% Mizar ND problem: t6_ami_6,ami_6,111,39 fof(dh_c1_6__ami_6,definition, ( ( v1_setfam_1(c1_6__ami_6) => ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_ami_1(A,c1_6__ami_6) & v5_ami_1(A,c1_6__ami_6) & v8_ami_1(A,c1_6__ami_6) & v10_ami_1(A,c1_6__ami_6) & l1_ami_1(A,c1_6__ami_6) ) => ! [B] : ( m1_subset_1(B,k4_card_3(u5_ami_1(c1_6__ami_6,A))) => ! [C] : ( m1_subset_1(C,k4_card_3(u5_ami_1(c1_6__ami_6,A))) => ! [D] : ( m1_struct_0(D,A,u2_ami_1(c1_6__ami_6,A)) => ! [E] : ( m1_subset_1(E,k3_ami_1(c1_6__ami_6,A,k2_ami_1(c1_6__ami_6,A))) => ! [F] : ( m1_subset_1(F,k3_ami_1(c1_6__ami_6,A,D)) => ( ( E = D & C = k8_ami_5(c1_6__ami_6,A,B,k16_ami_1(c1_6__ami_6,A,k2_ami_1(c1_6__ami_6,A),D,E,F)) ) => ( k13_ami_1(c1_6__ami_6,A,C,D) = F & k6_ami_1(c1_6__ami_6,A,C) = D & k6_ami_1(c1_6__ami_6,A,k9_ami_1(c1_6__ami_6,A,C)) = k1_funct_1(k4_ami_1(c1_6__ami_6,A,k13_ami_1(c1_6__ami_6,A,C,k6_ami_1(c1_6__ami_6,A,C)),C),k2_ami_1(c1_6__ami_6,A)) ) ) ) ) ) ) ) ) ) => ! [G] : ( v1_setfam_1(G) => ! [H] : ( ( ~ v3_struct_0(H) & ~ v2_ami_1(H,G) & v5_ami_1(H,G) & v8_ami_1(H,G) & v10_ami_1(H,G) & l1_ami_1(H,G) ) => ! [I] : ( m1_subset_1(I,k4_card_3(u5_ami_1(G,H))) => ! [J] : ( m1_subset_1(J,k4_card_3(u5_ami_1(G,H))) => ! [K] : ( m1_struct_0(K,H,u2_ami_1(G,H)) => ! [L] : ( m1_subset_1(L,k3_ami_1(G,H,k2_ami_1(G,H))) => ! [M] : ( m1_subset_1(M,k3_ami_1(G,H,K)) => ( ( L = K & J = k8_ami_5(G,H,I,k16_ami_1(G,H,k2_ami_1(G,H),K,L,M)) ) => ( k13_ami_1(G,H,J,K) = M & k6_ami_1(G,H,J) = K & k6_ami_1(G,H,k9_ami_1(G,H,J)) = k1_funct_1(k4_ami_1(G,H,k13_ami_1(G,H,J,k6_ami_1(G,H,J)),J),k2_ami_1(G,H)) ) ) ) ) ) ) ) ) ) ), introduced(definition,[new_symbol(c1_6__ami_6),file(ami_6,c1_6__ami_6)]), [interesting(0.8),axiom,file(ami_6,c1_6__ami_6)]). fof(dh_c2_6__ami_6,definition, ( ( ( ~ v3_struct_0(c2_6__ami_6) & ~ v2_ami_1(c2_6__ami_6,c1_6__ami_6) & v5_ami_1(c2_6__ami_6,c1_6__ami_6) & v8_ami_1(c2_6__ami_6,c1_6__ami_6) & v10_ami_1(c2_6__ami_6,c1_6__ami_6) & l1_ami_1(c2_6__ami_6,c1_6__ami_6) ) => ! [A] : ( m1_subset_1(A,k4_card_3(u5_ami_1(c1_6__ami_6,c2_6__ami_6))) => ! [B] : ( m1_subset_1(B,k4_card_3(u5_ami_1(c1_6__ami_6,c2_6__ami_6))) => ! [C] : ( m1_struct_0(C,c2_6__ami_6,u2_ami_1(c1_6__ami_6,c2_6__ami_6)) => ! [D] : ( m1_subset_1(D,k3_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6))) => ! [E] : ( m1_subset_1(E,k3_ami_1(c1_6__ami_6,c2_6__ami_6,C)) => ( ( D = C & B = k8_ami_5(c1_6__ami_6,c2_6__ami_6,A,k16_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6),C,D,E)) ) => ( k13_ami_1(c1_6__ami_6,c2_6__ami_6,B,C) = E & k6_ami_1(c1_6__ami_6,c2_6__ami_6,B) = C & k6_ami_1(c1_6__ami_6,c2_6__ami_6,k9_ami_1(c1_6__ami_6,c2_6__ami_6,B)) = k1_funct_1(k4_ami_1(c1_6__ami_6,c2_6__ami_6,k13_ami_1(c1_6__ami_6,c2_6__ami_6,B,k6_ami_1(c1_6__ami_6,c2_6__ami_6,B)),B),k2_ami_1(c1_6__ami_6,c2_6__ami_6)) ) ) ) ) ) ) ) ) => ! [F] : ( ( ~ v3_struct_0(F) & ~ v2_ami_1(F,c1_6__ami_6) & v5_ami_1(F,c1_6__ami_6) & v8_ami_1(F,c1_6__ami_6) & v10_ami_1(F,c1_6__ami_6) & l1_ami_1(F,c1_6__ami_6) ) => ! [G] : ( m1_subset_1(G,k4_card_3(u5_ami_1(c1_6__ami_6,F))) => ! [H] : ( m1_subset_1(H,k4_card_3(u5_ami_1(c1_6__ami_6,F))) => ! [I] : ( m1_struct_0(I,F,u2_ami_1(c1_6__ami_6,F)) => ! [J] : ( m1_subset_1(J,k3_ami_1(c1_6__ami_6,F,k2_ami_1(c1_6__ami_6,F))) => ! [K] : ( m1_subset_1(K,k3_ami_1(c1_6__ami_6,F,I)) => ( ( J = I & H = k8_ami_5(c1_6__ami_6,F,G,k16_ami_1(c1_6__ami_6,F,k2_ami_1(c1_6__ami_6,F),I,J,K)) ) => ( k13_ami_1(c1_6__ami_6,F,H,I) = K & k6_ami_1(c1_6__ami_6,F,H) = I & k6_ami_1(c1_6__ami_6,F,k9_ami_1(c1_6__ami_6,F,H)) = k1_funct_1(k4_ami_1(c1_6__ami_6,F,k13_ami_1(c1_6__ami_6,F,H,k6_ami_1(c1_6__ami_6,F,H)),H),k2_ami_1(c1_6__ami_6,F)) ) ) ) ) ) ) ) ) ), introduced(definition,[new_symbol(c2_6__ami_6),file(ami_6,c2_6__ami_6)]), [interesting(0.8),axiom,file(ami_6,c2_6__ami_6)]). fof(dh_c3_6__ami_6,definition, ( ( m1_subset_1(c3_6__ami_6,k4_card_3(u5_ami_1(c1_6__ami_6,c2_6__ami_6))) => ! [A] : ( m1_subset_1(A,k4_card_3(u5_ami_1(c1_6__ami_6,c2_6__ami_6))) => ! [B] : ( m1_struct_0(B,c2_6__ami_6,u2_ami_1(c1_6__ami_6,c2_6__ami_6)) => ! [C] : ( m1_subset_1(C,k3_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6))) => ! [D] : ( m1_subset_1(D,k3_ami_1(c1_6__ami_6,c2_6__ami_6,B)) => ( ( C = B & A = k8_ami_5(c1_6__ami_6,c2_6__ami_6,c3_6__ami_6,k16_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6),B,C,D)) ) => ( k13_ami_1(c1_6__ami_6,c2_6__ami_6,A,B) = D & k6_ami_1(c1_6__ami_6,c2_6__ami_6,A) = B & k6_ami_1(c1_6__ami_6,c2_6__ami_6,k9_ami_1(c1_6__ami_6,c2_6__ami_6,A)) = k1_funct_1(k4_ami_1(c1_6__ami_6,c2_6__ami_6,k13_ami_1(c1_6__ami_6,c2_6__ami_6,A,k6_ami_1(c1_6__ami_6,c2_6__ami_6,A)),A),k2_ami_1(c1_6__ami_6,c2_6__ami_6)) ) ) ) ) ) ) ) => ! [E] : ( m1_subset_1(E,k4_card_3(u5_ami_1(c1_6__ami_6,c2_6__ami_6))) => ! [F] : ( m1_subset_1(F,k4_card_3(u5_ami_1(c1_6__ami_6,c2_6__ami_6))) => ! [G] : ( m1_struct_0(G,c2_6__ami_6,u2_ami_1(c1_6__ami_6,c2_6__ami_6)) => ! [H] : ( m1_subset_1(H,k3_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6))) => ! [I] : ( m1_subset_1(I,k3_ami_1(c1_6__ami_6,c2_6__ami_6,G)) => ( ( H = G & F = k8_ami_5(c1_6__ami_6,c2_6__ami_6,E,k16_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6),G,H,I)) ) => ( k13_ami_1(c1_6__ami_6,c2_6__ami_6,F,G) = I & k6_ami_1(c1_6__ami_6,c2_6__ami_6,F) = G & k6_ami_1(c1_6__ami_6,c2_6__ami_6,k9_ami_1(c1_6__ami_6,c2_6__ami_6,F)) = k1_funct_1(k4_ami_1(c1_6__ami_6,c2_6__ami_6,k13_ami_1(c1_6__ami_6,c2_6__ami_6,F,k6_ami_1(c1_6__ami_6,c2_6__ami_6,F)),F),k2_ami_1(c1_6__ami_6,c2_6__ami_6)) ) ) ) ) ) ) ) ), introduced(definition,[new_symbol(c3_6__ami_6),file(ami_6,c3_6__ami_6)]), [interesting(0.8),axiom,file(ami_6,c3_6__ami_6)]). fof(dh_c4_6__ami_6,definition, ( ( m1_subset_1(c4_6__ami_6,k4_card_3(u5_ami_1(c1_6__ami_6,c2_6__ami_6))) => ! [A] : ( m1_struct_0(A,c2_6__ami_6,u2_ami_1(c1_6__ami_6,c2_6__ami_6)) => ! [B] : ( m1_subset_1(B,k3_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6))) => ! [C] : ( m1_subset_1(C,k3_ami_1(c1_6__ami_6,c2_6__ami_6,A)) => ( ( B = A & c4_6__ami_6 = k8_ami_5(c1_6__ami_6,c2_6__ami_6,c3_6__ami_6,k16_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6),A,B,C)) ) => ( k13_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6,A) = C & k6_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6) = A & k6_ami_1(c1_6__ami_6,c2_6__ami_6,k9_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)) = k1_funct_1(k4_ami_1(c1_6__ami_6,c2_6__ami_6,k13_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6,k6_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)),c4_6__ami_6),k2_ami_1(c1_6__ami_6,c2_6__ami_6)) ) ) ) ) ) ) => ! [D] : ( m1_subset_1(D,k4_card_3(u5_ami_1(c1_6__ami_6,c2_6__ami_6))) => ! [E] : ( m1_struct_0(E,c2_6__ami_6,u2_ami_1(c1_6__ami_6,c2_6__ami_6)) => ! [F] : ( m1_subset_1(F,k3_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6))) => ! [G] : ( m1_subset_1(G,k3_ami_1(c1_6__ami_6,c2_6__ami_6,E)) => ( ( F = E & D = k8_ami_5(c1_6__ami_6,c2_6__ami_6,c3_6__ami_6,k16_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6),E,F,G)) ) => ( k13_ami_1(c1_6__ami_6,c2_6__ami_6,D,E) = G & k6_ami_1(c1_6__ami_6,c2_6__ami_6,D) = E & k6_ami_1(c1_6__ami_6,c2_6__ami_6,k9_ami_1(c1_6__ami_6,c2_6__ami_6,D)) = k1_funct_1(k4_ami_1(c1_6__ami_6,c2_6__ami_6,k13_ami_1(c1_6__ami_6,c2_6__ami_6,D,k6_ami_1(c1_6__ami_6,c2_6__ami_6,D)),D),k2_ami_1(c1_6__ami_6,c2_6__ami_6)) ) ) ) ) ) ) ), introduced(definition,[new_symbol(c4_6__ami_6),file(ami_6,c4_6__ami_6)]), [interesting(0.8),axiom,file(ami_6,c4_6__ami_6)]). fof(dh_c5_6__ami_6,definition, ( ( m1_struct_0(c5_6__ami_6,c2_6__ami_6,u2_ami_1(c1_6__ami_6,c2_6__ami_6)) => ! [A] : ( m1_subset_1(A,k3_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6))) => ! [B] : ( m1_subset_1(B,k3_ami_1(c1_6__ami_6,c2_6__ami_6,c5_6__ami_6)) => ( ( A = c5_6__ami_6 & c4_6__ami_6 = k8_ami_5(c1_6__ami_6,c2_6__ami_6,c3_6__ami_6,k16_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6),c5_6__ami_6,A,B)) ) => ( k13_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6,c5_6__ami_6) = B & k6_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6) = c5_6__ami_6 & k6_ami_1(c1_6__ami_6,c2_6__ami_6,k9_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)) = k1_funct_1(k4_ami_1(c1_6__ami_6,c2_6__ami_6,k13_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6,k6_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)),c4_6__ami_6),k2_ami_1(c1_6__ami_6,c2_6__ami_6)) ) ) ) ) ) => ! [C] : ( m1_struct_0(C,c2_6__ami_6,u2_ami_1(c1_6__ami_6,c2_6__ami_6)) => ! [D] : ( m1_subset_1(D,k3_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6))) => ! [E] : ( m1_subset_1(E,k3_ami_1(c1_6__ami_6,c2_6__ami_6,C)) => ( ( D = C & c4_6__ami_6 = k8_ami_5(c1_6__ami_6,c2_6__ami_6,c3_6__ami_6,k16_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6),C,D,E)) ) => ( k13_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6,C) = E & k6_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6) = C & k6_ami_1(c1_6__ami_6,c2_6__ami_6,k9_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)) = k1_funct_1(k4_ami_1(c1_6__ami_6,c2_6__ami_6,k13_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6,k6_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)),c4_6__ami_6),k2_ami_1(c1_6__ami_6,c2_6__ami_6)) ) ) ) ) ) ), introduced(definition,[new_symbol(c5_6__ami_6),file(ami_6,c5_6__ami_6)]), [interesting(0.8),axiom,file(ami_6,c5_6__ami_6)]). fof(dh_c6_6__ami_6,definition, ( ( m1_subset_1(c6_6__ami_6,k3_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6))) => ! [A] : ( m1_subset_1(A,k3_ami_1(c1_6__ami_6,c2_6__ami_6,c5_6__ami_6)) => ( ( c6_6__ami_6 = c5_6__ami_6 & c4_6__ami_6 = k8_ami_5(c1_6__ami_6,c2_6__ami_6,c3_6__ami_6,k16_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6),c5_6__ami_6,c6_6__ami_6,A)) ) => ( k13_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6,c5_6__ami_6) = A & k6_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6) = c5_6__ami_6 & k6_ami_1(c1_6__ami_6,c2_6__ami_6,k9_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)) = k1_funct_1(k4_ami_1(c1_6__ami_6,c2_6__ami_6,k13_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6,k6_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)),c4_6__ami_6),k2_ami_1(c1_6__ami_6,c2_6__ami_6)) ) ) ) ) => ! [B] : ( m1_subset_1(B,k3_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6))) => ! [C] : ( m1_subset_1(C,k3_ami_1(c1_6__ami_6,c2_6__ami_6,c5_6__ami_6)) => ( ( B = c5_6__ami_6 & c4_6__ami_6 = k8_ami_5(c1_6__ami_6,c2_6__ami_6,c3_6__ami_6,k16_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6),c5_6__ami_6,B,C)) ) => ( k13_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6,c5_6__ami_6) = C & k6_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6) = c5_6__ami_6 & k6_ami_1(c1_6__ami_6,c2_6__ami_6,k9_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)) = k1_funct_1(k4_ami_1(c1_6__ami_6,c2_6__ami_6,k13_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6,k6_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)),c4_6__ami_6),k2_ami_1(c1_6__ami_6,c2_6__ami_6)) ) ) ) ) ), introduced(definition,[new_symbol(c6_6__ami_6),file(ami_6,c6_6__ami_6)]), [interesting(0.8),axiom,file(ami_6,c6_6__ami_6)]). fof(dh_c7_6__ami_6,definition, ( ( m1_subset_1(c7_6__ami_6,k3_ami_1(c1_6__ami_6,c2_6__ami_6,c5_6__ami_6)) => ( ( c6_6__ami_6 = c5_6__ami_6 & c4_6__ami_6 = k8_ami_5(c1_6__ami_6,c2_6__ami_6,c3_6__ami_6,k16_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6),c5_6__ami_6,c6_6__ami_6,c7_6__ami_6)) ) => ( k13_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6,c5_6__ami_6) = c7_6__ami_6 & k6_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6) = c5_6__ami_6 & k6_ami_1(c1_6__ami_6,c2_6__ami_6,k9_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)) = k1_funct_1(k4_ami_1(c1_6__ami_6,c2_6__ami_6,k13_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6,k6_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)),c4_6__ami_6),k2_ami_1(c1_6__ami_6,c2_6__ami_6)) ) ) ) => ! [A] : ( m1_subset_1(A,k3_ami_1(c1_6__ami_6,c2_6__ami_6,c5_6__ami_6)) => ( ( c6_6__ami_6 = c5_6__ami_6 & c4_6__ami_6 = k8_ami_5(c1_6__ami_6,c2_6__ami_6,c3_6__ami_6,k16_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6),c5_6__ami_6,c6_6__ami_6,A)) ) => ( k13_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6,c5_6__ami_6) = A & k6_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6) = c5_6__ami_6 & k6_ami_1(c1_6__ami_6,c2_6__ami_6,k9_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)) = k1_funct_1(k4_ami_1(c1_6__ami_6,c2_6__ami_6,k13_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6,k6_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)),c4_6__ami_6),k2_ami_1(c1_6__ami_6,c2_6__ami_6)) ) ) ) ), introduced(definition,[new_symbol(c7_6__ami_6),file(ami_6,c7_6__ami_6)]), [interesting(0.8),axiom,file(ami_6,c7_6__ami_6)]). fof(cc3_int_1,theorem,( ! [A] : ( v4_ordinal2(A) => v1_int_1(A) ) ), file(int_1,cc3_int_1), [interesting(0.9),axiom,file(int_1,cc3_int_1)]). fof(cc3_nat_1,theorem,( ! [A] : ( v4_ordinal2(A) => ( v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(nat_1,cc3_nat_1), [interesting(0.9),axiom,file(nat_1,cc3_nat_1)]). fof(cc4_int_1,theorem,( ! [A] : ( v1_int_1(A) => ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(int_1,cc4_int_1), [interesting(0.9),axiom,file(int_1,cc4_int_1)]). fof(fc12_membered,theorem,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => v1_membered(k2_tarski(A,B)) ) ), file(membered,fc12_membered), [interesting(0.9),axiom,file(membered,fc12_membered)]). fof(fc13_membered,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) ) ) ), file(membered,fc13_membered), [interesting(0.9),axiom,file(membered,fc13_membered)]). fof(fc14_membered,theorem,( ! [A,B] : ( ( v1_rat_1(A) & v1_rat_1(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) ) ) ), file(membered,fc14_membered), [interesting(0.9),axiom,file(membered,fc14_membered)]). fof(fc15_membered,theorem,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) ) ) ), file(membered,fc15_membered), [interesting(0.9),axiom,file(membered,fc15_membered)]). fof(fc16_membered,theorem,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) & v5_membered(k2_tarski(A,B)) ) ) ), file(membered,fc16_membered), [interesting(0.9),axiom,file(membered,fc16_membered)]). fof(rc1_nat_1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(nat_1,rc1_nat_1), [interesting(0.9),axiom,file(nat_1,rc1_nat_1)]). fof(rc2_int_1,theorem,( ? [A] : v1_int_1(A) ), file(int_1,rc2_int_1), [interesting(0.9),axiom,file(int_1,rc2_int_1)]). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), [interesting(0.9),axiom,file(relset_1,m1_relset_1)]). fof(cc10_membered,theorem,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,A) => v1_xcmplx_0(B) ) ) ), file(membered,cc10_membered), [interesting(0.9),axiom,file(membered,cc10_membered)]). fof(cc11_membered,theorem,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) ) ) ) ), file(membered,cc11_membered), [interesting(0.9),axiom,file(membered,cc11_membered)]). fof(cc12_membered,theorem,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_rat_1(B) ) ) ) ), file(membered,cc12_membered), [interesting(0.9),axiom,file(membered,cc12_membered)]). fof(cc13_membered,theorem,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc13_membered), [interesting(0.9),axiom,file(membered,cc13_membered)]). fof(cc14_membered,theorem,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v4_ordinal2(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc14_membered), [interesting(0.9),axiom,file(membered,cc14_membered)]). fof(cc16_membered,theorem,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_membered(B) ) ) ), file(membered,cc16_membered), [interesting(0.9),axiom,file(membered,cc16_membered)]). fof(cc17_membered,theorem,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) ) ) ) ), file(membered,cc17_membered), [interesting(0.9),axiom,file(membered,cc17_membered)]). fof(cc18_membered,theorem,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) ) ) ) ), file(membered,cc18_membered), [interesting(0.9),axiom,file(membered,cc18_membered)]). fof(cc19_membered,theorem,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) ) ) ) ), file(membered,cc19_membered), [interesting(0.9),axiom,file(membered,cc19_membered)]). fof(cc1_membered,theorem,( ! [A] : ( v5_membered(A) => v4_membered(A) ) ), file(membered,cc1_membered), [interesting(0.9),axiom,file(membered,cc1_membered)]). fof(cc1_tex_2,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( ~ v1_tex_2(B,k1_zfmisc_1(A)) => ~ v1_xboole_0(B) ) ) ) ), file(tex_2,cc1_tex_2), [interesting(0.9),axiom,file(tex_2,cc1_tex_2)]). fof(cc20_membered,theorem,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) ) ) ) ), file(membered,cc20_membered), [interesting(0.9),axiom,file(membered,cc20_membered)]). fof(cc2_membered,theorem,( ! [A] : ( v4_membered(A) => v3_membered(A) ) ), file(membered,cc2_membered), [interesting(0.9),axiom,file(membered,cc2_membered)]). fof(cc3_membered,theorem,( ! [A] : ( v3_membered(A) => v2_membered(A) ) ), file(membered,cc3_membered), [interesting(0.9),axiom,file(membered,cc3_membered)]). fof(cc4_membered,theorem,( ! [A] : ( v2_membered(A) => v1_membered(A) ) ), file(membered,cc4_membered), [interesting(0.9),axiom,file(membered,cc4_membered)]). fof(fc22_membered,theorem,( ! [A,B] : ( ( v1_membered(A) & v1_membered(B) ) => v1_membered(k2_xboole_0(A,B)) ) ), file(membered,fc22_membered), [interesting(0.9),axiom,file(membered,fc22_membered)]). fof(fc23_membered,theorem,( ! [A,B] : ( ( v2_membered(A) & v2_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc23_membered), [interesting(0.9),axiom,file(membered,fc23_membered)]). fof(fc24_membered,theorem,( ! [A,B] : ( ( v3_membered(A) & v3_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc24_membered), [interesting(0.9),axiom,file(membered,fc24_membered)]). fof(fc25_membered,theorem,( ! [A,B] : ( ( v4_membered(A) & v4_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc25_membered), [interesting(0.9),axiom,file(membered,fc25_membered)]). fof(fc26_membered,theorem,( ! [A,B] : ( ( v5_membered(A) & v5_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) & v5_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc26_membered), [interesting(0.9),axiom,file(membered,fc26_membered)]). fof(fc4_ami_1,theorem,( ! [A,B,C] : ( ( v1_setfam_1(B) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) ) => ( ~ v1_xboole_0(k4_card_3(C)) & v1_fraenkel(k4_card_3(C)) ) ) ), file(ami_1,fc4_ami_1), [interesting(0.9),axiom,file(ami_1,fc4_ami_1)]). fof(rc1_amistd_2,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_fraenkel(A) & v1_pralg_2(A) & v1_amistd_2(A) ) ), file(amistd_2,rc1_amistd_2), [interesting(0.9),axiom,file(amistd_2,rc1_amistd_2)]). fof(rc1_membered,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ), file(membered,rc1_membered), [interesting(0.9),axiom,file(membered,rc1_membered)]). fof(rc2_tex_2,theorem,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ), file(tex_2,rc2_tex_2), [interesting(0.9),axiom,file(tex_2,rc2_tex_2)]). fof(rc3_funct_1,theorem,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ), file(funct_1,rc3_funct_1), [interesting(0.9),axiom,file(funct_1,rc3_funct_1)]). fof(rc3_tex_2,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ), file(tex_2,rc3_tex_2), [interesting(0.9),axiom,file(tex_2,rc3_tex_2)]). fof(rc4_tex_2,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ), file(tex_2,rc4_tex_2), [interesting(0.9),axiom,file(tex_2,rc4_tex_2)]). fof(commutativity_k2_tarski,theorem,( ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ), file(tarski,k2_tarski), [interesting(0.9),axiom,file(tarski,k2_tarski)]). fof(redefinition_m2_relset_1,definition,( ! [A,B,C] : ( m2_relset_1(C,A,B) <=> m1_relset_1(C,A,B) ) ), file(relset_1,m2_relset_1), [interesting(0.9),axiom,file(relset_1,m2_relset_1)]). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]). fof(dt_k2_tarski,axiom,( $true ), file(tarski,k2_tarski), [interesting(0.9),axiom,file(tarski,k2_tarski)]). fof(dt_k7_ami_1,axiom,( $true ), file(ami_1,k7_ami_1), [interesting(0.9),axiom,file(ami_1,k7_ami_1)]). fof(dt_l1_struct_0,axiom,( $true ), file(struct_0,l1_struct_0), [interesting(0.9),axiom,file(struct_0,l1_struct_0)]). fof(dt_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ), file(relset_1,m2_relset_1), [interesting(0.9),axiom,file(relset_1,m2_relset_1)]). fof(cc15_membered,theorem,( ! [A] : ( v1_xboole_0(A) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc15_membered), [interesting(0.9),axiom,file(membered,cc15_membered)]). fof(cc1_amistd_2,theorem,( ! [A] : ( v1_amistd_2(A) => ( v1_fraenkel(A) & v1_pralg_2(A) ) ) ), file(amistd_2,cc1_amistd_2), [interesting(0.9),axiom,file(amistd_2,cc1_amistd_2)]). fof(cc1_fraenkel,theorem,( ! [A] : ( v1_fraenkel(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ) ), file(fraenkel,cc1_fraenkel), [interesting(0.9),axiom,file(fraenkel,cc1_fraenkel)]). fof(cc1_funct_1,theorem,( ! [A] : ( v1_xboole_0(A) => v1_funct_1(A) ) ), file(funct_1,cc1_funct_1), [interesting(0.9),axiom,file(funct_1,cc1_funct_1)]). fof(cc1_relat_1,theorem,( ! [A] : ( v1_xboole_0(A) => v1_relat_1(A) ) ), file(relat_1,cc1_relat_1), [interesting(0.9),axiom,file(relat_1,cc1_relat_1)]). fof(cc1_relset_1,theorem,( ! [A,B,C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => v1_relat_1(C) ) ), file(relset_1,cc1_relset_1), [interesting(0.9),axiom,file(relset_1,cc1_relset_1)]). fof(cc1_setfam_1,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_setfam_1(A) ) => ! [B] : ( m1_subset_1(B,A) => ~ v1_xboole_0(B) ) ) ), file(setfam_1,cc1_setfam_1), [interesting(0.9),axiom,file(setfam_1,cc1_setfam_1)]). fof(cc2_funct_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ) ), file(funct_1,cc2_funct_1), [interesting(0.9),axiom,file(funct_1,cc2_funct_1)]). fof(cc2_tex_2,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_xboole_0(B) => v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ), file(tex_2,cc2_tex_2), [interesting(0.9),axiom,file(tex_2,cc2_tex_2)]). fof(fc10_ami_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( ~ v1_xboole_0(k7_ami_1(A)) & v1_fraenkel(k7_ami_1(A)) ) ) ), file(ami_1,fc10_ami_1), [interesting(0.9),axiom,file(ami_1,fc10_ami_1)]). fof(fc1_amistd_2,theorem,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) & ~ v1_xboole_0(B) ) => ( v1_relat_1(k1_funct_4(A,B)) & v1_funct_1(k1_funct_4(A,B)) & ~ v1_xboole_0(k1_funct_4(A,B)) & v1_setfam_1(k1_funct_4(A,B)) ) ) ), file(amistd_2,fc1_amistd_2), [interesting(0.9),axiom,file(amistd_2,fc1_amistd_2)]). fof(fc1_struct_0,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ~ v1_xboole_0(u1_struct_0(A)) ) ), file(struct_0,fc1_struct_0), [interesting(0.9),axiom,file(struct_0,fc1_struct_0)]). fof(fc2_amistd_2,theorem,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) & ~ v1_xboole_0(B) ) => ( v1_relat_1(k1_funct_4(B,A)) & v1_funct_1(k1_funct_4(B,A)) & ~ v1_xboole_0(k1_funct_4(B,A)) & v1_setfam_1(k1_funct_4(B,A)) ) ) ), file(amistd_2,fc2_amistd_2), [interesting(0.9),axiom,file(amistd_2,fc2_amistd_2)]). fof(fc2_xboole_0,theorem,( ! [A,B] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k2_xboole_0(A,B)) ) ), file(xboole_0,fc2_xboole_0), [interesting(0.9),axiom,file(xboole_0,fc2_xboole_0)]). fof(fc3_setfam_1,theorem,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ( ~ v1_xboole_0(k2_tarski(A,B)) & v1_setfam_1(k2_tarski(A,B)) ) ) ), file(setfam_1,fc3_setfam_1), [interesting(0.9),axiom,file(setfam_1,fc3_setfam_1)]). fof(fc3_xboole_0,theorem,( ! [A,B] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k2_xboole_0(B,A)) ) ), file(xboole_0,fc3_xboole_0), [interesting(0.9),axiom,file(xboole_0,fc3_xboole_0)]). fof(rc1_fraenkel,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_fraenkel(A) ) ), file(fraenkel,rc1_fraenkel), [interesting(0.9),axiom,file(fraenkel,rc1_fraenkel)]). fof(rc1_relat_1,theorem,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) ) ), file(relat_1,rc1_relat_1), [interesting(0.9),axiom,file(relat_1,rc1_relat_1)]). fof(rc1_setfam_1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_setfam_1(A) ) ), file(setfam_1,rc1_setfam_1), [interesting(0.9),axiom,file(setfam_1,rc1_setfam_1)]). fof(rc1_xboole_0,theorem,( ? [A] : v1_xboole_0(A) ), file(xboole_0,rc1_xboole_0), [interesting(0.9),axiom,file(xboole_0,rc1_xboole_0)]). fof(rc2_funct_1,theorem,( ? [A] : ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) ), file(funct_1,rc2_funct_1), [interesting(0.9),axiom,file(funct_1,rc2_funct_1)]). fof(rc2_relat_1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) ) ), file(relat_1,rc2_relat_1), [interesting(0.9),axiom,file(relat_1,rc2_relat_1)]). fof(rc2_xboole_0,theorem,( ? [A] : ~ v1_xboole_0(A) ), file(xboole_0,rc2_xboole_0), [interesting(0.9),axiom,file(xboole_0,rc2_xboole_0)]). fof(rc3_struct_0,theorem,( ? [A] : ( l1_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc3_struct_0), [interesting(0.9),axiom,file(struct_0,rc3_struct_0)]). fof(rc5_struct_0,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) ) ) ), file(struct_0,rc5_struct_0), [interesting(0.9),axiom,file(struct_0,rc5_struct_0)]). fof(idempotence_k1_funct_4,theorem,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => k1_funct_4(A,A) = A ) ), file(funct_4,k1_funct_4), [interesting(0.9),axiom,file(funct_4,k1_funct_4)]). fof(commutativity_k2_xboole_0,theorem,( ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ), file(xboole_0,k2_xboole_0), [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]). fof(idempotence_k2_xboole_0,theorem,( ! [A,B] : k2_xboole_0(A,A) = A ), file(xboole_0,k2_xboole_0), [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]). fof(redefinition_m1_struct_0,definition,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_struct_0(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(struct_0,m1_struct_0), [interesting(0.9),axiom,file(struct_0,m1_struct_0)]). fof(redefinition_m2_subset_1,definition,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(subset_1,m2_subset_1), [interesting(0.9),axiom,file(subset_1,m2_subset_1)]). fof(dt_k13_finseq_1,axiom,( $true ), file(finseq_1,k13_finseq_1), [interesting(0.9),axiom,file(finseq_1,k13_finseq_1)]). fof(dt_k1_funct_4,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => ( v1_relat_1(k1_funct_4(A,B)) & v1_funct_1(k1_funct_4(A,B)) ) ) ), file(funct_4,k1_funct_4), [interesting(0.9),axiom,file(funct_4,k1_funct_4)]). fof(dt_k2_xboole_0,axiom,( $true ), file(xboole_0,k2_xboole_0), [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), [interesting(0.9),axiom,file(zfmisc_1,k2_zfmisc_1)]). fof(dt_k3_ami_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(B) & l1_ami_1(B,A) & m1_subset_1(C,u1_struct_0(B)) ) => m1_subset_1(k3_ami_1(A,B,C),k2_xboole_0(A,k2_tarski(u4_ami_1(A,B),u2_ami_1(A,B)))) ) ), file(ami_1,k3_ami_1), [interesting(0.9),axiom,file(ami_1,k3_ami_1)]). fof(dt_k3_tarski,axiom,( $true ), file(tarski,k3_tarski), [interesting(0.9),axiom,file(tarski,k3_tarski)]). fof(dt_k4_card_3,axiom,( $true ), file(card_3,k4_card_3), [interesting(0.9),axiom,file(card_3,k4_card_3)]). fof(dt_k4_funct_4,axiom,( $true ), file(funct_4,k4_funct_4), [interesting(0.9),axiom,file(funct_4,k4_funct_4)]). fof(dt_l1_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => l1_struct_0(B) ) ), file(ami_1,l1_ami_1), [interesting(0.9),axiom,file(ami_1,l1_ami_1)]). fof(dt_m1_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ! [C] : ( m1_ami_1(C,A,B) => m1_subset_1(C,k7_ami_1(u5_ami_1(A,B))) ) ) ), file(ami_1,m1_ami_1), [interesting(0.9),axiom,file(ami_1,m1_ami_1)]). fof(dt_m1_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_struct_0(C,A,B) => m1_subset_1(C,u1_struct_0(A)) ) ) ), file(struct_0,m1_struct_0), [interesting(0.9),axiom,file(struct_0,m1_struct_0)]). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), [interesting(0.9),axiom,file(subset_1,m1_subset_1)]). fof(dt_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) => m1_subset_1(C,A) ) ) ), file(subset_1,m2_subset_1), [interesting(0.9),axiom,file(subset_1,m2_subset_1)]). fof(dt_u1_struct_0,axiom,( $true ), file(struct_0,u1_struct_0), [interesting(0.9),axiom,file(struct_0,u1_struct_0)]). fof(dt_u2_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => m1_subset_1(u2_ami_1(A,B),k1_zfmisc_1(u1_struct_0(B))) ) ), file(ami_1,u2_ami_1), [interesting(0.9),axiom,file(ami_1,u2_ami_1)]). fof(dt_u3_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ~ v1_xboole_0(u3_ami_1(A,B)) ) ), file(ami_1,u3_ami_1), [interesting(0.9),axiom,file(ami_1,u3_ami_1)]). fof(dt_u4_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ( ~ v1_xboole_0(u4_ami_1(A,B)) & m1_subset_1(u4_ami_1(A,B),k1_zfmisc_1(k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))))) ) ) ), file(ami_1,u4_ami_1), [interesting(0.9),axiom,file(ami_1,u4_ami_1)]). fof(dt_u5_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ( v1_funct_1(u5_ami_1(A,B)) & v1_funct_2(u5_ami_1(A,B),u1_struct_0(B),k2_xboole_0(A,k2_tarski(u4_ami_1(A,B),u2_ami_1(A,B)))) & m2_relset_1(u5_ami_1(A,B),u1_struct_0(B),k2_xboole_0(A,k2_tarski(u4_ami_1(A,B),u2_ami_1(A,B)))) ) ) ), file(ami_1,u5_ami_1), [interesting(0.9),axiom,file(ami_1,u5_ami_1)]). fof(fc11_ami_1,theorem,( ! [A,B,C] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,u1_struct_0(B)) ) => ~ v1_xboole_0(k3_ami_1(A,B,C)) ) ), file(ami_1,fc11_ami_1), [interesting(0.9),axiom,file(ami_1,fc11_ami_1)]). fof(fc16_finseq_1,theorem,( ! [A] : ( ~ v1_xboole_0(k13_finseq_1(A)) & v1_fraenkel(k13_finseq_1(A)) ) ), file(finseq_1,fc16_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc16_finseq_1)]). fof(fc2_ami_1,theorem,( ! [A,B] : ( ( ~ v2_ami_1(B,A) & l1_ami_1(B,A) ) => ~ v1_xboole_0(u2_ami_1(A,B)) ) ), file(ami_1,fc2_ami_1), [interesting(0.9),axiom,file(ami_1,fc2_ami_1)]). fof(fc2_relat_1,theorem,( ! [A,B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => v1_relat_1(k2_xboole_0(A,B)) ) ), file(relat_1,fc2_relat_1), [interesting(0.9),axiom,file(relat_1,fc2_relat_1)]). fof(fc3_ami_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => v1_fraenkel(k4_card_3(A)) ) ), file(ami_1,fc3_ami_1), [interesting(0.9),axiom,file(ami_1,fc3_ami_1)]). fof(fc4_setfam_1,theorem,( ! [A,B] : ( ( v1_setfam_1(A) & v1_setfam_1(B) ) => v1_setfam_1(k2_xboole_0(A,B)) ) ), file(setfam_1,fc4_setfam_1), [interesting(0.9),axiom,file(setfam_1,fc4_setfam_1)]). fof(fc5_amistd_2,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_fraenkel(k4_card_3(A)) & v1_amistd_2(k4_card_3(A)) ) ) ), file(amistd_2,fc5_amistd_2), [interesting(0.9),axiom,file(amistd_2,fc5_amistd_2)]). fof(fc9_finseq_1,theorem,( ! [A] : ~ v1_xboole_0(k13_finseq_1(A)) ), file(finseq_1,fc9_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc9_finseq_1)]). fof(rc1_funct_1,theorem,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc1_funct_1), [interesting(0.9),axiom,file(funct_1,rc1_funct_1)]). fof(rc2_ami_1,theorem,( ! [A] : ? [B] : ( l1_ami_1(B,A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) ) ), file(ami_1,rc2_ami_1), [interesting(0.9),axiom,file(ami_1,rc2_ami_1)]). fof(idempotence_k8_ami_5,theorem,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v2_ami_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) & m1_ami_1(D,A,B) ) => k8_ami_5(A,B,C,C) = C ) ), file(ami_5,k8_ami_5), [interesting(0.9),axiom,file(ami_5,k8_ami_5)]). fof(redefinition_k13_ami_1,definition,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) & m1_subset_1(D,u2_ami_1(A,B)) ) => k13_ami_1(A,B,C,D) = k1_funct_1(C,D) ) ), file(ami_1,k13_ami_1), [interesting(0.9),axiom,file(ami_1,k13_ami_1)]). fof(redefinition_k16_ami_1,definition,( ! [A,B,C,D,E,F] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(E,k3_ami_1(A,B,C)) & m1_subset_1(F,k3_ami_1(A,B,D)) ) => k16_ami_1(A,B,C,D,E,F) = k4_funct_4(C,D,E,F) ) ), file(ami_1,k16_ami_1), [interesting(0.9),axiom,file(ami_1,k16_ami_1)]). fof(redefinition_k8_ami_5,definition,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v2_ami_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) & m1_ami_1(D,A,B) ) => k8_ami_5(A,B,C,D) = k1_funct_4(C,D) ) ), file(ami_5,k8_ami_5), [interesting(0.9),axiom,file(ami_5,k8_ami_5)]). fof(dt_k13_ami_1,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) & m1_subset_1(D,u2_ami_1(A,B)) ) => m2_subset_1(k13_ami_1(A,B,C,D),k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B)) ) ), file(ami_1,k13_ami_1), [interesting(0.9),axiom,file(ami_1,k13_ami_1)]). fof(dt_k16_ami_1,axiom,( ! [A,B,C,D,E,F] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(E,k3_ami_1(A,B,C)) & m1_subset_1(F,k3_ami_1(A,B,D)) ) => m1_ami_1(k16_ami_1(A,B,C,D,E,F),A,B) ) ), file(ami_1,k16_ami_1), [interesting(0.9),axiom,file(ami_1,k16_ami_1)]). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), [interesting(0.9),axiom,file(funct_1,k1_funct_1)]). fof(dt_k2_ami_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & l1_ami_1(B,A) ) => m1_subset_1(k2_ami_1(A,B),u1_struct_0(B)) ) ), file(ami_1,k2_ami_1), [interesting(0.9),axiom,file(ami_1,k2_ami_1)]). fof(dt_k4_ami_1,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v2_ami_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,u4_ami_1(A,B)) & m1_subset_1(D,k4_card_3(u5_ami_1(A,B))) ) => m1_subset_1(k4_ami_1(A,B,C,D),k4_card_3(u5_ami_1(A,B))) ) ), file(ami_1,k4_ami_1), [interesting(0.9),axiom,file(ami_1,k4_ami_1)]). fof(dt_k6_ami_1,axiom,( ! [A,B,C] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) ) => m1_struct_0(k6_ami_1(A,B,C),B,u2_ami_1(A,B)) ) ), file(ami_1,k6_ami_1), [interesting(0.9),axiom,file(ami_1,k6_ami_1)]). fof(dt_k8_ami_5,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v2_ami_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) & m1_ami_1(D,A,B) ) => m1_subset_1(k8_ami_5(A,B,C,D),k4_card_3(u5_ami_1(A,B))) ) ), file(ami_5,k8_ami_5), [interesting(0.9),axiom,file(ami_5,k8_ami_5)]). fof(dt_k9_ami_1,axiom,( ! [A,B,C] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) ) => m1_subset_1(k9_ami_1(A,B,C),k4_card_3(u5_ami_1(A,B))) ) ), file(ami_1,k9_ami_1), [interesting(0.9),axiom,file(ami_1,k9_ami_1)]). fof(dt_c1_6__ami_6,assumption,( v1_setfam_1(c1_6__ami_6) ), introduced(assumption,[file(ami_6,c1_6__ami_6)]), [interesting(0.8),axiom,file(ami_6,c1_6__ami_6)]). fof(dt_c2_6__ami_6,assumption, ( ~ v3_struct_0(c2_6__ami_6) & ~ v2_ami_1(c2_6__ami_6,c1_6__ami_6) & v5_ami_1(c2_6__ami_6,c1_6__ami_6) & v8_ami_1(c2_6__ami_6,c1_6__ami_6) & v10_ami_1(c2_6__ami_6,c1_6__ami_6) & l1_ami_1(c2_6__ami_6,c1_6__ami_6) ), introduced(assumption,[file(ami_6,c2_6__ami_6)]), [interesting(0.8),axiom,file(ami_6,c2_6__ami_6)]). fof(dt_c3_6__ami_6,assumption,( m1_subset_1(c3_6__ami_6,k4_card_3(u5_ami_1(c1_6__ami_6,c2_6__ami_6))) ), introduced(assumption,[file(ami_6,c3_6__ami_6)]), [interesting(0.8),axiom,file(ami_6,c3_6__ami_6)]). fof(dt_c4_6__ami_6,assumption,( m1_subset_1(c4_6__ami_6,k4_card_3(u5_ami_1(c1_6__ami_6,c2_6__ami_6))) ), introduced(assumption,[file(ami_6,c4_6__ami_6)]), [interesting(0.8),axiom,file(ami_6,c4_6__ami_6)]). fof(dt_c5_6__ami_6,assumption,( m1_struct_0(c5_6__ami_6,c2_6__ami_6,u2_ami_1(c1_6__ami_6,c2_6__ami_6)) ), introduced(assumption,[file(ami_6,c5_6__ami_6)]), [interesting(0.8),axiom,file(ami_6,c5_6__ami_6)]). fof(dt_c6_6__ami_6,assumption,( m1_subset_1(c6_6__ami_6,k3_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6))) ), introduced(assumption,[file(ami_6,c6_6__ami_6)]), [interesting(0.8),axiom,file(ami_6,c6_6__ami_6)]). fof(dt_c7_6__ami_6,assumption,( m1_subset_1(c7_6__ami_6,k3_ami_1(c1_6__ami_6,c2_6__ami_6,c5_6__ami_6)) ), introduced(assumption,[file(ami_6,c7_6__ami_6)]), [interesting(0.8),axiom,file(ami_6,c7_6__ami_6)]). fof(e1_6__ami_6,assumption,( c6_6__ami_6 = c5_6__ami_6 ), introduced(assumption,[file(ami_6,e1_6__ami_6)]), [interesting(0.8),axiom,file(ami_6,e1_6__ami_6)]). fof(e2_6__ami_6,assumption,( c4_6__ami_6 = k8_ami_5(c1_6__ami_6,c2_6__ami_6,c3_6__ami_6,k16_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6),c5_6__ami_6,c6_6__ami_6,c7_6__ami_6)) ), introduced(assumption,[file(ami_6,e2_6__ami_6)]), [interesting(0.8),axiom,file(ami_6,e2_6__ami_6)]). fof(cc3_tex_2,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_realset1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_tex_2(B,k1_zfmisc_1(A)) => ( v1_xboole_0(B) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ), file(tex_2,cc3_tex_2), [interesting(0.9),axiom,file(tex_2,cc3_tex_2)]). fof(cc4_tex_2,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_realset1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( ~ v1_xboole_0(B) => ( ~ v1_xboole_0(B) & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ), file(tex_2,cc4_tex_2), [interesting(0.9),axiom,file(tex_2,cc4_tex_2)]). fof(cc5_tex_2,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_realset1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( ( ~ v1_xboole_0(B) & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) => ( ~ v1_xboole_0(B) & v1_realset1(B) & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ), file(tex_2,cc5_tex_2), [interesting(0.9),axiom,file(tex_2,cc5_tex_2)]). fof(cc6_tex_2,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_realset1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( ( ~ v1_xboole_0(B) & v1_realset1(B) ) => ( ~ v1_xboole_0(B) & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ), file(tex_2,cc6_tex_2), [interesting(0.9),axiom,file(tex_2,cc6_tex_2)]). fof(cc7_tex_2,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_realset1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( ( ~ v1_xboole_0(B) & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) => ( ~ v1_xboole_0(B) & ~ v1_realset1(B) ) ) ) ) ), file(tex_2,cc7_tex_2), [interesting(0.9),axiom,file(tex_2,cc7_tex_2)]). fof(rc1_tex_2,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_realset1(A) ) ), file(tex_2,rc1_tex_2), [interesting(0.9),axiom,file(tex_2,rc1_tex_2)]). fof(rc5_tex_2,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_realset1(B) ) ) ), file(tex_2,rc5_tex_2), [interesting(0.9),axiom,file(tex_2,rc5_tex_2)]). fof(rc6_tex_2,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_realset1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_realset1(B) & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ), file(tex_2,rc6_tex_2), [interesting(0.9),axiom,file(tex_2,rc6_tex_2)]). fof(rc7_tex_2,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_realset1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & ~ v1_realset1(B) & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ), file(tex_2,rc7_tex_2), [interesting(0.9),axiom,file(tex_2,rc7_tex_2)]). fof(reflexivity_r1_tarski,theorem,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), [interesting(0.9),axiom,file(tarski,r1_tarski)]). fof(existence_m1_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), [interesting(0.9),axiom,file(relset_1,m1_relset_1)]). fof(cc1_finseq_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ) ), file(finseq_1,cc1_finseq_1), [interesting(0.9),axiom,file(finseq_1,cc1_finseq_1)]). fof(cc1_scmring1,theorem,( ! [A] : ( ~ v1_finset_1(A) => ( ~ v1_xboole_0(A) & ~ v1_realset1(A) ) ) ), file(scmring1,cc1_scmring1), [interesting(0.9),axiom,file(scmring1,cc1_scmring1)]). fof(fc17_finseq_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) => v1_finset_1(k1_relat_1(A)) ) ), file(finseq_1,fc17_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc17_finseq_1)]). fof(fc3_amistd_2,theorem,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ( v1_relat_1(k1_funct_4(A,B)) & v1_funct_1(k1_funct_4(A,B)) & v1_finset_1(k1_funct_4(A,B)) & v1_setfam_1(k1_funct_4(A,B)) ) ) ), file(amistd_2,fc3_amistd_2), [interesting(0.9),axiom,file(amistd_2,fc3_amistd_2)]). fof(rc1_finseq_1,theorem,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc1_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc1_finseq_1)]). fof(rc3_finseq_1,theorem,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc3_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc3_finseq_1)]). fof(rc3_relat_1,theorem,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) ) ), file(relat_1,rc3_relat_1), [interesting(0.9),axiom,file(relat_1,rc3_relat_1)]). fof(rc4_funct_1,theorem,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc4_funct_1), [interesting(0.9),axiom,file(funct_1,rc4_funct_1)]). fof(rc6_finseq_1,theorem,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc6_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc6_finseq_1)]). fof(rc7_finseq_1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc7_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc7_finseq_1)]). fof(rc8_finseq_1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc8_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc8_finseq_1)]). fof(existence_l1_struct_0,axiom,( ? [A] : l1_struct_0(A) ), file(struct_0,l1_struct_0), [interesting(0.9),axiom,file(struct_0,l1_struct_0)]). fof(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), [interesting(0.9),axiom,file(relset_1,m2_relset_1)]). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]). fof(fc12_relat_1,theorem, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) ), file(relat_1,fc12_relat_1), [interesting(0.9),axiom,file(relat_1,fc12_relat_1)]). fof(fc1_xboole_0,theorem,( v1_xboole_0(k1_xboole_0) ), file(xboole_0,fc1_xboole_0), [interesting(0.9),axiom,file(xboole_0,fc1_xboole_0)]). fof(fc2_finseq_1,theorem, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) & v1_funct_1(k1_xboole_0) & v2_funct_1(k1_xboole_0) & v1_finset_1(k1_xboole_0) & v1_finseq_1(k1_xboole_0) ), file(finseq_1,fc2_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc2_finseq_1)]). fof(fc4_relat_1,theorem, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) ), file(relat_1,fc4_relat_1), [interesting(0.9),axiom,file(relat_1,fc4_relat_1)]). fof(fc6_membered,theorem, ( v1_xboole_0(k1_xboole_0) & v1_membered(k1_xboole_0) & v2_membered(k1_xboole_0) & v3_membered(k1_xboole_0) & v4_membered(k1_xboole_0) & v5_membered(k1_xboole_0) ), file(membered,fc6_membered), [interesting(0.9),axiom,file(membered,fc6_membered)]). fof(t1_boole,theorem,( ! [A] : k2_xboole_0(A,k1_xboole_0) = A ), file(boole,t1_boole), [interesting(0.9),axiom,file(boole,t1_boole)]). fof(t3_subset,theorem,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), [interesting(0.9),axiom,file(subset,t3_subset)]). fof(t4_subset,theorem,( ! [A,B,C] : ( ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) ) => m1_subset_1(A,C) ) ), file(subset,t4_subset), [interesting(0.9),axiom,file(subset,t4_subset)]). fof(t5_subset,theorem,( ! [A,B,C] : ~ ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C) ) ), file(subset,t5_subset), [interesting(0.9),axiom,file(subset,t5_subset)]). fof(existence_l1_ami_1,axiom,( ! [A] : ? [B] : l1_ami_1(B,A) ), file(ami_1,l1_ami_1), [interesting(0.9),axiom,file(ami_1,l1_ami_1)]). fof(existence_m1_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ? [C] : m1_ami_1(C,A,B) ) ), file(ami_1,m1_ami_1), [interesting(0.9),axiom,file(ami_1,m1_ami_1)]). fof(existence_m1_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ? [C] : m1_struct_0(C,A,B) ) ), file(struct_0,m1_struct_0), [interesting(0.9),axiom,file(struct_0,m1_struct_0)]). fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), [interesting(0.9),axiom,file(subset_1,m1_subset_1)]). fof(existence_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ? [C] : m2_subset_1(C,A,B) ) ), file(subset_1,m2_subset_1), [interesting(0.9),axiom,file(subset_1,m2_subset_1)]). fof(fc5_relat_1,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) ) => ~ v1_xboole_0(k1_relat_1(A)) ) ), file(relat_1,fc5_relat_1), [interesting(0.9),axiom,file(relat_1,fc5_relat_1)]). fof(fc7_relat_1,theorem,( ! [A] : ( v1_xboole_0(A) => ( v1_xboole_0(k1_relat_1(A)) & v1_relat_1(k1_relat_1(A)) ) ) ), file(relat_1,fc7_relat_1), [interesting(0.9),axiom,file(relat_1,fc7_relat_1)]). fof(t2_subset,theorem,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), [interesting(0.9),axiom,file(subset,t2_subset)]). fof(t6_boole,theorem,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), [interesting(0.9),axiom,file(boole,t6_boole)]). fof(t8_boole,theorem,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), [interesting(0.9),axiom,file(boole,t8_boole)]). fof(antisymmetry_r2_hidden,theorem,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), [interesting(0.9),axiom,file(hidden,r2_hidden)]). fof(dt_k1_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), [interesting(0.9),axiom,file(relat_1,k1_relat_1)]). fof(t1_subset,theorem,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), [interesting(0.9),axiom,file(subset,t1_subset)]). fof(t7_boole,theorem,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), [interesting(0.9),axiom,file(boole,t7_boole)]). fof(commutativity_k2_struct_0,theorem,( ! [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), [interesting(0.9),axiom,file(struct_0,k2_struct_0)]). fof(redefinition_k2_struct_0,definition,( ! [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), [interesting(0.9),axiom,file(struct_0,k2_struct_0)]). 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), [interesting(0.9),axiom,file(struct_0,k2_struct_0)]). fof(fc11_finseq_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_finset_1(A) ) => v1_finset_1(k2_relat_1(A)) ) ), file(finseq_1,fc11_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc11_finseq_1)]). fof(fc6_relat_1,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) ) => ~ v1_xboole_0(k2_relat_1(A)) ) ), file(relat_1,fc6_relat_1), [interesting(0.9),axiom,file(relat_1,fc6_relat_1)]). fof(fc8_relat_1,theorem,( ! [A] : ( v1_xboole_0(A) => ( v1_xboole_0(k2_relat_1(A)) & v1_relat_1(k2_relat_1(A)) ) ) ), file(relat_1,fc8_relat_1), [interesting(0.9),axiom,file(relat_1,fc8_relat_1)]). fof(dt_k2_relat_1,axiom,( $true ), file(relat_1,k2_relat_1), [interesting(0.9),axiom,file(relat_1,k2_relat_1)]). fof(t65_funct_4,theorem,( ! [A,B,C,D] : ( k1_relat_1(k4_funct_4(A,B,C,D)) = k2_tarski(A,B) & r1_tarski(k2_relat_1(k4_funct_4(A,B,C,D)),k2_tarski(C,D)) ) ), file(funct_4,t65_funct_4), [interesting(0.9),axiom,file(funct_4,t65_funct_4)]). fof(e3_6__ami_6,plain,( k1_relat_1(k16_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6),c5_6__ami_6,c6_6__ami_6,c7_6__ami_6)) = k2_struct_0(c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6),c5_6__ami_6) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c5_6__ami_6,dt_c6_6__ami_6,dt_c7_6__ami_6])],[cc3_tex_2,cc4_tex_2,cc5_tex_2,cc6_tex_2,cc7_tex_2,rc1_tex_2,rc5_tex_2,rc6_tex_2,rc7_tex_2,existence_m1_relset_1,dt_m1_relset_1,cc1_finseq_1,cc1_fraenkel,cc1_scmring1,cc3_int_1,cc3_nat_1,cc4_int_1,fc11_finseq_1,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc17_finseq_1,rc1_finseq_1,rc1_fraenkel,rc1_nat_1,rc2_int_1,rc3_finseq_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_k3_tarski,dt_m2_relset_1,dt_u3_ami_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc1_tex_2,cc20_membered,cc2_funct_1,cc2_membered,cc3_membered,cc4_membered,fc10_ami_1,fc12_relat_1,fc16_finseq_1,fc1_xboole_0,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc4_relat_1,fc6_membered,fc9_finseq_1,rc1_funct_1,rc1_membered,rc2_funct_1,rc2_tex_2,rc3_tex_2,rc4_tex_2,t1_boole,t1_subset,t4_subset,t5_subset,commutativity_k2_xboole_0,idempotence_k2_xboole_0,dt_k2_xboole_0,dt_k7_ami_1,dt_u4_ami_1,dt_u5_ami_1,cc15_membered,cc1_funct_1,cc1_relat_1,cc1_setfam_1,cc2_tex_2,fc2_relat_1,fc2_xboole_0,fc3_setfam_1,fc3_xboole_0,fc4_setfam_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_relat_1,rc1_setfam_1,rc1_xboole_0,rc2_relat_1,rc2_xboole_0,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_ami_1,existence_l1_struct_0,existence_m1_ami_1,existence_m1_struct_0,existence_m1_subset_1,redefinition_m1_struct_0,dt_k1_zfmisc_1,dt_k3_ami_1,dt_l1_ami_1,dt_l1_struct_0,dt_m1_ami_1,dt_m1_struct_0,dt_m1_subset_1,dt_u1_struct_0,dt_u2_ami_1,fc11_ami_1,fc1_struct_0,fc2_ami_1,rc2_ami_1,rc3_struct_0,commutativity_k2_struct_0,commutativity_k2_tarski,reflexivity_r1_tarski,redefinition_k16_ami_1,redefinition_k2_struct_0,dt_k16_ami_1,dt_k1_relat_1,dt_k2_ami_1,dt_k2_relat_1,dt_k2_struct_0,dt_k2_tarski,dt_k4_funct_4,dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c5_6__ami_6,dt_c6_6__ami_6,dt_c7_6__ami_6,t3_subset,t65_funct_4]), [interesting(0.8),file(ami_6,e3_6__ami_6),[file(ami_6,e3_6__ami_6)]]). fof(d2_tarski,definition,( ! [A,B,C] : ( C = k2_tarski(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( D = A | D = B ) ) ) ), file(tarski,d2_tarski), [interesting(0.9),axiom,file(tarski,d2_tarski)]). fof(e6_6__ami_6,plain,( r2_hidden(c5_6__ami_6,k1_relat_1(k16_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6),c5_6__ami_6,c6_6__ami_6,c7_6__ami_6))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c5_6__ami_6,dt_c6_6__ami_6,dt_c7_6__ami_6])],[existence_m1_relset_1,dt_m1_relset_1,cc3_tex_2,cc4_tex_2,cc5_tex_2,cc6_tex_2,cc7_tex_2,rc1_tex_2,rc5_tex_2,rc6_tex_2,rc7_tex_2,existence_m2_relset_1,redefinition_m2_relset_1,dt_k13_finseq_1,dt_k2_zfmisc_1,dt_k3_tarski,dt_m2_relset_1,dt_u3_ami_1,cc1_finseq_1,cc1_fraenkel,cc1_relset_1,cc1_scmring1,cc3_int_1,cc3_nat_1,cc4_int_1,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_finseq_1,fc16_membered,fc17_finseq_1,fc9_finseq_1,rc1_finseq_1,rc1_fraenkel,rc1_nat_1,rc2_int_1,rc3_finseq_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_xboole_0,dt_k7_ami_1,dt_u4_ami_1,dt_u5_ami_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_tex_2,cc20_membered,cc2_funct_1,cc2_membered,cc3_membered,cc4_membered,fc10_ami_1,fc12_relat_1,fc1_xboole_0,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc2_relat_1,fc2_xboole_0,fc3_xboole_0,fc4_relat_1,fc4_setfam_1,fc6_membered,rc1_funct_1,rc1_membered,rc2_funct_1,rc2_tex_2,rc3_tex_2,rc4_tex_2,t1_boole,existence_l1_ami_1,existence_l1_struct_0,existence_m1_ami_1,existence_m1_struct_0,existence_m1_subset_1,redefinition_m1_struct_0,dt_k1_zfmisc_1,dt_k3_ami_1,dt_k4_funct_4,dt_l1_ami_1,dt_l1_struct_0,dt_m1_ami_1,dt_m1_struct_0,dt_m1_subset_1,dt_u1_struct_0,dt_u2_ami_1,cc15_membered,cc1_funct_1,cc1_relat_1,cc1_setfam_1,cc2_tex_2,fc11_ami_1,fc1_struct_0,fc2_ami_1,fc3_setfam_1,fc5_relat_1,fc7_relat_1,rc1_relat_1,rc1_setfam_1,rc1_xboole_0,rc2_ami_1,rc2_relat_1,rc2_xboole_0,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k2_struct_0,commutativity_k2_tarski,antisymmetry_r2_hidden,redefinition_k16_ami_1,redefinition_k2_struct_0,dt_k16_ami_1,dt_k1_relat_1,dt_k2_ami_1,dt_k2_struct_0,dt_k2_tarski,dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c5_6__ami_6,dt_c6_6__ami_6,dt_c7_6__ami_6,t1_subset,t7_boole,e3_6__ami_6,d2_tarski]), [interesting(0.8),file(ami_6,e6_6__ami_6),[file(ami_6,e6_6__ami_6)]]). fof(t14_funct_4,theorem,( ! [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(k1_funct_4(C,B),A) = k1_funct_1(B,A) ) ) ) ), file(funct_4,t14_funct_4), [interesting(0.9),axiom,file(funct_4,t14_funct_4)]). fof(e1_6_1__ami_6,plain,( k13_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6,c5_6__ami_6) = k1_funct_1(k16_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6),c5_6__ami_6,c6_6__ami_6,c7_6__ami_6),c5_6__ami_6) ), inference(mizar_by,[status(thm),assumptions([dt_c3_6__ami_6,dt_c4_6__ami_6,dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c5_6__ami_6,dt_c6_6__ami_6,dt_c7_6__ami_6,e2_6__ami_6])],[cc3_tex_2,cc4_tex_2,cc5_tex_2,cc6_tex_2,cc7_tex_2,rc1_tex_2,rc5_tex_2,rc6_tex_2,rc7_tex_2,reflexivity_r1_tarski,existence_m1_relset_1,dt_m1_relset_1,cc1_finseq_1,cc1_scmring1,cc1_tex_2,cc3_int_1,cc3_nat_1,cc4_int_1,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc17_finseq_1,fc3_amistd_2,fc4_ami_1,rc1_amistd_2,rc1_finseq_1,rc1_nat_1,rc2_int_1,rc2_tex_2,rc3_finseq_1,rc3_relat_1,rc3_tex_2,rc4_funct_1,rc4_tex_2,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,commutativity_k2_tarski,existence_l1_struct_0,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_tarski,dt_k7_ami_1,dt_l1_struct_0,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_amistd_2,cc1_fraenkel,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc2_tex_2,cc3_membered,cc4_membered,fc10_ami_1,fc12_relat_1,fc1_struct_0,fc1_xboole_0,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc3_setfam_1,fc4_relat_1,fc6_membered,rc1_fraenkel,rc1_membered,rc3_funct_1,rc3_struct_0,rc5_struct_0,t1_boole,t3_subset,t4_subset,t5_subset,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_l1_ami_1,existence_m1_ami_1,existence_m1_struct_0,existence_m1_subset_1,existence_m2_subset_1,redefinition_m1_struct_0,redefinition_m2_subset_1,dt_k13_finseq_1,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_ami_1,dt_k3_tarski,dt_k4_card_3,dt_k4_funct_4,dt_l1_ami_1,dt_m1_ami_1,dt_m1_struct_0,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,dt_u2_ami_1,dt_u3_ami_1,dt_u4_ami_1,dt_u5_ami_1,cc15_membered,cc1_funct_1,cc1_relat_1,cc1_setfam_1,cc2_funct_1,fc11_ami_1,fc16_finseq_1,fc1_amistd_2,fc2_ami_1,fc2_amistd_2,fc2_relat_1,fc2_xboole_0,fc3_ami_1,fc3_xboole_0,fc4_setfam_1,fc5_amistd_2,fc5_relat_1,fc7_relat_1,fc9_finseq_1,rc1_relat_1,rc1_setfam_1,rc1_xboole_0,rc2_ami_1,rc2_funct_1,rc2_relat_1,rc2_xboole_0,t2_subset,t6_boole,t8_boole,idempotence_k1_funct_4,idempotence_k8_ami_5,antisymmetry_r2_hidden,redefinition_k13_ami_1,redefinition_k16_ami_1,redefinition_k8_ami_5,dt_k13_ami_1,dt_k16_ami_1,dt_k1_funct_1,dt_k1_funct_4,dt_k1_relat_1,dt_k2_ami_1,dt_k8_ami_5,dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c3_6__ami_6,dt_c4_6__ami_6,dt_c5_6__ami_6,dt_c6_6__ami_6,dt_c7_6__ami_6,rc1_funct_1,t1_subset,t7_boole,e6_6__ami_6,e2_6__ami_6,t14_funct_4]), [interesting(0.65),file(ami_6,e1_6_1__ami_6),[file(ami_6,e1_6_1__ami_6)]]). fof(t48_ami_1,theorem,( ! [A,B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) ) => ( v10_ami_1(B,A) => ! [C] : ( m1_struct_0(C,B,u2_ami_1(A,B)) => k2_ami_1(A,B) != C ) ) ) ), file(ami_1,t48_ami_1), [interesting(0.9),axiom,file(ami_1,t48_ami_1)]). fof(e5_6__ami_6,plain,( k2_ami_1(c1_6__ami_6,c2_6__ami_6) != c5_6__ami_6 ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c5_6__ami_6])],[cc3_tex_2,cc4_tex_2,cc5_tex_2,cc6_tex_2,cc7_tex_2,rc1_tex_2,rc5_tex_2,rc6_tex_2,rc7_tex_2,cc1_finseq_1,cc1_scmring1,cc3_int_1,cc3_nat_1,cc4_int_1,rc1_finseq_1,rc1_nat_1,rc2_int_1,rc3_finseq_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_tex_2,cc20_membered,cc2_funct_1,cc2_membered,cc3_membered,cc4_membered,fc12_relat_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,fc6_membered,rc1_funct_1,rc1_membered,rc1_relat_1,rc2_funct_1,rc2_relat_1,rc2_tex_2,rc3_tex_2,rc4_tex_2,t1_subset,t4_subset,t5_subset,existence_l1_struct_0,existence_m1_subset_1,dt_k1_zfmisc_1,dt_l1_struct_0,dt_m1_subset_1,dt_u1_struct_0,cc15_membered,cc1_funct_1,cc1_relat_1,cc1_setfam_1,cc2_tex_2,fc1_struct_0,rc1_setfam_1,rc1_xboole_0,rc2_xboole_0,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,existence_l1_ami_1,existence_m1_struct_0,redefinition_m1_struct_0,dt_k2_ami_1,dt_l1_ami_1,dt_m1_struct_0,dt_u2_ami_1,dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c5_6__ami_6,fc2_ami_1,rc2_ami_1,t48_ami_1]), [interesting(0.8),file(ami_6,e5_6__ami_6),[file(ami_6,e5_6__ami_6)]]). fof(t66_funct_4,theorem,( ! [A,B,C,D] : ( A != B => ( k1_funct_1(k4_funct_4(A,B,C,D),A) = C & k1_funct_1(k4_funct_4(A,B,C,D),B) = D ) ) ), file(funct_4,t66_funct_4), [interesting(0.9),axiom,file(funct_4,t66_funct_4)]). fof(e2_6_1__ami_6,plain,( k1_funct_1(k16_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6),c5_6__ami_6,c6_6__ami_6,c7_6__ami_6),c5_6__ami_6) = c7_6__ami_6 ), inference(mizar_by,[status(thm),assumptions([dt_c6_6__ami_6,dt_c7_6__ami_6,dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c5_6__ami_6])],[cc3_tex_2,cc4_tex_2,cc5_tex_2,cc6_tex_2,cc7_tex_2,rc1_tex_2,rc5_tex_2,rc6_tex_2,rc7_tex_2,existence_m1_relset_1,dt_m1_relset_1,cc1_finseq_1,cc1_scmring1,cc3_int_1,cc3_nat_1,cc4_int_1,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,rc1_finseq_1,rc1_nat_1,rc2_int_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_k3_tarski,dt_m2_relset_1,dt_u3_ami_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_fraenkel,cc1_membered,cc1_relset_1,cc1_tex_2,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc12_relat_1,fc16_finseq_1,fc1_xboole_0,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc4_relat_1,fc6_membered,fc9_finseq_1,rc1_fraenkel,rc1_membered,rc2_tex_2,rc3_funct_1,rc3_tex_2,rc4_tex_2,t1_boole,t1_subset,t4_subset,t5_subset,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_l1_struct_0,dt_k1_zfmisc_1,dt_k2_tarski,dt_k2_xboole_0,dt_k7_ami_1,dt_l1_struct_0,dt_u4_ami_1,dt_u5_ami_1,cc15_membered,cc1_funct_1,cc1_relat_1,cc1_setfam_1,cc2_funct_1,cc2_tex_2,fc10_ami_1,fc1_struct_0,fc2_relat_1,fc2_xboole_0,fc3_setfam_1,fc3_xboole_0,fc4_setfam_1,rc1_relat_1,rc1_setfam_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,existence_l1_ami_1,existence_m1_ami_1,existence_m1_struct_0,existence_m1_subset_1,redefinition_m1_struct_0,dt_k3_ami_1,dt_l1_ami_1,dt_m1_ami_1,dt_m1_struct_0,dt_m1_subset_1,dt_u1_struct_0,dt_u2_ami_1,fc11_ami_1,fc2_ami_1,rc1_funct_1,rc2_ami_1,redefinition_k16_ami_1,dt_k16_ami_1,dt_k1_funct_1,dt_k2_ami_1,dt_k4_funct_4,dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c5_6__ami_6,dt_c6_6__ami_6,dt_c7_6__ami_6,e5_6__ami_6,t66_funct_4]), [interesting(0.65),file(ami_6,e2_6_1__ami_6),[file(ami_6,e2_6_1__ami_6)]]). fof(e7_6__ami_6,plain,( k13_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6,c5_6__ami_6) = c7_6__ami_6 ), inference(iterative_eq,[status(thm),assumptions([dt_c3_6__ami_6,dt_c4_6__ami_6,e2_6__ami_6,dt_c6_6__ami_6,dt_c7_6__ami_6,dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c5_6__ami_6])],[cc3_int_1,cc3_nat_1,cc4_int_1,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,rc1_nat_1,rc2_int_1,dt_m1_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_tex_2,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc4_ami_1,rc1_amistd_2,rc1_membered,rc2_tex_2,rc3_funct_1,rc3_tex_2,rc4_tex_2,commutativity_k2_tarski,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k2_tarski,dt_k7_ami_1,dt_l1_struct_0,dt_m2_relset_1,cc15_membered,cc1_amistd_2,cc1_fraenkel,cc1_funct_1,cc1_relat_1,cc1_relset_1,cc1_setfam_1,cc2_funct_1,cc2_tex_2,fc10_ami_1,fc1_struct_0,fc2_xboole_0,fc3_setfam_1,fc3_xboole_0,rc1_fraenkel,rc1_relat_1,rc1_setfam_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,rc3_struct_0,rc5_struct_0,commutativity_k2_xboole_0,idempotence_k2_xboole_0,redefinition_m1_struct_0,redefinition_m2_subset_1,dt_k13_finseq_1,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_ami_1,dt_k3_tarski,dt_k4_card_3,dt_k4_funct_4,dt_l1_ami_1,dt_m1_ami_1,dt_m1_struct_0,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,dt_u2_ami_1,dt_u3_ami_1,dt_u4_ami_1,dt_u5_ami_1,fc11_ami_1,fc16_finseq_1,fc2_ami_1,fc2_relat_1,fc3_ami_1,fc4_setfam_1,fc5_amistd_2,fc9_finseq_1,rc1_funct_1,rc2_ami_1,redefinition_k13_ami_1,redefinition_k16_ami_1,dt_k13_ami_1,dt_k16_ami_1,dt_k1_funct_1,dt_k2_ami_1,dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c4_6__ami_6,dt_c5_6__ami_6,dt_c6_6__ami_6,dt_c7_6__ami_6,e1_6_1__ami_6,e2_6_1__ami_6]), [interesting(0.8),file(ami_6,e7_6__ami_6),[file(ami_6,e7_6__ami_6)]]). fof(d15_ami_1,definition,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) => k6_ami_1(A,B,C) = k1_funct_1(C,k2_ami_1(A,B)) ) ) ) ), file(ami_1,d15_ami_1), [interesting(0.9),axiom,file(ami_1,d15_ami_1)]). fof(e1_6_2__ami_6,plain,( k6_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6) = k1_funct_1(c4_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c4_6__ami_6])],[cc3_tex_2,cc4_tex_2,cc5_tex_2,cc6_tex_2,cc7_tex_2,rc1_tex_2,rc5_tex_2,rc6_tex_2,rc7_tex_2,cc1_finseq_1,cc1_scmring1,cc3_int_1,cc3_nat_1,cc4_int_1,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,rc1_finseq_1,rc1_nat_1,rc2_int_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_tex_2,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc12_relat_1,fc1_xboole_0,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc4_relat_1,fc6_membered,rc1_amistd_2,rc1_membered,rc2_tex_2,rc3_funct_1,rc3_tex_2,rc4_tex_2,t1_boole,t1_subset,t4_subset,t5_subset,existence_m1_relset_1,dt_k13_finseq_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k3_tarski,dt_m1_relset_1,dt_u3_ami_1,cc15_membered,cc1_amistd_2,cc1_fraenkel,cc1_funct_1,cc1_relat_1,cc1_relset_1,cc1_setfam_1,cc2_funct_1,cc2_tex_2,fc16_finseq_1,fc2_xboole_0,fc3_setfam_1,fc3_xboole_0,fc4_ami_1,fc9_finseq_1,rc1_fraenkel,rc1_relat_1,rc1_setfam_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,rc5_struct_0,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_l1_struct_0,existence_m1_struct_0,existence_m2_relset_1,redefinition_m1_struct_0,redefinition_m2_relset_1,dt_k2_tarski,dt_k2_xboole_0,dt_l1_struct_0,dt_m1_struct_0,dt_m2_relset_1,dt_u1_struct_0,dt_u2_ami_1,dt_u4_ami_1,fc1_struct_0,fc2_ami_1,fc2_relat_1,fc3_ami_1,fc4_setfam_1,fc5_amistd_2,rc1_funct_1,rc3_struct_0,existence_l1_ami_1,existence_m1_subset_1,dt_k1_funct_1,dt_k2_ami_1,dt_k4_card_3,dt_k6_ami_1,dt_l1_ami_1,dt_m1_subset_1,dt_u5_ami_1,dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c4_6__ami_6,rc2_ami_1,d15_ami_1]), [interesting(0.65),file(ami_6,e1_6_2__ami_6),[file(ami_6,e1_6_2__ami_6)]]). fof(e4_6__ami_6,plain,( r2_hidden(k2_ami_1(c1_6__ami_6,c2_6__ami_6),k1_relat_1(k16_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6),c5_6__ami_6,c6_6__ami_6,c7_6__ami_6))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c5_6__ami_6,dt_c6_6__ami_6,dt_c7_6__ami_6])],[existence_m1_relset_1,dt_m1_relset_1,cc3_tex_2,cc4_tex_2,cc5_tex_2,cc6_tex_2,cc7_tex_2,rc1_tex_2,rc5_tex_2,rc6_tex_2,rc7_tex_2,existence_m2_relset_1,redefinition_m2_relset_1,dt_k13_finseq_1,dt_k2_zfmisc_1,dt_k3_tarski,dt_m2_relset_1,dt_u3_ami_1,cc1_finseq_1,cc1_fraenkel,cc1_relset_1,cc1_scmring1,cc3_int_1,cc3_nat_1,cc4_int_1,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_finseq_1,fc16_membered,fc17_finseq_1,fc9_finseq_1,rc1_finseq_1,rc1_fraenkel,rc1_nat_1,rc2_int_1,rc3_finseq_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_xboole_0,dt_k7_ami_1,dt_u4_ami_1,dt_u5_ami_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_tex_2,cc20_membered,cc2_funct_1,cc2_membered,cc3_membered,cc4_membered,fc10_ami_1,fc12_relat_1,fc1_xboole_0,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc2_relat_1,fc2_xboole_0,fc3_xboole_0,fc4_relat_1,fc4_setfam_1,fc6_membered,rc1_funct_1,rc1_membered,rc2_funct_1,rc2_tex_2,rc3_tex_2,rc4_tex_2,t1_boole,existence_l1_ami_1,existence_l1_struct_0,existence_m1_ami_1,existence_m1_struct_0,existence_m1_subset_1,redefinition_m1_struct_0,dt_k1_zfmisc_1,dt_k3_ami_1,dt_k4_funct_4,dt_l1_ami_1,dt_l1_struct_0,dt_m1_ami_1,dt_m1_struct_0,dt_m1_subset_1,dt_u1_struct_0,dt_u2_ami_1,cc15_membered,cc1_funct_1,cc1_relat_1,cc1_setfam_1,cc2_tex_2,fc11_ami_1,fc1_struct_0,fc2_ami_1,fc3_setfam_1,fc5_relat_1,fc7_relat_1,rc1_relat_1,rc1_setfam_1,rc1_xboole_0,rc2_ami_1,rc2_relat_1,rc2_xboole_0,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k2_struct_0,commutativity_k2_tarski,antisymmetry_r2_hidden,redefinition_k16_ami_1,redefinition_k2_struct_0,dt_k16_ami_1,dt_k1_relat_1,dt_k2_ami_1,dt_k2_struct_0,dt_k2_tarski,dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c5_6__ami_6,dt_c6_6__ami_6,dt_c7_6__ami_6,t1_subset,t7_boole,e3_6__ami_6,d2_tarski]), [interesting(0.8),file(ami_6,e4_6__ami_6),[file(ami_6,e4_6__ami_6)]]). fof(e2_6_2__ami_6,plain,( k1_funct_1(c4_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6)) = k1_funct_1(k16_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6),c5_6__ami_6,c6_6__ami_6,c7_6__ami_6),k2_ami_1(c1_6__ami_6,c2_6__ami_6)) ), inference(mizar_by,[status(thm),assumptions([dt_c3_6__ami_6,dt_c4_6__ami_6,e2_6__ami_6,dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c5_6__ami_6,dt_c6_6__ami_6,dt_c7_6__ami_6])],[cc3_tex_2,cc4_tex_2,cc5_tex_2,cc6_tex_2,cc7_tex_2,rc1_tex_2,rc5_tex_2,rc6_tex_2,rc7_tex_2,reflexivity_r1_tarski,existence_m1_relset_1,dt_k13_finseq_1,dt_k2_zfmisc_1,dt_k3_tarski,dt_m1_relset_1,dt_u3_ami_1,cc1_finseq_1,cc1_relset_1,cc1_scmring1,cc1_tex_2,cc3_int_1,cc3_nat_1,cc4_int_1,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_finseq_1,fc16_membered,fc17_finseq_1,fc3_amistd_2,fc4_ami_1,fc9_finseq_1,rc1_amistd_2,rc1_finseq_1,rc1_nat_1,rc2_int_1,rc2_tex_2,rc3_finseq_1,rc3_relat_1,rc3_tex_2,rc4_funct_1,rc4_tex_2,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_l1_struct_0,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_tarski,dt_k2_xboole_0,dt_k7_ami_1,dt_l1_struct_0,dt_m2_relset_1,dt_u4_ami_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_amistd_2,cc1_fraenkel,cc1_membered,cc20_membered,cc2_membered,cc2_tex_2,cc3_membered,cc4_membered,fc10_ami_1,fc12_relat_1,fc1_struct_0,fc1_xboole_0,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc2_relat_1,fc2_xboole_0,fc3_setfam_1,fc3_xboole_0,fc4_relat_1,fc4_setfam_1,fc6_membered,rc1_fraenkel,rc1_membered,rc3_funct_1,rc3_struct_0,rc5_struct_0,t1_boole,t3_subset,t4_subset,t5_subset,existence_l1_ami_1,existence_m1_ami_1,existence_m1_struct_0,existence_m1_subset_1,redefinition_m1_struct_0,dt_k3_ami_1,dt_k4_card_3,dt_k4_funct_4,dt_l1_ami_1,dt_m1_ami_1,dt_m1_struct_0,dt_m1_subset_1,dt_u1_struct_0,dt_u2_ami_1,dt_u5_ami_1,cc15_membered,cc1_funct_1,cc1_relat_1,cc1_setfam_1,cc2_funct_1,fc11_ami_1,fc1_amistd_2,fc2_ami_1,fc2_amistd_2,fc3_ami_1,fc5_amistd_2,fc5_relat_1,fc7_relat_1,rc1_relat_1,rc1_setfam_1,rc1_xboole_0,rc2_ami_1,rc2_funct_1,rc2_relat_1,rc2_xboole_0,t2_subset,t6_boole,t8_boole,idempotence_k1_funct_4,idempotence_k8_ami_5,antisymmetry_r2_hidden,redefinition_k16_ami_1,redefinition_k8_ami_5,dt_k16_ami_1,dt_k1_funct_1,dt_k1_funct_4,dt_k1_relat_1,dt_k2_ami_1,dt_k8_ami_5,dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c3_6__ami_6,dt_c4_6__ami_6,dt_c5_6__ami_6,dt_c6_6__ami_6,dt_c7_6__ami_6,rc1_funct_1,t1_subset,t7_boole,e2_6__ami_6,e4_6__ami_6,t14_funct_4]), [interesting(0.65),file(ami_6,e2_6_2__ami_6),[file(ami_6,e2_6_2__ami_6)]]). fof(e3_6_2__ami_6,plain,( k1_funct_1(k16_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6),c5_6__ami_6,c6_6__ami_6,c7_6__ami_6),k2_ami_1(c1_6__ami_6,c2_6__ami_6)) = c5_6__ami_6 ), inference(mizar_by,[status(thm),assumptions([dt_c6_6__ami_6,dt_c7_6__ami_6,e1_6__ami_6,dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c5_6__ami_6])],[cc3_tex_2,cc4_tex_2,cc5_tex_2,cc6_tex_2,cc7_tex_2,rc1_tex_2,rc5_tex_2,rc6_tex_2,rc7_tex_2,existence_m1_relset_1,dt_m1_relset_1,cc1_finseq_1,cc1_scmring1,cc3_int_1,cc3_nat_1,cc4_int_1,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,rc1_finseq_1,rc1_nat_1,rc2_int_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_k3_tarski,dt_m2_relset_1,dt_u3_ami_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_fraenkel,cc1_membered,cc1_relset_1,cc1_tex_2,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc12_relat_1,fc16_finseq_1,fc1_xboole_0,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc4_relat_1,fc6_membered,fc9_finseq_1,rc1_fraenkel,rc1_membered,rc2_tex_2,rc3_funct_1,rc3_tex_2,rc4_tex_2,t1_boole,t1_subset,t4_subset,t5_subset,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_l1_struct_0,dt_k1_zfmisc_1,dt_k2_tarski,dt_k2_xboole_0,dt_k7_ami_1,dt_l1_struct_0,dt_u4_ami_1,dt_u5_ami_1,cc15_membered,cc1_funct_1,cc1_relat_1,cc1_setfam_1,cc2_funct_1,cc2_tex_2,fc10_ami_1,fc1_struct_0,fc2_relat_1,fc2_xboole_0,fc3_setfam_1,fc3_xboole_0,fc4_setfam_1,rc1_relat_1,rc1_setfam_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,existence_l1_ami_1,existence_m1_ami_1,existence_m1_struct_0,existence_m1_subset_1,redefinition_m1_struct_0,dt_k3_ami_1,dt_l1_ami_1,dt_m1_ami_1,dt_m1_struct_0,dt_m1_subset_1,dt_u1_struct_0,dt_u2_ami_1,fc11_ami_1,fc2_ami_1,rc1_funct_1,rc2_ami_1,redefinition_k16_ami_1,dt_k16_ami_1,dt_k1_funct_1,dt_k2_ami_1,dt_k4_funct_4,dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c5_6__ami_6,dt_c6_6__ami_6,dt_c7_6__ami_6,e1_6__ami_6,e5_6__ami_6,t66_funct_4]), [interesting(0.65),file(ami_6,e3_6_2__ami_6),[file(ami_6,e3_6_2__ami_6)]]). fof(e8_6__ami_6,plain,( k6_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6) = c5_6__ami_6 ), inference(iterative_eq,[status(thm),assumptions([dt_c3_6__ami_6,dt_c4_6__ami_6,e2_6__ami_6,dt_c6_6__ami_6,dt_c7_6__ami_6,e1_6__ami_6,dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c5_6__ami_6])],[e1_6_2__ami_6,e2_6_2__ami_6,e3_6_2__ami_6]), [interesting(0.8),file(ami_6,e8_6__ami_6),[file(ami_6,e8_6__ami_6)]]). fof(dt_k8_ami_1,axiom,( ! [A,B,C] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) ) => m2_subset_1(k8_ami_1(A,B,C),k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B)) ) ), file(ami_1,k8_ami_1), [interesting(0.9),axiom,file(ami_1,k8_ami_1)]). fof(d18_ami_1,definition,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) => k9_ami_1(A,B,C) = k4_ami_1(A,B,k8_ami_1(A,B,C),C) ) ) ) ), file(ami_1,d18_ami_1), [interesting(0.9),axiom,file(ami_1,d18_ami_1)]). fof(e1_6_3__ami_6,plain,( k6_ami_1(c1_6__ami_6,c2_6__ami_6,k9_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)) = k6_ami_1(c1_6__ami_6,c2_6__ami_6,k4_ami_1(c1_6__ami_6,c2_6__ami_6,k8_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6),c4_6__ami_6)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c4_6__ami_6])],[cc3_tex_2,cc4_tex_2,cc5_tex_2,cc6_tex_2,cc7_tex_2,rc1_tex_2,rc5_tex_2,rc6_tex_2,rc7_tex_2,cc1_finseq_1,cc1_scmring1,cc3_int_1,cc3_nat_1,cc4_int_1,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,rc1_finseq_1,rc1_nat_1,rc2_int_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_tex_2,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc12_relat_1,fc1_xboole_0,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc4_relat_1,fc6_membered,rc1_amistd_2,rc1_membered,rc2_tex_2,rc3_funct_1,rc3_tex_2,rc4_tex_2,t1_boole,t1_subset,t4_subset,t5_subset,existence_m1_relset_1,dt_k1_zfmisc_1,dt_m1_relset_1,cc15_membered,cc1_amistd_2,cc1_fraenkel,cc1_funct_1,cc1_relat_1,cc1_relset_1,cc1_setfam_1,cc2_funct_1,cc2_tex_2,fc2_xboole_0,fc3_setfam_1,fc3_xboole_0,fc4_ami_1,rc1_fraenkel,rc1_relat_1,rc1_setfam_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,rc5_struct_0,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_l1_struct_0,existence_m1_struct_0,existence_m2_relset_1,existence_m2_subset_1,redefinition_m1_struct_0,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k13_finseq_1,dt_k2_tarski,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_tarski,dt_l1_struct_0,dt_m1_struct_0,dt_m2_relset_1,dt_m2_subset_1,dt_u1_struct_0,dt_u2_ami_1,dt_u3_ami_1,dt_u4_ami_1,fc16_finseq_1,fc1_struct_0,fc2_ami_1,fc2_relat_1,fc3_ami_1,fc4_setfam_1,fc5_amistd_2,fc9_finseq_1,rc1_funct_1,rc3_struct_0,existence_l1_ami_1,existence_m1_subset_1,dt_k4_ami_1,dt_k4_card_3,dt_k6_ami_1,dt_k8_ami_1,dt_k9_ami_1,dt_l1_ami_1,dt_m1_subset_1,dt_u5_ami_1,dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c4_6__ami_6,rc2_ami_1,d18_ami_1]), [interesting(0.65),file(ami_6,e1_6_3__ami_6),[file(ami_6,e1_6_3__ami_6)]]). fof(d17_ami_1,definition,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) => k8_ami_1(A,B,C) = k1_funct_1(C,k6_ami_1(A,B,C)) ) ) ) ), file(ami_1,d17_ami_1), [interesting(0.9),axiom,file(ami_1,d17_ami_1)]). fof(e2_6_3__ami_6,plain,( k6_ami_1(c1_6__ami_6,c2_6__ami_6,k4_ami_1(c1_6__ami_6,c2_6__ami_6,k8_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6),c4_6__ami_6)) = k6_ami_1(c1_6__ami_6,c2_6__ami_6,k4_ami_1(c1_6__ami_6,c2_6__ami_6,k13_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6,k6_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)),c4_6__ami_6)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c4_6__ami_6])],[cc3_tex_2,cc4_tex_2,cc5_tex_2,cc6_tex_2,cc7_tex_2,rc1_tex_2,rc5_tex_2,rc6_tex_2,rc7_tex_2,cc1_finseq_1,cc1_scmring1,cc3_int_1,cc3_nat_1,cc4_int_1,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,rc1_finseq_1,rc1_nat_1,rc2_int_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_tex_2,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc12_relat_1,fc1_xboole_0,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc4_relat_1,fc6_membered,rc1_amistd_2,rc1_membered,rc2_tex_2,rc3_funct_1,rc3_tex_2,rc4_tex_2,t1_boole,t1_subset,t4_subset,t5_subset,existence_m1_relset_1,dt_k1_zfmisc_1,dt_m1_relset_1,cc15_membered,cc1_amistd_2,cc1_fraenkel,cc1_funct_1,cc1_relat_1,cc1_relset_1,cc1_setfam_1,cc2_funct_1,cc2_tex_2,fc2_xboole_0,fc3_setfam_1,fc3_xboole_0,fc4_ami_1,rc1_fraenkel,rc1_relat_1,rc1_setfam_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,rc5_struct_0,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_l1_struct_0,existence_m1_struct_0,existence_m2_relset_1,existence_m2_subset_1,redefinition_m1_struct_0,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k13_finseq_1,dt_k2_tarski,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_tarski,dt_l1_struct_0,dt_m1_struct_0,dt_m2_relset_1,dt_m2_subset_1,dt_u1_struct_0,dt_u2_ami_1,dt_u3_ami_1,dt_u4_ami_1,fc16_finseq_1,fc1_struct_0,fc2_ami_1,fc2_relat_1,fc3_ami_1,fc4_setfam_1,fc5_amistd_2,fc9_finseq_1,rc1_funct_1,rc3_struct_0,existence_l1_ami_1,existence_m1_subset_1,redefinition_k13_ami_1,dt_k13_ami_1,dt_k1_funct_1,dt_k4_ami_1,dt_k4_card_3,dt_k6_ami_1,dt_k8_ami_1,dt_l1_ami_1,dt_m1_subset_1,dt_u5_ami_1,dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c4_6__ami_6,rc2_ami_1,d17_ami_1]), [interesting(0.65),file(ami_6,e2_6_3__ami_6),[file(ami_6,e2_6_3__ami_6)]]). fof(e3_6_3__ami_6,plain,( k6_ami_1(c1_6__ami_6,c2_6__ami_6,k4_ami_1(c1_6__ami_6,c2_6__ami_6,k13_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6,k6_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)),c4_6__ami_6)) = k1_funct_1(k4_ami_1(c1_6__ami_6,c2_6__ami_6,k13_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6,k6_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)),c4_6__ami_6),k2_ami_1(c1_6__ami_6,c2_6__ami_6)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c4_6__ami_6])],[cc3_tex_2,cc4_tex_2,cc5_tex_2,cc6_tex_2,cc7_tex_2,rc1_tex_2,rc5_tex_2,rc6_tex_2,rc7_tex_2,cc1_finseq_1,cc1_scmring1,cc3_int_1,cc3_nat_1,cc4_int_1,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,rc1_finseq_1,rc1_nat_1,rc2_int_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_tex_2,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc12_relat_1,fc1_xboole_0,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc4_relat_1,fc6_membered,rc1_amistd_2,rc1_membered,rc2_tex_2,rc3_funct_1,rc3_tex_2,rc4_tex_2,t1_boole,t1_subset,t4_subset,t5_subset,existence_m1_relset_1,dt_k1_zfmisc_1,dt_m1_relset_1,cc15_membered,cc1_amistd_2,cc1_fraenkel,cc1_funct_1,cc1_relat_1,cc1_relset_1,cc1_setfam_1,cc2_funct_1,cc2_tex_2,fc2_xboole_0,fc3_setfam_1,fc3_xboole_0,fc4_ami_1,rc1_fraenkel,rc1_relat_1,rc1_setfam_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,rc5_struct_0,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_l1_struct_0,existence_m1_struct_0,existence_m2_relset_1,existence_m2_subset_1,redefinition_m1_struct_0,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k13_finseq_1,dt_k2_tarski,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_tarski,dt_l1_struct_0,dt_m1_struct_0,dt_m2_relset_1,dt_m2_subset_1,dt_u1_struct_0,dt_u2_ami_1,dt_u3_ami_1,dt_u4_ami_1,fc16_finseq_1,fc1_struct_0,fc2_ami_1,fc2_relat_1,fc3_ami_1,fc4_setfam_1,fc5_amistd_2,fc9_finseq_1,rc1_funct_1,rc3_struct_0,existence_l1_ami_1,existence_m1_subset_1,redefinition_k13_ami_1,dt_k13_ami_1,dt_k1_funct_1,dt_k2_ami_1,dt_k4_ami_1,dt_k4_card_3,dt_k6_ami_1,dt_l1_ami_1,dt_m1_subset_1,dt_u5_ami_1,dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c4_6__ami_6,rc2_ami_1,d15_ami_1]), [interesting(0.65),file(ami_6,e3_6_3__ami_6),[file(ami_6,e3_6_3__ami_6)]]). fof(e9_6__ami_6,plain,( k6_ami_1(c1_6__ami_6,c2_6__ami_6,k9_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)) = k1_funct_1(k4_ami_1(c1_6__ami_6,c2_6__ami_6,k13_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6,k6_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)),c4_6__ami_6),k2_ami_1(c1_6__ami_6,c2_6__ami_6)) ), inference(iterative_eq,[status(thm),assumptions([dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c4_6__ami_6])],[cc3_int_1,cc3_nat_1,cc4_int_1,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,rc1_nat_1,rc2_int_1,dt_m1_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_tex_2,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc4_ami_1,rc1_amistd_2,rc1_membered,rc2_tex_2,rc3_funct_1,rc3_tex_2,rc4_tex_2,commutativity_k2_tarski,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k2_tarski,dt_l1_struct_0,dt_m2_relset_1,cc15_membered,cc1_amistd_2,cc1_fraenkel,cc1_funct_1,cc1_relat_1,cc1_relset_1,cc1_setfam_1,cc2_funct_1,cc2_tex_2,fc1_struct_0,fc2_xboole_0,fc3_setfam_1,fc3_xboole_0,rc1_fraenkel,rc1_relat_1,rc1_setfam_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,rc3_struct_0,rc5_struct_0,commutativity_k2_xboole_0,idempotence_k2_xboole_0,redefinition_m1_struct_0,redefinition_m2_subset_1,dt_k13_finseq_1,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_tarski,dt_k4_card_3,dt_l1_ami_1,dt_m1_struct_0,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,dt_u2_ami_1,dt_u3_ami_1,dt_u4_ami_1,dt_u5_ami_1,fc16_finseq_1,fc2_ami_1,fc2_relat_1,fc3_ami_1,fc4_setfam_1,fc5_amistd_2,fc9_finseq_1,rc1_funct_1,rc2_ami_1,redefinition_k13_ami_1,dt_k13_ami_1,dt_k1_funct_1,dt_k2_ami_1,dt_k4_ami_1,dt_k6_ami_1,dt_k8_ami_1,dt_k9_ami_1,dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c4_6__ami_6,e1_6_3__ami_6,e2_6_3__ami_6,e3_6_3__ami_6]), [interesting(0.8),file(ami_6,e9_6__ami_6),[file(ami_6,e9_6__ami_6)]]). fof(i10_6__ami_6,theorem,( $true ), introduced(tautology,[file(ami_6,i10_6__ami_6)]), [interesting(0.8),trivial,file(ami_6,i10_6__ami_6)]). fof(i9_6__ami_6,plain,( k6_ami_1(c1_6__ami_6,c2_6__ami_6,k9_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)) = k1_funct_1(k4_ami_1(c1_6__ami_6,c2_6__ami_6,k13_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6,k6_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)),c4_6__ami_6),k2_ami_1(c1_6__ami_6,c2_6__ami_6)) ), inference(conclusion,[status(thm),assumptions([dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c4_6__ami_6])],[cc3_int_1,cc3_nat_1,cc4_int_1,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,rc1_nat_1,rc2_int_1,dt_m1_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_tex_2,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc4_ami_1,rc1_amistd_2,rc1_membered,rc2_tex_2,rc3_funct_1,rc3_tex_2,rc4_tex_2,commutativity_k2_tarski,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k2_tarski,dt_l1_struct_0,dt_m2_relset_1,cc15_membered,cc1_amistd_2,cc1_fraenkel,cc1_funct_1,cc1_relat_1,cc1_relset_1,cc1_setfam_1,cc2_funct_1,cc2_tex_2,fc1_struct_0,fc2_xboole_0,fc3_setfam_1,fc3_xboole_0,rc1_fraenkel,rc1_relat_1,rc1_setfam_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,rc3_struct_0,rc5_struct_0,commutativity_k2_xboole_0,idempotence_k2_xboole_0,redefinition_m1_struct_0,redefinition_m2_subset_1,dt_k13_finseq_1,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_tarski,dt_k4_card_3,dt_l1_ami_1,dt_m1_struct_0,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,dt_u2_ami_1,dt_u3_ami_1,dt_u4_ami_1,dt_u5_ami_1,fc16_finseq_1,fc2_ami_1,fc2_relat_1,fc3_ami_1,fc4_setfam_1,fc5_amistd_2,fc9_finseq_1,rc1_funct_1,rc2_ami_1,redefinition_k13_ami_1,dt_k13_ami_1,dt_k1_funct_1,dt_k2_ami_1,dt_k4_ami_1,dt_k6_ami_1,dt_k9_ami_1,dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c4_6__ami_6,e9_6__ami_6,i10_6__ami_6]), [interesting(0.8),file(ami_6,i9_6__ami_6),[file(ami_6,i9_6__ami_6)]]). fof(i8_6__ami_6,plain, ( k6_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6) = c5_6__ami_6 & k6_ami_1(c1_6__ami_6,c2_6__ami_6,k9_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)) = k1_funct_1(k4_ami_1(c1_6__ami_6,c2_6__ami_6,k13_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6,k6_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)),c4_6__ami_6),k2_ami_1(c1_6__ami_6,c2_6__ami_6)) ), inference(conclusion,[status(thm),assumptions([dt_c3_6__ami_6,e2_6__ami_6,dt_c6_6__ami_6,dt_c7_6__ami_6,e1_6__ami_6,dt_c5_6__ami_6,dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c4_6__ami_6])],[cc3_int_1,cc3_nat_1,cc4_int_1,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,rc1_nat_1,rc2_int_1,dt_m1_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_tex_2,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc4_ami_1,rc1_amistd_2,rc1_membered,rc2_tex_2,rc3_funct_1,rc3_tex_2,rc4_tex_2,commutativity_k2_tarski,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k2_tarski,dt_l1_struct_0,dt_m2_relset_1,cc15_membered,cc1_amistd_2,cc1_fraenkel,cc1_funct_1,cc1_relat_1,cc1_relset_1,cc1_setfam_1,cc2_funct_1,cc2_tex_2,fc1_struct_0,fc2_xboole_0,fc3_setfam_1,fc3_xboole_0,rc1_fraenkel,rc1_relat_1,rc1_setfam_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,rc3_struct_0,rc5_struct_0,commutativity_k2_xboole_0,idempotence_k2_xboole_0,redefinition_m1_struct_0,redefinition_m2_subset_1,dt_k13_finseq_1,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_tarski,dt_k4_card_3,dt_l1_ami_1,dt_m1_struct_0,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,dt_u2_ami_1,dt_u3_ami_1,dt_u4_ami_1,dt_u5_ami_1,fc16_finseq_1,fc2_ami_1,fc2_relat_1,fc3_ami_1,fc4_setfam_1,fc5_amistd_2,fc9_finseq_1,rc1_funct_1,rc2_ami_1,redefinition_k13_ami_1,dt_k13_ami_1,dt_k1_funct_1,dt_k2_ami_1,dt_k4_ami_1,dt_k6_ami_1,dt_k9_ami_1,dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c4_6__ami_6,dt_c5_6__ami_6,e8_6__ami_6,i9_6__ami_6]), [interesting(0.8),file(ami_6,i8_6__ami_6),[file(ami_6,i8_6__ami_6)]]). fof(i7_6__ami_6,plain, ( k13_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6,c5_6__ami_6) = c7_6__ami_6 & k6_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6) = c5_6__ami_6 & k6_ami_1(c1_6__ami_6,c2_6__ami_6,k9_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)) = k1_funct_1(k4_ami_1(c1_6__ami_6,c2_6__ami_6,k13_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6,k6_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)),c4_6__ami_6),k2_ami_1(c1_6__ami_6,c2_6__ami_6)) ), inference(conclusion,[status(thm),assumptions([dt_c3_6__ami_6,e2_6__ami_6,dt_c6_6__ami_6,dt_c7_6__ami_6,e1_6__ami_6,dt_c5_6__ami_6,dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c4_6__ami_6])],[cc3_int_1,cc3_nat_1,cc4_int_1,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,rc1_nat_1,rc2_int_1,dt_m1_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_tex_2,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc4_ami_1,rc1_amistd_2,rc1_membered,rc2_tex_2,rc3_funct_1,rc3_tex_2,rc4_tex_2,commutativity_k2_tarski,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k2_tarski,dt_l1_struct_0,dt_m2_relset_1,cc15_membered,cc1_amistd_2,cc1_fraenkel,cc1_funct_1,cc1_relat_1,cc1_relset_1,cc1_setfam_1,cc2_funct_1,cc2_tex_2,fc1_struct_0,fc2_xboole_0,fc3_setfam_1,fc3_xboole_0,rc1_fraenkel,rc1_relat_1,rc1_setfam_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,rc3_struct_0,rc5_struct_0,commutativity_k2_xboole_0,idempotence_k2_xboole_0,redefinition_m1_struct_0,redefinition_m2_subset_1,dt_k13_finseq_1,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_ami_1,dt_k3_tarski,dt_k4_card_3,dt_l1_ami_1,dt_m1_struct_0,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,dt_u2_ami_1,dt_u3_ami_1,dt_u4_ami_1,dt_u5_ami_1,fc11_ami_1,fc16_finseq_1,fc2_ami_1,fc2_relat_1,fc3_ami_1,fc4_setfam_1,fc5_amistd_2,fc9_finseq_1,rc1_funct_1,rc2_ami_1,redefinition_k13_ami_1,dt_k13_ami_1,dt_k1_funct_1,dt_k2_ami_1,dt_k4_ami_1,dt_k6_ami_1,dt_k9_ami_1,dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c4_6__ami_6,dt_c5_6__ami_6,dt_c7_6__ami_6,e7_6__ami_6,i8_6__ami_6]), [interesting(0.8),file(ami_6,i7_6__ami_6),[file(ami_6,i7_6__ami_6)]]). fof(i7_6_tmp__ami_6,plain, ( ( c6_6__ami_6 = c5_6__ami_6 & c4_6__ami_6 = k8_ami_5(c1_6__ami_6,c2_6__ami_6,c3_6__ami_6,k16_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6),c5_6__ami_6,c6_6__ami_6,c7_6__ami_6)) ) => ( k13_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6,c5_6__ami_6) = c7_6__ami_6 & k6_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6) = c5_6__ami_6 & k6_ami_1(c1_6__ami_6,c2_6__ami_6,k9_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)) = k1_funct_1(k4_ami_1(c1_6__ami_6,c2_6__ami_6,k13_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6,k6_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)),c4_6__ami_6),k2_ami_1(c1_6__ami_6,c2_6__ami_6)) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c3_6__ami_6,dt_c6_6__ami_6,dt_c7_6__ami_6,dt_c5_6__ami_6,dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c4_6__ami_6]),discharge_asm(discharge,[e1_6__ami_6,e2_6__ami_6])],[e1_6__ami_6,e2_6__ami_6,i7_6__ami_6]), [interesting(0.8),i6_6__ami_6]). fof(i6_6__ami_6,plain, ( ( c6_6__ami_6 = c5_6__ami_6 & c4_6__ami_6 = k8_ami_5(c1_6__ami_6,c2_6__ami_6,c3_6__ami_6,k16_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6),c5_6__ami_6,c6_6__ami_6,c7_6__ami_6)) ) => ( k13_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6,c5_6__ami_6) = c7_6__ami_6 & k6_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6) = c5_6__ami_6 & k6_ami_1(c1_6__ami_6,c2_6__ami_6,k9_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)) = k1_funct_1(k4_ami_1(c1_6__ami_6,c2_6__ami_6,k13_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6,k6_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)),c4_6__ami_6),k2_ami_1(c1_6__ami_6,c2_6__ami_6)) ) ), inference(mizar_def_expansion,[status(thm),assumptions([dt_c3_6__ami_6,dt_c6_6__ami_6,dt_c7_6__ami_6,dt_c5_6__ami_6,dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c4_6__ami_6])],[i7_6_tmp__ami_6,cc3_int_1,cc3_nat_1,cc4_int_1,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,rc1_nat_1,rc2_int_1,dt_m1_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_tex_2,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc4_ami_1,rc1_amistd_2,rc1_membered,rc2_tex_2,rc3_funct_1,rc3_tex_2,rc4_tex_2,commutativity_k2_tarski,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k2_tarski,dt_k7_ami_1,dt_l1_struct_0,dt_m2_relset_1,cc15_membered,cc1_amistd_2,cc1_fraenkel,cc1_funct_1,cc1_relat_1,cc1_relset_1,cc1_setfam_1,cc2_funct_1,cc2_tex_2,fc10_ami_1,fc1_amistd_2,fc1_struct_0,fc2_amistd_2,fc2_xboole_0,fc3_setfam_1,fc3_xboole_0,rc1_fraenkel,rc1_relat_1,rc1_setfam_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,rc3_struct_0,rc5_struct_0,idempotence_k1_funct_4,commutativity_k2_xboole_0,idempotence_k2_xboole_0,redefinition_m1_struct_0,redefinition_m2_subset_1,dt_k13_finseq_1,dt_k1_funct_4,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_ami_1,dt_k3_tarski,dt_k4_card_3,dt_k4_funct_4,dt_l1_ami_1,dt_m1_ami_1,dt_m1_struct_0,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,dt_u2_ami_1,dt_u3_ami_1,dt_u4_ami_1,dt_u5_ami_1,fc11_ami_1,fc16_finseq_1,fc2_ami_1,fc2_relat_1,fc3_ami_1,fc4_setfam_1,fc5_amistd_2,fc9_finseq_1,rc1_funct_1,rc2_ami_1,idempotence_k8_ami_5,redefinition_k13_ami_1,redefinition_k16_ami_1,redefinition_k8_ami_5,dt_k13_ami_1,dt_k16_ami_1,dt_k1_funct_1,dt_k2_ami_1,dt_k4_ami_1,dt_k6_ami_1,dt_k8_ami_5,dt_k9_ami_1,dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c3_6__ami_6,dt_c4_6__ami_6,dt_c5_6__ami_6,dt_c6_6__ami_6,dt_c7_6__ami_6]), [interesting(0.8),file(ami_6,i6_6__ami_6),[file(ami_6,i6_6__ami_6)]]). fof(i6_6_tmp__ami_6,plain, ( m1_subset_1(c7_6__ami_6,k3_ami_1(c1_6__ami_6,c2_6__ami_6,c5_6__ami_6)) => ( ( c6_6__ami_6 = c5_6__ami_6 & c4_6__ami_6 = k8_ami_5(c1_6__ami_6,c2_6__ami_6,c3_6__ami_6,k16_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6),c5_6__ami_6,c6_6__ami_6,c7_6__ami_6)) ) => ( k13_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6,c5_6__ami_6) = c7_6__ami_6 & k6_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6) = c5_6__ami_6 & k6_ami_1(c1_6__ami_6,c2_6__ami_6,k9_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)) = k1_funct_1(k4_ami_1(c1_6__ami_6,c2_6__ami_6,k13_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6,k6_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)),c4_6__ami_6),k2_ami_1(c1_6__ami_6,c2_6__ami_6)) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c3_6__ami_6,dt_c6_6__ami_6,dt_c5_6__ami_6,dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c4_6__ami_6]),discharge_asm(discharge,[dt_c7_6__ami_6])],[dt_c7_6__ami_6,i6_6__ami_6]), [interesting(0.8),i5_6__ami_6]). fof(i5_6__ami_6,plain,( ! [A] : ( m1_subset_1(A,k3_ami_1(c1_6__ami_6,c2_6__ami_6,c5_6__ami_6)) => ( ( c6_6__ami_6 = c5_6__ami_6 & c4_6__ami_6 = k8_ami_5(c1_6__ami_6,c2_6__ami_6,c3_6__ami_6,k16_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6),c5_6__ami_6,c6_6__ami_6,A)) ) => ( k13_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6,c5_6__ami_6) = A & k6_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6) = c5_6__ami_6 & k6_ami_1(c1_6__ami_6,c2_6__ami_6,k9_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)) = k1_funct_1(k4_ami_1(c1_6__ami_6,c2_6__ami_6,k13_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6,k6_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)),c4_6__ami_6),k2_ami_1(c1_6__ami_6,c2_6__ami_6)) ) ) ) ), inference(let,[status(thm),assumptions([dt_c3_6__ami_6,dt_c6_6__ami_6,dt_c5_6__ami_6,dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c4_6__ami_6])],[i6_6_tmp__ami_6,dh_c7_6__ami_6]), [interesting(0.8),file(ami_6,i5_6__ami_6),[file(ami_6,i5_6__ami_6)]]). fof(i5_6_tmp__ami_6,plain, ( m1_subset_1(c6_6__ami_6,k3_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6))) => ! [A] : ( m1_subset_1(A,k3_ami_1(c1_6__ami_6,c2_6__ami_6,c5_6__ami_6)) => ( ( c6_6__ami_6 = c5_6__ami_6 & c4_6__ami_6 = k8_ami_5(c1_6__ami_6,c2_6__ami_6,c3_6__ami_6,k16_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6),c5_6__ami_6,c6_6__ami_6,A)) ) => ( k13_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6,c5_6__ami_6) = A & k6_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6) = c5_6__ami_6 & k6_ami_1(c1_6__ami_6,c2_6__ami_6,k9_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)) = k1_funct_1(k4_ami_1(c1_6__ami_6,c2_6__ami_6,k13_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6,k6_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)),c4_6__ami_6),k2_ami_1(c1_6__ami_6,c2_6__ami_6)) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c3_6__ami_6,dt_c5_6__ami_6,dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c4_6__ami_6]),discharge_asm(discharge,[dt_c6_6__ami_6])],[dt_c6_6__ami_6,i5_6__ami_6]), [interesting(0.8),i4_6__ami_6]). fof(i4_6__ami_6,plain,( ! [A] : ( m1_subset_1(A,k3_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6))) => ! [B] : ( m1_subset_1(B,k3_ami_1(c1_6__ami_6,c2_6__ami_6,c5_6__ami_6)) => ( ( A = c5_6__ami_6 & c4_6__ami_6 = k8_ami_5(c1_6__ami_6,c2_6__ami_6,c3_6__ami_6,k16_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6),c5_6__ami_6,A,B)) ) => ( k13_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6,c5_6__ami_6) = B & k6_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6) = c5_6__ami_6 & k6_ami_1(c1_6__ami_6,c2_6__ami_6,k9_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)) = k1_funct_1(k4_ami_1(c1_6__ami_6,c2_6__ami_6,k13_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6,k6_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)),c4_6__ami_6),k2_ami_1(c1_6__ami_6,c2_6__ami_6)) ) ) ) ) ), inference(let,[status(thm),assumptions([dt_c3_6__ami_6,dt_c5_6__ami_6,dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c4_6__ami_6])],[i5_6_tmp__ami_6,dh_c6_6__ami_6]), [interesting(0.8),file(ami_6,i4_6__ami_6),[file(ami_6,i4_6__ami_6)]]). fof(i4_6_tmp__ami_6,plain, ( m1_struct_0(c5_6__ami_6,c2_6__ami_6,u2_ami_1(c1_6__ami_6,c2_6__ami_6)) => ! [A] : ( m1_subset_1(A,k3_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6))) => ! [B] : ( m1_subset_1(B,k3_ami_1(c1_6__ami_6,c2_6__ami_6,c5_6__ami_6)) => ( ( A = c5_6__ami_6 & c4_6__ami_6 = k8_ami_5(c1_6__ami_6,c2_6__ami_6,c3_6__ami_6,k16_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6),c5_6__ami_6,A,B)) ) => ( k13_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6,c5_6__ami_6) = B & k6_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6) = c5_6__ami_6 & k6_ami_1(c1_6__ami_6,c2_6__ami_6,k9_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)) = k1_funct_1(k4_ami_1(c1_6__ami_6,c2_6__ami_6,k13_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6,k6_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)),c4_6__ami_6),k2_ami_1(c1_6__ami_6,c2_6__ami_6)) ) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c3_6__ami_6,dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c4_6__ami_6]),discharge_asm(discharge,[dt_c5_6__ami_6])],[dt_c5_6__ami_6,i4_6__ami_6]), [interesting(0.8),i3_6__ami_6]). fof(i3_6__ami_6,plain,( ! [A] : ( m1_struct_0(A,c2_6__ami_6,u2_ami_1(c1_6__ami_6,c2_6__ami_6)) => ! [B] : ( m1_subset_1(B,k3_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6))) => ! [C] : ( m1_subset_1(C,k3_ami_1(c1_6__ami_6,c2_6__ami_6,A)) => ( ( B = A & c4_6__ami_6 = k8_ami_5(c1_6__ami_6,c2_6__ami_6,c3_6__ami_6,k16_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6),A,B,C)) ) => ( k13_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6,A) = C & k6_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6) = A & k6_ami_1(c1_6__ami_6,c2_6__ami_6,k9_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)) = k1_funct_1(k4_ami_1(c1_6__ami_6,c2_6__ami_6,k13_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6,k6_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)),c4_6__ami_6),k2_ami_1(c1_6__ami_6,c2_6__ami_6)) ) ) ) ) ) ), inference(let,[status(thm),assumptions([dt_c3_6__ami_6,dt_c1_6__ami_6,dt_c2_6__ami_6,dt_c4_6__ami_6])],[i4_6_tmp__ami_6,dh_c5_6__ami_6]), [interesting(0.8),file(ami_6,i3_6__ami_6),[file(ami_6,i3_6__ami_6)]]). fof(i3_6_tmp__ami_6,plain, ( ( m1_subset_1(c3_6__ami_6,k4_card_3(u5_ami_1(c1_6__ami_6,c2_6__ami_6))) & m1_subset_1(c4_6__ami_6,k4_card_3(u5_ami_1(c1_6__ami_6,c2_6__ami_6))) ) => ! [A] : ( m1_struct_0(A,c2_6__ami_6,u2_ami_1(c1_6__ami_6,c2_6__ami_6)) => ! [B] : ( m1_subset_1(B,k3_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6))) => ! [C] : ( m1_subset_1(C,k3_ami_1(c1_6__ami_6,c2_6__ami_6,A)) => ( ( B = A & c4_6__ami_6 = k8_ami_5(c1_6__ami_6,c2_6__ami_6,c3_6__ami_6,k16_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6),A,B,C)) ) => ( k13_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6,A) = C & k6_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6) = A & k6_ami_1(c1_6__ami_6,c2_6__ami_6,k9_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)) = k1_funct_1(k4_ami_1(c1_6__ami_6,c2_6__ami_6,k13_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6,k6_ami_1(c1_6__ami_6,c2_6__ami_6,c4_6__ami_6)),c4_6__ami_6),k2_ami_1(c1_6__ami_6,c2_6__ami_6)) ) ) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_6__ami_6,dt_c2_6__ami_6]),discharge_asm(discharge,[dt_c3_6__ami_6,dt_c4_6__ami_6])],[dt_c3_6__ami_6,dt_c4_6__ami_6,i3_6__ami_6]), [interesting(0.8),i2_6__ami_6]). fof(i2_6__ami_6,plain,( ! [A] : ( m1_subset_1(A,k4_card_3(u5_ami_1(c1_6__ami_6,c2_6__ami_6))) => ! [B] : ( m1_subset_1(B,k4_card_3(u5_ami_1(c1_6__ami_6,c2_6__ami_6))) => ! [C] : ( m1_struct_0(C,c2_6__ami_6,u2_ami_1(c1_6__ami_6,c2_6__ami_6)) => ! [D] : ( m1_subset_1(D,k3_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6))) => ! [E] : ( m1_subset_1(E,k3_ami_1(c1_6__ami_6,c2_6__ami_6,C)) => ( ( D = C & B = k8_ami_5(c1_6__ami_6,c2_6__ami_6,A,k16_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6),C,D,E)) ) => ( k13_ami_1(c1_6__ami_6,c2_6__ami_6,B,C) = E & k6_ami_1(c1_6__ami_6,c2_6__ami_6,B) = C & k6_ami_1(c1_6__ami_6,c2_6__ami_6,k9_ami_1(c1_6__ami_6,c2_6__ami_6,B)) = k1_funct_1(k4_ami_1(c1_6__ami_6,c2_6__ami_6,k13_ami_1(c1_6__ami_6,c2_6__ami_6,B,k6_ami_1(c1_6__ami_6,c2_6__ami_6,B)),B),k2_ami_1(c1_6__ami_6,c2_6__ami_6)) ) ) ) ) ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_6__ami_6,dt_c2_6__ami_6])],[i3_6_tmp__ami_6,dh_c3_6__ami_6,dh_c4_6__ami_6]), [interesting(0.8),file(ami_6,i2_6__ami_6),[file(ami_6,i2_6__ami_6)]]). fof(i2_6_tmp__ami_6,plain, ( ( ~ v3_struct_0(c2_6__ami_6) & ~ v2_ami_1(c2_6__ami_6,c1_6__ami_6) & v5_ami_1(c2_6__ami_6,c1_6__ami_6) & v8_ami_1(c2_6__ami_6,c1_6__ami_6) & v10_ami_1(c2_6__ami_6,c1_6__ami_6) & l1_ami_1(c2_6__ami_6,c1_6__ami_6) ) => ! [A] : ( m1_subset_1(A,k4_card_3(u5_ami_1(c1_6__ami_6,c2_6__ami_6))) => ! [B] : ( m1_subset_1(B,k4_card_3(u5_ami_1(c1_6__ami_6,c2_6__ami_6))) => ! [C] : ( m1_struct_0(C,c2_6__ami_6,u2_ami_1(c1_6__ami_6,c2_6__ami_6)) => ! [D] : ( m1_subset_1(D,k3_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6))) => ! [E] : ( m1_subset_1(E,k3_ami_1(c1_6__ami_6,c2_6__ami_6,C)) => ( ( D = C & B = k8_ami_5(c1_6__ami_6,c2_6__ami_6,A,k16_ami_1(c1_6__ami_6,c2_6__ami_6,k2_ami_1(c1_6__ami_6,c2_6__ami_6),C,D,E)) ) => ( k13_ami_1(c1_6__ami_6,c2_6__ami_6,B,C) = E & k6_ami_1(c1_6__ami_6,c2_6__ami_6,B) = C & k6_ami_1(c1_6__ami_6,c2_6__ami_6,k9_ami_1(c1_6__ami_6,c2_6__ami_6,B)) = k1_funct_1(k4_ami_1(c1_6__ami_6,c2_6__ami_6,k13_ami_1(c1_6__ami_6,c2_6__ami_6,B,k6_ami_1(c1_6__ami_6,c2_6__ami_6,B)),B),k2_ami_1(c1_6__ami_6,c2_6__ami_6)) ) ) ) ) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_6__ami_6]),discharge_asm(discharge,[dt_c2_6__ami_6])],[dt_c2_6__ami_6,i2_6__ami_6]), [interesting(0.8),i1_6__ami_6]). fof(i1_6__ami_6,plain,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_ami_1(A,c1_6__ami_6) & v5_ami_1(A,c1_6__ami_6) & v8_ami_1(A,c1_6__ami_6) & v10_ami_1(A,c1_6__ami_6) & l1_ami_1(A,c1_6__ami_6) ) => ! [B] : ( m1_subset_1(B,k4_card_3(u5_ami_1(c1_6__ami_6,A))) => ! [C] : ( m1_subset_1(C,k4_card_3(u5_ami_1(c1_6__ami_6,A))) => ! [D] : ( m1_struct_0(D,A,u2_ami_1(c1_6__ami_6,A)) => ! [E] : ( m1_subset_1(E,k3_ami_1(c1_6__ami_6,A,k2_ami_1(c1_6__ami_6,A))) => ! [F] : ( m1_subset_1(F,k3_ami_1(c1_6__ami_6,A,D)) => ( ( E = D & C = k8_ami_5(c1_6__ami_6,A,B,k16_ami_1(c1_6__ami_6,A,k2_ami_1(c1_6__ami_6,A),D,E,F)) ) => ( k13_ami_1(c1_6__ami_6,A,C,D) = F & k6_ami_1(c1_6__ami_6,A,C) = D & k6_ami_1(c1_6__ami_6,A,k9_ami_1(c1_6__ami_6,A,C)) = k1_funct_1(k4_ami_1(c1_6__ami_6,A,k13_ami_1(c1_6__ami_6,A,C,k6_ami_1(c1_6__ami_6,A,C)),C),k2_ami_1(c1_6__ami_6,A)) ) ) ) ) ) ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_6__ami_6])],[i2_6_tmp__ami_6,dh_c2_6__ami_6]), [interesting(0.8),file(ami_6,i1_6__ami_6),[file(ami_6,i1_6__ami_6)]]). fof(i1_6_tmp__ami_6,plain, ( v1_setfam_1(c1_6__ami_6) => ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_ami_1(A,c1_6__ami_6) & v5_ami_1(A,c1_6__ami_6) & v8_ami_1(A,c1_6__ami_6) & v10_ami_1(A,c1_6__ami_6) & l1_ami_1(A,c1_6__ami_6) ) => ! [B] : ( m1_subset_1(B,k4_card_3(u5_ami_1(c1_6__ami_6,A))) => ! [C] : ( m1_subset_1(C,k4_card_3(u5_ami_1(c1_6__ami_6,A))) => ! [D] : ( m1_struct_0(D,A,u2_ami_1(c1_6__ami_6,A)) => ! [E] : ( m1_subset_1(E,k3_ami_1(c1_6__ami_6,A,k2_ami_1(c1_6__ami_6,A))) => ! [F] : ( m1_subset_1(F,k3_ami_1(c1_6__ami_6,A,D)) => ( ( E = D & C = k8_ami_5(c1_6__ami_6,A,B,k16_ami_1(c1_6__ami_6,A,k2_ami_1(c1_6__ami_6,A),D,E,F)) ) => ( k13_ami_1(c1_6__ami_6,A,C,D) = F & k6_ami_1(c1_6__ami_6,A,C) = D & k6_ami_1(c1_6__ami_6,A,k9_ami_1(c1_6__ami_6,A,C)) = k1_funct_1(k4_ami_1(c1_6__ami_6,A,k13_ami_1(c1_6__ami_6,A,C,k6_ami_1(c1_6__ami_6,A,C)),C),k2_ami_1(c1_6__ami_6,A)) ) ) ) ) ) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_6__ami_6])],[dt_c1_6__ami_6,i1_6__ami_6]), [interesting(1),t6_ami_6]). fof(t6_ami_6,theorem,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v10_ami_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) => ! [D] : ( m1_subset_1(D,k4_card_3(u5_ami_1(A,B))) => ! [E] : ( m1_struct_0(E,B,u2_ami_1(A,B)) => ! [F] : ( m1_subset_1(F,k3_ami_1(A,B,k2_ami_1(A,B))) => ! [G] : ( m1_subset_1(G,k3_ami_1(A,B,E)) => ( ( F = E & D = k8_ami_5(A,B,C,k16_ami_1(A,B,k2_ami_1(A,B),E,F,G)) ) => ( k13_ami_1(A,B,D,E) = G & k6_ami_1(A,B,D) = E & k6_ami_1(A,B,k9_ami_1(A,B,D)) = k1_funct_1(k4_ami_1(A,B,k13_ami_1(A,B,D,k6_ami_1(A,B,D)),D),k2_ami_1(A,B)) ) ) ) ) ) ) ) ) ) ), inference(let,[status(thm),assumptions([])],[i1_6_tmp__ami_6,dh_c1_6__ami_6]), [interesting(1),file(ami_6,t6_ami_6),[file(ami_6,t6_ami_6)]]).