% Mizar problem: t20_hessenbe,hessenbe,202,75 fof(t20_hessenbe,conjecture,( ! [A] : ( ( ~ v3_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & v2_anproj_2(A) & v3_anproj_2(A) & v6_anproj_2(A) & v7_anproj_2(A) & l1_collsp(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)) => ( ( r1_collsp(A,D,B,C) & r1_collsp(A,G,E,F) & r1_collsp(A,D,E,H) & r1_collsp(A,G,B,H) & r1_collsp(A,D,F,I) & r1_collsp(A,C,G,I) & r1_collsp(A,B,F,J) & r1_collsp(A,C,E,J) ) => ( B = C | D = C | E = F | G = E | G = F | r1_collsp(A,D,B,G) | r1_collsp(A,J,I,H) ) ) ) ) ) ) ) ) ) ) ) ) ), inference(mizar_bg_added,[status(thm)],[cc1_projdes1,d13_anproj_2,d14_anproj_2,d7_anproj_2,dt_l1_collsp,dt_l1_struct_0,dt_m1_subset_1,dt_u1_struct_0,existence_l1_collsp,existence_l1_struct_0,existence_m1_subset_1,rc2_anproj_2,t13_hessenbe,t14_hessenbe,t16_hessenbe,t3_hessenbe,t4_hessenbe,t8_hessenbe,t9_hessenbe]), [file(hessenbe,t20_hessenbe)]). fof(cc1_projdes1,axiom,( ! [A] : ( l1_collsp(A) => ( ( ~ v3_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & v2_anproj_2(A) & v3_anproj_2(A) & ~ v7_anproj_2(A) ) => ( ~ v3_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & v2_anproj_2(A) & v3_anproj_2(A) & v5_anproj_2(A) & ~ v7_anproj_2(A) ) ) ) ), file(projdes1,cc1_projdes1), []). fof(d13_anproj_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & v2_anproj_2(A) & v3_anproj_2(A) & l1_collsp(A) ) => ( v6_anproj_2(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [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_collsp(A,B,C,D) & r1_collsp(A,B,C,E) & r1_collsp(A,B,F,G) & r1_collsp(A,B,F,H) & r1_collsp(A,C,G,K) & r1_collsp(A,F,D,K) & r1_collsp(A,C,H,J) & r1_collsp(A,E,F,J) & r1_collsp(A,D,H,I) & r1_collsp(A,E,G,I) ) => ( B = D | B = E | D = E | C = D | C = E | B = G | B = H | G = H | F = G | F = H | r1_collsp(A,B,C,F) | r1_collsp(A,I,J,K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ), file(anproj_2,d13_anproj_2), []). fof(d14_anproj_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & v2_anproj_2(A) & v3_anproj_2(A) & l1_collsp(A) ) => ( v7_anproj_2(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ? [F] : ( m1_subset_1(F,u1_struct_0(A)) & r1_collsp(A,B,C,F) & r1_collsp(A,D,E,F) ) ) ) ) ) ) ) ), file(anproj_2,d14_anproj_2), []). fof(d7_anproj_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_collsp(A) ) => ( v2_collsp(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_collsp(A,B,C,B) & r1_collsp(A,B,B,C) & r1_collsp(A,B,C,C) ) ) ) ) ) ) ), file(anproj_2,d7_anproj_2), []). fof(dt_l1_collsp,axiom,( ! [A] : ( l1_collsp(A) => l1_struct_0(A) ) ), file(collsp,l1_collsp), []). fof(dt_l1_struct_0,axiom,( $true ), file(struct_0,l1_struct_0), []). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), []). fof(dt_u1_struct_0,axiom,( $true ), file(struct_0,u1_struct_0), []). fof(existence_l1_collsp,axiom,( ? [A] : l1_collsp(A) ), file(collsp,l1_collsp), []). fof(existence_l1_struct_0,axiom,( ? [A] : l1_struct_0(A) ), file(struct_0,l1_struct_0), []). fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), []). fof(rc2_anproj_2,axiom,( ? [A] : ( l1_collsp(A) & ~ v3_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & v2_anproj_2(A) & v3_anproj_2(A) ) ), file(anproj_2,rc2_anproj_2), []). fof(t13_hessenbe,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & v2_anproj_2(A) & v3_anproj_2(A) & l1_collsp(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)) => ~ ( ~ r1_collsp(A,B,C,D) & r1_collsp(A,B,C,E) & r1_collsp(A,D,F,E) & F != D & E != B & r1_collsp(A,F,B,D) ) ) ) ) ) ) ) ), file(hessenbe,t13_hessenbe), []). fof(t14_hessenbe,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & v2_anproj_2(A) & v3_anproj_2(A) & l1_collsp(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)) => ~ ( ~ r1_collsp(A,B,C,D) & r1_collsp(A,B,C,E) & r1_collsp(A,D,E,F) & B != E & E != F & r1_collsp(A,C,B,F) ) ) ) ) ) ) ) ), file(hessenbe,t14_hessenbe), []). fof(t16_hessenbe,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & v2_anproj_2(A) & v3_anproj_2(A) & l1_collsp(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)) => ~ ( ~ r1_collsp(A,B,C,D) & r1_collsp(A,B,C,E) & r1_collsp(A,D,F,B) & B != E & B != F & r1_collsp(A,E,B,F) ) ) ) ) ) ) ) ), file(hessenbe,t16_hessenbe), []). fof(t3_hessenbe,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & v2_anproj_2(A) & v3_anproj_2(A) & l1_collsp(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_collsp(A,B,C,D) => ( r1_collsp(A,C,D,B) & r1_collsp(A,D,B,C) & r1_collsp(A,C,B,D) & r1_collsp(A,B,D,C) & r1_collsp(A,D,C,B) ) ) ) ) ) ) ), file(hessenbe,t3_hessenbe), []). fof(t4_hessenbe,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & v2_anproj_2(A) & v3_anproj_2(A) & l1_collsp(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_collsp(A,B,C,D) & r1_collsp(A,B,C,E) ) => ( B = C | r1_collsp(A,B,D,E) ) ) ) ) ) ) ) ), file(hessenbe,t4_hessenbe), []). fof(t8_hessenbe,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & v2_anproj_2(A) & v3_anproj_2(A) & l1_collsp(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_collsp(A,B,C,D) & r1_collsp(A,B,C,E) & B != E & r1_collsp(A,B,E,D) ) ) ) ) ) ) ), file(hessenbe,t8_hessenbe), []). fof(t9_hessenbe,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & v2_anproj_2(A) & v3_anproj_2(A) & l1_collsp(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_collsp(A,B,C,E) & r1_collsp(A,B,D,E) ) => ( r1_collsp(A,B,C,D) | B = E ) ) ) ) ) ) ) ), file(hessenbe,t9_hessenbe), []).