% Mizar problem: t10_conmetr,conmetr,544,45 fof(t10_conmetr,conjecture,( ! [A] : ( ( ~ v3_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ( v4_conmetr(A) => v7_conmetr(A) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v1_analoaf,antisymmetry_r2_hidden,cc1_analmetr,d10_analmetr,d11_analmetr,d1_aff_1,d4_conmetr,d7_conmetr,dt_g1_analoaf,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k3_analmetr,dt_l1_analmetr,dt_l1_analoaf,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_analoaf,dt_u1_struct_0,existence_l1_analmetr,existence_l1_analoaf,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc2_analmetr,fc3_analmetr,fc4_analmetr,free_g1_analoaf,rc2_analmetr,redefinition_m2_relset_1,redefinition_r10_analmetr,redefinition_r11_analmetr,redefinition_r4_aff_1,reflexivity_r1_tarski,symmetry_r10_analmetr,symmetry_r11_analmetr,symmetry_r4_aff_1,t15_aff_1,t1_subset,t23_aff_1,t30_aff_1,t32_aff_1,t39_aff_1,t3_subset,t47_analmetr,t48_analmetr,t4_subset,t51_analmetr,t53_aff_1,t55_aff_1,t55_analmetr,t57_analmetr,t58_analmetr,t62_analmetr,t64_analmetr,t72_aff_1,t72_analmetr,t73_analmetr,t74_aff_1,t78_analmetr,t81_analmetr,t82_analmetr,t84_analmetr,t85_analmetr]), [file(conmetr,t10_conmetr)]). 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(antisymmetry_r2_hidden,axiom,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), []). fof(cc1_analmetr,axiom,( ! [A] : ( l1_analmetr(A) => ( ( ~ v3_struct_0(A) & v3_analmetr(A) ) => ( ~ v3_struct_0(A) & v2_analmetr(A) ) ) ) ), file(analmetr,cc1_analmetr), []). fof(d10_analmetr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_analmetr(A) ) => ( v3_analmetr(A) <=> ( ~ v3_struct_0(g1_analoaf(u1_struct_0(A),u1_analoaf(A))) & ~ v3_realset2(g1_analoaf(u1_struct_0(A),u1_analoaf(A))) & v1_diraf(g1_analoaf(u1_struct_0(A),u1_analoaf(A))) & v2_diraf(g1_analoaf(u1_struct_0(A),u1_analoaf(A))) & l1_analoaf(g1_analoaf(u1_struct_0(A),u1_analoaf(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)) => ( ( r5_analmetr(A,B,C,B,C) => B = C ) & r5_analmetr(A,B,C,D,D) & ( r5_analmetr(A,B,C,D,E) => ( r5_analmetr(A,B,C,E,D) & r5_analmetr(A,D,E,B,C) ) ) & ~ ( r5_analmetr(A,B,C,F,G) & r4_analmetr(A,B,C,H,I) & ~ r5_analmetr(A,F,G,H,I) & B != C ) & ~ ( r5_analmetr(A,B,C,F,G) & r5_analmetr(A,B,C,H,I) & ~ r4_analmetr(A,F,G,H,I) & B != C ) ) ) ) ) ) ) ) ) ) & ! [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)) & r5_analmetr(A,B,C,D,E) & D != E ) ) ) ) ) ) ) ), file(analmetr,d10_analmetr), []). fof(d11_analmetr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_analmetr(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)) => ( r6_analmetr(A,B,C,D) <=> r4_analmetr(A,B,C,B,D) ) ) ) ) ) ), file(analmetr,d11_analmetr), []). fof(d1_aff_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_aff_1(A,B,C,D) <=> r2_analoaf(A,B,C,B,D) ) ) ) ) ) ), file(aff_1,d1_aff_1), []). fof(d4_conmetr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ( v4_conmetr(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,k1_zfmisc_1(u1_struct_0(A))) => ! [K] : ( m1_subset_1(K,k1_zfmisc_1(u1_struct_0(A))) => ( ( r11_analmetr(A,J,K) & r2_hidden(B,J) & r2_hidden(D,J) & r2_hidden(G,J) & r2_hidden(I,J) & r2_hidden(C,K) & r2_hidden(E,K) & r2_hidden(F,K) & r2_hidden(H,K) & r5_analmetr(A,B,C,F,G) & r5_analmetr(A,C,D,G,H) & r5_analmetr(A,D,E,H,I) ) => ( r2_hidden(C,J) | r2_hidden(E,J) | r5_analmetr(A,B,E,F,I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ), file(conmetr,d4_conmetr), []). fof(d7_conmetr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ( v7_conmetr(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,k1_zfmisc_1(u1_struct_0(A))) => ! [K] : ( m1_subset_1(K,k1_zfmisc_1(u1_struct_0(A))) => ( ( r11_analmetr(A,J,K) & r2_hidden(B,J) & r2_hidden(D,J) & r2_hidden(F,J) & r2_hidden(H,J) & r2_hidden(C,K) & r2_hidden(E,K) & r2_hidden(G,K) & r2_hidden(I,K) & r4_analmetr(A,D,C,H,G) & r4_analmetr(A,C,B,G,F) & r4_analmetr(A,B,E,F,I) ) => ( r2_hidden(E,J) | r2_hidden(C,J) | r2_hidden(G,J) | r2_hidden(I,J) | r2_hidden(B,K) | r2_hidden(D,K) | r2_hidden(F,K) | r2_hidden(H,K) | r4_analmetr(A,D,E,H,I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ), file(conmetr,d7_conmetr), []). 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_k3_analmetr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_analmetr(A) ) => ( v1_analoaf(k3_analmetr(A)) & l1_analoaf(k3_analmetr(A)) ) ) ), file(analmetr,k3_analmetr), []). fof(dt_l1_analmetr,axiom,( ! [A] : ( l1_analmetr(A) => l1_analoaf(A) ) ), file(analmetr,l1_analmetr), []). fof(dt_l1_analoaf,axiom,( ! [A] : ( l1_analoaf(A) => l1_struct_0(A) ) ), file(analoaf,l1_analoaf), []). fof(dt_l1_struct_0,axiom,( $true ), file(struct_0,l1_struct_0), []). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), []). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), []). fof(dt_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_analmetr,axiom,( ? [A] : l1_analmetr(A) ), file(analmetr,l1_analmetr), []). fof(existence_l1_analoaf,axiom,( ? [A] : l1_analoaf(A) ), file(analoaf,l1_analoaf), []). fof(existence_l1_struct_0,axiom,( ? [A] : l1_struct_0(A) ), file(struct_0,l1_struct_0), []). fof(existence_m1_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), []). fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), []). fof(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), []). fof(fc2_analmetr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_analmetr(A) ) => ( ~ v3_struct_0(k3_analmetr(A)) & v1_analoaf(k3_analmetr(A)) ) ) ), file(analmetr,fc2_analmetr), []). fof(fc3_analmetr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_analmetr(A) & l1_analmetr(A) ) => ( ~ v3_struct_0(k3_analmetr(A)) & ~ v3_realset2(k3_analmetr(A)) & v1_analoaf(k3_analmetr(A)) & v1_diraf(k3_analmetr(A)) ) ) ), file(analmetr,fc3_analmetr), []). fof(fc4_analmetr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ( ~ v3_struct_0(k3_analmetr(A)) & ~ v3_realset2(k3_analmetr(A)) & v1_analoaf(k3_analmetr(A)) & v1_diraf(k3_analmetr(A)) & v2_diraf(k3_analmetr(A)) ) ) ), file(analmetr,fc4_analmetr), []). 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(rc2_analmetr,axiom,( ? [A] : ( l1_analmetr(A) & ~ v3_struct_0(A) ) ), file(analmetr,rc2_analmetr), []). fof(redefinition_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) <=> m1_relset_1(C,A,B) ) ), file(relset_1,m2_relset_1), []). fof(redefinition_r10_analmetr,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_analmetr(A) & l1_analmetr(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ( r10_analmetr(A,B,C) <=> r9_analmetr(A,B,C) ) ) ), file(analmetr,r10_analmetr), []). fof(redefinition_r11_analmetr,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_analmetr(A) & l1_analmetr(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ( r11_analmetr(A,B,C) <=> r8_analmetr(A,B,C) ) ) ), file(analmetr,r11_analmetr), []). fof(redefinition_r4_aff_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ( r4_aff_1(A,B,C) <=> r3_aff_1(A,B,C) ) ) ), file(aff_1,r4_aff_1), []). fof(reflexivity_r1_tarski,axiom,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), []). fof(symmetry_r10_analmetr,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_analmetr(A) & l1_analmetr(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ( r10_analmetr(A,B,C) => r10_analmetr(A,C,B) ) ) ), file(analmetr,r10_analmetr), []). fof(symmetry_r11_analmetr,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_analmetr(A) & l1_analmetr(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ( r11_analmetr(A,B,C) => r11_analmetr(A,C,B) ) ) ), file(analmetr,r11_analmetr), []). fof(symmetry_r4_aff_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ( r4_aff_1(A,B,C) => r4_aff_1(A,C,B) ) ) ), file(aff_1,r4_aff_1), []). fof(t15_aff_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_aff_1(A,B,C,D) => ( r1_aff_1(A,B,D,C) & r1_aff_1(A,C,B,D) & r1_aff_1(A,C,D,B) & r1_aff_1(A,D,B,C) & r1_aff_1(A,D,C,B) ) ) ) ) ) ) ), file(aff_1,t15_aff_1), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t23_aff_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(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)) => ( ( r1_aff_1(A,B,D,E) & r2_analoaf(A,C,D,C,E) ) => ( r1_aff_1(A,B,C,D) | D = E ) ) ) ) ) ) ) ), file(aff_1,t23_aff_1), []). fof(t30_aff_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,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(A))) => ~ ( v1_aff_1(D,A) & v1_aff_1(E,A) & r2_hidden(B,D) & r2_hidden(C,D) & r2_hidden(B,E) & r2_hidden(C,E) & B != C & D != E ) ) ) ) ) ) ), file(aff_1,t30_aff_1), []). fof(t32_aff_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v1_aff_1(C,A) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( B != D & r2_hidden(D,C) ) ) ) ) ) ) ), file(aff_1,t32_aff_1), []). fof(t39_aff_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(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,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_aff_1(E,A) & r2_hidden(B,E) & r2_hidden(C,E) & r1_aff_1(A,B,C,D) ) => ( B = C | r2_hidden(D,E) ) ) ) ) ) ) ) ), file(aff_1,t39_aff_1), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t47_analmetr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) <=> m1_subset_1(B,u1_struct_0(k3_analmetr(A))) ) ) ), file(analmetr,t47_analmetr), []). fof(t48_analmetr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_analmetr(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(k3_analmetr(A))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k3_analmetr(A))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k3_analmetr(A))) => ! [I] : ( m1_subset_1(I,u1_struct_0(k3_analmetr(A))) => ( ( B = F & C = G & D = H & E = I ) => ( r4_analmetr(A,B,C,D,E) <=> r2_analoaf(k3_analmetr(A),F,G,H,I) ) ) ) ) ) ) ) ) ) ) ) ), file(analmetr,t48_analmetr), []). fof(t4_subset,axiom,( ! [A,B,C] : ( ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) ) => m1_subset_1(A,C) ) ), file(subset,t4_subset), []). fof(t51_analmetr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_analmetr(A) ) => ( v3_analmetr(A) <=> ( ~ ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => B = C ) ) & ! [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)) => ( r4_analmetr(A,B,C,C,B) & r4_analmetr(A,B,C,D,D) & ~ ( r4_analmetr(A,B,C,F,G) & r4_analmetr(A,B,C,H,I) & ~ r4_analmetr(A,F,G,H,I) & B != C ) & ( r4_analmetr(A,B,C,B,D) => r4_analmetr(A,C,B,C,D) ) & ? [J] : ( m1_subset_1(J,u1_struct_0(A)) & r4_analmetr(A,B,C,D,J) & r4_analmetr(A,B,D,C,J) ) & ~ ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,u1_struct_0(A)) => ! [L] : ( m1_subset_1(L,u1_struct_0(A)) => r4_analmetr(A,J,K,J,L) ) ) ) & ? [J] : ( m1_subset_1(J,u1_struct_0(A)) & r4_analmetr(A,B,C,D,J) & D != J ) & ~ ( r4_analmetr(A,B,C,C,E) & C != B & ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ~ ( r4_analmetr(A,D,C,C,J) & r4_analmetr(A,D,B,E,J) ) ) ) & ( r5_analmetr(A,B,C,B,C) => B = C ) & r5_analmetr(A,B,C,D,D) & ( r5_analmetr(A,B,C,D,E) => ( r5_analmetr(A,B,C,E,D) & r5_analmetr(A,D,E,B,C) ) ) & ~ ( r5_analmetr(A,B,C,F,G) & r4_analmetr(A,B,C,H,I) & ~ r5_analmetr(A,F,G,H,I) & B != C ) & ~ ( r5_analmetr(A,B,C,F,G) & r5_analmetr(A,B,C,H,I) & ~ r4_analmetr(A,F,G,H,I) & B != C ) & ? [J] : ( m1_subset_1(J,u1_struct_0(A)) & r5_analmetr(A,B,C,D,J) & D != J ) & ~ ( ~ r4_analmetr(A,B,C,D,E) & ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ~ ( r4_analmetr(A,B,C,B,J) & r4_analmetr(A,D,E,D,J) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ), file(analmetr,t51_analmetr), []). fof(t53_aff_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(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,k1_zfmisc_1(u1_struct_0(A))) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(A))) => ( ( r2_hidden(B,F) & r2_hidden(C,F) & r2_hidden(D,G) & r2_hidden(E,G) & r3_aff_1(A,F,G) ) => r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) ) ) ), file(aff_1,t53_aff_1), []). fof(t55_aff_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_aff_1(B,A) => r3_aff_1(A,B,B) ) ) ) ), file(aff_1,t55_aff_1), []). fof(t55_analmetr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_analmetr(A) & l1_analmetr(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(k3_analmetr(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k3_analmetr(A))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k3_analmetr(A))) => ( ( B = E & C = F & D = G ) => ( r6_analmetr(A,B,C,D) <=> r1_aff_1(k3_analmetr(A),E,F,G) ) ) ) ) ) ) ) ) ) ), file(analmetr,t55_analmetr), []). fof(t57_analmetr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) <=> m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_analmetr(A)))) ) ) ), file(analmetr,t57_analmetr), []). fof(t58_analmetr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_analmetr(A)))) => ( B = C => ( v4_analmetr(B,A) <=> v1_aff_1(C,k3_analmetr(A)) ) ) ) ) ) ), file(analmetr,t58_analmetr), []). fof(t62_analmetr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,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(A))) => ( ( r7_analmetr(A,B,C,D) => v4_analmetr(D,A) ) & ( r8_analmetr(A,D,E) => ( v4_analmetr(D,A) & v4_analmetr(E,A) ) ) ) ) ) ) ) ) ), file(analmetr,t62_analmetr), []). fof(t64_analmetr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_analmetr(A) & l1_analmetr(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))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_analmetr(A)))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k3_analmetr(A)))) => ( ( B = D & C = E ) => ( r9_analmetr(A,B,C) <=> r4_aff_1(k3_analmetr(A),D,E) ) ) ) ) ) ) ) ), file(analmetr,t64_analmetr), []). fof(t72_aff_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(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))) => ~ ( v1_aff_1(B,A) & v1_aff_1(C,A) & ~ r4_aff_1(A,B,C) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(D,B) & r2_hidden(D,C) ) ) ) ) ) ) ), file(aff_1,t72_aff_1), []). fof(t72_analmetr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ r11_analmetr(A,B,B) ) ) ), file(analmetr,t72_analmetr), []). fof(t73_analmetr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_analmetr(A) & l1_analmetr(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))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ~ ( ( r11_analmetr(A,B,C) | r11_analmetr(A,C,B) ) & ( r10_analmetr(A,B,D) | r10_analmetr(A,D,B) ) & ~ ( r11_analmetr(A,C,D) & r11_analmetr(A,D,C) ) ) ) ) ) ) ), file(analmetr,t73_analmetr), []). fof(t74_aff_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(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) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r1_aff_1(A,B,C,F) & r1_aff_1(A,D,E,F) ) ) ) ) ) ) ) ) ), file(aff_1,t74_aff_1), []). fof(t78_analmetr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_analmetr(A) & l1_analmetr(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))) => ! [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)) => ( ( r2_hidden(D,B) & r2_hidden(E,B) & r2_hidden(F,C) & r2_hidden(G,C) & r11_analmetr(A,B,C) ) => r5_analmetr(A,D,E,F,G) ) ) ) ) ) ) ) ) ), file(analmetr,t78_analmetr), []). fof(t81_analmetr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_analmetr(A) & l1_analmetr(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)) => ( r4_analmetr(A,B,C,D,E) => ( r4_analmetr(A,B,C,E,D) & r4_analmetr(A,C,B,D,E) & r4_analmetr(A,C,B,E,D) & r4_analmetr(A,D,E,B,C) & r4_analmetr(A,D,E,C,B) & r4_analmetr(A,E,D,B,C) & r4_analmetr(A,E,D,C,B) ) ) ) ) ) ) ) ), file(analmetr,t81_analmetr), []). fof(t82_analmetr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_analmetr(A) & l1_analmetr(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)) => ~ ( B != C & ~ ( ~ ( r4_analmetr(A,B,C,D,E) & r4_analmetr(A,B,C,F,G) ) & ~ ( r4_analmetr(A,B,C,D,E) & r4_analmetr(A,F,G,B,C) ) & ~ ( r4_analmetr(A,D,E,B,C) & r4_analmetr(A,F,G,B,C) ) & ~ ( r4_analmetr(A,D,E,B,C) & r4_analmetr(A,B,C,F,G) ) ) & ~ r4_analmetr(A,D,E,F,G) ) ) ) ) ) ) ) ) ), file(analmetr,t82_analmetr), []). fof(t84_analmetr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_analmetr(A) & l1_analmetr(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)) => ~ ( B != C & ~ ( ~ ( r4_analmetr(A,B,C,D,E) & r5_analmetr(A,B,C,F,G) ) & ~ ( r4_analmetr(A,B,C,F,G) & r5_analmetr(A,B,C,D,E) ) & ~ ( r4_analmetr(A,B,C,D,E) & r5_analmetr(A,F,G,B,C) ) & ~ ( r4_analmetr(A,B,C,F,G) & r5_analmetr(A,D,E,B,C) ) & ~ ( r4_analmetr(A,D,E,B,C) & r5_analmetr(A,F,G,B,C) ) & ~ ( r4_analmetr(A,F,G,B,C) & r5_analmetr(A,D,E,B,C) ) & ~ ( r4_analmetr(A,D,E,B,C) & r5_analmetr(A,B,C,F,G) ) & ~ ( r4_analmetr(A,F,G,B,C) & r5_analmetr(A,B,C,D,E) ) ) & ~ r5_analmetr(A,D,E,F,G) ) ) ) ) ) ) ) ) ), file(analmetr,t84_analmetr), []). fof(t85_analmetr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_analmetr(A) & l1_analmetr(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)) => ~ ( B != C & ~ ( ~ ( r5_analmetr(A,B,C,D,E) & r5_analmetr(A,B,C,F,G) ) & ~ ( r5_analmetr(A,B,C,D,E) & r5_analmetr(A,F,G,B,C) ) & ~ ( r5_analmetr(A,D,E,B,C) & r5_analmetr(A,F,G,B,C) ) & ~ ( r5_analmetr(A,D,E,B,C) & r5_analmetr(A,B,C,F,G) ) ) & ~ r4_analmetr(A,D,E,F,G) ) ) ) ) ) ) ) ) ), file(analmetr,t85_analmetr), []).