% Mizar problem: t39_osafree,osafree,5140,66 fof(t39_osafree,conjecture,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => v1_osafree(k24_osafree(A,B),A,k16_osafree(A,B)) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v1_lang1,abstractness_v4_msualg_1,antisymmetry_r2_hidden,cc1_dtconstr,cc1_msualg_1,cc1_msualg_4,cc1_osalg_1,cc1_partfun1,cc1_pboole,cc1_relset_1,cc2_msualg_1,cc2_osalg_4,cc2_pboole,cc3_pboole,cc4_osalg_4,cc4_trees_3,cc5_osalg_4,cc5_trees_3,cc6_osalg_4,cc6_trees_3,commutativity_k2_tarski,commutativity_k2_xboole_0,d11_osafree,d14_osalg_4,d18_osafree,d18_pboole,d19_osafree,d1_funct_2,d1_msafree,d22_osalg_4,d23_osalg_4,d24_osafree,d24_osalg_4,d25_osafree,d26_osafree,d27_osafree,d29_osalg_4,d2_osafree,d30_osalg_4,d5_funct_1,d5_osafree,d5_tarski,d6_osalg_4,d8_osalg_4,d9_osalg_4,dt_g1_lang1,dt_g3_msualg_1,dt_k13_finseq_1,dt_k13_pboole,dt_k15_osafree,dt_k15_osalg_4,dt_k16_osafree,dt_k16_osalg_4,dt_k17_osalg_4,dt_k18_osalg_4,dt_k19_osalg_4,dt_k1_funct_1,dt_k1_msafree,dt_k1_msualg_3,dt_k1_osafree,dt_k1_osalg_4,dt_k1_relat_1,dt_k1_tarski,dt_k1_trees_4,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k21_osafree,dt_k22_osafree,dt_k22_osalg_4,dt_k23_osafree,dt_k23_osalg_4,dt_k24_osafree,dt_k2_card_3,dt_k2_osafree,dt_k2_osalg_4,dt_k2_partfun1,dt_k2_relat_1,dt_k2_tarski,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_card_3,dt_k3_finseq_2,dt_k3_msafree,dt_k3_msualg_3,dt_k3_osalg_4,dt_k3_tarski,dt_k4_dtconstr,dt_k4_osalg_4,dt_k4_relset_1,dt_k4_tarski,dt_k5_osafree,dt_k5_osalg_4,dt_k5_relat_1,dt_k5_trees_3,dt_k6_eqrel_1,dt_k6_osalg_4,dt_k6_pboole,dt_k7_eqrel_1,dt_k7_funct_2,dt_k7_osafree,dt_k7_osalg_4,dt_k7_pboole,dt_k7_relat_1,dt_k8_eqrel_1,dt_k8_funct_2,dt_k8_osafree,dt_k8_osalg_4,dt_k8_pboole,dt_k8_relset_1,dt_l1_lang1,dt_l1_msualg_1,dt_l1_orders_2,dt_l1_osalg_1,dt_l1_struct_0,dt_l2_msualg_1,dt_l2_osalg_1,dt_l3_msualg_1,dt_l3_osalg_1,dt_m1_dtconstr,dt_m1_eqrel_1,dt_m1_finseq_2,dt_m1_msualg_4,dt_m1_osafree,dt_m1_osalg_4,dt_m1_pboole,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_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_orders_2,existence_l1_osalg_1,existence_l1_struct_0,existence_l2_msualg_1,existence_l2_osalg_1,existence_l3_msualg_1,existence_l3_osalg_1,existence_m1_dtconstr,existence_m1_eqrel_1,existence_m1_finseq_2,existence_m1_msualg_4,existence_m1_osafree,existence_m1_osalg_4,existence_m1_pboole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,existence_m3_pboole,existence_m3_trees_2,existence_m4_pboole,existence_m4_trees_3,existence_m5_trees_3,fc10_osafree,fc1_dtconstr,fc1_msafree,fc1_msualg_1,fc1_osafree,fc1_osalg_4,fc1_pboole,fc1_struct_0,fc1_subset_1,fc1_xboole_0,fc22_trees_3,fc26_trees_3,fc2_dtconstr,fc2_msafree,fc2_osafree,fc2_osalg_4,fc2_pboole,fc2_subset_1,fc2_xboole_0,fc3_dtconstr,fc3_msafree,fc3_osalg_4,fc3_subset_1,fc3_xboole_0,fc4_osafree,fc4_osalg_4,fc4_subset_1,fc5_osafree,fc6_trees_3,fc7_funcop_1,fc8_funcop_1,fc8_osafree,fc9_osafree,fraenkel_a_3_0_osalg_4,free_g1_lang1,free_g3_msualg_1,idempotence_k2_xboole_0,rc10_osalg_1,rc11_osalg_1,rc12_osalg_1,rc13_osalg_1,rc1_dtconstr,rc1_funcop_1,rc1_msualg_4,rc1_osalg_4,rc1_pboole,rc1_subset_1,rc1_xboole_0,rc2_msualg_4,rc2_partfun1,rc2_pboole,rc2_subset_1,rc2_trees_3,rc2_xboole_0,rc3_msualg_4,rc3_osalg_4,rc3_pboole,rc3_struct_0,rc4_osalg_4,rc4_pboole,rc4_trees_3,rc5_msualg_1,rc5_osalg_1,rc5_osalg_4,rc5_pboole,rc5_struct_0,rc6_msualg_1,rc6_osalg_4,rc7_osalg_4,rc8_osalg_4,redefinition_k1_msualg_3,redefinition_k2_partfun1,redefinition_k3_finseq_2,redefinition_k3_msafree,redefinition_k3_msualg_3,redefinition_k4_relset_1,redefinition_k7_funct_2,redefinition_k7_pboole,redefinition_k8_eqrel_1,redefinition_k8_funct_2,redefinition_k8_pboole,redefinition_k8_relset_1,redefinition_m1_dtconstr,redefinition_m2_relset_1,redefinition_m2_subset_1,redefinition_m5_trees_3,redefinition_r3_orders_2,redefinition_r6_pboole,reflexivity_r1_tarski,reflexivity_r2_pboole,reflexivity_r3_orders_2,reflexivity_r6_pboole,symmetry_r6_pboole,t10_osafree,t12_relset_1,t18_funct_2,t1_boole,t1_subset,t23_funct_1,t26_osalg_4,t27_osalg_4,t2_msualg_3,t2_subset,t2_tarski,t38_osafree,t3_funct_2,t3_subset,t4_funct_2,t4_subset,t5_subset,t6_boole,t70_funct_1,t72_funct_1,t76_funct_1,t7_boole,t8_boole,t91_relat_1]), [file(osafree,t39_osafree)]). 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_dtconstr,axiom,( ! [A,B] : ( m1_subset_1(B,k3_finseq_2(A)) => v1_finseq_1(B) ) ), file(dtconstr,cc1_dtconstr), []). fof(cc1_msualg_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k2_relat_1(u4_msualg_1(A,B))) => ~ v1_xboole_0(C) ) ) ), file(msualg_1,cc1_msualg_1), []). fof(cc1_msualg_4,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => ! [D] : ( m1_msualg_4(D,A,B,C) => v1_msualg_4(D) ) ) ), file(msualg_4,cc1_msualg_4), []). fof(cc1_osalg_1,axiom,( ! [A] : ( l3_osalg_1(A) => ( v4_osalg_1(A) => ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) ) ) ) ), file(osalg_1,cc1_osalg_1), []). fof(cc1_partfun1,axiom,( ! [A] : ( ( v1_relat_1(A) & v3_relat_2(A) & v8_relat_2(A) ) => ( v1_relat_1(A) & v1_relat_2(A) ) ) ), file(partfun1,cc1_partfun1), []). 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_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_msualg_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k2_relat_1(k6_pboole(u1_struct_0(A),u4_msualg_1(A,B)))) => ~ v1_xboole_0(C) ) ) ), file(msualg_1,cc2_msualg_1), []). fof(cc2_osalg_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k2_osalg_4(A)) => ~ v1_xboole_0(B) ) ) ), file(osalg_4,cc2_osalg_4), []). 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_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_osalg_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_osalg_4(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k2_osalg_4(A)) => ( ~ v1_xboole_0(B) & v1_waybel_0(B,A) ) ) ) ), file(osalg_4,cc4_osalg_4), []). 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(cc5_osalg_4,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & v5_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_osalg_4(C,A,B) => ( ( v3_msualg_4(C,A,B) & v3_osalg_4(C,A,B) ) => ( v1_msualg_4(C) & v3_msualg_4(C,A,B) & v4_msualg_4(C,A,B) ) ) ) ) ), file(osalg_4,cc5_osalg_4), []). 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(cc6_osalg_4,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & v5_msualg_1(B,A) & v12_osalg_1(B,A) & v13_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_osalg_4(C,A,B) => ( ( v3_msualg_4(C,A,B) & v4_msualg_4(C,A,B) ) => ( v1_msualg_4(C) & v3_msualg_4(C,A,B) & v4_msualg_4(C,A,B) & v3_osalg_4(C,A,B) ) ) ) ) ), file(osalg_4,cc6_osalg_4), []). fof(cc6_trees_3,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & ~ v1_xboole_0(B) ) => ! [C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_funct_2(C,A,B) ) => ( v1_funct_1(C) & v1_funct_2(C,A,B) & v3_trees_2(C) ) ) ) ) ), file(trees_3,cc6_trees_3), []). fof(commutativity_k2_tarski,axiom,( ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ), file(tarski,k2_tarski), []). fof(commutativity_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ), file(xboole_0,k2_xboole_0), []). fof(d11_osafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => k8_osafree(A,B) = g3_msualg_1(A,k5_osafree(A,B),k7_osafree(A,B)) ) ) ), file(osafree,d11_osafree), []). fof(d14_osalg_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( ( v5_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v3_msualg_4(C,A,B) & m1_osalg_4(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k1_funct_1(u4_msualg_1(A,B),D)) => k8_osalg_4(A,B,C,D,E) = k6_eqrel_1(k4_osalg_4(A,u4_msualg_1(A,B),k3_osalg_4(A,D)),k5_osalg_4(A,B,C,k3_osalg_4(A,D)),E) ) ) ) ) ) ), file(osalg_4,d14_osalg_4), []). fof(d18_osafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( ( v3_msualg_4(C,A,k8_osafree(A,B)) & v4_msualg_4(C,A,k8_osafree(A,B)) & v3_osalg_4(C,A,k8_osafree(A,B)) & m1_osalg_4(C,A,k8_osafree(A,B)) ) => ( C = k15_osafree(A,B) <=> ! [D] : ( ( v3_msualg_4(D,A,k8_osafree(A,B)) & v4_msualg_4(D,A,k8_osafree(A,B)) & v3_osalg_4(D,A,k8_osafree(A,B)) & m1_osalg_4(D,A,k8_osafree(A,B)) ) => r2_pboole(u1_struct_0(A),C,D) ) ) ) ) ) ), file(osafree,d18_osafree), []). fof(d18_pboole,axiom,( ! [A,B] : ( m1_pboole(B,A) => ! [C] : ( m1_pboole(C,A) => ! [D] : ( m1_pboole(D,A) => ( m3_pboole(D,A,B,C) <=> ! [E] : ( r2_hidden(E,A) => ( v1_funct_1(k1_funct_1(D,E)) & v1_funct_2(k1_funct_1(D,E),k1_funct_1(B,E),k1_funct_1(C,E)) & m2_relset_1(k1_funct_1(D,E),k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) ) ), file(pboole,d18_pboole), []). fof(d19_osafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => k16_osafree(A,B) = k16_osalg_4(A,k8_osafree(A,B),k15_osafree(A,B)) ) ) ), file(osafree,d19_osafree), []). fof(d1_funct_2,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => ( ( ( B = k1_xboole_0 => A = k1_xboole_0 ) => ( v1_funct_2(C,A,B) <=> A = k4_relset_1(A,B,C) ) ) & ( B = k1_xboole_0 => ( A = k1_xboole_0 | ( v1_funct_2(C,A,B) <=> C = k1_xboole_0 ) ) ) ) ) ), file(funct_2,d1_funct_2), []). fof(d1_msafree,axiom,( ! [A,B] : ( m1_pboole(B,A) => ! [C] : ( m1_pboole(C,A) => ! [D] : ( m4_pboole(D,A,B) => ! [E] : ( m3_pboole(E,A,B,C) => ! [F] : ( m3_pboole(F,A,D,C) => ( F = k1_msafree(A,B,C,D,E) <=> ! [G] : ( r2_hidden(G,A) => ! [H] : ( ( v1_funct_1(H) & v1_funct_2(H,k1_funct_1(B,G),k1_funct_1(C,G)) & m2_relset_1(H,k1_funct_1(B,G),k1_funct_1(C,G)) ) => ( H = k1_funct_1(E,G) => k1_funct_1(F,G) = k8_relset_1(k1_funct_1(B,G),k1_funct_1(C,G),H,k1_funct_1(D,G)) ) ) ) ) ) ) ) ) ) ), file(msafree,d1_msafree), []). fof(d22_osalg_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( ( v5_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v3_msualg_4(C,A,B) & v4_msualg_4(C,A,B) & m1_osalg_4(C,A,B) ) => k16_osalg_4(A,B,C) = g3_msualg_1(A,k7_osalg_4(A,B,C),k15_osalg_4(A,B,C)) ) ) ) ), file(osalg_4,d22_osalg_4), []). fof(d23_osalg_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( ( v5_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v3_msualg_4(C,A,B) & v4_msualg_4(C,A,B) & m1_osalg_4(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k1_funct_1(u4_msualg_1(A,B),D),k6_osalg_4(A,B,C,D)) & m2_relset_1(E,k1_funct_1(u4_msualg_1(A,B),D),k6_osalg_4(A,B,C,D)) ) => ( E = k17_osalg_4(A,B,C,D) <=> ! [F] : ( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,B),D)) => k8_funct_2(k1_funct_1(u4_msualg_1(A,B),D),k6_osalg_4(A,B,C,D),E,F) = k8_osalg_4(A,B,C,D,F) ) ) ) ) ) ) ) ), file(osalg_4,d23_osalg_4), []). fof(d24_osafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_funct_1(u4_msualg_1(A,k8_osafree(A,B)),C))) => ( D = k21_osafree(A,B,C) <=> ! [E] : ( r2_hidden(E,D) <=> ? [F] : ( r2_hidden(F,k1_funct_1(B,C)) & E = k1_trees_4(k4_tarski(F,C)) ) ) ) ) ) ) ) ), file(osafree,d24_osafree), []). fof(d24_osalg_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( ( v5_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v3_msualg_4(C,A,B) & v4_msualg_4(C,A,B) & m1_osalg_4(C,A,B) ) => ! [D] : ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,k16_osalg_4(A,B,C))) => ( D = k18_osalg_4(A,B,C) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,k16_osalg_4(A,B,C)),D,E) = k17_osalg_4(A,B,C,E) ) ) ) ) ) ) ), file(osalg_4,d24_osalg_4), []). fof(d25_osafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B))) => ( C = k22_osafree(A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k1_funct_1(C,D) = k21_osafree(A,B,D) ) ) ) ) ) ), file(osafree,d25_osafree), []). fof(d26_osafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_funct_1(u4_msualg_1(A,k16_osafree(A,B)),C))) => ( D = k23_osafree(A,B,C) <=> ! [E] : ( r2_hidden(E,D) <=> ? [F] : ( r2_hidden(F,k1_funct_1(B,C)) & E = k1_funct_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B)),u4_msualg_1(A,k16_osalg_4(A,k8_osafree(A,B),k15_osafree(A,B))),k18_osalg_4(A,k8_osafree(A,B),k15_osafree(A,B)),C),k1_trees_4(k4_tarski(F,C))) ) ) ) ) ) ) ) ), file(osafree,d26_osafree), []). fof(d27_osafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( m1_osafree(C,A,k16_osafree(A,B)) => ( C = k24_osafree(A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k1_funct_1(C,D) = k23_osafree(A,B,D) ) ) ) ) ) ), file(osafree,d27_osafree), []). fof(d29_osalg_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( ( v5_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v5_msualg_1(C,A) & v12_osalg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) => ! [E] : ( ( v3_msualg_4(E,A,B) & v4_msualg_4(E,A,B) & m1_osalg_4(E,A,B) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r1_msualg_3(A,B,C,D) & v1_osalg_3(D,A) & r2_pboole(u1_struct_0(A),E,k19_osalg_4(A,B,C,D)) ) => ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,k1_funct_1(u4_msualg_1(A,k16_osalg_4(A,B,E)),F),k1_funct_1(u4_msualg_1(A,C),F)) & m2_relset_1(G,k1_funct_1(u4_msualg_1(A,k16_osalg_4(A,B,E)),F),k1_funct_1(u4_msualg_1(A,C),F)) ) => ( G = k22_osalg_4(A,B,C,D,E,F) <=> ! [H] : ( m1_subset_1(H,k1_funct_1(u4_msualg_1(A,B),F)) => k1_funct_1(G,k8_osalg_4(A,B,E,F,H)) = k8_funct_2(k1_funct_1(u4_msualg_1(A,B),F),k1_funct_1(u4_msualg_1(A,C),F),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),D,F),H) ) ) ) ) ) ) ) ) ) ) ), file(osalg_4,d29_osalg_4), []). fof(d2_osafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & v13_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_osafree(C,A,B) => ( v1_osafree(C,A,B) <=> ! [D] : ( ( v5_msualg_1(D,A) & v12_osalg_1(D,A) & v13_osalg_1(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( m3_pboole(E,u1_struct_0(A),C,u4_msualg_1(A,D)) => ? [F] : ( m3_pboole(F,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,D)) & r1_msualg_3(A,B,D,F) & v1_osalg_3(F,A) & r6_pboole(u1_struct_0(A),k1_msafree(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,D),C,F),E) ) ) ) ) ) ) ) ), file(osafree,d2_osafree), []). fof(d30_osalg_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( ( v5_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v5_msualg_1(C,A) & v12_osalg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) => ! [E] : ( ( v3_msualg_4(E,A,B) & v4_msualg_4(E,A,B) & m1_osalg_4(E,A,B) ) => ! [F] : ( m3_pboole(F,u1_struct_0(A),u4_msualg_1(A,k16_osalg_4(A,B,E)),u4_msualg_1(A,C)) => ( F = k23_osalg_4(A,B,C,D,E) <=> ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,k16_osalg_4(A,B,E)),u4_msualg_1(A,C),F,G) = k22_osalg_4(A,B,C,D,E,G) ) ) ) ) ) ) ) ) ), file(osalg_4,d30_osalg_4), []). fof(d5_funct_1,axiom,( ! [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), []). fof(d5_osafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( m1_pboole(B,u1_struct_0(A)) => k2_osafree(A,B) = g1_lang1(k2_xboole_0(k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))),k3_card_3(k3_msafree(u1_struct_0(A),B))),k1_osafree(A,B)) ) ) ), file(osafree,d5_osafree), []). fof(d5_tarski,axiom,( ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ), file(tarski,d5_tarski), []). fof(d6_osalg_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => k2_osalg_4(A) = k8_eqrel_1(u1_struct_0(A),k1_osalg_4(A)) ) ), file(osalg_4,d6_osalg_4), []). fof(d8_osalg_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k3_osalg_4(A,B) = k6_eqrel_1(u1_struct_0(A),k1_osalg_4(A),B) ) ) ), file(osalg_4,d8_osalg_4), []). fof(d9_osalg_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_pboole(B,u1_struct_0(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(u1_struct_0(A)),k2_osalg_4(A)) => k4_osalg_4(A,B,C) = k3_tarski(a_3_0_osalg_4(A,B,C)) ) ) ) ), file(osalg_4,d9_osalg_4), []). 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_k13_finseq_1,axiom,( $true ), file(finseq_1,k13_finseq_1), []). fof(dt_k13_pboole,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_funcop_1(B) ) => ( v1_relat_1(k13_pboole(A,B)) & v1_funct_1(k13_pboole(A,B)) & v1_funcop_1(k13_pboole(A,B)) ) ) ), file(pboole,k13_pboole), []). fof(dt_k15_osafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ( v3_msualg_4(k15_osafree(A,B),A,k8_osafree(A,B)) & v4_msualg_4(k15_osafree(A,B),A,k8_osafree(A,B)) & v3_osalg_4(k15_osafree(A,B),A,k8_osafree(A,B)) & m1_osalg_4(k15_osafree(A,B),A,k8_osafree(A,B)) ) ) ), file(osafree,k15_osafree), []). fof(dt_k15_osalg_4,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) & v5_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) & v3_msualg_4(C,A,B) & v4_msualg_4(C,A,B) & m1_osalg_4(C,A,B) ) => m3_pboole(k15_osalg_4(A,B,C),u1_msualg_1(A),k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k7_osalg_4(A,B,C))),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k7_osalg_4(A,B,C))) ) ), file(osalg_4,k15_osalg_4), []). fof(dt_k16_osafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ( v4_msualg_1(k16_osafree(A,B),A) & v5_msualg_1(k16_osafree(A,B),A) & v12_osalg_1(k16_osafree(A,B),A) & v13_osalg_1(k16_osafree(A,B),A) & l3_msualg_1(k16_osafree(A,B),A) ) ) ), file(osafree,k16_osafree), []). fof(dt_k16_osalg_4,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) & v5_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) & v3_msualg_4(C,A,B) & v4_msualg_4(C,A,B) & m1_osalg_4(C,A,B) ) => ( v12_osalg_1(k16_osalg_4(A,B,C),A) & l3_msualg_1(k16_osalg_4(A,B,C),A) ) ) ), file(osalg_4,k16_osalg_4), []). fof(dt_k17_osalg_4,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) & v5_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) & v3_msualg_4(C,A,B) & v4_msualg_4(C,A,B) & m1_osalg_4(C,A,B) & m1_subset_1(D,u1_struct_0(A)) ) => ( v1_funct_1(k17_osalg_4(A,B,C,D)) & v1_funct_2(k17_osalg_4(A,B,C,D),k1_funct_1(u4_msualg_1(A,B),D),k6_osalg_4(A,B,C,D)) & m2_relset_1(k17_osalg_4(A,B,C,D),k1_funct_1(u4_msualg_1(A,B),D),k6_osalg_4(A,B,C,D)) ) ) ), file(osalg_4,k17_osalg_4), []). fof(dt_k18_osalg_4,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) & v5_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) & v3_msualg_4(C,A,B) & v4_msualg_4(C,A,B) & m1_osalg_4(C,A,B) ) => m3_pboole(k18_osalg_4(A,B,C),u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,k16_osalg_4(A,B,C))) ) ), file(osalg_4,k18_osalg_4), []). fof(dt_k19_osalg_4,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) & v5_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) & v5_msualg_1(C,A) & v12_osalg_1(C,A) & l3_msualg_1(C,A) & m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) ) => ( v3_msualg_4(k19_osalg_4(A,B,C,D),A,B) & v4_msualg_4(k19_osalg_4(A,B,C,D),A,B) & m1_osalg_4(k19_osalg_4(A,B,C,D),A,B) ) ) ), file(osalg_4,k19_osalg_4), []). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). fof(dt_k1_msafree,axiom,( ! [A,B,C,D,E] : ( ( m1_pboole(B,A) & m1_pboole(C,A) & m4_pboole(D,A,B) & m3_pboole(E,A,B,C) ) => m3_pboole(k1_msafree(A,B,C,D,E),A,D,C) ) ), file(msafree,k1_msafree), []). fof(dt_k1_msualg_3,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(A) & m1_pboole(B,A) & m1_pboole(C,A) & m3_pboole(D,A,B,C) & m1_subset_1(E,A) ) => ( v1_funct_1(k1_msualg_3(A,B,C,D,E)) & v1_funct_2(k1_msualg_3(A,B,C,D,E),k1_funct_1(B,E),k1_funct_1(C,E)) & m2_relset_1(k1_msualg_3(A,B,C,D,E),k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ), file(msualg_3,k1_msualg_3), []). fof(dt_k1_osafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & m1_pboole(B,u1_struct_0(A)) ) => m2_relset_1(k1_osafree(A,B),k2_xboole_0(k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))),k3_card_3(k3_msafree(u1_struct_0(A),B))),k3_finseq_2(k2_xboole_0(k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))),k3_card_3(k3_msafree(u1_struct_0(A),B))))) ) ), file(osafree,k1_osafree), []). fof(dt_k1_osalg_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ( v1_partfun1(k1_osalg_4(A),u1_struct_0(A),u1_struct_0(A)) & v3_relat_2(k1_osalg_4(A)) & v8_relat_2(k1_osalg_4(A)) & m2_relset_1(k1_osalg_4(A),u1_struct_0(A),u1_struct_0(A)) ) ) ), file(osalg_4,k1_osalg_4), []). fof(dt_k1_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), []). fof(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), []). fof(dt_k1_trees_4,axiom,( ! [A] : ( v1_relat_1(k1_trees_4(A)) & v1_funct_1(k1_trees_4(A)) & v3_trees_2(k1_trees_4(A)) ) ), file(trees_4,k1_trees_4), []). 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_k21_osafree,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k21_osafree(A,B,C),k1_zfmisc_1(k1_funct_1(u4_msualg_1(A,k8_osafree(A,B)),C))) ) ), file(osafree,k21_osafree), []). fof(dt_k22_osafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => m4_pboole(k22_osafree(A,B),u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B))) ) ), file(osafree,k22_osafree), []). fof(dt_k22_osalg_4,axiom,( ! [A,B,C,D,E,F] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) & v5_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) & v5_msualg_1(C,A) & v12_osalg_1(C,A) & l3_msualg_1(C,A) & m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) & v3_msualg_4(E,A,B) & v4_msualg_4(E,A,B) & m1_osalg_4(E,A,B) & m1_subset_1(F,u1_struct_0(A)) ) => ( v1_funct_1(k22_osalg_4(A,B,C,D,E,F)) & v1_funct_2(k22_osalg_4(A,B,C,D,E,F),k1_funct_1(u4_msualg_1(A,k16_osalg_4(A,B,E)),F),k1_funct_1(u4_msualg_1(A,C),F)) & m2_relset_1(k22_osalg_4(A,B,C,D,E,F),k1_funct_1(u4_msualg_1(A,k16_osalg_4(A,B,E)),F),k1_funct_1(u4_msualg_1(A,C),F)) ) ) ), file(osalg_4,k22_osalg_4), []). fof(dt_k23_osafree,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k23_osafree(A,B,C),k1_zfmisc_1(k1_funct_1(u4_msualg_1(A,k16_osafree(A,B)),C))) ) ), file(osafree,k23_osafree), []). fof(dt_k23_osalg_4,axiom,( ! [A,B,C,D,E] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) & v5_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) & v5_msualg_1(C,A) & v12_osalg_1(C,A) & l3_msualg_1(C,A) & m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) & v3_msualg_4(E,A,B) & v4_msualg_4(E,A,B) & m1_osalg_4(E,A,B) ) => m3_pboole(k23_osalg_4(A,B,C,D,E),u1_struct_0(A),u4_msualg_1(A,k16_osalg_4(A,B,E)),u4_msualg_1(A,C)) ) ), file(osalg_4,k23_osalg_4), []). fof(dt_k24_osafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => m1_osafree(k24_osafree(A,B),A,k16_osafree(A,B)) ) ), file(osafree,k24_osafree), []). fof(dt_k2_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k2_card_3(A)) & v1_funct_1(k2_card_3(A)) ) ) ), file(card_3,k2_card_3), []). fof(dt_k2_osafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & m1_pboole(B,u1_struct_0(A)) ) => l1_lang1(k2_osafree(A,B)) ) ), file(osafree,k2_osafree), []). fof(dt_k2_osalg_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ( ~ v1_xboole_0(k2_osalg_4(A)) & m1_subset_1(k2_osalg_4(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ) ), file(osalg_4,k2_osalg_4), []). fof(dt_k2_partfun1,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & m1_relset_1(C,A,B) ) => ( v1_funct_1(k2_partfun1(A,B,C,D)) & m2_relset_1(k2_partfun1(A,B,C,D),A,B) ) ) ), file(partfun1,k2_partfun1), []). fof(dt_k2_relat_1,axiom,( $true ), file(relat_1,k2_relat_1), []). fof(dt_k2_tarski,axiom,( $true ), file(tarski,k2_tarski), []). fof(dt_k2_xboole_0,axiom,( $true ), file(xboole_0,k2_xboole_0), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). fof(dt_k3_card_3,axiom,( $true ), file(card_3,k3_card_3), []). 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_k3_msafree,axiom,( ! [A,B] : ( m1_pboole(B,A) => m1_pboole(k3_msafree(A,B),A) ) ), file(msafree,k3_msafree), []). fof(dt_k3_msualg_3,axiom,( ! [A,B,C,D,E,F] : ( ( m1_pboole(B,A) & v2_relat_1(C) & m1_pboole(C,A) & v2_relat_1(D) & m1_pboole(D,A) & m3_pboole(E,A,B,C) & m3_pboole(F,A,C,D) ) => m3_pboole(k3_msualg_3(A,B,C,D,E,F),A,B,D) ) ), file(msualg_3,k3_msualg_3), []). fof(dt_k3_osalg_4,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) ) => m2_subset_1(k3_osalg_4(A,B),k1_zfmisc_1(u1_struct_0(A)),k2_osalg_4(A)) ) ), file(osalg_4,k3_osalg_4), []). fof(dt_k3_tarski,axiom,( $true ), file(tarski,k3_tarski), []). fof(dt_k4_dtconstr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_lang1(A) ) => m1_subset_1(k4_dtconstr(A),k1_zfmisc_1(k5_trees_3(u1_struct_0(A)))) ) ), file(dtconstr,k4_dtconstr), []). fof(dt_k4_osalg_4,axiom,( $true ), file(osalg_4,k4_osalg_4), []). fof(dt_k4_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(relset_1,k4_relset_1), []). fof(dt_k4_tarski,axiom,( $true ), file(tarski,k4_tarski), []). fof(dt_k5_osafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ( v11_osalg_1(k5_osafree(A,B),A) & m1_pboole(k5_osafree(A,B),u1_struct_0(A)) ) ) ), file(osafree,k5_osafree), []). fof(dt_k5_osalg_4,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) & v3_msualg_4(C,A,B) & m1_osalg_4(C,A,B) & m1_subset_1(D,k2_osalg_4(A)) ) => ( v1_partfun1(k5_osalg_4(A,B,C,D),k4_osalg_4(A,u4_msualg_1(A,B),D),k4_osalg_4(A,u4_msualg_1(A,B),D)) & v3_relat_2(k5_osalg_4(A,B,C,D)) & v8_relat_2(k5_osalg_4(A,B,C,D)) & m2_relset_1(k5_osalg_4(A,B,C,D),k4_osalg_4(A,u4_msualg_1(A,B),D),k4_osalg_4(A,u4_msualg_1(A,B),D)) ) ) ), file(osalg_4,k5_osalg_4), []). 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_eqrel_1,axiom,( ! [A,B,C] : ( ( v1_relat_2(B) & v3_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) ) => m1_subset_1(k6_eqrel_1(A,B,C),k1_zfmisc_1(A)) ) ), file(eqrel_1,k6_eqrel_1), []). fof(dt_k6_osalg_4,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) & v3_msualg_4(C,A,B) & m1_osalg_4(C,A,B) & m1_subset_1(D,u1_struct_0(A)) ) => m1_subset_1(k6_osalg_4(A,B,C,D),k1_zfmisc_1(k8_eqrel_1(k4_osalg_4(A,u4_msualg_1(A,B),k3_osalg_4(A,D)),k5_osalg_4(A,B,C,k3_osalg_4(A,D))))) ) ), file(osalg_4,k6_osalg_4), []). 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_eqrel_1,axiom,( ! [A,B] : ( ( v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) ) => m1_subset_1(k7_eqrel_1(A,B),k1_zfmisc_1(k1_zfmisc_1(A))) ) ), file(eqrel_1,k7_eqrel_1), []). fof(dt_k7_funct_2,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(D,A,B) & m1_relset_1(D,A,B) & v1_funct_1(E) & v1_funct_2(E,B,C) & m1_relset_1(E,B,C) ) => ( v1_funct_1(k7_funct_2(A,B,C,D,E)) & v1_funct_2(k7_funct_2(A,B,C,D,E),A,C) & m2_relset_1(k7_funct_2(A,B,C,D,E),A,C) ) ) ), file(funct_2,k7_funct_2), []). fof(dt_k7_osafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => m3_pboole(k7_osafree(A,B),u1_msualg_1(A),k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k5_osafree(A,B))),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k5_osafree(A,B))) ) ), file(osafree,k7_osafree), []). fof(dt_k7_osalg_4,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) & v3_msualg_4(C,A,B) & m1_osalg_4(C,A,B) ) => ( v11_osalg_1(k7_osalg_4(A,B,C),A) & m1_pboole(k7_osalg_4(A,B,C),u1_struct_0(A)) ) ) ), file(osalg_4,k7_osalg_4), []). 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_k7_relat_1,axiom,( ! [A,B] : ( v1_relat_1(A) => v1_relat_1(k7_relat_1(A,B)) ) ), file(relat_1,k7_relat_1), []). fof(dt_k8_eqrel_1,axiom,( ! [A,B] : ( ( v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) ) => m1_eqrel_1(k8_eqrel_1(A,B),A) ) ), file(eqrel_1,k8_eqrel_1), []). fof(dt_k8_funct_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,A) ) => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ), file(funct_2,k8_funct_2), []). fof(dt_k8_osafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ( v12_osalg_1(k8_osafree(A,B),A) & l3_msualg_1(k8_osafree(A,B),A) ) ) ), file(osafree,k8_osafree), []). fof(dt_k8_osalg_4,axiom,( ! [A,B,C,D,E] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) & v5_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) & v3_msualg_4(C,A,B) & m1_osalg_4(C,A,B) & m1_subset_1(D,u1_struct_0(A)) & m1_subset_1(E,k1_funct_1(u4_msualg_1(A,B),D)) ) => m1_subset_1(k8_osalg_4(A,B,C,D,E),k6_osalg_4(A,B,C,D)) ) ), file(osalg_4,k8_osalg_4), []). fof(dt_k8_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) & v2_relat_1(D) & m1_pboole(D,B) ) => ( v2_relat_1(k8_pboole(A,B,C,D)) & m1_pboole(k8_pboole(A,B,C,D),A) ) ) ), file(pboole,k8_pboole), []). fof(dt_k8_relset_1,axiom,( ! [A,B,C,D] : ( m1_relset_1(C,A,B) => m2_relset_1(k8_relset_1(A,B,C,D),A,B) ) ), file(relset_1,k8_relset_1), []). 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_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => l1_struct_0(A) ) ), file(orders_2,l1_orders_2), []). fof(dt_l1_osalg_1,axiom,( ! [A] : ( l1_osalg_1(A) => l1_msualg_1(A) ) ), file(osalg_1,l1_osalg_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_l2_osalg_1,axiom,( ! [A] : ( l2_osalg_1(A) => ( l1_msualg_1(A) & l1_orders_2(A) ) ) ), file(osalg_1,l2_osalg_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_l3_osalg_1,axiom,( ! [A] : ( l3_osalg_1(A) => ( l1_osalg_1(A) & l2_osalg_1(A) ) ) ), file(osalg_1,l3_osalg_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_eqrel_1,axiom,( ! [A,B] : ( m1_eqrel_1(B,A) => m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) ), file(eqrel_1,m1_eqrel_1), []). fof(dt_m1_finseq_2,axiom,( $true ), file(finseq_2,m1_finseq_2), []). fof(dt_m1_msualg_4,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => ! [D] : ( m1_msualg_4(D,A,B,C) => m1_pboole(D,A) ) ) ), file(msualg_4,m1_msualg_4), []). fof(dt_m1_osafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_osafree(C,A,B) => m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) ) ) ), file(osafree,m1_osafree), []). fof(dt_m1_osalg_4,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_osalg_4(C,A,B) => m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) ) ) ), file(osalg_4,m1_osalg_4), []). 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_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), []). 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_orders_2,axiom,( ? [A] : l1_orders_2(A) ), file(orders_2,l1_orders_2), []). fof(existence_l1_osalg_1,axiom,( ? [A] : l1_osalg_1(A) ), file(osalg_1,l1_osalg_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_l2_osalg_1,axiom,( ? [A] : l2_osalg_1(A) ), file(osalg_1,l2_osalg_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_l3_osalg_1,axiom,( ? [A] : l3_osalg_1(A) ), file(osalg_1,l3_osalg_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_eqrel_1,axiom,( ! [A] : ? [B] : m1_eqrel_1(B,A) ), file(eqrel_1,m1_eqrel_1), []). fof(existence_m1_finseq_2,axiom,( ! [A] : ? [B] : m1_finseq_2(B,A) ), file(finseq_2,m1_finseq_2), []). fof(existence_m1_msualg_4,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => ? [D] : m1_msualg_4(D,A,B,C) ) ), file(msualg_4,m1_msualg_4), []). fof(existence_m1_osafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ? [C] : m1_osafree(C,A,B) ) ), file(osafree,m1_osafree), []). fof(existence_m1_osalg_4,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ? [C] : m1_osalg_4(C,A,B) ) ), file(osalg_4,m1_osalg_4), []). 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_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), []). 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_osafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ( v1_relat_1(k24_osafree(A,B)) & v2_relat_1(k24_osafree(A,B)) & ~ v3_relat_1(k24_osafree(A,B)) & v1_funct_1(k24_osafree(A,B)) ) ) ), file(osafree,fc10_osafree), []). fof(fc1_dtconstr,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_relset_1(B,A,k3_finseq_2(A)) ) => ( ~ v3_struct_0(g1_lang1(A,B)) & v1_lang1(g1_lang1(A,B)) ) ) ), file(dtconstr,fc1_dtconstr), []). fof(fc1_msafree,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v2_relat_1(B) & m1_pboole(B,A) ) => ( v1_relat_1(k2_card_3(B)) & v2_relat_1(k2_card_3(B)) & v1_funct_1(k2_card_3(B)) ) ) ), file(msafree,fc1_msafree), []). 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_osafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & m1_pboole(B,u1_struct_0(A)) ) => ( ~ v3_struct_0(k2_osafree(A,B)) & v1_lang1(k2_osafree(A,B)) ) ) ), file(osafree,fc1_osafree), []). fof(fc1_osalg_4,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) & v5_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) & v3_msualg_4(C,A,B) & m1_osalg_4(C,A,B) & m1_subset_1(D,u1_struct_0(A)) ) => ~ v1_xboole_0(k6_osalg_4(A,B,C,D)) ) ), file(osalg_4,fc1_osalg_4), []). 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(fc1_xboole_0,axiom,( v1_xboole_0(k1_xboole_0) ), file(xboole_0,fc1_xboole_0), []). fof(fc22_trees_3,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & ~ v1_xboole_0(B) & v1_trees_1(B) ) => ( ~ v1_xboole_0(k2_xboole_0(A,B)) & v1_trees_1(k2_xboole_0(A,B)) ) ) ), file(trees_3,fc22_trees_3), []). fof(fc26_trees_3,axiom,( ! [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), []). fof(fc2_dtconstr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v1_dtconstr(A) & l1_lang1(A) ) => ( ~ v1_xboole_0(k4_dtconstr(A)) & v3_trees_3(k4_dtconstr(A)) ) ) ), file(dtconstr,fc2_dtconstr), []). fof(fc2_msafree,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v2_relat_1(B) & m1_pboole(B,A) ) => ~ v1_xboole_0(k3_card_3(B)) ) ), file(msafree,fc2_msafree), []). fof(fc2_osafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ( ~ v3_struct_0(k2_osafree(A,B)) & v1_lang1(k2_osafree(A,B)) & v1_dtconstr(k2_osafree(A,B)) & v2_dtconstr(k2_osafree(A,B)) & v3_dtconstr(k2_osafree(A,B)) ) ) ), file(osafree,fc2_osafree), []). fof(fc2_osalg_4,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) & v5_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) & v3_msualg_4(C,A,B) & m1_osalg_4(C,A,B) ) => ( v1_relat_1(k7_osalg_4(A,B,C)) & v2_relat_1(k7_osalg_4(A,B,C)) & ~ v3_relat_1(k7_osalg_4(A,B,C)) & v1_funct_1(k7_osalg_4(A,B,C)) & v11_osalg_1(k7_osalg_4(A,B,C),A) ) ) ), file(osalg_4,fc2_osalg_4), []). 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(fc2_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) ), file(subset_1,fc2_subset_1), []). fof(fc2_xboole_0,axiom,( ! [A,B] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k2_xboole_0(A,B)) ) ), file(xboole_0,fc2_xboole_0), []). fof(fc3_dtconstr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_dtconstr(A) & l1_lang1(A) ) => ( ~ v1_xboole_0(k4_dtconstr(A)) & v3_trees_3(k4_dtconstr(A)) ) ) ), file(dtconstr,fc3_dtconstr), []). 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(fc3_osalg_4,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) & v5_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) & v3_msualg_4(C,A,B) & v4_msualg_4(C,A,B) & m1_osalg_4(C,A,B) ) => ( v4_msualg_1(k16_osalg_4(A,B,C),A) & v5_msualg_1(k16_osalg_4(A,B,C),A) & v12_osalg_1(k16_osalg_4(A,B,C),A) ) ) ), file(osalg_4,fc3_osalg_4), []). fof(fc3_subset_1,axiom,( ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ), file(subset_1,fc3_subset_1), []). fof(fc3_xboole_0,axiom,( ! [A,B] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k2_xboole_0(B,A)) ) ), file(xboole_0,fc3_xboole_0), []). fof(fc4_osafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ( v1_relat_1(k5_osafree(A,B)) & v2_relat_1(k5_osafree(A,B)) & ~ v3_relat_1(k5_osafree(A,B)) & v1_funct_1(k5_osafree(A,B)) & v11_osalg_1(k5_osafree(A,B),A) ) ) ), file(osafree,fc4_osafree), []). fof(fc4_osalg_4,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) & v5_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) & v3_msualg_4(C,A,B) & v4_msualg_4(C,A,B) & v3_osalg_4(C,A,B) & m1_osalg_4(C,A,B) ) => ( v4_msualg_1(k16_osalg_4(A,B,C),A) & v5_msualg_1(k16_osalg_4(A,B,C),A) & v12_osalg_1(k16_osalg_4(A,B,C),A) & v13_osalg_1(k16_osalg_4(A,B,C),A) ) ) ), file(osalg_4,fc4_osalg_4), []). 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_osafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ( v4_msualg_1(k8_osafree(A,B),A) & v5_msualg_1(k8_osafree(A,B),A) & v12_osalg_1(k8_osafree(A,B),A) ) ) ), file(osafree,fc5_osafree), []). 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_osafree,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => ~ v1_xboole_0(k21_osafree(A,B,C)) ) ), file(osafree,fc8_osafree), []). fof(fc9_osafree,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => ~ v1_xboole_0(k23_osafree(A,B,C)) ) ), file(osafree,fc9_osafree), []). fof(fraenkel_a_3_0_osalg_4,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) & m1_pboole(C,u1_struct_0(B)) & m2_subset_1(D,k1_zfmisc_1(u1_struct_0(B)),k2_osalg_4(B)) ) => ( r2_hidden(A,a_3_0_osalg_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k1_funct_1(C,E) & r2_hidden(E,D) ) ) ) ), file(osalg_4,a_3_0_osalg_4), []). 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(idempotence_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,A) = A ), file(xboole_0,k2_xboole_0), []). fof(rc10_osalg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( m1_pboole(B,u1_struct_0(A)) & v1_relat_1(B) & v1_funct_1(B) & v11_osalg_1(B,A) ) ) ), file(osalg_1,rc10_osalg_1), []). fof(rc11_osalg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( m1_pboole(B,u1_struct_0(A)) & v1_relat_1(B) & v2_relat_1(B) & v1_funct_1(B) & v11_osalg_1(B,A) ) ) ), file(osalg_1,rc11_osalg_1), []). fof(rc12_osalg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ? [B] : ( l3_msualg_1(B,A) & v4_msualg_1(B,A) & v5_msualg_1(B,A) & v12_osalg_1(B,A) ) ) ), file(osalg_1,rc12_osalg_1), []). fof(rc13_osalg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ? [B] : ( l3_msualg_1(B,A) & v4_msualg_1(B,A) & v5_msualg_1(B,A) & v12_osalg_1(B,A) & v13_osalg_1(B,A) ) ) ), file(osalg_1,rc13_osalg_1), []). fof(rc1_dtconstr,axiom,( ? [A] : ( l1_lang1(A) & ~ v3_struct_0(A) & v1_lang1(A) & v1_dtconstr(A) & v2_dtconstr(A) & v3_dtconstr(A) ) ), file(dtconstr,rc1_dtconstr), []). 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_msualg_4,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_msualg_4(B) ) ), file(msualg_4,rc1_msualg_4), []). fof(rc1_osalg_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( m1_pboole(B,u1_struct_0(A)) & v1_relat_1(B) & v1_funct_1(B) & v11_osalg_1(B,A) & v1_msualg_4(B) ) ) ), file(osalg_4,rc1_osalg_4), []). fof(rc1_pboole,axiom,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A) ) ), file(pboole,rc1_pboole), []). 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(rc1_xboole_0,axiom,( ? [A] : v1_xboole_0(A) ), file(xboole_0,rc1_xboole_0), []). fof(rc2_msualg_4,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & l3_msualg_1(B,A) ) => ? [C] : ( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) & v1_relat_1(C) & v1_funct_1(C) & v1_msualg_4(C) & v3_msualg_4(C,A,B) ) ) ), file(msualg_4,rc2_msualg_4), []). fof(rc2_partfun1,axiom,( ! [A,B] : ? [C] : ( m1_relset_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C) ) ), file(partfun1,rc2_partfun1), []). 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_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(rc2_xboole_0,axiom,( ? [A] : ~ v1_xboole_0(A) ), file(xboole_0,rc2_xboole_0), []). fof(rc3_msualg_4,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) ) => ? [C] : ( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) & v1_relat_1(C) & v1_funct_1(C) & v1_msualg_4(C) & v3_msualg_4(C,A,B) & v4_msualg_4(C,A,B) ) ) ), file(msualg_4,rc3_msualg_4), []). fof(rc3_osalg_4,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ? [C] : ( m1_osalg_4(C,A,B) & v1_relat_1(C) & v1_funct_1(C) & v1_msualg_4(C) & v3_msualg_4(C,A,B) ) ) ), file(osalg_4,rc3_osalg_4), []). 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_struct_0,axiom,( ? [A] : ( l1_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc3_struct_0), []). fof(rc4_osalg_4,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & v5_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ? [C] : ( m1_osalg_4(C,A,B) & v1_relat_1(C) & v1_funct_1(C) & v1_msualg_4(C) & v3_msualg_4(C,A,B) & v4_msualg_4(C,A,B) ) ) ), file(osalg_4,rc4_osalg_4), []). 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(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_osalg_1,axiom,( ? [A] : ( l1_osalg_1(A) & ~ v3_struct_0(A) & ~ v2_msualg_1(A) ) ), file(osalg_1,rc5_osalg_1), []). fof(rc5_osalg_4,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_osalg_4(A) ) ), file(osalg_4,rc5_osalg_4), []). 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(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_osalg_4,axiom,( ? [A] : ( l3_osalg_1(A) & ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) ) ), file(osalg_4,rc6_osalg_4), []). fof(rc7_osalg_4,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & v5_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ? [C] : ( m1_osalg_4(C,A,B) & v1_relat_1(C) & v1_funct_1(C) & v1_msualg_4(C) & v3_msualg_4(C,A,B) & v4_msualg_4(C,A,B) & v3_osalg_4(C,A,B) ) ) ), file(osalg_4,rc7_osalg_4), []). fof(rc8_osalg_4,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & v5_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ? [C] : ( m1_osalg_4(C,A,B) & v1_relat_1(C) & v1_funct_1(C) & v1_msualg_4(C) & v3_msualg_4(C,A,B) & v3_osalg_4(C,A,B) ) ) ), file(osalg_4,rc8_osalg_4), []). fof(redefinition_k1_msualg_3,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(A) & m1_pboole(B,A) & m1_pboole(C,A) & m3_pboole(D,A,B,C) & m1_subset_1(E,A) ) => k1_msualg_3(A,B,C,D,E) = k1_funct_1(D,E) ) ), file(msualg_3,k1_msualg_3), []). fof(redefinition_k2_partfun1,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & m1_relset_1(C,A,B) ) => k2_partfun1(A,B,C,D) = k7_relat_1(C,D) ) ), file(partfun1,k2_partfun1), []). fof(redefinition_k3_finseq_2,axiom,( ! [A] : k3_finseq_2(A) = k13_finseq_1(A) ), file(finseq_2,k3_finseq_2), []). fof(redefinition_k3_msafree,axiom,( ! [A,B] : ( m1_pboole(B,A) => k3_msafree(A,B) = k2_card_3(B) ) ), file(msafree,k3_msafree), []). fof(redefinition_k3_msualg_3,axiom,( ! [A,B,C,D,E,F] : ( ( m1_pboole(B,A) & v2_relat_1(C) & m1_pboole(C,A) & v2_relat_1(D) & m1_pboole(D,A) & m3_pboole(E,A,B,C) & m3_pboole(F,A,C,D) ) => k3_msualg_3(A,B,C,D,E,F) = k13_pboole(E,F) ) ), file(msualg_3,k3_msualg_3), []). fof(redefinition_k4_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => k4_relset_1(A,B,C) = k1_relat_1(C) ) ), file(relset_1,k4_relset_1), []). fof(redefinition_k7_funct_2,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(D,A,B) & m1_relset_1(D,A,B) & v1_funct_1(E) & v1_funct_2(E,B,C) & m1_relset_1(E,B,C) ) => k7_funct_2(A,B,C,D,E) = k5_relat_1(D,E) ) ), file(funct_2,k7_funct_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_k8_eqrel_1,axiom,( ! [A,B] : ( ( v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) ) => k8_eqrel_1(A,B) = k7_eqrel_1(A,B) ) ), file(eqrel_1,k8_eqrel_1), []). fof(redefinition_k8_funct_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,A) ) => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ), file(funct_2,k8_funct_2), []). fof(redefinition_k8_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) & v2_relat_1(D) & m1_pboole(D,B) ) => k8_pboole(A,B,C,D) = k5_relat_1(C,D) ) ), file(pboole,k8_pboole), []). fof(redefinition_k8_relset_1,axiom,( ! [A,B,C,D] : ( m1_relset_1(C,A,B) => k8_relset_1(A,B,C,D) = k7_relat_1(C,D) ) ), file(relset_1,k8_relset_1), []). 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_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,B) ) ) ), file(subset_1,m2_subset_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(redefinition_r3_orders_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => ( r3_orders_2(A,B,C) <=> r1_orders_2(A,B,C) ) ) ), file(orders_2,r3_orders_2), []). fof(redefinition_r6_pboole,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => ( r6_pboole(A,B,C) <=> B = C ) ) ), file(pboole,r6_pboole), []). 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(reflexivity_r3_orders_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => r3_orders_2(A,B,B) ) ), file(orders_2,r3_orders_2), []). fof(reflexivity_r6_pboole,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => r6_pboole(A,B,B) ) ), file(pboole,r6_pboole), []). fof(symmetry_r6_pboole,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => ( r6_pboole(A,B,C) => r6_pboole(A,C,B) ) ) ), file(pboole,r6_pboole), []). fof(t10_osafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( r2_hidden(E,k1_funct_1(B,C)) => ( m1_dtconstr(k1_trees_4(k4_tarski(E,C)),u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B))) & ! [F] : k4_tarski(F,u1_struct_0(A)) != k1_funct_1(k1_trees_4(k4_tarski(E,C)),k1_xboole_0) & ( r2_hidden(k1_trees_4(k4_tarski(E,C)),k1_funct_1(u4_msualg_1(A,k8_osafree(A,B)),D)) => r3_orders_2(A,C,D) ) & ( r3_orders_2(A,C,D) => r2_hidden(k1_trees_4(k4_tarski(E,C)),k1_funct_1(u4_msualg_1(A,k8_osafree(A,B)),D)) ) ) ) ) ) ) ) ), file(osafree,t10_osafree), []). fof(t12_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => ( r1_tarski(k1_relat_1(C),A) & r1_tarski(k2_relat_1(C),B) ) ) ), file(relset_1,t12_relset_1), []). fof(t18_funct_2,axiom,( ! [A,B,C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) ) => ( ! [E] : ( r2_hidden(E,A) => k1_funct_1(C,E) = k1_funct_1(D,E) ) => C = D ) ) ) ), file(funct_2,t18_funct_2), []). fof(t1_boole,axiom,( ! [A] : k2_xboole_0(A,k1_xboole_0) = A ), file(boole,t1_boole), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t23_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(A,k1_relat_1(B)) => k1_funct_1(k5_relat_1(B,C),A) = k1_funct_1(C,k1_funct_1(B,A)) ) ) ) ), file(funct_1,t23_funct_1), []). fof(t26_osalg_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( ( v5_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v5_msualg_1(C,A) & v12_osalg_1(C,A) & v13_osalg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) => ( ( r1_msualg_3(A,B,C,D) & v1_osalg_3(D,A) ) => v3_osalg_4(k19_osalg_4(A,B,C,D),A,B) ) ) ) ) ) ), file(osalg_4,t26_osalg_4), []). fof(t27_osalg_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( ( v5_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v5_msualg_1(C,A) & v12_osalg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) => ! [E] : ( ( v3_msualg_4(E,A,B) & v4_msualg_4(E,A,B) & m1_osalg_4(E,A,B) ) => ( ( r1_msualg_3(A,B,C,D) & v1_osalg_3(D,A) & r2_pboole(u1_struct_0(A),E,k19_osalg_4(A,B,C,D)) ) => ( r1_msualg_3(A,k16_osalg_4(A,B,E),C,k23_osalg_4(A,B,C,D,E)) & v1_osalg_3(k23_osalg_4(A,B,C,D,E),A) ) ) ) ) ) ) ) ), file(osalg_4,t27_osalg_4), []). fof(t2_msualg_3,axiom,( ! [A,B] : ( m1_pboole(B,A) => ! [C] : ( m1_pboole(C,A) => ! [D] : ( m1_pboole(D,A) => ! [E] : ( m3_pboole(E,A,B,C) => ! [F] : ( m3_pboole(F,A,C,D) => ( k1_relat_1(k13_pboole(E,F)) = A & ! [G] : ( r2_hidden(G,A) => k1_funct_1(k13_pboole(E,F),G) = k5_relat_1(k1_funct_1(E,G),k1_funct_1(F,G)) ) ) ) ) ) ) ) ), file(msualg_3,t2_msualg_3), []). 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(t38_osafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( ( v5_msualg_1(C,A) & v12_osalg_1(C,A) & v13_osalg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( m3_pboole(D,u1_struct_0(A),k22_osafree(A,B),u4_msualg_1(A,C)) => ? [E] : ( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B)),u4_msualg_1(A,C)) & r1_msualg_3(A,k8_osafree(A,B),C,E) & v1_osalg_3(E,A) & r6_pboole(u1_struct_0(A),k1_msafree(u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B)),u4_msualg_1(A,C),k22_osafree(A,B),E),D) ) ) ) ) ) ), file(osafree,t38_osafree), []). fof(t3_funct_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_funct_1(A) & v1_funct_2(A,k1_relat_1(A),k2_relat_1(A)) & m2_relset_1(A,k1_relat_1(A),k2_relat_1(A)) ) ) ), file(funct_2,t3_funct_2), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t4_funct_2,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_tarski(k2_relat_1(B),A) => ( v1_funct_1(B) & v1_funct_2(B,k1_relat_1(B),A) & m2_relset_1(B,k1_relat_1(B),A) ) ) ) ), file(funct_2,t4_funct_2), []). 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(t70_funct_1,axiom,( ! [A,B,C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(B,k1_relat_1(k7_relat_1(C,A))) => k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B) ) ) ), file(funct_1,t70_funct_1), []). fof(t72_funct_1,axiom,( ! [A,B,C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(B,A) => k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B) ) ) ), file(funct_1,t72_funct_1), []). fof(t76_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_tarski(k1_relat_1(k7_relat_1(B,A)),k1_relat_1(B)) & r1_tarski(k2_relat_1(k7_relat_1(B,A)),k2_relat_1(B)) ) ) ), file(funct_1,t76_funct_1), []). 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), []). fof(t91_relat_1,axiom,( ! [A,B] : ( v1_relat_1(B) => ( r1_tarski(A,k1_relat_1(B)) => k1_relat_1(k7_relat_1(B,A)) = A ) ) ), file(relat_1,t91_relat_1), []).