% Mizar problem: t10_yellow11,yellow11,2353,72 fof(t10_yellow11,conjecture,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ( ~ ( ? [B] : ( v4_yellow_0(B,A) & v5_yellow_0(B,A) & v6_yellow_0(B,A) & m1_yellow_0(B,A) & r5_waybel_1(k2_yellow11,B) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( B != C & B != D & B != E & B != F & C != D & C != E & C != F & D != E & D != F & E != F & k12_lattice3(A,B,C) = B & k12_lattice3(A,B,D) = B & k12_lattice3(A,B,E) = B & k12_lattice3(A,C,F) = C & k12_lattice3(A,D,F) = D & k12_lattice3(A,E,F) = E & k12_lattice3(A,C,D) = B & k12_lattice3(A,C,E) = B & k12_lattice3(A,D,E) = B & k13_lattice3(A,C,D) = F & k13_lattice3(A,C,E) = F & k13_lattice3(A,D,E) = F ) ) ) ) ) ) ) & ~ ( ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ? [F] : ( m1_subset_1(F,u1_struct_0(A)) & B != C & B != D & B != E & B != F & C != D & C != E & C != F & D != E & D != F & E != F & k12_lattice3(A,B,C) = B & k12_lattice3(A,B,D) = B & k12_lattice3(A,B,E) = B & k12_lattice3(A,C,F) = C & k12_lattice3(A,D,F) = D & k12_lattice3(A,E,F) = E & k12_lattice3(A,C,D) = B & k12_lattice3(A,C,E) = B & k12_lattice3(A,D,E) = B & k13_lattice3(A,C,D) = F & k13_lattice3(A,C,E) = F & k13_lattice3(A,D,E) = F ) ) ) ) ) & ! [B] : ( ( v4_yellow_0(B,A) & v5_yellow_0(B,A) & v6_yellow_0(B,A) & m1_yellow_0(B,A) ) => ~ r5_waybel_1(k2_yellow11,B) ) ) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v1_orders_2,antisymmetry_r2_hidden,cc11_yellow_0,cc12_yellow_0,cc1_finset_1,cc1_lattice3,cc1_relset_1,cc1_yellow_0,cc2_finset_1,cc2_lattice3,cc2_yellow_0,cc3_yellow_0,cc4_yellow_0,cc5_yellow_0,cc6_yellow_0,cc7_yellow_0,cc8_yellow_0,commutativity_k12_lattice3,commutativity_k13_lattice3,commutativity_k2_struct_0,commutativity_k2_tarski,connectedness_r1_ordinal1,connectedness_r1_xreal_0,d10_xboole_0,d13_yellow_0,d15_yellow_0,d16_yellow_0,d17_yellow_0,d1_enumset1,d1_funct_2,d1_struct_0,d1_tarski,d1_waybel_1,d2_yellow11,d38_waybel_0,d3_enumset1,d3_tarski,d5_funct_1,d8_waybel_1,dt_g1_orders_2,dt_k10_lattice3,dt_k11_lattice3,dt_k12_lattice3,dt_k13_lattice3,dt_k1_enumset1,dt_k1_funct_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_tarski,dt_k1_waybel_0,dt_k1_wellord2,dt_k1_xboole_0,dt_k1_yellow_0,dt_k1_yellow_1,dt_k1_yellow_2,dt_k1_zfmisc_1,dt_k2_funct_1,dt_k2_relat_1,dt_k2_struct_0,dt_k2_tarski,dt_k2_yellow11,dt_k2_yellow_0,dt_k2_yellow_1,dt_k2_zfmisc_1,dt_k3_enumset1,dt_k4_relset_1,dt_k4_xboole_0,dt_k5_numbers,dt_k5_ordinal2,dt_k5_yellow_0,dt_k7_yellow_2,dt_k8_funct_2,dt_k8_yellow_2,dt_l1_orders_2,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m1_yellow_0,dt_m2_relset_1,dt_m2_subset_1,dt_u1_orders_2,dt_u1_struct_0,existence_l1_orders_2,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m1_yellow_0,existence_m2_relset_1,existence_m2_subset_1,fc12_finset_1,fc14_finset_1,fc1_finset_1,fc1_orders_2,fc1_struct_0,fc1_xboole_0,fc1_yellow_0,fc2_finset_1,fc2_orders_2,fc3_finset_1,fc3_orders_2,fc3_yellow11,fc4_yellow11,fc5_finset_1,fc5_yellow_1,fc6_yellow_1,free_g1_orders_2,rc1_finset_1,rc1_lattice3,rc1_orders_2,rc1_xboole_0,rc1_yellow_0,rc2_lattice3,rc2_orders_2,rc2_xboole_0,rc2_yellow_0,rc3_finset_1,rc3_struct_0,rc3_yellow_0,rc4_finset_1,rc4_yellow_0,rc5_struct_0,redefinition_k12_lattice3,redefinition_k13_lattice3,redefinition_k1_waybel_0,redefinition_k1_yellow_1,redefinition_k1_yellow_2,redefinition_k2_struct_0,redefinition_k4_relset_1,redefinition_k5_numbers,redefinition_k7_yellow_2,redefinition_k8_funct_2,redefinition_k8_yellow_2,redefinition_m2_relset_1,redefinition_m2_subset_1,redefinition_r1_ordinal1,redefinition_r3_orders_2,reflexivity_r1_ordinal1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,reflexivity_r3_orders_2,reflexivity_r5_waybel_1,s1_funct_2__e12_15_2_4__yellow11,spc0_boole,spc1_boole,spc1_numerals,spc2_boole,spc2_numerals,spc3_boole,spc3_numerals,t1_card_5,t1_numerals,t1_real,t1_subset,t1_yellow11,t1_yellow_1,t1_yellow_5,t20_yellow_0,t21_yellow_0,t22_yellow_0,t23_yellow_0,t24_yellow_0,t25_yellow_0,t26_orders_2,t2_subset,t2_xboole_1,t2_yellow11,t2_yellow_5,t3_boole,t3_subset,t3_xboole_1,t3_yellow_1,t40_yellow_0,t41_yellow_0,t4_boole,t4_real,t4_subset,t4_yellow11,t56_card_1,t5_subset,t5_yellow11,t60_yellow_0,t61_yellow_0,t66_waybel_0,t6_boole,t7_boole,t8_boole]), [file(yellow11,t10_yellow11)]). fof(abstractness_v1_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_orders_2(A) => A = g1_orders_2(u1_struct_0(A),u1_orders_2(A)) ) ) ), file(orders_2,v1_orders_2), []). fof(antisymmetry_r2_hidden,axiom,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), []). fof(cc11_yellow_0,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( ( ~ v3_struct_0(B) & v4_yellow_0(B,A) & v5_yellow_0(B,A) ) => ( ~ v3_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v2_lattice3(B) & v4_yellow_0(B,A) & v5_yellow_0(B,A) ) ) ) ) ), file(yellow_0,cc11_yellow_0), []). fof(cc12_yellow_0,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( ( ~ v3_struct_0(B) & v4_yellow_0(B,A) & v6_yellow_0(B,A) ) => ( ~ v3_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v4_yellow_0(B,A) & v6_yellow_0(B,A) ) ) ) ) ), file(yellow_0,cc12_yellow_0), []). fof(cc1_finset_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_finset_1(A) ) ), file(finset_1,cc1_finset_1), []). fof(cc1_lattice3,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_lattice3(A) => ~ v3_struct_0(A) ) ) ), file(lattice3,cc1_lattice3), []). 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(cc1_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v3_lattice3(A) ) => ( ~ v3_struct_0(A) & v1_lattice3(A) & v2_lattice3(A) ) ) ) ), file(yellow_0,cc1_yellow_0), []). fof(cc2_finset_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_finset_1(B) ) ) ), file(finset_1,cc2_finset_1), []). fof(cc2_lattice3,axiom,( ! [A] : ( l1_orders_2(A) => ( v2_lattice3(A) => ~ v3_struct_0(A) ) ) ), file(lattice3,cc2_lattice3), []). fof(cc2_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_realset2(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v3_lattice3(A) ) ) ) ), file(yellow_0,cc2_yellow_0), []). fof(cc3_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v3_lattice3(A) ) => ( ~ v3_struct_0(A) & v3_yellow_0(A) ) ) ) ), file(yellow_0,cc3_yellow_0), []). fof(cc4_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ( v3_yellow_0(A) => ( v1_yellow_0(A) & v2_yellow_0(A) ) ) ) ), file(yellow_0,cc4_yellow_0), []). fof(cc5_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( v1_yellow_0(A) & v2_yellow_0(A) ) => v3_yellow_0(A) ) ) ), file(yellow_0,cc5_yellow_0), []). fof(cc6_yellow_0,axiom,( ! [A] : ( ( v2_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( v4_yellow_0(B,A) => ( v2_orders_2(B) & v4_yellow_0(B,A) ) ) ) ) ), file(yellow_0,cc6_yellow_0), []). fof(cc7_yellow_0,axiom,( ! [A] : ( ( v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( v4_yellow_0(B,A) => ( v3_orders_2(B) & v4_yellow_0(B,A) ) ) ) ) ), file(yellow_0,cc7_yellow_0), []). fof(cc8_yellow_0,axiom,( ! [A] : ( ( v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( v4_yellow_0(B,A) => ( v4_orders_2(B) & v4_yellow_0(B,A) ) ) ) ) ), file(yellow_0,cc8_yellow_0), []). fof(commutativity_k12_lattice3,axiom,( ! [A,B,C] : ( ( v4_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => k12_lattice3(A,B,C) = k12_lattice3(A,C,B) ) ), file(lattice3,k12_lattice3), []). fof(commutativity_k13_lattice3,axiom,( ! [A,B,C] : ( ( v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => k13_lattice3(A,B,C) = k13_lattice3(A,C,B) ) ), file(lattice3,k13_lattice3), []). fof(commutativity_k2_struct_0,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => k2_struct_0(A,B,C) = k2_struct_0(A,C,B) ) ), file(struct_0,k2_struct_0), []). fof(commutativity_k2_tarski,axiom,( ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ), file(tarski,k2_tarski), []). fof(connectedness_r1_ordinal1,axiom,( ! [A,B] : ( ( v3_ordinal1(A) & v3_ordinal1(B) ) => ( r1_ordinal1(A,B) | r1_ordinal1(B,A) ) ) ), file(ordinal1,r1_ordinal1), []). fof(connectedness_r1_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( r1_xreal_0(A,B) | r1_xreal_0(B,A) ) ) ), file(xreal_0,r1_xreal_0), []). fof(d10_xboole_0,axiom,( ! [A,B] : ( A = B <=> ( r1_tarski(A,B) & r1_tarski(B,A) ) ) ), file(xboole_0,d10_xboole_0), []). fof(d13_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ( m1_yellow_0(B,A) <=> ( r1_tarski(u1_struct_0(B),u1_struct_0(A)) & r1_tarski(u1_orders_2(B),u1_orders_2(A)) ) ) ) ) ), file(yellow_0,d13_yellow_0), []). fof(d15_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( v1_orders_2(C) & v4_yellow_0(C,A) & m1_yellow_0(C,A) ) => ( C = k5_yellow_0(A,B) <=> u1_struct_0(C) = B ) ) ) ) ), file(yellow_0,d15_yellow_0), []). fof(d16_yellow_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( v5_yellow_0(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r2_hidden(C,u1_struct_0(B)) & r2_hidden(D,u1_struct_0(B)) & r2_yellow_0(A,k2_struct_0(A,C,D)) ) => r2_hidden(k2_yellow_0(A,k2_struct_0(A,C,D)),u1_struct_0(B)) ) ) ) ) ) ) ), file(yellow_0,d16_yellow_0), []). fof(d17_yellow_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( v6_yellow_0(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r2_hidden(C,u1_struct_0(B)) & r2_hidden(D,u1_struct_0(B)) & r1_yellow_0(A,k2_struct_0(A,C,D)) ) => r2_hidden(k1_yellow_0(A,k2_struct_0(A,C,D)),u1_struct_0(B)) ) ) ) ) ) ) ), file(yellow_0,d17_yellow_0), []). fof(d1_enumset1,axiom,( ! [A,B,C,D] : ( D = k1_enumset1(A,B,C) <=> ! [E] : ( r2_hidden(E,D) <=> ~ ( E != A & E != B & E != C ) ) ) ), file(enumset1,d1_enumset1), []). 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_struct_0,axiom,( ! [A] : ( l1_struct_0(A) => ( v3_struct_0(A) <=> v1_xboole_0(u1_struct_0(A)) ) ) ), file(struct_0,d1_struct_0), []). fof(d1_tarski,axiom,( ! [A,B] : ( B = k1_tarski(A) <=> ! [C] : ( r2_hidden(C,B) <=> C = A ) ) ), file(tarski,d1_tarski), []). fof(d1_waybel_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l1_struct_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ( v2_funct_1(C) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( k7_yellow_2(u1_struct_0(A),B,C,D) = k7_yellow_2(u1_struct_0(A),B,C,E) => D = E ) ) ) ) ) ) ) ), file(waybel_1,d1_waybel_1), []). fof(d2_yellow11,axiom,( k2_yellow11 = k2_yellow_1(k3_enumset1(0,1,k4_xboole_0(2,1),k4_xboole_0(3,2),3)) ), file(yellow11,d2_yellow11), []). fof(d38_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ( ~ ( ~ v3_struct_0(A) & ~ v3_struct_0(B) & ~ ( v23_waybel_0(C,A,B) <=> ( v2_funct_1(C) & v5_orders_3(C,A,B) & ? [D] : ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) & D = k2_funct_1(C) & v5_orders_3(D,B,A) ) ) ) ) & ( ~ ( ~ v3_struct_0(A) & ~ v3_struct_0(B) ) => ( v23_waybel_0(C,A,B) <=> ( v3_struct_0(A) & v3_struct_0(B) ) ) ) ) ) ) ) ), file(waybel_0,d38_waybel_0), []). fof(d3_enumset1,axiom,( ! [A,B,C,D,E,F] : ( F = k3_enumset1(A,B,C,D,E) <=> ! [G] : ( r2_hidden(G,F) <=> ~ ( G != A & G != B & G != C & G != D & G != E ) ) ) ), file(enumset1,d3_enumset1), []). fof(d3_tarski,axiom,( ! [A,B] : ( r1_tarski(A,B) <=> ! [C] : ( r2_hidden(C,A) => r2_hidden(C,B) ) ) ), file(tarski,d3_tarski), []). 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(d8_waybel_1,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ( r5_waybel_1(A,B) <=> ? [C] : ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v23_waybel_0(C,A,B) ) ) ) ) ), file(waybel_1,d8_waybel_1), []). fof(dt_g1_orders_2,axiom,( ! [A,B] : ( m1_relset_1(B,A,A) => ( v1_orders_2(g1_orders_2(A,B)) & l1_orders_2(g1_orders_2(A,B)) ) ) ), file(orders_2,g1_orders_2), []). fof(dt_k10_lattice3,axiom,( ! [A,B,C] : ( ( l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k10_lattice3(A,B,C),u1_struct_0(A)) ) ), file(lattice3,k10_lattice3), []). fof(dt_k11_lattice3,axiom,( ! [A,B,C] : ( ( l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k11_lattice3(A,B,C),u1_struct_0(A)) ) ), file(lattice3,k11_lattice3), []). fof(dt_k12_lattice3,axiom,( ! [A,B,C] : ( ( v4_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k12_lattice3(A,B,C),u1_struct_0(A)) ) ), file(lattice3,k12_lattice3), []). fof(dt_k13_lattice3,axiom,( ! [A,B,C] : ( ( v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k13_lattice3(A,B,C),u1_struct_0(A)) ) ), file(lattice3,k13_lattice3), []). fof(dt_k1_enumset1,axiom,( $true ), file(enumset1,k1_enumset1), []). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), []). 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_waybel_0,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v3_struct_0(B) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(A)) ) => m1_subset_1(k1_waybel_0(A,B,C,D),u1_struct_0(B)) ) ), file(waybel_0,k1_waybel_0), []). fof(dt_k1_wellord2,axiom,( ! [A] : v1_relat_1(k1_wellord2(A)) ), file(wellord2,k1_wellord2), []). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), []). fof(dt_k1_yellow_0,axiom,( ! [A,B] : ( l1_orders_2(A) => m1_subset_1(k1_yellow_0(A,B),u1_struct_0(A)) ) ), file(yellow_0,k1_yellow_0), []). fof(dt_k1_yellow_1,axiom,( ! [A] : ( v1_relat_2(k1_yellow_1(A)) & v4_relat_2(k1_yellow_1(A)) & v8_relat_2(k1_yellow_1(A)) & v1_partfun1(k1_yellow_1(A),A,A) & m2_relset_1(k1_yellow_1(A),A,A) ) ), file(yellow_1,k1_yellow_1), []). fof(dt_k1_yellow_2,axiom,( ! [A,B,C] : ( ( l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => m1_subset_1(k1_yellow_2(A,B,C),k1_zfmisc_1(u1_struct_0(B))) ) ), file(yellow_2,k1_yellow_2), []). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), []). fof(dt_k2_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k2_funct_1(A)) & v1_funct_1(k2_funct_1(A)) ) ) ), file(funct_1,k2_funct_1), []). fof(dt_k2_relat_1,axiom,( $true ), file(relat_1,k2_relat_1), []). fof(dt_k2_struct_0,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k2_struct_0(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ), file(struct_0,k2_struct_0), []). fof(dt_k2_tarski,axiom,( $true ), file(tarski,k2_tarski), []). fof(dt_k2_yellow11,axiom,( l1_orders_2(k2_yellow11) ), file(yellow11,k2_yellow11), []). fof(dt_k2_yellow_0,axiom,( ! [A,B] : ( l1_orders_2(A) => m1_subset_1(k2_yellow_0(A,B),u1_struct_0(A)) ) ), file(yellow_0,k2_yellow_0), []). fof(dt_k2_yellow_1,axiom,( ! [A] : ( v1_orders_2(k2_yellow_1(A)) & l1_orders_2(k2_yellow_1(A)) ) ), file(yellow_1,k2_yellow_1), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). fof(dt_k3_enumset1,axiom,( $true ), file(enumset1,k3_enumset1), []). 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_xboole_0,axiom,( $true ), file(xboole_0,k4_xboole_0), []). fof(dt_k5_numbers,axiom,( m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ), file(numbers,k5_numbers), []). fof(dt_k5_ordinal2,axiom,( $true ), file(ordinal2,k5_ordinal2), []). fof(dt_k5_yellow_0,axiom,( ! [A,B] : ( ( l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v1_orders_2(k5_yellow_0(A,B)) & v4_yellow_0(k5_yellow_0(A,B),A) & m1_yellow_0(k5_yellow_0(A,B),A) ) ) ), file(yellow_0,k5_yellow_0), []). fof(dt_k7_yellow_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v3_struct_0(B) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,A,u1_struct_0(B)) & m1_relset_1(C,A,u1_struct_0(B)) & m1_subset_1(D,A) ) => m1_subset_1(k7_yellow_2(A,B,C,D),u1_struct_0(B)) ) ), file(yellow_2,k7_yellow_2), []). 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_yellow_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(B) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,A,u1_struct_0(B)) & m1_relset_1(C,A,u1_struct_0(B)) ) => m1_subset_1(k8_yellow_2(A,B,C),k1_zfmisc_1(u1_struct_0(B))) ) ), file(yellow_2,k8_yellow_2), []). fof(dt_l1_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => l1_struct_0(A) ) ), file(orders_2,l1_orders_2), []). fof(dt_l1_struct_0,axiom,( $true ), file(struct_0,l1_struct_0), []). 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_m1_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_yellow_0(B,A) => l1_orders_2(B) ) ) ), file(yellow_0,m1_yellow_0), []). 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_u1_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => m2_relset_1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)) ) ), file(orders_2,u1_orders_2), []). fof(dt_u1_struct_0,axiom,( $true ), file(struct_0,u1_struct_0), []). fof(existence_l1_orders_2,axiom,( ? [A] : l1_orders_2(A) ), file(orders_2,l1_orders_2), []). fof(existence_l1_struct_0,axiom,( ? [A] : l1_struct_0(A) ), file(struct_0,l1_struct_0), []). 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_m1_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ? [B] : m1_yellow_0(B,A) ) ), file(yellow_0,m1_yellow_0), []). 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(fc12_finset_1,axiom,( ! [A,B] : ( v1_finset_1(A) => v1_finset_1(k4_xboole_0(A,B)) ) ), file(finset_1,fc12_finset_1), []). fof(fc14_finset_1,axiom,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_zfmisc_1(A,B)) ) ), file(finset_1,fc14_finset_1), []). fof(fc1_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)) ) ), file(finset_1,fc1_finset_1), []). fof(fc1_orders_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_relset_1(B,A,A) ) => ( ~ v3_struct_0(g1_orders_2(A,B)) & v1_orders_2(g1_orders_2(A,B)) ) ) ), file(orders_2,fc1_orders_2), []). 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_xboole_0,axiom,( v1_xboole_0(k1_xboole_0) ), file(xboole_0,fc1_xboole_0), []). fof(fc1_yellow_0,axiom,( ! [A,B] : ( m1_relset_1(B,k1_tarski(A),k1_tarski(A)) => ( ~ v3_struct_0(g1_orders_2(k1_tarski(A),B)) & v1_orders_2(g1_orders_2(k1_tarski(A),B)) & v3_realset2(g1_orders_2(k1_tarski(A),B)) ) ) ), file(yellow_0,fc1_yellow_0), []). fof(fc2_finset_1,axiom,( ! [A,B] : ( ~ v1_xboole_0(k2_tarski(A,B)) & v1_finset_1(k2_tarski(A,B)) ) ), file(finset_1,fc2_finset_1), []). fof(fc2_orders_2,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ( v1_relat_1(u1_orders_2(A)) & v1_relat_2(u1_orders_2(A)) & v4_relat_2(u1_orders_2(A)) & v8_relat_2(u1_orders_2(A)) & v1_partfun1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)) ) ) ), file(orders_2,fc2_orders_2), []). fof(fc3_finset_1,axiom,( ! [A,B,C] : v1_finset_1(k1_enumset1(A,B,C)) ), file(finset_1,fc3_finset_1), []). fof(fc3_orders_2,axiom,( ! [A,B] : ( ( v1_relat_2(B) & v4_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) ) => ( v1_orders_2(g1_orders_2(A,B)) & v2_orders_2(g1_orders_2(A,B)) & v3_orders_2(g1_orders_2(A,B)) & v4_orders_2(g1_orders_2(A,B)) ) ) ), file(orders_2,fc3_orders_2), []). fof(fc3_yellow11,axiom, ( v1_orders_2(k2_yellow11) & v2_orders_2(k2_yellow11) & v3_orders_2(k2_yellow11) & v4_orders_2(k2_yellow11) ), file(yellow11,fc3_yellow11), []). fof(fc4_yellow11,axiom, ( ~ v3_struct_0(k2_yellow11) & v1_lattice3(k2_yellow11) & v2_lattice3(k2_yellow11) ), file(yellow11,fc4_yellow11), []). fof(fc5_finset_1,axiom,( ! [A,B,C,D,E] : v1_finset_1(k3_enumset1(A,B,C,D,E)) ), file(finset_1,fc5_finset_1), []). fof(fc5_yellow_1,axiom,( ! [A] : ( v1_orders_2(k2_yellow_1(A)) & v2_orders_2(k2_yellow_1(A)) & v3_orders_2(k2_yellow_1(A)) & v4_orders_2(k2_yellow_1(A)) ) ), file(yellow_1,fc5_yellow_1), []). fof(fc6_yellow_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ v3_struct_0(k2_yellow_1(A)) & v1_orders_2(k2_yellow_1(A)) & v2_orders_2(k2_yellow_1(A)) & v3_orders_2(k2_yellow_1(A)) & v4_orders_2(k2_yellow_1(A)) ) ) ), file(yellow_1,fc6_yellow_1), []). fof(free_g1_orders_2,axiom,( ! [A,B] : ( m1_relset_1(B,A,A) => ! [C,D] : ( g1_orders_2(A,B) = g1_orders_2(C,D) => ( A = C & B = D ) ) ) ), file(orders_2,g1_orders_2), []). fof(rc1_finset_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) ) ), file(finset_1,rc1_finset_1), []). fof(rc1_lattice3,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v1_orders_2(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v3_lattice3(A) ) ), file(lattice3,rc1_lattice3), []). fof(rc1_orders_2,axiom,( ? [A] : ( l1_orders_2(A) & v1_orders_2(A) ) ), file(orders_2,rc1_orders_2), []). fof(rc1_xboole_0,axiom,( ? [A] : v1_xboole_0(A) ), file(xboole_0,rc1_xboole_0), []). fof(rc1_yellow_0,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v1_orders_2(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v3_realset2(A) ) ), file(yellow_0,rc1_yellow_0), []). fof(rc2_lattice3,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v1_orders_2(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) ) ), file(lattice3,rc2_lattice3), []). fof(rc2_orders_2,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v1_orders_2(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) ) ), file(orders_2,rc2_orders_2), []). fof(rc2_xboole_0,axiom,( ? [A] : ~ v1_xboole_0(A) ), file(xboole_0,rc2_xboole_0), []). fof(rc2_yellow_0,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) ) ), file(yellow_0,rc2_yellow_0), []). fof(rc3_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc3_finset_1), []). fof(rc3_struct_0,axiom,( ? [A] : ( l1_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc3_struct_0), []). fof(rc3_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ? [B] : ( m1_yellow_0(B,A) & v1_orders_2(B) & v4_yellow_0(B,A) ) ) ), file(yellow_0,rc3_yellow_0), []). fof(rc4_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc4_finset_1), []). fof(rc4_yellow_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ? [B] : ( m1_yellow_0(B,A) & ~ v3_struct_0(B) & v1_orders_2(B) & v4_yellow_0(B,A) ) ) ), file(yellow_0,rc4_yellow_0), []). 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(redefinition_k12_lattice3,axiom,( ! [A,B,C] : ( ( v4_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => k12_lattice3(A,B,C) = k11_lattice3(A,B,C) ) ), file(lattice3,k12_lattice3), []). fof(redefinition_k13_lattice3,axiom,( ! [A,B,C] : ( ( v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => k13_lattice3(A,B,C) = k10_lattice3(A,B,C) ) ), file(lattice3,k13_lattice3), []). fof(redefinition_k1_waybel_0,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v3_struct_0(B) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(A)) ) => k1_waybel_0(A,B,C,D) = k1_funct_1(C,D) ) ), file(waybel_0,k1_waybel_0), []). fof(redefinition_k1_yellow_1,axiom,( ! [A] : k1_yellow_1(A) = k1_wellord2(A) ), file(yellow_1,k1_yellow_1), []). fof(redefinition_k1_yellow_2,axiom,( ! [A,B,C] : ( ( l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => k1_yellow_2(A,B,C) = k2_relat_1(C) ) ), file(yellow_2,k1_yellow_2), []). fof(redefinition_k2_struct_0,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => k2_struct_0(A,B,C) = k2_tarski(B,C) ) ), file(struct_0,k2_struct_0), []). 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_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_k7_yellow_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v3_struct_0(B) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,A,u1_struct_0(B)) & m1_relset_1(C,A,u1_struct_0(B)) & m1_subset_1(D,A) ) => k7_yellow_2(A,B,C,D) = k1_funct_1(C,D) ) ), file(yellow_2,k7_yellow_2), []). 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_yellow_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(B) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,A,u1_struct_0(B)) & m1_relset_1(C,A,u1_struct_0(B)) ) => k8_yellow_2(A,B,C) = k2_relat_1(C) ) ), file(yellow_2,k8_yellow_2), []). 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_r1_ordinal1,axiom,( ! [A,B] : ( ( v3_ordinal1(A) & v3_ordinal1(B) ) => ( r1_ordinal1(A,B) <=> r1_tarski(A,B) ) ) ), file(ordinal1,r1_ordinal1), []). 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(reflexivity_r1_ordinal1,axiom,( ! [A,B] : ( ( v3_ordinal1(A) & v3_ordinal1(B) ) => r1_ordinal1(A,A) ) ), file(ordinal1,r1_ordinal1), []). fof(reflexivity_r1_tarski,axiom,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), []). fof(reflexivity_r1_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => r1_xreal_0(A,A) ) ), file(xreal_0,r1_xreal_0), []). 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_r5_waybel_1,axiom,( ! [A,B] : ( ( l1_orders_2(A) & l1_orders_2(B) ) => r5_waybel_1(A,A) ) ), file(waybel_1,r5_waybel_1), []). fof(s1_funct_2__e12_15_2_4__yellow11,axiom,( ! [A,B,C,D,E,F,G,H,I,J,K,L] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(A)) & m1_subset_1(E,u1_struct_0(A)) & m1_subset_1(F,u1_struct_0(A)) & m1_subset_1(G,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(H,u1_struct_0(k2_yellow11)) & m1_subset_1(I,u1_struct_0(k2_yellow11)) & m1_subset_1(J,u1_struct_0(k2_yellow11)) & m1_subset_1(K,u1_struct_0(k2_yellow11)) & m1_subset_1(L,u1_struct_0(k2_yellow11)) ) => ( ! [M] : ~ ( r2_hidden(M,u1_struct_0(k2_yellow11)) & ! [N] : ~ ( r2_hidden(N,G) & ! [O] : ( m1_subset_1(O,u1_struct_0(k2_yellow11)) => ( O = M => ( ( O = H => N = B ) & ( O = I => N = C ) & ( O = J => N = D ) & ( O = K => N = E ) & ( O = L => N = F ) ) ) ) ) ) => ? [M] : ( v1_funct_1(M) & v1_funct_2(M,u1_struct_0(k2_yellow11),G) & m2_relset_1(M,u1_struct_0(k2_yellow11),G) & ! [N] : ( r2_hidden(N,u1_struct_0(k2_yellow11)) => ! [P] : ( m1_subset_1(P,u1_struct_0(k2_yellow11)) => ( P = N => ( ( P = H => k1_funct_1(M,N) = B ) & ( P = I => k1_funct_1(M,N) = C ) & ( P = J => k1_funct_1(M,N) = D ) & ( P = K => k1_funct_1(M,N) = E ) & ( P = L => k1_funct_1(M,N) = F ) ) ) ) ) ) ) ) ), file(yellow11,s1_funct_2__e12_15_2_4__yellow11), []). fof(spc0_boole,axiom,( v1_xboole_0(0) ), file(boole,spc0_boole), []). fof(spc1_boole,axiom,( ~ v1_xboole_0(1) ), file(boole,spc1_boole), []). fof(spc1_numerals,axiom, ( v2_xreal_0(1) & m1_subset_1(1,k5_numbers) ), file(numerals,spc1_numerals), []). fof(spc2_boole,axiom,( ~ v1_xboole_0(2) ), file(boole,spc2_boole), []). fof(spc2_numerals,axiom, ( v2_xreal_0(2) & m1_subset_1(2,k5_numbers) ), file(numerals,spc2_numerals), []). fof(spc3_boole,axiom,( ~ v1_xboole_0(3) ), file(boole,spc3_boole), []). fof(spc3_numerals,axiom, ( v2_xreal_0(3) & m1_subset_1(3,k5_numbers) ), file(numerals,spc3_numerals), []). fof(t1_card_5,axiom, ( 1 = k1_tarski(0) & 2 = k2_tarski(0,1) ), file(card_5,t1_card_5), []). fof(t1_numerals,axiom,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), []). fof(t1_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & v2_xreal_0(A) ) => v2_xreal_0(B) ) ) ) ), file(real,t1_real), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t1_yellow11,axiom,( 3 = k1_enumset1(0,1,2) ), file(yellow11,t1_yellow11), []). fof(t1_yellow_1,axiom,( ! [A] : ( u1_struct_0(k2_yellow_1(A)) = A & u1_orders_2(k2_yellow_1(A)) = k1_yellow_1(A) ) ), file(yellow_1,t1_yellow_1), []). fof(t1_yellow_5,axiom,( ! [A] : ( ( v2_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k13_lattice3(A,B,B) = B ) ) ), file(yellow_5,t1_yellow_5), []). fof(t20_yellow_0,axiom,( ! [A] : ( ( v4_orders_2(A) & l1_orders_2(A) ) => ( v1_lattice3(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_yellow_0(A,k2_tarski(B,C)) ) ) ) ) ), file(yellow_0,t20_yellow_0), []). fof(t21_yellow_0,axiom,( ! [A] : ( ( v4_orders_2(A) & l1_orders_2(A) ) => ( v2_lattice3(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r2_yellow_0(A,k2_tarski(B,C)) ) ) ) ) ), file(yellow_0,t21_yellow_0), []). fof(t22_yellow_0,axiom,( ! [A] : ( ( v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( D = k13_lattice3(A,B,C) <=> ( r1_orders_2(A,B,D) & r1_orders_2(A,C,D) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r1_orders_2(A,B,E) & r1_orders_2(A,C,E) ) => r1_orders_2(A,D,E) ) ) ) ) ) ) ) ) ), file(yellow_0,t22_yellow_0), []). fof(t23_yellow_0,axiom,( ! [A] : ( ( v4_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( D = k12_lattice3(A,B,C) <=> ( r1_orders_2(A,D,B) & r1_orders_2(A,D,C) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r1_orders_2(A,E,B) & r1_orders_2(A,E,C) ) => r1_orders_2(A,E,D) ) ) ) ) ) ) ) ) ), file(yellow_0,t23_yellow_0), []). fof(t24_yellow_0,axiom,( ! [A] : ( ( v2_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( B = k13_lattice3(A,B,C) <=> r1_orders_2(A,C,B) ) ) ) ) ), file(yellow_0,t24_yellow_0), []). fof(t25_yellow_0,axiom,( ! [A] : ( ( v2_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( B = k12_lattice3(A,B,C) <=> r3_orders_2(A,B,C) ) ) ) ) ), file(yellow_0,t25_yellow_0), []). fof(t26_orders_2,axiom,( ! [A] : ( ( v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r1_orders_2(A,B,C) & r1_orders_2(A,C,D) ) => r1_orders_2(A,B,D) ) ) ) ) ) ), file(orders_2,t26_orders_2), []). 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_xboole_1,axiom,( ! [A] : r1_tarski(k1_xboole_0,A) ), file(xboole_1,t2_xboole_1), []). fof(t2_yellow11,axiom,( k4_xboole_0(2,1) = k1_tarski(1) ), file(yellow11,t2_yellow11), []). fof(t2_yellow_5,axiom,( ! [A] : ( ( v2_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k12_lattice3(A,B,B) = B ) ) ), file(yellow_5,t2_yellow_5), []). fof(t3_boole,axiom,( ! [A] : k4_xboole_0(A,k1_xboole_0) = A ), file(boole,t3_boole), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t3_xboole_1,axiom,( ! [A] : ( r1_tarski(A,k1_xboole_0) => A = k1_xboole_0 ) ), file(xboole_1,t3_xboole_1), []). fof(t3_yellow_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k2_yellow_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_yellow_1(A))) => ( r3_orders_2(k2_yellow_1(A),B,C) <=> r1_tarski(B,C) ) ) ) ) ), file(yellow_1,t3_yellow_1), []). fof(t40_yellow_0,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k2_yellow_0(A,k2_struct_0(A,B,C)) = k12_lattice3(A,B,C) ) ) ) ), file(yellow_0,t40_yellow_0), []). fof(t41_yellow_0,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_yellow_0(A,k2_struct_0(A,B,C)) = k13_lattice3(A,B,C) ) ) ) ), file(yellow_0,t41_yellow_0), []). fof(t4_boole,axiom,( ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ), file(boole,t4_boole), []). fof(t4_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xreal_0(A,B) & ~ v2_xreal_0(B) & v2_xreal_0(A) ) ) ) ), file(real,t4_real), []). 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(t4_yellow11,axiom,( k4_xboole_0(3,2) = k1_tarski(2) ), file(yellow11,t4_yellow11), []). fof(t56_card_1,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( r1_xreal_0(A,B) <=> r1_ordinal1(A,B) ) ) ) ), file(card_1,t56_card_1), []). 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(t5_yellow11,axiom,( ! [A] : ( ( v2_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k12_lattice3(A,B,C) = C <=> k13_lattice3(A,B,C) = B ) ) ) ) ), file(yellow11,t5_yellow11), []). fof(t60_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_yellow_0(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ( E = C & F = D & r1_orders_2(B,E,F) ) => r1_orders_2(A,C,D) ) ) ) ) ) ) ) ), file(yellow_0,t60_yellow_0), []). fof(t61_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( v4_yellow_0(B,A) & m1_yellow_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ( E = C & F = D & r1_orders_2(A,C,D) & r2_hidden(E,u1_struct_0(B)) & r2_hidden(F,u1_struct_0(B)) ) => r1_orders_2(B,E,F) ) ) ) ) ) ) ) ), file(yellow_0,t61_yellow_0), []). fof(t66_waybel_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ( v23_waybel_0(C,A,B) <=> ( v2_funct_1(C) & k2_relat_1(C) = u1_struct_0(B) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_orders_2(A,D,E) <=> r1_orders_2(B,k1_waybel_0(A,B,C,D),k1_waybel_0(A,B,C,E)) ) ) ) ) ) ) ) ) ), file(waybel_0,t66_waybel_0), []). 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), []).