% Mizar problem: t16_dirort,dirort,549,48 fof(t16_dirort,conjecture,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( ~ v3_struct_0(D) & v1_dirort(D) & l1_analoaf(D) ) => ( ( r1_analmetr(A,B,C) & D = k7_analort(A,B,C) ) => ( v6_dirort(D) & v4_dirort(D) & v3_dirort(D) & v2_dirort(D) ) ) ) ) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v1_analoaf,d4_dirort,d5_dirort,d6_dirort,d8_analort,d8_dirort,dt_g1_analoaf,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_analort,dt_k7_analort,dt_l1_analoaf,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_rlvect_1,dt_l2_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_analoaf,dt_u1_struct_0,existence_l1_analoaf,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_rlvect_1,existence_l2_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc2_analort,free_g1_analoaf,rc1_analoaf,rc1_dirort,rc2_analoaf,redefinition_m2_relset_1,t19_analort,t43_analort,t47_analort,t49_analort,t57_analort]), [file(dirort,t16_dirort)]). fof(abstractness_v1_analoaf,axiom,( ! [A] : ( l1_analoaf(A) => ( v1_analoaf(A) => A = g1_analoaf(u1_struct_0(A),u1_analoaf(A)) ) ) ), file(analoaf,v1_analoaf), []). fof(d4_dirort,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v1_dirort(A) & l1_analoaf(A) ) => ( v2_dirort(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ~ ( r2_analoaf(A,B,C,E,F) & r2_analoaf(A,H,I,E,F) & r2_analoaf(A,H,I,D,G) & H != I & E != F & ~ r2_analoaf(A,B,C,D,G) ) ) ) ) ) ) ) ) ) ) ) ), file(dirort,d4_dirort), []). fof(d5_dirort,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v1_dirort(A) & l1_analoaf(A) ) => ( v3_dirort(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ~ ( r2_analoaf(A,B,C,E,F) & r2_analoaf(A,E,F,H,I) & r2_analoaf(A,D,G,H,I) & H != I & E != F & ~ r2_analoaf(A,B,C,D,G) ) ) ) ) ) ) ) ) ) ) ) ), file(dirort,d5_dirort), []). fof(d6_dirort,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v1_dirort(A) & l1_analoaf(A) ) => ( v4_dirort(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ~ ( r2_analoaf(A,B,C,E,F) & r2_analoaf(A,E,F,H,I) & r2_analoaf(A,B,C,D,G) & B != C & E != F & ~ r2_analoaf(A,D,G,H,I) ) ) ) ) ) ) ) ) ) ) ) ), file(dirort,d6_dirort), []). fof(d8_analort,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k7_analort(A,B,C) = g1_analoaf(u1_struct_0(A),k5_analort(A,B,C)) ) ) ) ), file(analort,d8_analort), []). fof(d8_dirort,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v1_dirort(A) & l1_analoaf(A) ) => ( v6_dirort(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_analoaf(A,B,C,D,E) => r2_analoaf(A,D,E,B,C) ) ) ) ) ) ) ) ), file(dirort,d8_dirort), []). fof(dt_g1_analoaf,axiom,( ! [A,B] : ( m1_relset_1(B,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A)) => ( v1_analoaf(g1_analoaf(A,B)) & l1_analoaf(g1_analoaf(A,B)) ) ) ), file(analoaf,g1_analoaf), []). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). fof(dt_k5_analort,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m2_relset_1(k5_analort(A,B,C),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) ) ), file(analort,k5_analort), []). fof(dt_k7_analort,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => ( v1_analoaf(k7_analort(A,B,C)) & l1_analoaf(k7_analort(A,B,C)) ) ) ), file(analort,k7_analort), []). fof(dt_l1_analoaf,axiom,( ! [A] : ( l1_analoaf(A) => l1_struct_0(A) ) ), file(analoaf,l1_analoaf), []). fof(dt_l1_rlvect_1,axiom,( ! [A] : ( l1_rlvect_1(A) => l2_struct_0(A) ) ), file(rlvect_1,l1_rlvect_1), []). fof(dt_l1_struct_0,axiom,( $true ), file(struct_0,l1_struct_0), []). fof(dt_l2_rlvect_1,axiom,( ! [A] : ( l2_rlvect_1(A) => l1_rlvect_1(A) ) ), file(rlvect_1,l2_rlvect_1), []). fof(dt_l2_struct_0,axiom,( ! [A] : ( l2_struct_0(A) => l1_struct_0(A) ) ), file(struct_0,l2_struct_0), []). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), []). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), []). fof(dt_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ), file(relset_1,m2_relset_1), []). fof(dt_u1_analoaf,axiom,( ! [A] : ( l1_analoaf(A) => m2_relset_1(u1_analoaf(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) ) ), file(analoaf,u1_analoaf), []). fof(dt_u1_struct_0,axiom,( $true ), file(struct_0,u1_struct_0), []). fof(existence_l1_analoaf,axiom,( ? [A] : l1_analoaf(A) ), file(analoaf,l1_analoaf), []). fof(existence_l1_rlvect_1,axiom,( ? [A] : l1_rlvect_1(A) ), file(rlvect_1,l1_rlvect_1), []). fof(existence_l1_struct_0,axiom,( ? [A] : l1_struct_0(A) ), file(struct_0,l1_struct_0), []). fof(existence_l2_rlvect_1,axiom,( ? [A] : l2_rlvect_1(A) ), file(rlvect_1,l2_rlvect_1), []). fof(existence_l2_struct_0,axiom,( ? [A] : l2_struct_0(A) ), file(struct_0,l2_struct_0), []). fof(existence_m1_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), []). fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), []). fof(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), []). fof(fc2_analort,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => ( ~ v3_struct_0(k7_analort(A,B,C)) & v1_analoaf(k7_analort(A,B,C)) ) ) ), file(analort,fc2_analort), []). fof(free_g1_analoaf,axiom,( ! [A,B] : ( m1_relset_1(B,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A)) => ! [C,D] : ( g1_analoaf(A,B) = g1_analoaf(C,D) => ( A = C & B = D ) ) ) ), file(analoaf,g1_analoaf), []). fof(rc1_analoaf,axiom,( ? [A] : ( l1_analoaf(A) & v1_analoaf(A) ) ), file(analoaf,rc1_analoaf), []). fof(rc1_dirort,axiom,( ? [A] : ( l1_analoaf(A) & ~ v3_struct_0(A) & v1_dirort(A) ) ), file(dirort,rc1_dirort), []). fof(rc2_analoaf,axiom,( ? [A] : ( l1_analoaf(A) & ~ v3_struct_0(A) & v1_analoaf(A) ) ), file(analoaf,rc2_analoaf), []). fof(redefinition_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) <=> m1_relset_1(C,A,B) ) ), file(relset_1,m2_relset_1), []). fof(t19_analort,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r1_analmetr(A,B,C) & r2_analort(A,B,C,D,E,F,G) ) => r2_analort(A,B,C,F,G,D,E) ) ) ) ) ) ) ) ) ), file(analort,t19_analort), []). fof(t43_analort,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,u1_struct_0(A)) => ~ ( r1_analmetr(A,B,C) & r2_analort(A,B,C,D,E,F,G) & r2_analort(A,B,C,H,I,F,G) & r2_analort(A,B,C,H,I,J,K) & H != I & F != G & ~ r2_analort(A,B,C,D,E,J,K) ) ) ) ) ) ) ) ) ) ) ) ) ), file(analort,t43_analort), []). fof(t47_analort,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,u1_struct_0(A)) => ~ ( r1_analmetr(A,B,C) & r2_analort(A,B,C,D,E,F,G) & r2_analort(A,B,C,F,G,H,I) & r2_analort(A,B,C,J,K,H,I) & ~ r2_analort(A,B,C,D,E,J,K) & F != G & H != I ) ) ) ) ) ) ) ) ) ) ) ) ), file(analort,t47_analort), []). fof(t49_analort,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,u1_struct_0(A)) => ~ ( r1_analmetr(A,B,C) & r2_analort(A,B,C,D,E,F,G) & r2_analort(A,B,C,F,G,H,I) & r2_analort(A,B,C,D,E,J,K) & ~ r2_analort(A,B,C,J,K,H,I) & F != G & D != E ) ) ) ) ) ) ) ) ) ) ) ) ), file(analort,t49_analort), []). fof(t57_analort,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(k7_analort(A,F,G))) => ! [I] : ( m1_subset_1(I,u1_struct_0(k7_analort(A,F,G))) => ! [J] : ( m1_subset_1(J,u1_struct_0(k7_analort(A,F,G))) => ! [K] : ( m1_subset_1(K,u1_struct_0(k7_analort(A,F,G))) => ( ( B = H & C = I & D = J & E = K ) => ( r2_analoaf(k7_analort(A,F,G),H,I,J,K) <=> r2_analort(A,F,G,B,C,D,E) ) ) ) ) ) ) ) ) ) ) ) ) ) ), file(analort,t57_analort), []).