% Mizar ND problem: t6_connsp_1,connsp_1,105,47 fof(dh_c1_6__connsp_1,definition, ( ( ( v2_pre_topc(c1_6__connsp_1) & l1_pre_topc(c1_6__connsp_1) ) => ! [A] : ( m1_pre_topc(A,c1_6__connsp_1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_6__connsp_1))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_6__connsp_1))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ( ( D = B & E = C & r1_connsp_1(A,D,E) ) => r1_connsp_1(c1_6__connsp_1,B,C) ) ) ) ) ) ) ) => ! [F] : ( ( v2_pre_topc(F) & l1_pre_topc(F) ) => ! [G] : ( m1_pre_topc(G,F) => ! [H] : ( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(F))) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(F))) => ! [J] : ( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(G))) => ! [K] : ( m1_subset_1(K,k1_zfmisc_1(u1_struct_0(G))) => ( ( J = H & K = I & r1_connsp_1(G,J,K) ) => r1_connsp_1(F,H,I) ) ) ) ) ) ) ) ), introduced(definition,[new_symbol(c1_6__connsp_1),file(connsp_1,c1_6__connsp_1)]), [interesting(0.8),axiom,file(connsp_1,c1_6__connsp_1)]). fof(dh_c2_6__connsp_1,definition, ( ( m1_pre_topc(c2_6__connsp_1,c1_6__connsp_1) => ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_6__connsp_1))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_6__connsp_1))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c2_6__connsp_1))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(c2_6__connsp_1))) => ( ( C = A & D = B & r1_connsp_1(c2_6__connsp_1,C,D) ) => r1_connsp_1(c1_6__connsp_1,A,B) ) ) ) ) ) ) => ! [E] : ( m1_pre_topc(E,c1_6__connsp_1) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(c1_6__connsp_1))) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(c1_6__connsp_1))) => ! [H] : ( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(E))) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(E))) => ( ( H = F & I = G & r1_connsp_1(E,H,I) ) => r1_connsp_1(c1_6__connsp_1,F,G) ) ) ) ) ) ) ), introduced(definition,[new_symbol(c2_6__connsp_1),file(connsp_1,c2_6__connsp_1)]), [interesting(0.8),axiom,file(connsp_1,c2_6__connsp_1)]). fof(dh_c3_6__connsp_1,definition, ( ( m1_subset_1(c3_6__connsp_1,k1_zfmisc_1(u1_struct_0(c1_6__connsp_1))) => ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_6__connsp_1))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c2_6__connsp_1))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c2_6__connsp_1))) => ( ( B = c3_6__connsp_1 & C = A & r1_connsp_1(c2_6__connsp_1,B,C) ) => r1_connsp_1(c1_6__connsp_1,c3_6__connsp_1,A) ) ) ) ) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(c1_6__connsp_1))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(c1_6__connsp_1))) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(c2_6__connsp_1))) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(c2_6__connsp_1))) => ( ( F = D & G = E & r1_connsp_1(c2_6__connsp_1,F,G) ) => r1_connsp_1(c1_6__connsp_1,D,E) ) ) ) ) ) ), introduced(definition,[new_symbol(c3_6__connsp_1),file(connsp_1,c3_6__connsp_1)]), [interesting(0.8),axiom,file(connsp_1,c3_6__connsp_1)]). fof(dh_c4_6__connsp_1,definition, ( ( m1_subset_1(c4_6__connsp_1,k1_zfmisc_1(u1_struct_0(c1_6__connsp_1))) => ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c2_6__connsp_1))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c2_6__connsp_1))) => ( ( A = c3_6__connsp_1 & B = c4_6__connsp_1 & r1_connsp_1(c2_6__connsp_1,A,B) ) => r1_connsp_1(c1_6__connsp_1,c3_6__connsp_1,c4_6__connsp_1) ) ) ) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_6__connsp_1))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(c2_6__connsp_1))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(c2_6__connsp_1))) => ( ( D = c3_6__connsp_1 & E = C & r1_connsp_1(c2_6__connsp_1,D,E) ) => r1_connsp_1(c1_6__connsp_1,c3_6__connsp_1,C) ) ) ) ) ), introduced(definition,[new_symbol(c4_6__connsp_1),file(connsp_1,c4_6__connsp_1)]), [interesting(0.8),axiom,file(connsp_1,c4_6__connsp_1)]). fof(dh_c5_6__connsp_1,definition, ( ( m1_subset_1(c5_6__connsp_1,k1_zfmisc_1(u1_struct_0(c2_6__connsp_1))) => ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c2_6__connsp_1))) => ( ( c5_6__connsp_1 = c3_6__connsp_1 & A = c4_6__connsp_1 & r1_connsp_1(c2_6__connsp_1,c5_6__connsp_1,A) ) => r1_connsp_1(c1_6__connsp_1,c3_6__connsp_1,c4_6__connsp_1) ) ) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c2_6__connsp_1))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c2_6__connsp_1))) => ( ( B = c3_6__connsp_1 & C = c4_6__connsp_1 & r1_connsp_1(c2_6__connsp_1,B,C) ) => r1_connsp_1(c1_6__connsp_1,c3_6__connsp_1,c4_6__connsp_1) ) ) ) ), introduced(definition,[new_symbol(c5_6__connsp_1),file(connsp_1,c5_6__connsp_1)]), [interesting(0.8),axiom,file(connsp_1,c5_6__connsp_1)]). fof(dh_c6_6__connsp_1,definition, ( ( m1_subset_1(c6_6__connsp_1,k1_zfmisc_1(u1_struct_0(c2_6__connsp_1))) => ( ( c5_6__connsp_1 = c3_6__connsp_1 & c6_6__connsp_1 = c4_6__connsp_1 & r1_connsp_1(c2_6__connsp_1,c5_6__connsp_1,c6_6__connsp_1) ) => r1_connsp_1(c1_6__connsp_1,c3_6__connsp_1,c4_6__connsp_1) ) ) => ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c2_6__connsp_1))) => ( ( c5_6__connsp_1 = c3_6__connsp_1 & A = c4_6__connsp_1 & r1_connsp_1(c2_6__connsp_1,c5_6__connsp_1,A) ) => r1_connsp_1(c1_6__connsp_1,c3_6__connsp_1,c4_6__connsp_1) ) ) ), introduced(definition,[new_symbol(c6_6__connsp_1),file(connsp_1,c6_6__connsp_1)]), [interesting(0.8),axiom,file(connsp_1,c6_6__connsp_1)]). fof(e1_6__connsp_1,assumption,( c5_6__connsp_1 = c3_6__connsp_1 ), introduced(assumption,[file(connsp_1,e1_6__connsp_1)]), [interesting(0.8),axiom,file(connsp_1,e1_6__connsp_1)]). fof(e2_6__connsp_1,assumption,( c6_6__connsp_1 = c4_6__connsp_1 ), introduced(assumption,[file(connsp_1,e2_6__connsp_1)]), [interesting(0.8),axiom,file(connsp_1,e2_6__connsp_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_m1_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_pre_topc(B,A) => l1_pre_topc(B) ) ) ), file(pre_topc,m1_pre_topc), [interesting(0.9),axiom,file(pre_topc,m1_pre_topc)]). 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(cc15_membered,theorem,( ! [A] : ( v1_xboole_0(A) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc15_membered), [interesting(0.9),axiom,file(membered,cc15_membered)]). fof(cc16_membered,theorem,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_membered(B) ) ) ), file(membered,cc16_membered), [interesting(0.9),axiom,file(membered,cc16_membered)]). fof(cc17_membered,theorem,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) ) ) ) ), file(membered,cc17_membered), [interesting(0.9),axiom,file(membered,cc17_membered)]). fof(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_pre_topc,theorem,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => v2_pre_topc(B) ) ) ), file(pre_topc,cc1_pre_topc), [interesting(0.9),axiom,file(pre_topc,cc1_pre_topc)]). 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(fc27_membered,theorem,( ! [A,B] : ( v1_membered(A) => v1_membered(k3_xboole_0(A,B)) ) ), file(membered,fc27_membered), [interesting(0.9),axiom,file(membered,fc27_membered)]). fof(fc28_membered,theorem,( ! [A,B] : ( v1_membered(A) => v1_membered(k3_xboole_0(B,A)) ) ), file(membered,fc28_membered), [interesting(0.9),axiom,file(membered,fc28_membered)]). fof(fc29_membered,theorem,( ! [A,B] : ( v2_membered(A) => ( v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) ) ) ), file(membered,fc29_membered), [interesting(0.9),axiom,file(membered,fc29_membered)]). fof(fc30_membered,theorem,( ! [A,B] : ( v2_membered(A) => ( v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) ) ) ), file(membered,fc30_membered), [interesting(0.9),axiom,file(membered,fc30_membered)]). fof(fc31_membered,theorem,( ! [A,B] : ( v3_membered(A) => ( v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) ) ) ), file(membered,fc31_membered), [interesting(0.9),axiom,file(membered,fc31_membered)]). fof(fc32_membered,theorem,( ! [A,B] : ( v3_membered(A) => ( v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) ) ) ), file(membered,fc32_membered), [interesting(0.9),axiom,file(membered,fc32_membered)]). fof(fc33_membered,theorem,( ! [A,B] : ( v4_membered(A) => ( v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) ) ) ), file(membered,fc33_membered), [interesting(0.9),axiom,file(membered,fc33_membered)]). fof(fc34_membered,theorem,( ! [A,B] : ( v4_membered(A) => ( v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) & v4_membered(k3_xboole_0(B,A)) ) ) ), file(membered,fc34_membered), [interesting(0.9),axiom,file(membered,fc34_membered)]). fof(fc35_membered,theorem,( ! [A,B] : ( v5_membered(A) => ( v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) & v5_membered(k3_xboole_0(A,B)) ) ) ), file(membered,fc35_membered), [interesting(0.9),axiom,file(membered,fc35_membered)]). fof(fc36_membered,theorem,( ! [A,B] : ( v5_membered(A) => ( v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) & v4_membered(k3_xboole_0(B,A)) & v5_membered(k3_xboole_0(B,A)) ) ) ), file(membered,fc36_membered), [interesting(0.9),axiom,file(membered,fc36_membered)]). 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(rc1_subset_1,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) ) ) ), file(subset_1,rc1_subset_1), [interesting(0.9),axiom,file(subset_1,rc1_subset_1)]). fof(rc2_subset_1,theorem,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) ) ), file(subset_1,rc2_subset_1), [interesting(0.9),axiom,file(subset_1,rc2_subset_1)]). fof(commutativity_k3_xboole_0,theorem,( ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ), file(xboole_0,k3_xboole_0), [interesting(0.9),axiom,file(xboole_0,k3_xboole_0)]). fof(idempotence_k3_xboole_0,theorem,( ! [A,B] : k3_xboole_0(A,A) = A ), file(xboole_0,k3_xboole_0), [interesting(0.9),axiom,file(xboole_0,k3_xboole_0)]). fof(commutativity_k5_subset_1,theorem,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k5_subset_1(A,B,C) = k5_subset_1(A,C,B) ) ), file(subset_1,k5_subset_1), [interesting(0.9),axiom,file(subset_1,k5_subset_1)]). fof(idempotence_k5_subset_1,theorem,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k5_subset_1(A,B,B) = B ) ), file(subset_1,k5_subset_1), [interesting(0.9),axiom,file(subset_1,k5_subset_1)]). fof(symmetry_r1_connsp_1,theorem,( ! [A,B,C] : ( ( l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ( r1_connsp_1(A,B,C) => r1_connsp_1(A,C,B) ) ) ), file(connsp_1,r1_connsp_1), [interesting(0.9),axiom,file(connsp_1,r1_connsp_1)]). fof(symmetry_r1_xboole_0,theorem,( ! [A,B] : ( r1_xboole_0(A,B) => r1_xboole_0(B,A) ) ), file(xboole_0,r1_xboole_0), [interesting(0.9),axiom,file(xboole_0,r1_xboole_0)]). fof(redefinition_k5_subset_1,definition,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k5_subset_1(A,B,C) = k3_xboole_0(B,C) ) ), file(subset_1,k5_subset_1), [interesting(0.9),axiom,file(subset_1,k5_subset_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(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]). fof(dt_k3_xboole_0,axiom,( $true ), file(xboole_0,k3_xboole_0), [interesting(0.9),axiom,file(xboole_0,k3_xboole_0)]). fof(dt_k5_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => m1_subset_1(k5_subset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(subset_1,k5_subset_1), [interesting(0.9),axiom,file(subset_1,k5_subset_1)]). fof(dt_k6_pre_topc,axiom,( ! [A,B] : ( ( l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(k6_pre_topc(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ), file(pre_topc,k6_pre_topc), [interesting(0.9),axiom,file(pre_topc,k6_pre_topc)]). fof(dt_l1_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => l1_struct_0(A) ) ), file(pre_topc,l1_pre_topc), [interesting(0.9),axiom,file(pre_topc,l1_pre_topc)]). 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_u1_struct_0,axiom,( $true ), file(struct_0,u1_struct_0), [interesting(0.9),axiom,file(struct_0,u1_struct_0)]). fof(dt_c1_6__connsp_1,assumption, ( v2_pre_topc(c1_6__connsp_1) & l1_pre_topc(c1_6__connsp_1) ), introduced(assumption,[file(connsp_1,c1_6__connsp_1)]), [interesting(0.8),axiom,file(connsp_1,c1_6__connsp_1)]). fof(dt_c2_6__connsp_1,assumption,( m1_pre_topc(c2_6__connsp_1,c1_6__connsp_1) ), introduced(assumption,[file(connsp_1,c2_6__connsp_1)]), [interesting(0.8),axiom,file(connsp_1,c2_6__connsp_1)]). fof(dt_c3_6__connsp_1,assumption,( m1_subset_1(c3_6__connsp_1,k1_zfmisc_1(u1_struct_0(c1_6__connsp_1))) ), introduced(assumption,[file(connsp_1,c3_6__connsp_1)]), [interesting(0.8),axiom,file(connsp_1,c3_6__connsp_1)]). fof(dt_c4_6__connsp_1,assumption,( m1_subset_1(c4_6__connsp_1,k1_zfmisc_1(u1_struct_0(c1_6__connsp_1))) ), introduced(assumption,[file(connsp_1,c4_6__connsp_1)]), [interesting(0.8),axiom,file(connsp_1,c4_6__connsp_1)]). fof(dt_c5_6__connsp_1,assumption,( m1_subset_1(c5_6__connsp_1,k1_zfmisc_1(u1_struct_0(c2_6__connsp_1))) ), introduced(assumption,[file(connsp_1,c5_6__connsp_1)]), [interesting(0.8),axiom,file(connsp_1,c5_6__connsp_1)]). fof(dt_c6_6__connsp_1,assumption,( m1_subset_1(c6_6__connsp_1,k1_zfmisc_1(u1_struct_0(c2_6__connsp_1))) ), introduced(assumption,[file(connsp_1,c6_6__connsp_1)]), [interesting(0.8),axiom,file(connsp_1,c6_6__connsp_1)]). fof(fc1_subset_1,theorem,( ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ), file(subset_1,fc1_subset_1), [interesting(0.9),axiom,file(subset_1,fc1_subset_1)]). fof(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(e3_6__connsp_1,assumption, ( k5_subset_1(u1_struct_0(c2_6__connsp_1),k6_pre_topc(c2_6__connsp_1,c5_6__connsp_1),c6_6__connsp_1) = k1_xboole_0 & k5_subset_1(u1_struct_0(c2_6__connsp_1),c5_6__connsp_1,k6_pre_topc(c2_6__connsp_1,c6_6__connsp_1)) = k1_xboole_0 ), introduced(assumption,[file(connsp_1,e3_6__connsp_1)]), [interesting(0.8),axiom,file(connsp_1,e3_6__connsp_1)]). fof(d7_xboole_0,definition,( ! [A,B] : ( r1_xboole_0(A,B) <=> k3_xboole_0(A,B) = k1_xboole_0 ) ), file(xboole_0,d7_xboole_0), [interesting(0.9),axiom,file(xboole_0,d7_xboole_0)]). fof(d1_connsp_1,definition,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r1_connsp_1(A,B,C) <=> ( r1_xboole_0(k6_pre_topc(A,B),C) & r1_xboole_0(B,k6_pre_topc(A,C)) ) ) ) ) ) ), file(connsp_1,d1_connsp_1), [interesting(0.9),axiom,file(connsp_1,d1_connsp_1)]). 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(existence_m1_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ? [B] : m1_pre_topc(B,A) ) ), file(pre_topc,m1_pre_topc), [interesting(0.9),axiom,file(pre_topc,m1_pre_topc)]). 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(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(reflexivity_r1_tarski,theorem,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), [interesting(0.9),axiom,file(tarski,r1_tarski)]). 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(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(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(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(existence_l1_pre_topc,axiom,( ? [A] : l1_pre_topc(A) ), file(pre_topc,l1_pre_topc), [interesting(0.9),axiom,file(pre_topc,l1_pre_topc)]). 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(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(de_c7_6__connsp_1,definition,( c7_6__connsp_1 = c5_6__connsp_1 ), introduced(definition,[new_symbol(c7_6__connsp_1),file(connsp_1,c7_6__connsp_1)]), [interesting(0.8),axiom,file(connsp_1,c7_6__connsp_1)]). fof(t39_pre_topc,theorem,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ), file(pre_topc,t39_pre_topc), [interesting(0.9),axiom,file(pre_topc,t39_pre_topc)]). fof(e4_6__connsp_1,plain, ( m1_subset_1(c5_6__connsp_1,k1_zfmisc_1(u1_struct_0(c1_6__connsp_1))) & m1_subset_1(c6_6__connsp_1,k1_zfmisc_1(u1_struct_0(c1_6__connsp_1))) ), inference(mizar_by,[status(thm),assumptions([dt_c2_6__connsp_1,dt_c1_6__connsp_1,dt_c5_6__connsp_1,dt_c6_6__connsp_1])],[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,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,t1_subset,t4_subset,t5_subset,t8_boole,reflexivity_r1_tarski,existence_l1_struct_0,dt_l1_struct_0,dt_c2_6__connsp_1,cc15_membered,cc1_pre_topc,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,existence_l1_pre_topc,existence_m1_pre_topc,existence_m1_subset_1,dt_k1_zfmisc_1,dt_l1_pre_topc,dt_m1_pre_topc,dt_m1_subset_1,dt_u1_struct_0,dt_c1_6__connsp_1,dt_c5_6__connsp_1,dt_c6_6__connsp_1,fc1_subset_1,t3_subset,t39_pre_topc]), [interesting(0.8),file(connsp_1,e4_6__connsp_1),[file(connsp_1,e4_6__connsp_1)]]). fof(dt_c7_6__connsp_1,plain,( m1_subset_1(c7_6__connsp_1,k1_zfmisc_1(u1_struct_0(c1_6__connsp_1))) ), inference(mizar_by,[status(thm),assumptions([dt_c2_6__connsp_1,dt_c1_6__connsp_1,dt_c5_6__connsp_1,dt_c6_6__connsp_1])],[antisymmetry_r2_hidden,existence_m1_pre_topc,dt_k1_xboole_0,dt_m1_pre_topc,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_pre_topc,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_l1_pre_topc,existence_l1_struct_0,dt_l1_pre_topc,dt_l1_struct_0,dt_c2_6__connsp_1,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_6__connsp_1,dt_c5_6__connsp_1,dt_c6_6__connsp_1,fc1_subset_1,t3_subset,de_c7_6__connsp_1,e4_6__connsp_1]), [interesting(0.8),file(connsp_1,c7_6__connsp_1),[file(connsp_1,c7_6__connsp_1)]]). fof(de_c8_6__connsp_1,definition,( c8_6__connsp_1 = c6_6__connsp_1 ), introduced(definition,[new_symbol(c8_6__connsp_1),file(connsp_1,c8_6__connsp_1)]), [interesting(0.8),axiom,file(connsp_1,c8_6__connsp_1)]). fof(dt_c8_6__connsp_1,plain,( m1_subset_1(c8_6__connsp_1,k1_zfmisc_1(u1_struct_0(c1_6__connsp_1))) ), inference(mizar_by,[status(thm),assumptions([dt_c2_6__connsp_1,dt_c1_6__connsp_1,dt_c5_6__connsp_1,dt_c6_6__connsp_1])],[antisymmetry_r2_hidden,existence_m1_pre_topc,dt_k1_xboole_0,dt_m1_pre_topc,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_pre_topc,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_l1_pre_topc,existence_l1_struct_0,dt_l1_pre_topc,dt_l1_struct_0,dt_c2_6__connsp_1,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_6__connsp_1,dt_c5_6__connsp_1,dt_c6_6__connsp_1,fc1_subset_1,t3_subset,de_c8_6__connsp_1,e4_6__connsp_1]), [interesting(0.8),file(connsp_1,c8_6__connsp_1),[file(connsp_1,c8_6__connsp_1)]]). fof(t2_boole,theorem,( ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ), file(boole,t2_boole), [interesting(0.9),axiom,file(boole,t2_boole)]). fof(rc6_pre_topc,theorem,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(B,A) ) ) ), file(pre_topc,rc6_pre_topc), [interesting(0.9),axiom,file(pre_topc,rc6_pre_topc)]). fof(fc5_pre_topc,theorem,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => v4_pre_topc(k2_pre_topc(A),A) ) ), file(pre_topc,fc5_pre_topc), [interesting(0.9),axiom,file(pre_topc,fc5_pre_topc)]). fof(dt_k2_pre_topc,axiom,( ! [A] : ( l1_struct_0(A) => m1_subset_1(k2_pre_topc(A),k1_zfmisc_1(u1_struct_0(A))) ) ), file(pre_topc,k2_pre_topc), [interesting(0.9),axiom,file(pre_topc,k2_pre_topc)]). fof(t47_pre_topc,theorem,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( C = D => k6_pre_topc(B,D) = k3_xboole_0(k6_pre_topc(A,C),k2_pre_topc(B)) ) ) ) ) ) ), file(pre_topc,t47_pre_topc), [interesting(0.9),axiom,file(pre_topc,t47_pre_topc)]). fof(e1_6_2__connsp_1,plain,( k5_subset_1(u1_struct_0(c2_6__connsp_1),c5_6__connsp_1,k6_pre_topc(c2_6__connsp_1,c6_6__connsp_1)) = k3_xboole_0(c5_6__connsp_1,k3_xboole_0(k2_pre_topc(c2_6__connsp_1),k6_pre_topc(c1_6__connsp_1,c8_6__connsp_1))) ), inference(mizar_by,[status(thm),assumptions([dt_c2_6__connsp_1,dt_c1_6__connsp_1,dt_c5_6__connsp_1,dt_c6_6__connsp_1])],[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,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc6_membered,rc1_membered,rc6_pre_topc,t1_subset,t2_boole,t4_subset,t5_subset,reflexivity_r1_tarski,existence_l1_struct_0,dt_l1_struct_0,cc15_membered,cc1_pre_topc,fc5_pre_topc,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,commutativity_k5_subset_1,idempotence_k5_subset_1,existence_l1_pre_topc,existence_m1_pre_topc,existence_m1_subset_1,redefinition_k5_subset_1,dt_k1_zfmisc_1,dt_k2_pre_topc,dt_k3_xboole_0,dt_k5_subset_1,dt_k6_pre_topc,dt_l1_pre_topc,dt_m1_pre_topc,dt_m1_subset_1,dt_u1_struct_0,dt_c1_6__connsp_1,dt_c2_6__connsp_1,dt_c5_6__connsp_1,dt_c6_6__connsp_1,dt_c8_6__connsp_1,de_c8_6__connsp_1,fc1_subset_1,t3_subset,t47_pre_topc]), [interesting(0.65),file(connsp_1,e1_6_2__connsp_1),[file(connsp_1,e1_6_2__connsp_1)]]). fof(t16_xboole_1,theorem,( ! [A,B,C] : k3_xboole_0(k3_xboole_0(A,B),C) = k3_xboole_0(A,k3_xboole_0(B,C)) ), file(xboole_1,t16_xboole_1), [interesting(0.9),axiom,file(xboole_1,t16_xboole_1)]). fof(e2_6_2__connsp_1,plain,( k3_xboole_0(c5_6__connsp_1,k3_xboole_0(k2_pre_topc(c2_6__connsp_1),k6_pre_topc(c1_6__connsp_1,c8_6__connsp_1))) = k3_xboole_0(k5_subset_1(u1_struct_0(c2_6__connsp_1),c5_6__connsp_1,k2_pre_topc(c2_6__connsp_1)),k6_pre_topc(c1_6__connsp_1,c8_6__connsp_1)) ), inference(mizar_by,[status(thm),assumptions([dt_c2_6__connsp_1,dt_c1_6__connsp_1,dt_c5_6__connsp_1,dt_c6_6__connsp_1])],[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,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc6_membered,rc1_membered,t1_subset,t2_boole,t4_subset,t5_subset,reflexivity_r1_tarski,cc15_membered,rc1_subset_1,rc2_subset_1,rc6_pre_topc,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_pre_topc,existence_m1_subset_1,dt_k1_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_pre_topc,dt_m1_subset_1,dt_c6_6__connsp_1,cc1_pre_topc,fc1_subset_1,fc5_pre_topc,t3_subset,commutativity_k3_xboole_0,idempotence_k3_xboole_0,commutativity_k5_subset_1,idempotence_k5_subset_1,redefinition_k5_subset_1,dt_k2_pre_topc,dt_k3_xboole_0,dt_k5_subset_1,dt_k6_pre_topc,dt_u1_struct_0,dt_c1_6__connsp_1,dt_c2_6__connsp_1,dt_c5_6__connsp_1,dt_c8_6__connsp_1,de_c8_6__connsp_1,t16_xboole_1]), [interesting(0.65),file(connsp_1,e2_6_2__connsp_1),[file(connsp_1,e2_6_2__connsp_1)]]). fof(t15_pre_topc,theorem,( ! [A] : ( l1_struct_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k5_subset_1(u1_struct_0(A),B,k2_pre_topc(A)) = B ) ) ), file(pre_topc,t15_pre_topc), [interesting(0.9),axiom,file(pre_topc,t15_pre_topc)]). fof(e3_6_2__connsp_1,plain,( k3_xboole_0(k5_subset_1(u1_struct_0(c2_6__connsp_1),c5_6__connsp_1,k2_pre_topc(c2_6__connsp_1)),k6_pre_topc(c1_6__connsp_1,c8_6__connsp_1)) = k5_subset_1(u1_struct_0(c1_6__connsp_1),c7_6__connsp_1,k6_pre_topc(c1_6__connsp_1,c8_6__connsp_1)) ), inference(mizar_by,[status(thm),assumptions([dt_c2_6__connsp_1,dt_c1_6__connsp_1,dt_c5_6__connsp_1,dt_c6_6__connsp_1])],[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,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc6_membered,rc1_membered,rc6_pre_topc,t1_subset,t2_boole,t4_subset,t5_subset,reflexivity_r1_tarski,existence_l1_pre_topc,existence_m1_pre_topc,dt_l1_pre_topc,dt_m1_pre_topc,dt_c6_6__connsp_1,cc15_membered,cc1_pre_topc,fc5_pre_topc,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,commutativity_k5_subset_1,idempotence_k5_subset_1,existence_l1_struct_0,existence_m1_subset_1,redefinition_k5_subset_1,dt_k1_zfmisc_1,dt_k2_pre_topc,dt_k3_xboole_0,dt_k5_subset_1,dt_k6_pre_topc,dt_l1_struct_0,dt_m1_subset_1,dt_u1_struct_0,dt_c1_6__connsp_1,dt_c2_6__connsp_1,dt_c5_6__connsp_1,dt_c7_6__connsp_1,dt_c8_6__connsp_1,de_c7_6__connsp_1,de_c8_6__connsp_1,fc1_subset_1,t3_subset,t15_pre_topc]), [interesting(0.65),file(connsp_1,e3_6_2__connsp_1),[file(connsp_1,e3_6_2__connsp_1)]]). fof(e6_6__connsp_1,plain,( k5_subset_1(u1_struct_0(c2_6__connsp_1),c5_6__connsp_1,k6_pre_topc(c2_6__connsp_1,c6_6__connsp_1)) = k5_subset_1(u1_struct_0(c1_6__connsp_1),c7_6__connsp_1,k6_pre_topc(c1_6__connsp_1,c8_6__connsp_1)) ), inference(iterative_eq,[status(thm),assumptions([dt_c2_6__connsp_1,dt_c1_6__connsp_1,dt_c5_6__connsp_1,dt_c6_6__connsp_1])],[cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,rc1_membered,cc15_membered,rc1_subset_1,rc2_subset_1,rc6_pre_topc,dt_k1_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_pre_topc,dt_m1_subset_1,cc1_pre_topc,fc1_subset_1,fc5_pre_topc,commutativity_k3_xboole_0,idempotence_k3_xboole_0,commutativity_k5_subset_1,idempotence_k5_subset_1,redefinition_k5_subset_1,dt_k2_pre_topc,dt_k3_xboole_0,dt_k5_subset_1,dt_k6_pre_topc,dt_u1_struct_0,dt_c1_6__connsp_1,dt_c2_6__connsp_1,dt_c5_6__connsp_1,dt_c6_6__connsp_1,dt_c7_6__connsp_1,dt_c8_6__connsp_1,e1_6_2__connsp_1,e2_6_2__connsp_1,e3_6_2__connsp_1]), [interesting(0.8),file(connsp_1,e6_6__connsp_1),[file(connsp_1,e6_6__connsp_1)]]). fof(e1_6_1__connsp_1,plain,( k5_subset_1(u1_struct_0(c2_6__connsp_1),k6_pre_topc(c2_6__connsp_1,c5_6__connsp_1),c6_6__connsp_1) = k3_xboole_0(k3_xboole_0(k6_pre_topc(c1_6__connsp_1,c7_6__connsp_1),k2_pre_topc(c2_6__connsp_1)),c6_6__connsp_1) ), inference(mizar_by,[status(thm),assumptions([dt_c2_6__connsp_1,dt_c1_6__connsp_1,dt_c5_6__connsp_1,dt_c6_6__connsp_1])],[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,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc6_membered,rc1_membered,rc6_pre_topc,t1_subset,t2_boole,t4_subset,t5_subset,reflexivity_r1_tarski,existence_l1_struct_0,dt_l1_struct_0,cc15_membered,cc1_pre_topc,fc5_pre_topc,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,commutativity_k5_subset_1,idempotence_k5_subset_1,existence_l1_pre_topc,existence_m1_pre_topc,existence_m1_subset_1,redefinition_k5_subset_1,dt_k1_zfmisc_1,dt_k2_pre_topc,dt_k3_xboole_0,dt_k5_subset_1,dt_k6_pre_topc,dt_l1_pre_topc,dt_m1_pre_topc,dt_m1_subset_1,dt_u1_struct_0,dt_c1_6__connsp_1,dt_c2_6__connsp_1,dt_c5_6__connsp_1,dt_c6_6__connsp_1,dt_c7_6__connsp_1,de_c7_6__connsp_1,fc1_subset_1,t3_subset,t47_pre_topc]), [interesting(0.65),file(connsp_1,e1_6_1__connsp_1),[file(connsp_1,e1_6_1__connsp_1)]]). fof(e2_6_1__connsp_1,plain,( k3_xboole_0(k3_xboole_0(k6_pre_topc(c1_6__connsp_1,c7_6__connsp_1),k2_pre_topc(c2_6__connsp_1)),c6_6__connsp_1) = k3_xboole_0(k6_pre_topc(c1_6__connsp_1,c7_6__connsp_1),k5_subset_1(u1_struct_0(c2_6__connsp_1),c6_6__connsp_1,k2_pre_topc(c2_6__connsp_1))) ), inference(mizar_by,[status(thm),assumptions([dt_c2_6__connsp_1,dt_c1_6__connsp_1,dt_c5_6__connsp_1,dt_c6_6__connsp_1])],[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,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc6_membered,rc1_membered,t1_subset,t2_boole,t4_subset,t5_subset,reflexivity_r1_tarski,cc15_membered,rc1_subset_1,rc2_subset_1,rc6_pre_topc,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_pre_topc,existence_m1_subset_1,dt_k1_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_pre_topc,dt_m1_subset_1,dt_c5_6__connsp_1,cc1_pre_topc,fc1_subset_1,fc5_pre_topc,t3_subset,commutativity_k3_xboole_0,idempotence_k3_xboole_0,commutativity_k5_subset_1,idempotence_k5_subset_1,redefinition_k5_subset_1,dt_k2_pre_topc,dt_k3_xboole_0,dt_k5_subset_1,dt_k6_pre_topc,dt_u1_struct_0,dt_c1_6__connsp_1,dt_c2_6__connsp_1,dt_c6_6__connsp_1,dt_c7_6__connsp_1,de_c7_6__connsp_1,t16_xboole_1]), [interesting(0.65),file(connsp_1,e2_6_1__connsp_1),[file(connsp_1,e2_6_1__connsp_1)]]). fof(e3_6_1__connsp_1,plain,( k3_xboole_0(k6_pre_topc(c1_6__connsp_1,c7_6__connsp_1),k5_subset_1(u1_struct_0(c2_6__connsp_1),c6_6__connsp_1,k2_pre_topc(c2_6__connsp_1))) = k5_subset_1(u1_struct_0(c1_6__connsp_1),k6_pre_topc(c1_6__connsp_1,c7_6__connsp_1),c8_6__connsp_1) ), inference(mizar_by,[status(thm),assumptions([dt_c2_6__connsp_1,dt_c1_6__connsp_1,dt_c5_6__connsp_1,dt_c6_6__connsp_1])],[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,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc6_membered,rc1_membered,rc6_pre_topc,t1_subset,t2_boole,t4_subset,t5_subset,reflexivity_r1_tarski,existence_l1_pre_topc,existence_m1_pre_topc,dt_l1_pre_topc,dt_m1_pre_topc,dt_c5_6__connsp_1,cc15_membered,cc1_pre_topc,fc5_pre_topc,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,commutativity_k5_subset_1,idempotence_k5_subset_1,existence_l1_struct_0,existence_m1_subset_1,redefinition_k5_subset_1,dt_k1_zfmisc_1,dt_k2_pre_topc,dt_k3_xboole_0,dt_k5_subset_1,dt_k6_pre_topc,dt_l1_struct_0,dt_m1_subset_1,dt_u1_struct_0,dt_c1_6__connsp_1,dt_c2_6__connsp_1,dt_c6_6__connsp_1,dt_c7_6__connsp_1,dt_c8_6__connsp_1,de_c7_6__connsp_1,de_c8_6__connsp_1,fc1_subset_1,t3_subset,t15_pre_topc]), [interesting(0.65),file(connsp_1,e3_6_1__connsp_1),[file(connsp_1,e3_6_1__connsp_1)]]). fof(e5_6__connsp_1,plain,( k5_subset_1(u1_struct_0(c2_6__connsp_1),k6_pre_topc(c2_6__connsp_1,c5_6__connsp_1),c6_6__connsp_1) = k5_subset_1(u1_struct_0(c1_6__connsp_1),k6_pre_topc(c1_6__connsp_1,c7_6__connsp_1),c8_6__connsp_1) ), inference(iterative_eq,[status(thm),assumptions([dt_c2_6__connsp_1,dt_c1_6__connsp_1,dt_c5_6__connsp_1,dt_c6_6__connsp_1])],[cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,rc1_membered,cc15_membered,rc1_subset_1,rc2_subset_1,rc6_pre_topc,dt_k1_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_pre_topc,dt_m1_subset_1,cc1_pre_topc,fc1_subset_1,fc5_pre_topc,commutativity_k3_xboole_0,idempotence_k3_xboole_0,commutativity_k5_subset_1,idempotence_k5_subset_1,redefinition_k5_subset_1,dt_k2_pre_topc,dt_k3_xboole_0,dt_k5_subset_1,dt_k6_pre_topc,dt_u1_struct_0,dt_c1_6__connsp_1,dt_c2_6__connsp_1,dt_c5_6__connsp_1,dt_c6_6__connsp_1,dt_c7_6__connsp_1,dt_c8_6__connsp_1,e1_6_1__connsp_1,e2_6_1__connsp_1,e3_6_1__connsp_1]), [interesting(0.8),file(connsp_1,e5_6__connsp_1),[file(connsp_1,e5_6__connsp_1)]]). fof(e7_6__connsp_1,plain, ( r1_xboole_0(k6_pre_topc(c1_6__connsp_1,c7_6__connsp_1),c8_6__connsp_1) & r1_xboole_0(c7_6__connsp_1,k6_pre_topc(c1_6__connsp_1,c8_6__connsp_1)) ), inference(mizar_by,[status(thm),assumptions([e3_6__connsp_1,dt_c2_6__connsp_1,dt_c1_6__connsp_1,dt_c5_6__connsp_1,dt_c6_6__connsp_1])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,t1_subset,t4_subset,t5_subset,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_pre_topc,existence_m1_subset_1,dt_k1_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_pre_topc,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_pre_topc,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc1_subset_1,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,rc1_membered,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t7_boole,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,commutativity_k5_subset_1,idempotence_k5_subset_1,symmetry_r1_xboole_0,redefinition_k5_subset_1,dt_k1_xboole_0,dt_k3_xboole_0,dt_k5_subset_1,dt_k6_pre_topc,dt_u1_struct_0,dt_c1_6__connsp_1,dt_c2_6__connsp_1,dt_c5_6__connsp_1,dt_c6_6__connsp_1,dt_c7_6__connsp_1,dt_c8_6__connsp_1,de_c7_6__connsp_1,de_c8_6__connsp_1,fc6_membered,t2_boole,t6_boole,e6_6__connsp_1,e3_6__connsp_1,e5_6__connsp_1,d7_xboole_0]), [interesting(0.8),file(connsp_1,e7_6__connsp_1),[file(connsp_1,e7_6__connsp_1)]]). fof(e8_6__connsp_1,plain,( r1_connsp_1(c1_6__connsp_1,c3_6__connsp_1,c4_6__connsp_1) ), inference(mizar_by,[status(thm),assumptions([dt_c3_6__connsp_1,dt_c4_6__connsp_1,e3_6__connsp_1,dt_c2_6__connsp_1,dt_c1_6__connsp_1,dt_c5_6__connsp_1,dt_c6_6__connsp_1,e1_6__connsp_1,e2_6__connsp_1])],[antisymmetry_r2_hidden,existence_m1_pre_topc,dt_k1_xboole_0,dt_m1_pre_topc,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_pre_topc,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_l1_struct_0,dt_l1_struct_0,dt_c2_6__connsp_1,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,symmetry_r1_connsp_1,symmetry_r1_xboole_0,existence_l1_pre_topc,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k6_pre_topc,dt_l1_pre_topc,dt_m1_subset_1,dt_u1_struct_0,dt_c1_6__connsp_1,dt_c3_6__connsp_1,dt_c4_6__connsp_1,dt_c5_6__connsp_1,dt_c6_6__connsp_1,dt_c7_6__connsp_1,dt_c8_6__connsp_1,de_c7_6__connsp_1,de_c8_6__connsp_1,fc1_subset_1,t3_subset,e7_6__connsp_1,e1_6__connsp_1,e2_6__connsp_1,d1_connsp_1]), [interesting(0.8),file(connsp_1,e8_6__connsp_1),[file(connsp_1,e8_6__connsp_1)]]). fof(i7_6__connsp_1,theorem,( $true ), introduced(tautology,[file(connsp_1,i7_6__connsp_1)]), [interesting(0.8),trivial,file(connsp_1,i7_6__connsp_1)]). fof(i6_6__connsp_1,plain,( r1_connsp_1(c1_6__connsp_1,c3_6__connsp_1,c4_6__connsp_1) ), inference(conclusion,[status(thm),assumptions([dt_c3_6__connsp_1,dt_c4_6__connsp_1,e3_6__connsp_1,dt_c2_6__connsp_1,dt_c1_6__connsp_1,dt_c5_6__connsp_1,dt_c6_6__connsp_1,e1_6__connsp_1,e2_6__connsp_1])],[e8_6__connsp_1,i7_6__connsp_1]), [interesting(0.8),file(connsp_1,i6_6__connsp_1),[file(connsp_1,i6_6__connsp_1)]]). fof(i6_6_tmp__connsp_1,plain, ( ( k5_subset_1(u1_struct_0(c2_6__connsp_1),k6_pre_topc(c2_6__connsp_1,c5_6__connsp_1),c6_6__connsp_1) = k1_xboole_0 & k5_subset_1(u1_struct_0(c2_6__connsp_1),c5_6__connsp_1,k6_pre_topc(c2_6__connsp_1,c6_6__connsp_1)) = k1_xboole_0 ) => r1_connsp_1(c1_6__connsp_1,c3_6__connsp_1,c4_6__connsp_1) ), inference(discharge_asm,[status(thm),assumptions([dt_c3_6__connsp_1,dt_c4_6__connsp_1,dt_c2_6__connsp_1,dt_c1_6__connsp_1,dt_c5_6__connsp_1,dt_c6_6__connsp_1,e1_6__connsp_1,e2_6__connsp_1]),discharge_asm(discharge,[e3_6__connsp_1])],[e3_6__connsp_1,i6_6__connsp_1]), [interesting(0.8),i5_6__connsp_1]). fof(i5_6__connsp_1,plain,( ~ ( r1_connsp_1(c2_6__connsp_1,c5_6__connsp_1,c6_6__connsp_1) & ~ r1_connsp_1(c1_6__connsp_1,c3_6__connsp_1,c4_6__connsp_1) ) ), inference(mizar_def_expansion,[status(thm),assumptions([dt_c3_6__connsp_1,dt_c4_6__connsp_1,dt_c2_6__connsp_1,dt_c1_6__connsp_1,dt_c5_6__connsp_1,dt_c6_6__connsp_1,e1_6__connsp_1,e2_6__connsp_1])],[i6_6_tmp__connsp_1,d7_xboole_0,d1_connsp_1,dt_l1_struct_0,dt_m1_pre_topc,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_pre_topc,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,rc1_membered,rc1_subset_1,rc2_subset_1,commutativity_k3_xboole_0,idempotence_k3_xboole_0,commutativity_k5_subset_1,idempotence_k5_subset_1,symmetry_r1_connsp_1,symmetry_r1_xboole_0,redefinition_k5_subset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k3_xboole_0,dt_k5_subset_1,dt_k6_pre_topc,dt_l1_pre_topc,dt_m1_subset_1,dt_u1_struct_0,dt_c1_6__connsp_1,dt_c2_6__connsp_1,dt_c3_6__connsp_1,dt_c4_6__connsp_1,dt_c5_6__connsp_1,dt_c6_6__connsp_1,fc1_subset_1,fc6_membered]), [interesting(0.8),file(connsp_1,i5_6__connsp_1),[file(connsp_1,i5_6__connsp_1)]]). fof(i4_6__connsp_1,plain, ( ( c5_6__connsp_1 = c3_6__connsp_1 & c6_6__connsp_1 = c4_6__connsp_1 & r1_connsp_1(c2_6__connsp_1,c5_6__connsp_1,c6_6__connsp_1) ) => r1_connsp_1(c1_6__connsp_1,c3_6__connsp_1,c4_6__connsp_1) ), inference(discharge_asm,[status(thm),assumptions([dt_c3_6__connsp_1,dt_c4_6__connsp_1,dt_c2_6__connsp_1,dt_c1_6__connsp_1,dt_c5_6__connsp_1,dt_c6_6__connsp_1]),discharge_asm(discharge,[e1_6__connsp_1,e2_6__connsp_1])],[e1_6__connsp_1,e2_6__connsp_1,i5_6__connsp_1]), [interesting(0.8),file(connsp_1,i4_6__connsp_1),[file(connsp_1,i4_6__connsp_1)]]). fof(i4_6_tmp__connsp_1,plain, ( ( m1_subset_1(c5_6__connsp_1,k1_zfmisc_1(u1_struct_0(c2_6__connsp_1))) & m1_subset_1(c6_6__connsp_1,k1_zfmisc_1(u1_struct_0(c2_6__connsp_1))) ) => ( ( c5_6__connsp_1 = c3_6__connsp_1 & c6_6__connsp_1 = c4_6__connsp_1 & r1_connsp_1(c2_6__connsp_1,c5_6__connsp_1,c6_6__connsp_1) ) => r1_connsp_1(c1_6__connsp_1,c3_6__connsp_1,c4_6__connsp_1) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c3_6__connsp_1,dt_c4_6__connsp_1,dt_c2_6__connsp_1,dt_c1_6__connsp_1]),discharge_asm(discharge,[dt_c5_6__connsp_1,dt_c6_6__connsp_1])],[dt_c5_6__connsp_1,dt_c6_6__connsp_1,i4_6__connsp_1]), [interesting(0.8),i3_6__connsp_1]). fof(i3_6__connsp_1,plain,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c2_6__connsp_1))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c2_6__connsp_1))) => ( ( A = c3_6__connsp_1 & B = c4_6__connsp_1 & r1_connsp_1(c2_6__connsp_1,A,B) ) => r1_connsp_1(c1_6__connsp_1,c3_6__connsp_1,c4_6__connsp_1) ) ) ) ), inference(let,[status(thm),assumptions([dt_c3_6__connsp_1,dt_c4_6__connsp_1,dt_c2_6__connsp_1,dt_c1_6__connsp_1])],[i4_6_tmp__connsp_1,dh_c5_6__connsp_1,dh_c6_6__connsp_1]), [interesting(0.8),file(connsp_1,i3_6__connsp_1),[file(connsp_1,i3_6__connsp_1)]]). fof(i3_6_tmp__connsp_1,plain, ( ( m1_subset_1(c3_6__connsp_1,k1_zfmisc_1(u1_struct_0(c1_6__connsp_1))) & m1_subset_1(c4_6__connsp_1,k1_zfmisc_1(u1_struct_0(c1_6__connsp_1))) ) => ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c2_6__connsp_1))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c2_6__connsp_1))) => ( ( A = c3_6__connsp_1 & B = c4_6__connsp_1 & r1_connsp_1(c2_6__connsp_1,A,B) ) => r1_connsp_1(c1_6__connsp_1,c3_6__connsp_1,c4_6__connsp_1) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c2_6__connsp_1,dt_c1_6__connsp_1]),discharge_asm(discharge,[dt_c3_6__connsp_1,dt_c4_6__connsp_1])],[dt_c3_6__connsp_1,dt_c4_6__connsp_1,i3_6__connsp_1]), [interesting(0.8),i2_6__connsp_1]). fof(i2_6__connsp_1,plain,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_6__connsp_1))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_6__connsp_1))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c2_6__connsp_1))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(c2_6__connsp_1))) => ( ( C = A & D = B & r1_connsp_1(c2_6__connsp_1,C,D) ) => r1_connsp_1(c1_6__connsp_1,A,B) ) ) ) ) ) ), inference(let,[status(thm),assumptions([dt_c2_6__connsp_1,dt_c1_6__connsp_1])],[i3_6_tmp__connsp_1,dh_c3_6__connsp_1,dh_c4_6__connsp_1]), [interesting(0.8),file(connsp_1,i2_6__connsp_1),[file(connsp_1,i2_6__connsp_1)]]). fof(i2_6_tmp__connsp_1,plain, ( m1_pre_topc(c2_6__connsp_1,c1_6__connsp_1) => ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_6__connsp_1))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_6__connsp_1))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c2_6__connsp_1))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(c2_6__connsp_1))) => ( ( C = A & D = B & r1_connsp_1(c2_6__connsp_1,C,D) ) => r1_connsp_1(c1_6__connsp_1,A,B) ) ) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_6__connsp_1]),discharge_asm(discharge,[dt_c2_6__connsp_1])],[dt_c2_6__connsp_1,i2_6__connsp_1]), [interesting(0.8),i1_6__connsp_1]). fof(i1_6__connsp_1,plain,( ! [A] : ( m1_pre_topc(A,c1_6__connsp_1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_6__connsp_1))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_6__connsp_1))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ( ( D = B & E = C & r1_connsp_1(A,D,E) ) => r1_connsp_1(c1_6__connsp_1,B,C) ) ) ) ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_6__connsp_1])],[i2_6_tmp__connsp_1,dh_c2_6__connsp_1]), [interesting(0.8),file(connsp_1,i1_6__connsp_1),[file(connsp_1,i1_6__connsp_1)]]). fof(i1_6_tmp__connsp_1,plain, ( ( v2_pre_topc(c1_6__connsp_1) & l1_pre_topc(c1_6__connsp_1) ) => ! [A] : ( m1_pre_topc(A,c1_6__connsp_1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_6__connsp_1))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_6__connsp_1))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ( ( D = B & E = C & r1_connsp_1(A,D,E) ) => r1_connsp_1(c1_6__connsp_1,B,C) ) ) ) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_6__connsp_1])],[dt_c1_6__connsp_1,i1_6__connsp_1]), [interesting(1),t6_connsp_1]). fof(t6_connsp_1,theorem,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(B))) => ( ( E = C & F = D & r1_connsp_1(B,E,F) ) => r1_connsp_1(A,C,D) ) ) ) ) ) ) ) ), inference(let,[status(thm),assumptions([])],[i1_6_tmp__connsp_1,dh_c1_6__connsp_1]), [interesting(1),file(connsp_1,t6_connsp_1),[file(connsp_1,t6_connsp_1)]]).