] : ( ( v2_relat_1(B) & m1_pboole(B,A) ) => ( v1_relat_1(k6_pboole(A,B)) & v2_relat_1(k6_pboole(A,B)) & ~ v3_relat_1(k6_pboole(A,B)) & v1_funct_1(k6_pboole(A,B)) ) ) ), file(pboole,fc1_pboole), []). fof(fc1_struct_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ~ v1_xboole_0(u1_struct_0(A)) ) ), file(struct_0,fc1_struct_0), []). fof(fc1_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ), file(subset_1,fc1_subset_1), []). fof(fc2_catalg_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & ~ v1_catalg_1(B,A) & l3_msualg_1(B,A) ) => ( v1_relat_1(u4_msualg_1(A,B)) & ~ v3_relat_1(u4_msualg_1(A,B)) & v1_funct_1(u4_msualg_1(A,B)) ) ) ), file(catalg_1,fc2_catalg_1), []). fof(fc2_finseq_1,axiom, ( 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), []). fof(fc2_msaterm,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ( ~ v1_xboole_0(k1_msaterm(A,B)) & v3_trees_3(k1_msaterm(A,B)) ) ) ), file(msaterm,fc2_msaterm), []). fof(fc2_msualg_9,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ( v4_msualg_1(k11_msafree(A,B),A) & v5_msualg_1(k11_msafree(A,B),A) & v2_msafree(k11_msafree(A,B),A) ) ) ), file(msualg_9,fc2_msualg_9), []). fof(fc2_pboole,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v2_relat_1(B) & m1_pboole(B,A) & m1_subset_1(C,A) ) => ~ v1_xboole_0(k1_funct_1(B,C)) ) ), file(pboole,fc2_pboole), []). fof(fc3_msafree,axiom,( ! [A] : ( ( ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ~ v1_xboole_0(u1_msualg_1(A)) ) ), file(msafree,fc3_msafree), []). fof(fc4_msafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & m1_pboole(B,u1_struct_0(A)) ) => ( ~ v3_struct_0(k5_msafree(A,B)) & v1_lang1(k5_msafree(A,B)) ) ) ), file(msafree,fc4_msafree), []). fof(fc4_relat_1,axiom, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) ), file(relat_1,fc4_relat_1), []). fof(fc4_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ), file(subset_1,fc4_subset_1), []). fof(fc5_msafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ( ~ v3_struct_0(k5_msafree(A,B)) & v1_lang1(k5_msafree(A,B)) & v1_dtconstr(k5_msafree(A,B)) & v2_dtconstr(k5_msafree(A,B)) & v3_dtconstr(k5_msafree(A,B)) ) ) ), file(msafree,fc5_msafree), []). fof(fc6_msualg_2,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) ) => ( v4_msualg_1(g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)),A) & v5_msualg_1(g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)),A) ) ) ), file(msualg_2,fc6_msualg_2), []). fof(fc6_trees_3,axiom,( ! [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), []). fof(fc7_funcop_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => ( v1_relat_1(k1_funct_1(A,B)) & v1_funct_1(k1_funct_1(A,B)) ) ) ), file(funcop_1,fc7_funcop_1), []). fof(fc8_funcop_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => ( v1_relat_1(k5_relat_1(B,A)) & v1_funct_1(k5_relat_1(B,A)) & v1_funcop_1(k5_relat_1(B,A)) ) ) ), file(funcop_1,fc8_funcop_1), []). fof(fc8_msafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ( v4_msualg_1(k11_msafree(A,B),A) & v5_msualg_1(k11_msafree(A,B),A) ) ) ), file(msafree,fc8_msafree), []). fof(fc9_finseq_1,axiom,( ! [A] : ~ v1_xboole_0(k13_finseq_1(A)) ), file(finseq_1,fc9_finseq_1), []). fof(fc9_relat_1,axiom,( ! [A,B] : ( ( v1_xboole_0(A) & v1_relat_1(B) ) => ( v1_xboole_0(k5_relat_1(A,B)) & v1_relat_1(k5_relat_1(A,B)) ) ) ), file(relat_1,fc9_relat_1), []). fof(fraenkel_a_4_0_msafree3,axiom,( ! [A,B,C,D,E] : ( ( ~ v2_msualg_1(B) & v1_instalg1(B) & l1_msualg_1(B) & v2_relat_1(C) & m1_pboole(C,u1_struct_0(B)) & m1_pboole(D,u1_struct_0(B)) & m1_subset_1(E,u1_struct_0(B)) ) => ( r2_hidden(A,a_4_0_msafree3(B,C,D,E)) <=> ? [F] : ( m1_dtconstr(F,u1_struct_0(k5_msafree(B,C)),k5_trees_3(u1_struct_0(k5_msafree(B,C))),k1_msaterm(B,C)) & A = F & k7_msaterm(B,C,F) = E & r2_pboole(u1_struct_0(B),k4_msafree3(B,C,F),D) ) ) ) ), file(msafree3,a_4_0_msafree3), []). fof(free_g1_lang1,axiom,( ! [A,B] : ( m1_relset_1(B,A,k3_finseq_2(A)) => ! [C,D] : ( g1_lang1(A,B) = g1_lang1(C,D) => ( A = C & B = D ) ) ) ), file(lang1,g1_lang1), []). fof(free_g3_msualg_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) & m1_pboole(B,u1_struct_0(A)) & m3_pboole(C,u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),B)),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),B)) ) => ! [D,E,F] : ( g3_msualg_1(A,B,C) = g3_msualg_1(D,E,F) => ( A = D & B = E & C = F ) ) ) ), file(msualg_1,g3_msualg_1), []). fof(rc1_catalg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ? [B] : ( l3_msualg_1(B,A) & v4_msualg_1(B,A) & v5_msualg_1(B,A) & v1_msafree1(B,A) & ~ v1_catalg_1(B,A) ) ) ), file(catalg_1,rc1_catalg_1), []). fof(rc1_finseq_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc1_finseq_1), []). fof(rc1_funcop_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) ), file(funcop_1,rc1_funcop_1), []). fof(rc1_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc1_funct_1), []). fof(rc1_index_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & ~ v3_relat_1(B) & v1_funct_1(B) ) ) ), file(index_1,rc1_index_1), []). fof(rc1_instalg1,axiom,( ? [A] : ( l1_msualg_1(A) & ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v1_instalg1(A) ) ), file(instalg1,rc1_instalg1), []). fof(rc1_msafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ? [B] : ( l3_msualg_1(B,A) & v4_msualg_1(B,A) & v5_msualg_1(B,A) & v2_msafree(B,A) ) ) ), file(msafree,rc1_msafree), []). fof(rc1_msualg_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ? [B] : ( l3_msualg_1(B,A) & v5_msualg_1(B,A) & v1_msualg_6(B,A) ) ) ), file(msualg_6,rc1_msualg_6), []). fof(rc1_pboole,axiom,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A) ) ), file(pboole,rc1_pboole), []). fof(rc1_relat_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) ) ), file(relat_1,rc1_relat_1), []). fof(rc1_subset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) ) ) ), file(subset_1,rc1_subset_1), []). fof(rc2_catalg_1,axiom,( ? [A] : ( v1_relat_1(A) & ~ v3_relat_1(A) & v1_funct_1(A) ) ), file(catalg_1,rc2_catalg_1), []). fof(rc2_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) ), file(funct_1,rc2_funct_1), []). fof(rc2_pboole,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v3_relat_1(B) & v1_funct_1(B) ) ), file(pboole,rc2_pboole), []). fof(rc2_relat_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) ) ), file(relat_1,rc2_relat_1), []). fof(rc2_subset_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) ) ), file(subset_1,rc2_subset_1), []). fof(rc2_trees_3,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) & v3_trees_3(A) ) ), file(trees_3,rc2_trees_3), []). fof(rc3_finseq_1,axiom,( ? [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), []). fof(rc3_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ), file(funct_1,rc3_funct_1), []). fof(rc3_pboole,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v2_relat_1(B) & v1_funct_1(B) ) ), file(pboole,rc3_pboole), []). fof(rc3_relat_1,axiom,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) ) ), file(relat_1,rc3_relat_1), []). fof(rc3_struct_0,axiom,( ? [A] : ( l1_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc3_struct_0), []). fof(rc4_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc4_funct_1), []). fof(rc4_pboole,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_funcop_1(B) ) ), file(pboole,rc4_pboole), []). fof(rc4_trees_3,axiom,( ! [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), []). fof(rc4_trees_9,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v3_trees_2(A) & v3_trees_9(A) & v4_trees_9(A) ) ), file(trees_9,rc4_trees_9), []). fof(rc5_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc5_funct_1), []). fof(rc5_msualg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) ) => ? [B] : ( l3_msualg_1(B,A) & v4_msualg_1(B,A) ) ) ), file(msualg_1,rc5_msualg_1), []). fof(rc5_pboole,axiom,( ! [A,B] : ( ( v2_relat_1(B) & m1_pboole(B,A) ) => ? [C] : ( m4_pboole(C,A,B) & v1_relat_1(C) & v2_relat_1(C) & v1_funct_1(C) ) ) ), file(pboole,rc5_pboole), []). fof(rc5_struct_0,axiom,( ! [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), []). fof(rc5_trees_2,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) ), file(trees_2,rc5_trees_2), []). fof(rc6_finseq_1,axiom,( ? [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), []). fof(rc6_msualg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) ) => ? [B] : ( l3_msualg_1(B,A) & v4_msualg_1(B,A) & v5_msualg_1(B,A) ) ) ), file(msualg_1,rc6_msualg_1), []). fof(rc6_trees_2,axiom,( ! [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), []). fof(rc7_finseq_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc7_finseq_1), []). fof(rc7_trees_2,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v3_trees_2(A) ) ), file(trees_2,rc7_trees_2), []). fof(rc8_finseq_1,axiom,( ? [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), []). fof(rc8_trees_2,axiom,( ! [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), []). fof(rc9_trees_2,axiom,( ! [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), []). fof(redefinition_k3_finseq_2,axiom,( ! [A] : k3_finseq_2(A) = k13_finseq_1(A) ), file(finseq_2,k3_finseq_2), []). fof(redefinition_k7_pboole,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_pboole(D,B) ) => k7_pboole(A,B,C,D) = k5_relat_1(C,D) ) ), file(pboole,k7_pboole), []). fof(redefinition_m1_dtconstr,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m4_trees_3(B,A) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(B)) ) => ! [D] : ( m1_dtconstr(D,A,B,C) <=> m1_subset_1(D,C) ) ) ), file(dtconstr,m1_dtconstr), []). fof(redefinition_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) <=> m1_relset_1(C,A,B) ) ), file(relset_1,m2_relset_1), []). fof(redefinition_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) <=> m1_subset_1(C,B) ) ) ), file(trees_3,m5_trees_3), []). fof(reflexivity_r1_tarski,axiom,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), []). fof(reflexivity_r2_pboole,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => r2_pboole(A,B,B) ) ), file(pboole,r2_pboole), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t2_subset,axiom,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), []). fof(t2_tarski,axiom,( ! [A,B] : ( ! [C] : ( r2_hidden(C,A) <=> r2_hidden(C,B) ) => A = B ) ), file(tarski,t2_tarski), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t4_subset,axiom,( ! [A,B,C] : ( ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) ) => m1_subset_1(A,C) ) ), file(subset,t4_subset), []). fof(t5_subset,axiom,( ! [A,B,C] : ~ ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C) ) ), file(subset,t5_subset), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []).