% Mizar ND problem: t3_anproj_2,anproj_2,118,71 fof(dh_c1_6__anproj_2,definition, ( ( ( ~ v3_struct_0(c1_6__anproj_2) & v3_rlvect_1(c1_6__anproj_2) & v4_rlvect_1(c1_6__anproj_2) & v5_rlvect_1(c1_6__anproj_2) & v6_rlvect_1(c1_6__anproj_2) & v7_rlvect_1(c1_6__anproj_2) & l2_rlvect_1(c1_6__anproj_2) ) => ! [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) => ! [B] : ( m1_subset_1(B,u1_struct_0(c1_6__anproj_2)) => ! [C] : ( m1_subset_1(C,u1_struct_0(c1_6__anproj_2)) => ( ( ! [D] : ( m1_subset_1(D,u1_struct_0(c1_6__anproj_2)) => ? [E] : ( m1_subset_1(E,k1_numbers) & ? [F] : ( m1_subset_1(F,k1_numbers) & ? [G] : ( m1_subset_1(G,k1_numbers) & D = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,A,E),k3_rlvect_1(c1_6__anproj_2,B,F)),k3_rlvect_1(c1_6__anproj_2,C,G)) ) ) ) ) & ! [D] : ( m1_subset_1(D,k1_numbers) => ! [E] : ( m1_subset_1(E,k1_numbers) => ! [F] : ( m1_subset_1(F,k1_numbers) => ( k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,A,D),k3_rlvect_1(c1_6__anproj_2,B,E)),k3_rlvect_1(c1_6__anproj_2,C,F)) = k1_rlvect_1(c1_6__anproj_2) => ( D = 0 & E = 0 & F = 0 ) ) ) ) ) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(c1_6__anproj_2)) => ! [E] : ( m1_subset_1(E,u1_struct_0(c1_6__anproj_2)) => ? [F] : ( m1_subset_1(F,u1_struct_0(c1_6__anproj_2)) & r2_anproj_1(c1_6__anproj_2,A,B,F) & r2_anproj_1(c1_6__anproj_2,D,E,F) & v8_rlvect_1(F,c1_6__anproj_2) ) ) ) ) ) ) ) ) => ! [H] : ( ( ~ v3_struct_0(H) & v3_rlvect_1(H) & v4_rlvect_1(H) & v5_rlvect_1(H) & v6_rlvect_1(H) & v7_rlvect_1(H) & l2_rlvect_1(H) ) => ! [I] : ( m1_subset_1(I,u1_struct_0(H)) => ! [J] : ( m1_subset_1(J,u1_struct_0(H)) => ! [K] : ( m1_subset_1(K,u1_struct_0(H)) => ( ( ! [L] : ( m1_subset_1(L,u1_struct_0(H)) => ? [M] : ( m1_subset_1(M,k1_numbers) & ? [N] : ( m1_subset_1(N,k1_numbers) & ? [O] : ( m1_subset_1(O,k1_numbers) & L = k4_rlvect_1(H,k4_rlvect_1(H,k3_rlvect_1(H,I,M),k3_rlvect_1(H,J,N)),k3_rlvect_1(H,K,O)) ) ) ) ) & ! [L] : ( m1_subset_1(L,k1_numbers) => ! [M] : ( m1_subset_1(M,k1_numbers) => ! [N] : ( m1_subset_1(N,k1_numbers) => ( k4_rlvect_1(H,k4_rlvect_1(H,k3_rlvect_1(H,I,L),k3_rlvect_1(H,J,M)),k3_rlvect_1(H,K,N)) = k1_rlvect_1(H) => ( L = 0 & M = 0 & N = 0 ) ) ) ) ) ) => ! [L] : ( m1_subset_1(L,u1_struct_0(H)) => ! [M] : ( m1_subset_1(M,u1_struct_0(H)) => ? [N] : ( m1_subset_1(N,u1_struct_0(H)) & r2_anproj_1(H,I,J,N) & r2_anproj_1(H,L,M,N) & v8_rlvect_1(N,H) ) ) ) ) ) ) ) ) ), introduced(definition,[new_symbol(c1_6__anproj_2),file(anproj_2,c1_6__anproj_2)]), [interesting(0.8),axiom,file(anproj_2,c1_6__anproj_2)]). fof(dh_c2_6__anproj_2,definition, ( ( m1_subset_1(c2_6__anproj_2,u1_struct_0(c1_6__anproj_2)) => ! [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) => ! [B] : ( m1_subset_1(B,u1_struct_0(c1_6__anproj_2)) => ( ( ! [C] : ( m1_subset_1(C,u1_struct_0(c1_6__anproj_2)) => ? [D] : ( m1_subset_1(D,k1_numbers) & ? [E] : ( m1_subset_1(E,k1_numbers) & ? [F] : ( m1_subset_1(F,k1_numbers) & C = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,D),k3_rlvect_1(c1_6__anproj_2,A,E)),k3_rlvect_1(c1_6__anproj_2,B,F)) ) ) ) ) & ! [C] : ( m1_subset_1(C,k1_numbers) => ! [D] : ( m1_subset_1(D,k1_numbers) => ! [E] : ( m1_subset_1(E,k1_numbers) => ( k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,C),k3_rlvect_1(c1_6__anproj_2,A,D)),k3_rlvect_1(c1_6__anproj_2,B,E)) = k1_rlvect_1(c1_6__anproj_2) => ( C = 0 & D = 0 & E = 0 ) ) ) ) ) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(c1_6__anproj_2)) => ! [D] : ( m1_subset_1(D,u1_struct_0(c1_6__anproj_2)) => ? [E] : ( m1_subset_1(E,u1_struct_0(c1_6__anproj_2)) & r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,A,E) & r2_anproj_1(c1_6__anproj_2,C,D,E) & v8_rlvect_1(E,c1_6__anproj_2) ) ) ) ) ) ) ) => ! [G] : ( m1_subset_1(G,u1_struct_0(c1_6__anproj_2)) => ! [H] : ( m1_subset_1(H,u1_struct_0(c1_6__anproj_2)) => ! [I] : ( m1_subset_1(I,u1_struct_0(c1_6__anproj_2)) => ( ( ! [J] : ( m1_subset_1(J,u1_struct_0(c1_6__anproj_2)) => ? [K] : ( m1_subset_1(K,k1_numbers) & ? [L] : ( m1_subset_1(L,k1_numbers) & ? [M] : ( m1_subset_1(M,k1_numbers) & J = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,G,K),k3_rlvect_1(c1_6__anproj_2,H,L)),k3_rlvect_1(c1_6__anproj_2,I,M)) ) ) ) ) & ! [J] : ( m1_subset_1(J,k1_numbers) => ! [K] : ( m1_subset_1(K,k1_numbers) => ! [L] : ( m1_subset_1(L,k1_numbers) => ( k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,G,J),k3_rlvect_1(c1_6__anproj_2,H,K)),k3_rlvect_1(c1_6__anproj_2,I,L)) = k1_rlvect_1(c1_6__anproj_2) => ( J = 0 & K = 0 & L = 0 ) ) ) ) ) ) => ! [J] : ( m1_subset_1(J,u1_struct_0(c1_6__anproj_2)) => ! [K] : ( m1_subset_1(K,u1_struct_0(c1_6__anproj_2)) => ? [L] : ( m1_subset_1(L,u1_struct_0(c1_6__anproj_2)) & r2_anproj_1(c1_6__anproj_2,G,H,L) & r2_anproj_1(c1_6__anproj_2,J,K,L) & v8_rlvect_1(L,c1_6__anproj_2) ) ) ) ) ) ) ) ), introduced(definition,[new_symbol(c2_6__anproj_2),file(anproj_2,c2_6__anproj_2)]), [interesting(0.8),axiom,file(anproj_2,c2_6__anproj_2)]). fof(dh_c3_6__anproj_2,definition, ( ( m1_subset_1(c3_6__anproj_2,u1_struct_0(c1_6__anproj_2)) => ! [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) => ( ( ! [B] : ( m1_subset_1(B,u1_struct_0(c1_6__anproj_2)) => ? [C] : ( m1_subset_1(C,k1_numbers) & ? [D] : ( m1_subset_1(D,k1_numbers) & ? [E] : ( m1_subset_1(E,k1_numbers) & B = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,C),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,D)),k3_rlvect_1(c1_6__anproj_2,A,E)) ) ) ) ) & ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,k1_numbers) => ! [D] : ( m1_subset_1(D,k1_numbers) => ( k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,B),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,C)),k3_rlvect_1(c1_6__anproj_2,A,D)) = k1_rlvect_1(c1_6__anproj_2) => ( B = 0 & C = 0 & D = 0 ) ) ) ) ) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(c1_6__anproj_2)) => ! [C] : ( m1_subset_1(C,u1_struct_0(c1_6__anproj_2)) => ? [D] : ( m1_subset_1(D,u1_struct_0(c1_6__anproj_2)) & r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,D) & r2_anproj_1(c1_6__anproj_2,B,C,D) & v8_rlvect_1(D,c1_6__anproj_2) ) ) ) ) ) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(c1_6__anproj_2)) => ! [G] : ( m1_subset_1(G,u1_struct_0(c1_6__anproj_2)) => ( ( ! [H] : ( m1_subset_1(H,u1_struct_0(c1_6__anproj_2)) => ? [I] : ( m1_subset_1(I,k1_numbers) & ? [J] : ( m1_subset_1(J,k1_numbers) & ? [K] : ( m1_subset_1(K,k1_numbers) & H = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,I),k3_rlvect_1(c1_6__anproj_2,F,J)),k3_rlvect_1(c1_6__anproj_2,G,K)) ) ) ) ) & ! [H] : ( m1_subset_1(H,k1_numbers) => ! [I] : ( m1_subset_1(I,k1_numbers) => ! [J] : ( m1_subset_1(J,k1_numbers) => ( k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,H),k3_rlvect_1(c1_6__anproj_2,F,I)),k3_rlvect_1(c1_6__anproj_2,G,J)) = k1_rlvect_1(c1_6__anproj_2) => ( H = 0 & I = 0 & J = 0 ) ) ) ) ) ) => ! [H] : ( m1_subset_1(H,u1_struct_0(c1_6__anproj_2)) => ! [I] : ( m1_subset_1(I,u1_struct_0(c1_6__anproj_2)) => ? [J] : ( m1_subset_1(J,u1_struct_0(c1_6__anproj_2)) & r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,F,J) & r2_anproj_1(c1_6__anproj_2,H,I,J) & v8_rlvect_1(J,c1_6__anproj_2) ) ) ) ) ) ) ), introduced(definition,[new_symbol(c3_6__anproj_2),file(anproj_2,c3_6__anproj_2)]), [interesting(0.8),axiom,file(anproj_2,c3_6__anproj_2)]). fof(dh_c4_6__anproj_2,definition, ( ( m1_subset_1(c4_6__anproj_2,u1_struct_0(c1_6__anproj_2)) => ( ( ! [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) => ? [B] : ( m1_subset_1(B,k1_numbers) & ? [C] : ( m1_subset_1(C,k1_numbers) & ? [D] : ( m1_subset_1(D,k1_numbers) & A = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,B),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,C)),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,D)) ) ) ) ) & ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,k1_numbers) => ( k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,A),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,B)),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,C)) = k1_rlvect_1(c1_6__anproj_2) => ( A = 0 & B = 0 & C = 0 ) ) ) ) ) ) => ! [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) => ! [B] : ( m1_subset_1(B,u1_struct_0(c1_6__anproj_2)) => ? [C] : ( m1_subset_1(C,u1_struct_0(c1_6__anproj_2)) & r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,C) & r2_anproj_1(c1_6__anproj_2,A,B,C) & v8_rlvect_1(C,c1_6__anproj_2) ) ) ) ) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(c1_6__anproj_2)) => ( ( ! [F] : ( m1_subset_1(F,u1_struct_0(c1_6__anproj_2)) => ? [G] : ( m1_subset_1(G,k1_numbers) & ? [H] : ( m1_subset_1(H,k1_numbers) & ? [I] : ( m1_subset_1(I,k1_numbers) & F = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,G),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,H)),k3_rlvect_1(c1_6__anproj_2,E,I)) ) ) ) ) & ! [F] : ( m1_subset_1(F,k1_numbers) => ! [G] : ( m1_subset_1(G,k1_numbers) => ! [H] : ( m1_subset_1(H,k1_numbers) => ( k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,F),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,G)),k3_rlvect_1(c1_6__anproj_2,E,H)) = k1_rlvect_1(c1_6__anproj_2) => ( F = 0 & G = 0 & H = 0 ) ) ) ) ) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(c1_6__anproj_2)) => ! [G] : ( m1_subset_1(G,u1_struct_0(c1_6__anproj_2)) => ? [H] : ( m1_subset_1(H,u1_struct_0(c1_6__anproj_2)) & r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,H) & r2_anproj_1(c1_6__anproj_2,F,G,H) & v8_rlvect_1(H,c1_6__anproj_2) ) ) ) ) ) ), introduced(definition,[new_symbol(c4_6__anproj_2),file(anproj_2,c4_6__anproj_2)]), [interesting(0.8),axiom,file(anproj_2,c4_6__anproj_2)]). fof(e1_6__anproj_2,assumption,( ! [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) => ? [B] : ( m1_subset_1(B,k1_numbers) & ? [C] : ( m1_subset_1(C,k1_numbers) & ? [D] : ( m1_subset_1(D,k1_numbers) & A = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,B),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,C)),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,D)) ) ) ) ) ), introduced(assumption,[file(anproj_2,e1_6__anproj_2)]), [interesting(0.8),axiom,file(anproj_2,e1_6__anproj_2)]). fof(e2_6__anproj_2,assumption,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,k1_numbers) => ( k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,A),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,B)),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,C)) = k1_rlvect_1(c1_6__anproj_2) => ( A = 0 & B = 0 & C = 0 ) ) ) ) ) ), introduced(assumption,[file(anproj_2,e2_6__anproj_2)]), [interesting(0.8),axiom,file(anproj_2,e2_6__anproj_2)]). fof(dh_c5_6__anproj_2,definition, ( ( m1_subset_1(c5_6__anproj_2,u1_struct_0(c1_6__anproj_2)) => ! [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) => ? [B] : ( m1_subset_1(B,u1_struct_0(c1_6__anproj_2)) & r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,B) & r2_anproj_1(c1_6__anproj_2,c5_6__anproj_2,A,B) & v8_rlvect_1(B,c1_6__anproj_2) ) ) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(c1_6__anproj_2)) => ! [D] : ( m1_subset_1(D,u1_struct_0(c1_6__anproj_2)) => ? [E] : ( m1_subset_1(E,u1_struct_0(c1_6__anproj_2)) & r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,E) & r2_anproj_1(c1_6__anproj_2,C,D,E) & v8_rlvect_1(E,c1_6__anproj_2) ) ) ) ), introduced(definition,[new_symbol(c5_6__anproj_2),file(anproj_2,c5_6__anproj_2)]), [interesting(0.8),axiom,file(anproj_2,c5_6__anproj_2)]). fof(dh_c6_6__anproj_2,definition, ( ( m1_subset_1(c6_6__anproj_2,u1_struct_0(c1_6__anproj_2)) => ? [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) & r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,A) & r2_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2,A) & v8_rlvect_1(A,c1_6__anproj_2) ) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(c1_6__anproj_2)) => ? [C] : ( m1_subset_1(C,u1_struct_0(c1_6__anproj_2)) & r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,C) & r2_anproj_1(c1_6__anproj_2,c5_6__anproj_2,B,C) & v8_rlvect_1(C,c1_6__anproj_2) ) ) ), introduced(definition,[new_symbol(c6_6__anproj_2),file(anproj_2,c6_6__anproj_2)]), [interesting(0.8),axiom,file(anproj_2,c6_6__anproj_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_l2_struct_0,axiom,( ? [A] : l2_struct_0(A) ), file(struct_0,l2_struct_0), [interesting(0.9),axiom,file(struct_0,l2_struct_0)]). fof(dt_l2_struct_0,axiom,( ! [A] : ( l2_struct_0(A) => l1_struct_0(A) ) ), file(struct_0,l2_struct_0), [interesting(0.9),axiom,file(struct_0,l2_struct_0)]). fof(rc4_struct_0,theorem,( ? [A] : ( l2_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc4_struct_0), [interesting(0.9),axiom,file(struct_0,rc4_struct_0)]). 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_l1_rlvect_1,axiom,( ? [A] : l1_rlvect_1(A) ), file(rlvect_1,l1_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,l1_rlvect_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_k5_ordinal2,axiom,( $true ), file(ordinal2,k5_ordinal2), [interesting(0.9),axiom,file(ordinal2,k5_ordinal2)]). fof(dt_l1_rlvect_1,axiom,( ! [A] : ( l1_rlvect_1(A) => l2_struct_0(A) ) ), file(rlvect_1,l1_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,l1_rlvect_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(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(cc6_membered,theorem,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v1_membered(A) & v2_membered(A) ) ) ), file(membered,cc6_membered), [interesting(0.9),axiom,file(membered,cc6_membered)]). fof(cc9_membered,theorem,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k5_numbers)) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc9_membered), [interesting(0.9),axiom,file(membered,cc9_membered)]). 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(fc5_membered,theorem, ( v1_membered(k5_ordinal2) & v2_membered(k5_ordinal2) & v3_membered(k5_ordinal2) & v4_membered(k5_ordinal2) & v5_membered(k5_ordinal2) ), file(membered,fc5_membered), [interesting(0.9),axiom,file(membered,fc5_membered)]). 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(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(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(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(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_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_l2_rlvect_1,axiom,( ? [A] : l2_rlvect_1(A) ), file(rlvect_1,l2_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,l2_rlvect_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(redefinition_k5_numbers,definition,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), [interesting(0.9),axiom,file(numbers,k5_numbers)]). 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_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), [interesting(0.9),axiom,file(numbers,k1_numbers)]). fof(dt_k5_numbers,axiom,( m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ), file(numbers,k5_numbers), [interesting(0.9),axiom,file(numbers,k5_numbers)]). 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_l2_rlvect_1,axiom,( ! [A] : ( l2_rlvect_1(A) => l1_rlvect_1(A) ) ), file(rlvect_1,l2_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,l2_rlvect_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(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(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_membered,theorem, ( ~ v1_xboole_0(k1_numbers) & v1_membered(k1_numbers) & v2_membered(k1_numbers) ), file(membered,fc2_membered), [interesting(0.9),axiom,file(membered,fc2_membered)]). 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(t1_numerals,theorem,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), [interesting(0.9),axiom,file(numerals,t1_numerals)]). 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(symmetry_r1_anproj_1,theorem,( ! [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)) ) => ( r1_anproj_1(A,B,C) => r1_anproj_1(A,C,B) ) ) ), file(anproj_1,r1_anproj_1), [interesting(0.9),axiom,file(anproj_1,r1_anproj_1)]). fof(reflexivity_r1_anproj_1,theorem,( ! [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)) ) => r1_anproj_1(A,B,B) ) ), file(anproj_1,r1_anproj_1), [interesting(0.9),axiom,file(anproj_1,r1_anproj_1)]). 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(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__anproj_2,assumption, ( ~ v3_struct_0(c1_6__anproj_2) & v3_rlvect_1(c1_6__anproj_2) & v4_rlvect_1(c1_6__anproj_2) & v5_rlvect_1(c1_6__anproj_2) & v6_rlvect_1(c1_6__anproj_2) & v7_rlvect_1(c1_6__anproj_2) & l2_rlvect_1(c1_6__anproj_2) ), introduced(assumption,[file(anproj_2,c1_6__anproj_2)]), [interesting(0.8),axiom,file(anproj_2,c1_6__anproj_2)]). fof(dt_c2_6__anproj_2,assumption,( m1_subset_1(c2_6__anproj_2,u1_struct_0(c1_6__anproj_2)) ), introduced(assumption,[file(anproj_2,c2_6__anproj_2)]), [interesting(0.8),axiom,file(anproj_2,c2_6__anproj_2)]). fof(dt_c3_6__anproj_2,assumption,( m1_subset_1(c3_6__anproj_2,u1_struct_0(c1_6__anproj_2)) ), introduced(assumption,[file(anproj_2,c3_6__anproj_2)]), [interesting(0.8),axiom,file(anproj_2,c3_6__anproj_2)]). fof(dt_c5_6__anproj_2,assumption,( m1_subset_1(c5_6__anproj_2,u1_struct_0(c1_6__anproj_2)) ), introduced(assumption,[file(anproj_2,c5_6__anproj_2)]), [interesting(0.8),axiom,file(anproj_2,c5_6__anproj_2)]). fof(dt_c6_6__anproj_2,assumption,( m1_subset_1(c6_6__anproj_2,u1_struct_0(c1_6__anproj_2)) ), introduced(assumption,[file(anproj_2,c6_6__anproj_2)]), [interesting(0.8),axiom,file(anproj_2,c6_6__anproj_2)]). fof(dh_c7_6__anproj_2,definition, ( ? [A] : ( m1_subset_1(A,k1_numbers) & ? [B] : ( m1_subset_1(B,k1_numbers) & ? [C] : ( m1_subset_1(C,k1_numbers) & c5_6__anproj_2 = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,A),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,B)),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,C)) ) ) ) => ( m1_subset_1(c7_6__anproj_2,k1_numbers) & ? [D] : ( m1_subset_1(D,k1_numbers) & ? [E] : ( m1_subset_1(E,k1_numbers) & c5_6__anproj_2 = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,c7_6__anproj_2),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,D)),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,E)) ) ) ) ), introduced(definition,[new_symbol(c7_6__anproj_2),file(anproj_2,c7_6__anproj_2)]), [interesting(0.8),axiom,file(anproj_2,c7_6__anproj_2)]). fof(dh_c8_6__anproj_2,definition, ( ? [A] : ( m1_subset_1(A,k1_numbers) & ? [B] : ( m1_subset_1(B,k1_numbers) & c5_6__anproj_2 = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,c7_6__anproj_2),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,A)),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,B)) ) ) => ( m1_subset_1(c8_6__anproj_2,k1_numbers) & ? [C] : ( m1_subset_1(C,k1_numbers) & c5_6__anproj_2 = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,c7_6__anproj_2),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,c8_6__anproj_2)),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,C)) ) ) ), introduced(definition,[new_symbol(c8_6__anproj_2),file(anproj_2,c8_6__anproj_2)]), [interesting(0.8),axiom,file(anproj_2,c8_6__anproj_2)]). fof(dh_c9_6__anproj_2,definition, ( ? [A] : ( m1_subset_1(A,k1_numbers) & c5_6__anproj_2 = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,c7_6__anproj_2),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,c8_6__anproj_2)),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,A)) ) => ( m1_subset_1(c9_6__anproj_2,k1_numbers) & c5_6__anproj_2 = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,c7_6__anproj_2),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,c8_6__anproj_2)),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,c9_6__anproj_2)) ) ), introduced(definition,[new_symbol(c9_6__anproj_2),file(anproj_2,c9_6__anproj_2)]), [interesting(0.8),axiom,file(anproj_2,c9_6__anproj_2)]). fof(dt_k2_rlvect_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k2_rlvect_1(A,B,C),u1_struct_0(A)) ) ), file(rlvect_1,k2_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,k2_rlvect_1)]). fof(commutativity_k4_rlvect_1,theorem,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => k4_rlvect_1(A,B,C) = k4_rlvect_1(A,C,B) ) ), file(rlvect_1,k4_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,k4_rlvect_1)]). fof(redefinition_k4_rlvect_1,definition,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => k4_rlvect_1(A,B,C) = k2_rlvect_1(A,B,C) ) ), file(rlvect_1,k4_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,k4_rlvect_1)]). fof(dt_k3_rlvect_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l2_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,k1_numbers) ) => m1_subset_1(k3_rlvect_1(A,B,C),u1_struct_0(A)) ) ), file(rlvect_1,k3_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,k3_rlvect_1)]). fof(dt_k4_rlvect_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k4_rlvect_1(A,B,C),u1_struct_0(A)) ) ), file(rlvect_1,k4_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,k4_rlvect_1)]). fof(dt_c4_6__anproj_2,assumption,( m1_subset_1(c4_6__anproj_2,u1_struct_0(c1_6__anproj_2)) ), introduced(assumption,[file(anproj_2,c4_6__anproj_2)]), [interesting(0.8),axiom,file(anproj_2,c4_6__anproj_2)]). fof(e3_6__anproj_2,plain,( ? [A] : ( m1_subset_1(A,k1_numbers) & ? [B] : ( m1_subset_1(B,k1_numbers) & ? [C] : ( m1_subset_1(C,k1_numbers) & c5_6__anproj_2 = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,A),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,B)),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,C)) ) ) ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2])],[antisymmetry_r2_hidden,existence_l2_struct_0,dt_k1_xboole_0,dt_l2_struct_0,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,fc6_membered,rc1_membered,rc4_struct_0,t1_subset,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_rlvect_1,dt_k2_rlvect_1,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_rlvect_1,cc10_membered,cc11_membered,cc15_membered,cc4_membered,fc1_struct_0,rc3_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k4_rlvect_1,existence_m1_subset_1,redefinition_k4_rlvect_1,dt_k1_numbers,dt_k3_rlvect_1,dt_k4_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,fc2_membered,e1_6__anproj_2]), [interesting(0.8),file(anproj_2,e3_6__anproj_2),[file(anproj_2,e3_6__anproj_2)]]). fof(dt_c9_6__anproj_2,plain,( m1_subset_1(c9_6__anproj_2,k1_numbers) ), inference(consider,[status(thm),assumptions([dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2])],[dh_c7_6__anproj_2,dh_c8_6__anproj_2,dh_c9_6__anproj_2,e3_6__anproj_2]), [interesting(0.8),file(anproj_2,c9_6__anproj_2),[file(anproj_2,c9_6__anproj_2)]]). fof(spc0_numerals,theorem, ( v2_xreal_0(0) & m2_subset_1(0,k1_numbers,k5_numbers) & m1_subset_1(0,k5_numbers) & m1_subset_1(0,k1_numbers) ), file(numerals,spc0_numerals), [interesting(0.9),axiom,file(numerals,spc0_numerals)]). fof(spc0_boole,theorem,( v1_xboole_0(0) ), file(boole,spc0_boole), [interesting(0.9),axiom,file(boole,spc0_boole)]). fof(e1_6_4__anproj_2,assumption, ( ~ r1_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2) & v8_rlvect_1(c5_6__anproj_2,c1_6__anproj_2) & v8_rlvect_1(c6_6__anproj_2,c1_6__anproj_2) & c9_6__anproj_2 != 0 ), introduced(assumption,[file(anproj_2,e1_6_4__anproj_2)]), [interesting(0.65),axiom,file(anproj_2,e1_6_4__anproj_2)]). fof(dh_c10_6__anproj_2,definition, ( ? [A] : ( m1_subset_1(A,k1_numbers) & ? [B] : ( m1_subset_1(B,k1_numbers) & ? [C] : ( m1_subset_1(C,k1_numbers) & c6_6__anproj_2 = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,A),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,B)),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,C)) ) ) ) => ( m1_subset_1(c10_6__anproj_2,k1_numbers) & ? [D] : ( m1_subset_1(D,k1_numbers) & ? [E] : ( m1_subset_1(E,k1_numbers) & c6_6__anproj_2 = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,c10_6__anproj_2),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,D)),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,E)) ) ) ) ), introduced(definition,[new_symbol(c10_6__anproj_2),file(anproj_2,c10_6__anproj_2)]), [interesting(0.8),axiom,file(anproj_2,c10_6__anproj_2)]). fof(dh_c11_6__anproj_2,definition, ( ? [A] : ( m1_subset_1(A,k1_numbers) & ? [B] : ( m1_subset_1(B,k1_numbers) & c6_6__anproj_2 = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,c10_6__anproj_2),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,A)),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,B)) ) ) => ( m1_subset_1(c11_6__anproj_2,k1_numbers) & ? [C] : ( m1_subset_1(C,k1_numbers) & c6_6__anproj_2 = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,c10_6__anproj_2),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,c11_6__anproj_2)),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,C)) ) ) ), introduced(definition,[new_symbol(c11_6__anproj_2),file(anproj_2,c11_6__anproj_2)]), [interesting(0.8),axiom,file(anproj_2,c11_6__anproj_2)]). fof(dh_c12_6__anproj_2,definition, ( ? [A] : ( m1_subset_1(A,k1_numbers) & c6_6__anproj_2 = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,c10_6__anproj_2),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,c11_6__anproj_2)),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,A)) ) => ( m1_subset_1(c12_6__anproj_2,k1_numbers) & c6_6__anproj_2 = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,c10_6__anproj_2),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,c11_6__anproj_2)),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,c12_6__anproj_2)) ) ), introduced(definition,[new_symbol(c12_6__anproj_2),file(anproj_2,c12_6__anproj_2)]), [interesting(0.8),axiom,file(anproj_2,c12_6__anproj_2)]). fof(e5_6__anproj_2,plain,( ? [A] : ( m1_subset_1(A,k1_numbers) & ? [B] : ( m1_subset_1(B,k1_numbers) & ? [C] : ( m1_subset_1(C,k1_numbers) & c6_6__anproj_2 = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,A),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,B)),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,C)) ) ) ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c6_6__anproj_2,e1_6__anproj_2])],[antisymmetry_r2_hidden,existence_l2_struct_0,dt_k1_xboole_0,dt_l2_struct_0,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,fc6_membered,rc1_membered,rc4_struct_0,t1_subset,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_rlvect_1,dt_k2_rlvect_1,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_rlvect_1,cc10_membered,cc11_membered,cc15_membered,cc4_membered,fc1_struct_0,rc3_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k4_rlvect_1,existence_m1_subset_1,redefinition_k4_rlvect_1,dt_k1_numbers,dt_k3_rlvect_1,dt_k4_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c6_6__anproj_2,fc2_membered,e1_6__anproj_2]), [interesting(0.8),file(anproj_2,e5_6__anproj_2),[file(anproj_2,e5_6__anproj_2)]]). fof(dt_c12_6__anproj_2,plain,( m1_subset_1(c12_6__anproj_2,k1_numbers) ), inference(consider,[status(thm),assumptions([dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c6_6__anproj_2,e1_6__anproj_2])],[dh_c10_6__anproj_2,dh_c11_6__anproj_2,dh_c12_6__anproj_2,e5_6__anproj_2]), [interesting(0.8),file(anproj_2,c12_6__anproj_2),[file(anproj_2,c12_6__anproj_2)]]). fof(e1_6_4_2__anproj_2,assumption,( c12_6__anproj_2 != 0 ), introduced(assumption,[file(anproj_2,e1_6_4_2__anproj_2)]), [interesting(0.5),axiom,file(anproj_2,e1_6_4_2__anproj_2)]). fof(involutiveness_k5_xcmplx_0,theorem,( ! [A] : ( v1_xcmplx_0(A) => k5_xcmplx_0(k5_xcmplx_0(A)) = A ) ), file(xcmplx_0,k5_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k5_xcmplx_0)]). fof(dt_k5_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_xcmplx_0(k5_xcmplx_0(A)) ) ), file(xcmplx_0,k5_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k5_xcmplx_0)]). fof(spc10_arithm,theorem,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k3_xcmplx_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) = k5_xcmplx_0(k3_xcmplx_0(A,B)) ) ), file(arithm,spc10_arithm), [interesting(0.9),axiom,file(arithm,spc10_arithm)]). fof(spc2_arithm,theorem,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(A,k4_xcmplx_0(1)) = k4_xcmplx_0(A) ) ), file(arithm,spc2_arithm), [interesting(0.9),axiom,file(arithm,spc2_arithm)]). fof(spc7_arithm,theorem,( ! [A,B,C] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) ) => k3_xcmplx_0(k3_xcmplx_0(A,B),C) = k3_xcmplx_0(A,k3_xcmplx_0(B,C)) ) ), file(arithm,spc6_arithm), [interesting(0.9),axiom,file(arithm,spc6_arithm)]). fof(t3_arithm,theorem,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(1,A) = A ) ), file(arithm,t3_arithm), [interesting(0.9),axiom,file(arithm,t3_arithm)]). fof(involutiveness_k1_real_1,theorem,( ! [A] : ( m1_subset_1(A,k1_numbers) => k1_real_1(k1_real_1(A)) = A ) ), file(real_1,k1_real_1), [interesting(0.9),axiom,file(real_1,k1_real_1)]). fof(involutiveness_k2_real_1,theorem,( ! [A] : ( m1_subset_1(A,k1_numbers) => k2_real_1(k2_real_1(A)) = A ) ), file(real_1,k2_real_1), [interesting(0.9),axiom,file(real_1,k2_real_1)]). fof(commutativity_k3_xcmplx_0,theorem,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k3_xcmplx_0(A,B) = k3_xcmplx_0(B,A) ) ), file(xcmplx_0,k3_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k3_xcmplx_0)]). fof(commutativity_k4_real_1,theorem,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k4_real_1(A,B) = k4_real_1(B,A) ) ), file(real_1,k4_real_1), [interesting(0.9),axiom,file(real_1,k4_real_1)]). fof(involutiveness_k4_xcmplx_0,theorem,( ! [A] : ( v1_xcmplx_0(A) => k4_xcmplx_0(k4_xcmplx_0(A)) = A ) ), file(xcmplx_0,k4_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k4_xcmplx_0)]). fof(redefinition_k1_real_1,definition,( ! [A] : ( m1_subset_1(A,k1_numbers) => k1_real_1(A) = k4_xcmplx_0(A) ) ), file(real_1,k1_real_1), [interesting(0.9),axiom,file(real_1,k1_real_1)]). fof(redefinition_k2_real_1,definition,( ! [A] : ( m1_subset_1(A,k1_numbers) => k2_real_1(A) = k5_xcmplx_0(A) ) ), file(real_1,k2_real_1), [interesting(0.9),axiom,file(real_1,k2_real_1)]). fof(redefinition_k4_real_1,definition,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k4_real_1(A,B) = k3_xcmplx_0(A,B) ) ), file(real_1,k4_real_1), [interesting(0.9),axiom,file(real_1,k4_real_1)]). fof(dt_k1_real_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => m1_subset_1(k1_real_1(A),k1_numbers) ) ), file(real_1,k1_real_1), [interesting(0.9),axiom,file(real_1,k1_real_1)]). fof(dt_k2_real_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => m1_subset_1(k2_real_1(A),k1_numbers) ) ), file(real_1,k2_real_1), [interesting(0.9),axiom,file(real_1,k2_real_1)]). fof(dt_k3_xcmplx_0,axiom,( $true ), file(xcmplx_0,k3_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k3_xcmplx_0)]). fof(dt_k4_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k4_real_1(A,B),k1_numbers) ) ), file(real_1,k4_real_1), [interesting(0.9),axiom,file(real_1,k4_real_1)]). fof(dt_k4_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_xcmplx_0(k4_xcmplx_0(A)) ) ), file(xcmplx_0,k4_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k4_xcmplx_0)]). fof(rqRealNeg__k4_xcmplx_0__rm1_r1,theorem,( k4_xcmplx_0(k4_xcmplx_0(1)) = 1 ), file(arithm,rqRealNeg__k4_xcmplx_0__rm1_r1), [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rm1_r1)]). fof(spc1_numerals,theorem, ( v2_xreal_0(1) & m2_subset_1(1,k1_numbers,k5_numbers) & m1_subset_1(1,k5_numbers) & m1_subset_1(1,k1_numbers) ), file(numerals,spc1_numerals), [interesting(0.9),axiom,file(numerals,spc1_numerals)]). fof(spc1_boole,theorem,( ~ v1_xboole_0(1) ), file(boole,spc1_boole), [interesting(0.9),axiom,file(boole,spc1_boole)]). fof(t2_arithm,theorem,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(A,0) = 0 ) ), file(arithm,t2_arithm), [interesting(0.9),axiom,file(arithm,t2_arithm)]). fof(rqRealMult__k3_xcmplx_0__r0_r0_r0,theorem,( k3_xcmplx_0(0,0) = 0 ), file(arithm,rqRealMult__k3_xcmplx_0__r0_r0_r0), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r0_r0_r0)]). fof(rqRealMult__k3_xcmplx_0__r0_r1_r0,theorem,( k3_xcmplx_0(0,1) = 0 ), file(arithm,rqRealMult__k3_xcmplx_0__r0_r1_r0), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r0_r1_r0)]). fof(rqRealMult__k3_xcmplx_0__r1_r0_r0,theorem,( k3_xcmplx_0(1,0) = 0 ), file(arithm,rqRealMult__k3_xcmplx_0__r1_r0_r0), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_r0_r0)]). fof(rqRealNeg__k4_xcmplx_0__r0_r0,theorem,( k4_xcmplx_0(0) = 0 ), file(arithm,rqRealNeg__k4_xcmplx_0__r0_r0), [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__r0_r0)]). fof(t11_anproj_1,theorem,( ! [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)) => ( ( v8_rlvect_1(B,A) & v8_rlvect_1(C,A) ) => ( r1_anproj_1(A,B,C) | ( r2_anproj_1(A,B,C,D) <=> ? [E] : ( m1_subset_1(E,k1_numbers) & ? [F] : ( m1_subset_1(F,k1_numbers) & D = k4_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,C,F)) ) ) ) ) ) ) ) ) ) ), file(anproj_1,t11_anproj_1), [interesting(0.9),axiom,file(anproj_1,t11_anproj_1)]). fof(rqRealNeg__k4_xcmplx_0__r1_rm1,theorem,( k4_xcmplx_0(1) = k4_xcmplx_0(1) ), file(arithm,rqRealNeg__k4_xcmplx_0__r1_rm1), [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__r1_rm1)]). fof(rqRealMult__k3_xcmplx_0__r1_r1_r1,theorem,( k3_xcmplx_0(1,1) = 1 ), file(arithm,rqRealMult__k3_xcmplx_0__r1_r1_r1), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_r1_r1)]). fof(e8_6_4_2__anproj_2,plain,( r2_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,1),k3_rlvect_1(c1_6__anproj_2,c6_6__anproj_2,k1_real_1(k4_real_1(c9_6__anproj_2,k2_real_1(c12_6__anproj_2)))))) ), inference(mizar_by,[status(thm),assumptions([dt_c6_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2,e1_6_4__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l2_struct_0,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l2_struct_0,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc4_struct_0,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,involutiveness_k5_xcmplx_0,existence_l1_rlvect_1,existence_l1_struct_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k2_rlvect_1,dt_k5_numbers,dt_k5_xcmplx_0,dt_l1_rlvect_1,dt_l1_struct_0,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc4_membered,fc1_struct_0,rc3_struct_0,spc10_arithm,spc2_arithm,spc7_arithm,t1_numerals,t2_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,involutiveness_k1_real_1,involutiveness_k2_real_1,commutativity_k3_xcmplx_0,commutativity_k4_real_1,commutativity_k4_rlvect_1,involutiveness_k4_xcmplx_0,symmetry_r1_anproj_1,reflexivity_r1_anproj_1,existence_l2_rlvect_1,existence_m1_subset_1,redefinition_k1_real_1,redefinition_k2_real_1,redefinition_k4_real_1,redefinition_k4_rlvect_1,dt_k1_numbers,dt_k1_real_1,dt_k2_real_1,dt_k3_rlvect_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_k4_rlvect_1,dt_k4_xcmplx_0,dt_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c12_6__anproj_2,dt_c1_6__anproj_2,dt_c5_6__anproj_2,dt_c6_6__anproj_2,dt_c9_6__anproj_2,fc2_membered,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealNeg__k4_xcmplx_0__rm1_r1,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e1_6_4__anproj_2,t11_anproj_1,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealMult__k3_xcmplx_0__r1_r1_r1]), [interesting(0.5),file(anproj_2,e8_6_4_2__anproj_2),[file(anproj_2,e8_6_4_2__anproj_2)]]). fof(e1_6_4_2_1__anproj_2,assumption,( ~ v8_rlvect_1(k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,1),k3_rlvect_1(c1_6__anproj_2,c6_6__anproj_2,k1_real_1(k4_real_1(c9_6__anproj_2,k2_real_1(c12_6__anproj_2))))),c1_6__anproj_2) ), introduced(assumption,[file(anproj_2,e1_6_4_2_1__anproj_2)]), [interesting(0.35),axiom,file(anproj_2,e1_6_4_2_1__anproj_2)]). fof(dt_k5_rlvect_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) ) => m1_subset_1(k5_rlvect_1(A,B),u1_struct_0(A)) ) ), file(rlvect_1,k5_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,k5_rlvect_1)]). fof(dt_k1_rlvect_1,axiom,( ! [A] : ( l2_struct_0(A) => m1_subset_1(k1_rlvect_1(A),u1_struct_0(A)) ) ), file(rlvect_1,k1_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,k1_rlvect_1)]). fof(d13_rlvect_1,definition,( ! [A] : ( ( ~ v3_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v8_rlvect_1(B,A) <=> B != k1_rlvect_1(A) ) ) ) ), file(rlvect_1,d13_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,d13_rlvect_1)]). fof(e1_6_4_2_1_1__anproj_2,plain,( k1_rlvect_1(c1_6__anproj_2) = k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,1),k3_rlvect_1(c1_6__anproj_2,c6_6__anproj_2,k1_real_1(k4_real_1(c9_6__anproj_2,k2_real_1(c12_6__anproj_2))))) ), inference(mizar_by,[status(thm),assumptions([dt_c6_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2,e1_6_4_2_1__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,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,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,involutiveness_k5_xcmplx_0,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_rlvect_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_rlvect_1,dt_k5_numbers,dt_k5_xcmplx_0,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_rlvect_1,dt_m2_subset_1,cc15_membered,fc1_struct_0,fc2_membered,rc3_struct_0,spc10_arithm,spc2_arithm,spc7_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,involutiveness_k1_real_1,involutiveness_k2_real_1,commutativity_k3_xcmplx_0,commutativity_k4_real_1,commutativity_k4_rlvect_1,involutiveness_k4_xcmplx_0,existence_l2_struct_0,existence_m1_subset_1,redefinition_k1_real_1,redefinition_k2_real_1,redefinition_k4_real_1,redefinition_k4_rlvect_1,dt_k1_real_1,dt_k1_rlvect_1,dt_k2_real_1,dt_k3_rlvect_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_k4_rlvect_1,dt_k4_xcmplx_0,dt_l2_struct_0,dt_m1_subset_1,dt_u1_struct_0,dt_c12_6__anproj_2,dt_c1_6__anproj_2,dt_c5_6__anproj_2,dt_c6_6__anproj_2,dt_c9_6__anproj_2,rc4_struct_0,rqRealNeg__k4_xcmplx_0__rm1_r1,spc1_numerals,spc1_boole,e1_6_4_2_1__anproj_2,d13_rlvect_1,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealMult__k3_xcmplx_0__r1_r1_r1]), [interesting(0.2),file(anproj_2,e1_6_4_2_1_1__anproj_2),[file(anproj_2,e1_6_4_2_1_1__anproj_2)]]). fof(t38_rlvect_1,theorem,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( ( ~ v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & l2_rlvect_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => k3_rlvect_1(B,k5_rlvect_1(B,C),A) = k3_rlvect_1(B,C,k1_real_1(A)) ) ) ) ), file(rlvect_1,t38_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,t38_rlvect_1)]). fof(e2_6_4_2_1_1__anproj_2,plain,( k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,1),k3_rlvect_1(c1_6__anproj_2,c6_6__anproj_2,k1_real_1(k4_real_1(c9_6__anproj_2,k2_real_1(c12_6__anproj_2))))) = k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,1),k3_rlvect_1(c1_6__anproj_2,k5_rlvect_1(c1_6__anproj_2,c6_6__anproj_2),k4_real_1(c9_6__anproj_2,k2_real_1(c12_6__anproj_2)))) ), inference(mizar_by,[status(thm),assumptions([dt_c6_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l2_struct_0,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l2_struct_0,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc4_struct_0,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,involutiveness_k5_xcmplx_0,existence_l1_rlvect_1,existence_l1_struct_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k2_rlvect_1,dt_k5_numbers,dt_k5_xcmplx_0,dt_l1_rlvect_1,dt_l1_struct_0,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc4_membered,fc1_struct_0,rc3_struct_0,spc10_arithm,spc2_arithm,spc7_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,involutiveness_k1_real_1,involutiveness_k2_real_1,commutativity_k3_xcmplx_0,commutativity_k4_real_1,commutativity_k4_rlvect_1,involutiveness_k4_xcmplx_0,existence_l2_rlvect_1,existence_m1_subset_1,redefinition_k1_real_1,redefinition_k2_real_1,redefinition_k4_real_1,redefinition_k4_rlvect_1,dt_k1_numbers,dt_k1_real_1,dt_k2_real_1,dt_k3_rlvect_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_k4_rlvect_1,dt_k4_xcmplx_0,dt_k5_rlvect_1,dt_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c12_6__anproj_2,dt_c1_6__anproj_2,dt_c5_6__anproj_2,dt_c6_6__anproj_2,dt_c9_6__anproj_2,fc2_membered,rqRealNeg__k4_xcmplx_0__rm1_r1,spc1_numerals,spc1_boole,t38_rlvect_1,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealMult__k3_xcmplx_0__r1_r1_r1]), [interesting(0.2),file(anproj_2,e2_6_4_2_1_1__anproj_2),[file(anproj_2,e2_6_4_2_1_1__anproj_2)]]). fof(t39_rlvect_1,theorem,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( ( ~ v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & l2_rlvect_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => k3_rlvect_1(B,k5_rlvect_1(B,C),A) = k5_rlvect_1(B,k3_rlvect_1(B,C,A)) ) ) ) ), file(rlvect_1,t39_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,t39_rlvect_1)]). fof(e3_6_4_2_1_1__anproj_2,plain,( k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,1),k3_rlvect_1(c1_6__anproj_2,k5_rlvect_1(c1_6__anproj_2,c6_6__anproj_2),k4_real_1(c9_6__anproj_2,k2_real_1(c12_6__anproj_2)))) = k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,1),k5_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c6_6__anproj_2,k4_real_1(c9_6__anproj_2,k2_real_1(c12_6__anproj_2))))) ), inference(mizar_by,[status(thm),assumptions([dt_c6_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l2_struct_0,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l2_struct_0,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc4_struct_0,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,involutiveness_k5_xcmplx_0,existence_l1_rlvect_1,existence_l1_struct_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k2_rlvect_1,dt_k5_numbers,dt_k5_xcmplx_0,dt_l1_rlvect_1,dt_l1_struct_0,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc4_membered,fc1_struct_0,rc3_struct_0,spc10_arithm,spc7_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,involutiveness_k2_real_1,commutativity_k3_xcmplx_0,commutativity_k4_real_1,commutativity_k4_rlvect_1,existence_l2_rlvect_1,existence_m1_subset_1,redefinition_k2_real_1,redefinition_k4_real_1,redefinition_k4_rlvect_1,dt_k1_numbers,dt_k2_real_1,dt_k3_rlvect_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_k4_rlvect_1,dt_k5_rlvect_1,dt_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c12_6__anproj_2,dt_c1_6__anproj_2,dt_c5_6__anproj_2,dt_c6_6__anproj_2,dt_c9_6__anproj_2,fc2_membered,spc1_numerals,spc1_boole,t39_rlvect_1,rqRealMult__k3_xcmplx_0__r1_r1_r1]), [interesting(0.2),file(anproj_2,e3_6_4_2_1_1__anproj_2),[file(anproj_2,e3_6_4_2_1_1__anproj_2)]]). fof(e2_6_4_2_1__anproj_2,plain,( k1_rlvect_1(c1_6__anproj_2) = k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,1),k5_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c6_6__anproj_2,k4_real_1(c9_6__anproj_2,k2_real_1(c12_6__anproj_2))))) ), inference(iterative_eq,[status(thm),assumptions([e1_6_4_2_1__anproj_2,dt_c6_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2])],[e1_6_4_2_1_1__anproj_2,e2_6_4_2_1_1__anproj_2,e3_6_4_2_1_1__anproj_2]), [interesting(0.35),file(anproj_2,e2_6_4_2_1__anproj_2),[file(anproj_2,e2_6_4_2_1__anproj_2)]]). fof(d10_rlvect_1,definition,( ! [A] : ( ( ~ v3_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( ( v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( C = k5_rlvect_1(A,B) <=> k2_rlvect_1(A,B,C) = k1_rlvect_1(A) ) ) ) ) ) ), file(rlvect_1,d10_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,d10_rlvect_1)]). fof(e3_6_4_2_1__anproj_2,plain,( k5_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,1)) = k5_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c6_6__anproj_2,k4_real_1(c9_6__anproj_2,k2_real_1(c12_6__anproj_2)))) ), inference(mizar_by,[status(thm),assumptions([e1_6_4_2_1__anproj_2,dt_c6_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,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,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,involutiveness_k5_xcmplx_0,existence_l1_struct_0,existence_l2_rlvect_1,existence_l2_struct_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_k5_xcmplx_0,dt_l1_struct_0,dt_l2_rlvect_1,dt_l2_struct_0,dt_m2_subset_1,cc15_membered,fc1_struct_0,fc2_membered,rc3_struct_0,rc4_struct_0,spc10_arithm,spc7_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,involutiveness_k2_real_1,commutativity_k3_xcmplx_0,commutativity_k4_real_1,commutativity_k4_rlvect_1,existence_l1_rlvect_1,existence_m1_subset_1,redefinition_k2_real_1,redefinition_k4_real_1,redefinition_k4_rlvect_1,dt_k1_rlvect_1,dt_k2_real_1,dt_k2_rlvect_1,dt_k3_rlvect_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_k4_rlvect_1,dt_k5_rlvect_1,dt_l1_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c12_6__anproj_2,dt_c1_6__anproj_2,dt_c5_6__anproj_2,dt_c6_6__anproj_2,dt_c9_6__anproj_2,spc1_numerals,spc1_boole,e2_6_4_2_1__anproj_2,d10_rlvect_1,rqRealMult__k3_xcmplx_0__r1_r1_r1]), [interesting(0.35),file(anproj_2,e3_6_4_2_1__anproj_2),[file(anproj_2,e3_6_4_2_1__anproj_2)]]). fof(t31_rlvect_1,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k5_rlvect_1(A,B) = k5_rlvect_1(A,C) => B = C ) ) ) ) ), file(rlvect_1,t31_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,t31_rlvect_1)]). fof(e4_6_4_2_1__anproj_2,plain,( k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,1) = k3_rlvect_1(c1_6__anproj_2,c6_6__anproj_2,k4_real_1(c9_6__anproj_2,k2_real_1(c12_6__anproj_2))) ), inference(mizar_by,[status(thm),assumptions([e1_6_4_2_1__anproj_2,dt_c6_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,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,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,involutiveness_k5_xcmplx_0,existence_l1_struct_0,existence_l2_rlvect_1,existence_l2_struct_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_k5_xcmplx_0,dt_l1_struct_0,dt_l2_rlvect_1,dt_l2_struct_0,dt_m2_subset_1,cc15_membered,fc1_struct_0,fc2_membered,rc3_struct_0,rc4_struct_0,spc10_arithm,spc7_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,involutiveness_k2_real_1,commutativity_k3_xcmplx_0,commutativity_k4_real_1,existence_l1_rlvect_1,existence_m1_subset_1,redefinition_k2_real_1,redefinition_k4_real_1,dt_k2_real_1,dt_k3_rlvect_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_k5_rlvect_1,dt_l1_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c12_6__anproj_2,dt_c1_6__anproj_2,dt_c5_6__anproj_2,dt_c6_6__anproj_2,dt_c9_6__anproj_2,spc1_numerals,spc1_boole,e3_6_4_2_1__anproj_2,t31_rlvect_1,rqRealMult__k3_xcmplx_0__r1_r1_r1]), [interesting(0.35),file(anproj_2,e4_6_4_2_1__anproj_2),[file(anproj_2,e4_6_4_2_1__anproj_2)]]). fof(t203_xcmplx_1,theorem,( k5_xcmplx_0(0) = 0 ), file(xcmplx_1,t203_xcmplx_1), [interesting(0.9),axiom,file(xcmplx_1,t203_xcmplx_1)]). fof(e2_6_4_2__anproj_2,plain,( k2_real_1(c12_6__anproj_2) != 0 ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c6_6__anproj_2,e1_6__anproj_2,e1_6_4_2__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,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,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,fc2_membered,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,involutiveness_k2_real_1,involutiveness_k5_xcmplx_0,redefinition_k2_real_1,dt_k2_real_1,dt_k5_xcmplx_0,dt_c12_6__anproj_2,spc0_numerals,spc0_boole,e1_6_4_2__anproj_2,t203_xcmplx_1]), [interesting(0.5),file(anproj_2,e2_6_4_2__anproj_2),[file(anproj_2,e2_6_4_2__anproj_2)]]). fof(t6_xcmplx_1,theorem,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ~ ( k3_xcmplx_0(A,B) = 0 & A != 0 & B != 0 ) ) ) ), file(xcmplx_1,t6_xcmplx_1), [interesting(0.9),axiom,file(xcmplx_1,t6_xcmplx_1)]). fof(e3_6_4_2__anproj_2,plain,( k4_real_1(c9_6__anproj_2,k2_real_1(c12_6__anproj_2)) != 0 ), inference(mizar_by,[status(thm),assumptions([dt_c5_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c6_6__anproj_2,e1_6__anproj_2,e1_6_4_2__anproj_2,e1_6_4__anproj_2])],[reflexivity_r1_tarski,existence_l2_struct_0,dt_l2_struct_0,rc4_struct_0,antisymmetry_r2_hidden,existence_l1_rlvect_1,existence_l1_struct_0,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l1_rlvect_1,dt_l1_struct_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,cc6_membered,cc9_membered,fc1_struct_0,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,involutiveness_k5_xcmplx_0,existence_l2_rlvect_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_k5_xcmplx_0,dt_l2_rlvect_1,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,cc15_membered,fc2_membered,spc10_arithm,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,involutiveness_k2_real_1,commutativity_k3_xcmplx_0,commutativity_k4_real_1,involutiveness_k4_xcmplx_0,symmetry_r1_anproj_1,reflexivity_r1_anproj_1,redefinition_k2_real_1,redefinition_k4_real_1,dt_k2_real_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_k4_xcmplx_0,dt_c12_6__anproj_2,dt_c1_6__anproj_2,dt_c5_6__anproj_2,dt_c6_6__anproj_2,dt_c9_6__anproj_2,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,rqRealNeg__k4_xcmplx_0__rm1_r1,spc2_arithm,spc7_arithm,t2_arithm,t3_arithm,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e2_6_4_2__anproj_2,e1_6_4__anproj_2,t6_xcmplx_1,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealNeg__k4_xcmplx_0__r1_rm1]), [interesting(0.5),file(anproj_2,e3_6_4_2__anproj_2),[file(anproj_2,e3_6_4_2__anproj_2)]]). fof(d2_anproj_1,definition,( ! [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)) => ( r1_anproj_1(A,B,C) <=> ? [D] : ( m1_subset_1(D,k1_numbers) & ? [E] : ( m1_subset_1(E,k1_numbers) & k3_rlvect_1(A,B,D) = k3_rlvect_1(A,C,E) & D != 0 & E != 0 ) ) ) ) ) ) ), file(anproj_1,d2_anproj_1), [interesting(0.9),axiom,file(anproj_1,d2_anproj_1)]). fof(e5_6_4_2_1__anproj_2,plain,( ~ $true ), inference(mizar_by,[status(thm),assumptions([e1_6_4_2_1__anproj_2,dt_c5_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c6_6__anproj_2,e1_6__anproj_2,e1_6_4_2__anproj_2,e1_6_4__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l2_struct_0,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l2_struct_0,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc4_struct_0,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,involutiveness_k5_xcmplx_0,existence_l1_rlvect_1,existence_l1_struct_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k5_numbers,dt_k5_xcmplx_0,dt_l1_rlvect_1,dt_l1_struct_0,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc4_membered,fc1_struct_0,rc3_struct_0,spc10_arithm,spc7_arithm,t1_numerals,t2_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,involutiveness_k2_real_1,commutativity_k3_xcmplx_0,commutativity_k4_real_1,symmetry_r1_anproj_1,reflexivity_r1_anproj_1,existence_l2_rlvect_1,existence_m1_subset_1,redefinition_k2_real_1,redefinition_k4_real_1,dt_k1_numbers,dt_k2_real_1,dt_k3_rlvect_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c12_6__anproj_2,dt_c1_6__anproj_2,dt_c5_6__anproj_2,dt_c6_6__anproj_2,dt_c9_6__anproj_2,fc2_membered,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e4_6_4_2_1__anproj_2,e1_6_4__anproj_2,e3_6_4_2__anproj_2,d2_anproj_1,rqRealMult__k3_xcmplx_0__r1_r1_r1]), [interesting(0.35),file(anproj_2,e5_6_4_2_1__anproj_2),[file(anproj_2,e5_6_4_2_1__anproj_2)]]). fof(i2_6_4_2_1__anproj_2,theorem,( $true ), introduced(tautology,[file(anproj_2,i2_6_4_2_1__anproj_2)]), [interesting(0.35),trivial,file(anproj_2,i2_6_4_2_1__anproj_2)]). fof(i1_6_4_2_1__anproj_2,plain,( ~ $true ), inference(conclusion,[status(thm),assumptions([e1_6_4_2_1__anproj_2,dt_c5_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c6_6__anproj_2,e1_6__anproj_2,e1_6_4_2__anproj_2,e1_6_4__anproj_2])],[e5_6_4_2_1__anproj_2,i2_6_4_2_1__anproj_2]), [interesting(0.35),file(anproj_2,i1_6_4_2_1__anproj_2),[file(anproj_2,i1_6_4_2_1__anproj_2)]]). fof(e4_6_4_2__anproj_2,plain,( v8_rlvect_1(k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,1),k3_rlvect_1(c1_6__anproj_2,c6_6__anproj_2,k1_real_1(k4_real_1(c9_6__anproj_2,k2_real_1(c12_6__anproj_2))))),c1_6__anproj_2) ), inference(discharge_asm,[status(thm),assumptions([dt_c5_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c6_6__anproj_2,e1_6__anproj_2,e1_6_4_2__anproj_2,e1_6_4__anproj_2]),discharge_asm(discharge,[e1_6_4_2_1__anproj_2])],[e1_6_4_2_1__anproj_2,i1_6_4_2_1__anproj_2]), [interesting(0.5),file(anproj_2,e4_6_4_2__anproj_2),[file(anproj_2,e4_6_4_2__anproj_2)]]). fof(commutativity_k2_xcmplx_0,theorem,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ), file(xcmplx_0,k2_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k2_xcmplx_0)]). fof(dt_k2_xcmplx_0,axiom,( $true ), file(xcmplx_0,k2_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k2_xcmplx_0)]). fof(spc5_arithm,theorem,( ! [A,B,C] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) ) => k3_xcmplx_0(k2_xcmplx_0(A,B),C) = k2_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,C)) ) ), file(arithm,spc5_arithm), [interesting(0.9),axiom,file(arithm,spc5_arithm)]). fof(spc6_arithm,theorem,( ! [A,B,C] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) ) => k2_xcmplx_0(k2_xcmplx_0(A,B),C) = k2_xcmplx_0(A,k2_xcmplx_0(B,C)) ) ), file(arithm,spc6_arithm), [interesting(0.9),axiom,file(arithm,spc6_arithm)]). fof(spc8_arithm,theorem,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k2_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(B)) = k4_xcmplx_0(k2_xcmplx_0(A,B)) ) ), file(arithm,spc8_arithm), [interesting(0.9),axiom,file(arithm,spc8_arithm)]). fof(commutativity_k3_real_1,theorem,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k3_real_1(A,B) = k3_real_1(B,A) ) ), file(real_1,k3_real_1), [interesting(0.9),axiom,file(real_1,k3_real_1)]). fof(redefinition_k3_real_1,definition,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k3_real_1(A,B) = k2_xcmplx_0(A,B) ) ), file(real_1,k3_real_1), [interesting(0.9),axiom,file(real_1,k3_real_1)]). fof(dt_k3_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k3_real_1(A,B),k1_numbers) ) ), file(real_1,k3_real_1), [interesting(0.9),axiom,file(real_1,k3_real_1)]). fof(dt_c10_6__anproj_2,plain,( m1_subset_1(c10_6__anproj_2,k1_numbers) ), inference(consider,[status(thm),assumptions([dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c6_6__anproj_2,e1_6__anproj_2])],[dh_c10_6__anproj_2,e5_6__anproj_2]), [interesting(0.8),file(anproj_2,c10_6__anproj_2),[file(anproj_2,c10_6__anproj_2)]]). fof(dt_c11_6__anproj_2,plain,( m1_subset_1(c11_6__anproj_2,k1_numbers) ), inference(consider,[status(thm),assumptions([dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c6_6__anproj_2,e1_6__anproj_2])],[dh_c10_6__anproj_2,dh_c11_6__anproj_2,e5_6__anproj_2]), [interesting(0.8),file(anproj_2,c11_6__anproj_2),[file(anproj_2,c11_6__anproj_2)]]). fof(dt_c7_6__anproj_2,plain,( m1_subset_1(c7_6__anproj_2,k1_numbers) ), inference(consider,[status(thm),assumptions([dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2])],[dh_c7_6__anproj_2,e3_6__anproj_2]), [interesting(0.8),file(anproj_2,c7_6__anproj_2),[file(anproj_2,c7_6__anproj_2)]]). fof(dt_c8_6__anproj_2,plain,( m1_subset_1(c8_6__anproj_2,k1_numbers) ), inference(consider,[status(thm),assumptions([dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2])],[dh_c7_6__anproj_2,dh_c8_6__anproj_2,e3_6__anproj_2]), [interesting(0.8),file(anproj_2,c8_6__anproj_2),[file(anproj_2,c8_6__anproj_2)]]). fof(rqRealAdd__k2_xcmplx_0__r0_r0_r0,theorem,( k2_xcmplx_0(0,0) = 0 ), file(arithm,rqRealAdd__k2_xcmplx_0__r0_r0_r0), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_r0_r0)]). fof(rqRealAdd__k2_xcmplx_0__r0_r1_r1,theorem,( k2_xcmplx_0(0,1) = 1 ), file(arithm,rqRealAdd__k2_xcmplx_0__r0_r1_r1), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_r1_r1)]). fof(rqRealAdd__k2_xcmplx_0__r0_r2_r2,theorem,( k2_xcmplx_0(0,2) = 2 ), file(arithm,rqRealAdd__k2_xcmplx_0__r0_r2_r2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_r2_r2)]). fof(rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,theorem,( k2_xcmplx_0(0,k4_xcmplx_0(1)) = k4_xcmplx_0(1) ), file(arithm,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1)]). fof(rqRealAdd__k2_xcmplx_0__r0_rm2_rm2,theorem,( k2_xcmplx_0(0,k4_xcmplx_0(2)) = k4_xcmplx_0(2) ), file(arithm,rqRealAdd__k2_xcmplx_0__r0_rm2_rm2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_rm2_rm2)]). fof(rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2,theorem,( k2_xcmplx_0(0,k7_xcmplx_0(1,2)) = k7_xcmplx_0(1,2) ), file(arithm,rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2)]). fof(rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2,theorem,( k2_xcmplx_0(0,k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ), file(arithm,rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2)]). fof(rqRealAdd__k2_xcmplx_0__r1_r0_r1,theorem,( k2_xcmplx_0(1,0) = 1 ), file(arithm,rqRealAdd__k2_xcmplx_0__r1_r0_r1), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_r0_r1)]). fof(rqRealAdd__k2_xcmplx_0__r1_r1_r2,theorem,( k2_xcmplx_0(1,1) = 2 ), file(arithm,rqRealAdd__k2_xcmplx_0__r1_r1_r2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_r1_r2)]). fof(rqRealAdd__k2_xcmplx_0__r1_rm1_r0,theorem,( k2_xcmplx_0(1,k4_xcmplx_0(1)) = 0 ), file(arithm,rqRealAdd__k2_xcmplx_0__r1_rm1_r0), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_rm1_r0)]). fof(rqRealAdd__k2_xcmplx_0__r1_rm2_rm1,theorem,( k2_xcmplx_0(1,k4_xcmplx_0(2)) = k4_xcmplx_0(1) ), file(arithm,rqRealAdd__k2_xcmplx_0__r1_rm2_rm1), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_rm2_rm1)]). fof(rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2,theorem,( k2_xcmplx_0(1,k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(1,2) ), file(arithm,rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2)]). fof(rqRealAdd__k2_xcmplx_0__r2_r0_r2,theorem,( k2_xcmplx_0(2,0) = 2 ), file(arithm,rqRealAdd__k2_xcmplx_0__r2_r0_r2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r2_r0_r2)]). fof(rqRealAdd__k2_xcmplx_0__r2_rm1_r1,theorem,( k2_xcmplx_0(2,k4_xcmplx_0(1)) = 1 ), file(arithm,rqRealAdd__k2_xcmplx_0__r2_rm1_r1), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r2_rm1_r1)]). fof(rqRealAdd__k2_xcmplx_0__r2_rm2_r0,theorem,( k2_xcmplx_0(2,k4_xcmplx_0(2)) = 0 ), file(arithm,rqRealAdd__k2_xcmplx_0__r2_rm2_r0), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r2_rm2_r0)]). fof(rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,theorem,( k2_xcmplx_0(k4_xcmplx_0(1),0) = k4_xcmplx_0(1) ), file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1)]). fof(rqRealAdd__k2_xcmplx_0__rm1_r1_r0,theorem,( k2_xcmplx_0(k4_xcmplx_0(1),1) = 0 ), file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r1_r0), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r1_r0)]). fof(rqRealAdd__k2_xcmplx_0__rm1_r2_r1,theorem,( k2_xcmplx_0(k4_xcmplx_0(1),2) = 1 ), file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r2_r1), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r2_r1)]). fof(rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2,theorem,( k2_xcmplx_0(k4_xcmplx_0(1),k4_xcmplx_0(1)) = k4_xcmplx_0(2) ), file(arithm,rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2)]). fof(rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2,theorem,( k2_xcmplx_0(k4_xcmplx_0(1),k7_xcmplx_0(1,2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ), file(arithm,rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2)]). fof(rqRealAdd__k2_xcmplx_0__rm2_r0_rm2,theorem,( k2_xcmplx_0(k4_xcmplx_0(2),0) = k4_xcmplx_0(2) ), file(arithm,rqRealAdd__k2_xcmplx_0__rm2_r0_rm2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm2_r0_rm2)]). fof(rqRealAdd__k2_xcmplx_0__rm2_r1_rm1,theorem,( k2_xcmplx_0(k4_xcmplx_0(2),1) = k4_xcmplx_0(1) ), file(arithm,rqRealAdd__k2_xcmplx_0__rm2_r1_rm1), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm2_r1_rm1)]). fof(rqRealAdd__k2_xcmplx_0__rm2_r2_r0,theorem,( k2_xcmplx_0(k4_xcmplx_0(2),2) = 0 ), file(arithm,rqRealAdd__k2_xcmplx_0__rm2_r2_r0), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm2_r2_r0)]). fof(rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2,theorem,( k2_xcmplx_0(k7_xcmplx_0(1,2),0) = k7_xcmplx_0(1,2) ), file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2)]). fof(rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2,theorem,( k2_xcmplx_0(k7_xcmplx_0(1,2),k4_xcmplx_0(1)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ), file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2)]). fof(rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1,theorem,( k2_xcmplx_0(k7_xcmplx_0(1,2),k7_xcmplx_0(1,2)) = 1 ), file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1)]). fof(rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0,theorem,( k2_xcmplx_0(k7_xcmplx_0(1,2),k7_xcmplx_0(k4_xcmplx_0(1),2)) = 0 ), file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0)]). fof(rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2,theorem,( k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),1) = k7_xcmplx_0(1,2) ), file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2)]). fof(rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0,theorem,( k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(1,2)) = 0 ), file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0)]). fof(rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1,theorem,( k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(k4_xcmplx_0(1),2)) = k4_xcmplx_0(1) ), file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1)]). fof(spc11_arithm,theorem,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k7_xcmplx_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) = k7_xcmplx_0(B,A) ) ), file(arithm,spc11_arithm), [interesting(0.9),axiom,file(arithm,spc11_arithm)]). fof(spc12_arithm,theorem,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k3_xcmplx_0(A,k5_xcmplx_0(B)) = k7_xcmplx_0(A,B) ) ), file(arithm,spc12_arithm), [interesting(0.9),axiom,file(arithm,spc12_arithm)]). fof(spc1_arithm,theorem,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k2_xcmplx_0(A,k4_xcmplx_0(B)) = k6_xcmplx_0(A,B) ) ), file(arithm,spc1_arithm), [interesting(0.9),axiom,file(arithm,spc1_arithm)]). fof(spc3_arithm,theorem,( ! [A] : ( v1_xcmplx_0(A) => k7_xcmplx_0(1,A) = k5_xcmplx_0(A) ) ), file(arithm,spc3_arithm), [interesting(0.9),axiom,file(arithm,spc3_arithm)]). fof(spc4_arithm,theorem,( ! [A,B,C] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) ) => k3_xcmplx_0(A,k7_xcmplx_0(B,C)) = k7_xcmplx_0(k3_xcmplx_0(A,B),C) ) ), file(arithm,spc4_arithm), [interesting(0.9),axiom,file(arithm,spc4_arithm)]). fof(spc9_arithm,theorem,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k6_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(B)) = k6_xcmplx_0(B,A) ) ), file(arithm,spc9_arithm), [interesting(0.9),axiom,file(arithm,spc9_arithm)]). fof(t1_arithm,theorem,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(A,0) = A ) ), file(arithm,t1_arithm), [interesting(0.9),axiom,file(arithm,t1_arithm)]). fof(t4_arithm,theorem,( ! [A] : ( v1_xcmplx_0(A) => k6_xcmplx_0(A,0) = A ) ), file(arithm,t4_arithm), [interesting(0.9),axiom,file(arithm,t4_arithm)]). fof(t5_arithm,theorem,( ! [A] : ( v1_xcmplx_0(A) => k7_xcmplx_0(0,A) = 0 ) ), file(arithm,t5_arithm), [interesting(0.9),axiom,file(arithm,t5_arithm)]). fof(t6_arithm,theorem,( ! [A] : ( v1_xcmplx_0(A) => k7_xcmplx_0(A,1) = A ) ), file(arithm,t6_arithm), [interesting(0.9),axiom,file(arithm,t6_arithm)]). fof(dt_k6_xcmplx_0,axiom,( $true ), file(xcmplx_0,k6_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k6_xcmplx_0)]). fof(dt_k7_xcmplx_0,axiom,( $true ), file(xcmplx_0,k7_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k7_xcmplx_0)]). fof(rqRealDiff__k6_xcmplx_0__r0_r0_r0,theorem,( k6_xcmplx_0(0,0) = 0 ), file(arithm,rqRealDiff__k6_xcmplx_0__r0_r0_r0), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_r0_r0)]). fof(rqRealDiff__k6_xcmplx_0__r0_r2_rm2,theorem,( k6_xcmplx_0(0,2) = k4_xcmplx_0(2) ), file(arithm,rqRealDiff__k6_xcmplx_0__r0_r2_rm2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_r2_rm2)]). fof(rqRealDiff__k6_xcmplx_0__r0_rm1_r1,theorem,( k6_xcmplx_0(0,k4_xcmplx_0(1)) = 1 ), file(arithm,rqRealDiff__k6_xcmplx_0__r0_rm1_r1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_rm1_r1)]). fof(rqRealDiff__k6_xcmplx_0__r0_rm2_r2,theorem,( k6_xcmplx_0(0,k4_xcmplx_0(2)) = 2 ), file(arithm,rqRealDiff__k6_xcmplx_0__r0_rm2_r2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_rm2_r2)]). fof(rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2,theorem,( k6_xcmplx_0(0,k7_xcmplx_0(1,2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ), file(arithm,rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2)]). fof(rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2,theorem,( k6_xcmplx_0(0,k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(1,2) ), file(arithm,rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2)]). fof(rqRealDiff__k6_xcmplx_0__r1_r0_r1,theorem,( k6_xcmplx_0(1,0) = 1 ), file(arithm,rqRealDiff__k6_xcmplx_0__r1_r0_r1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_r0_r1)]). fof(rqRealDiff__k6_xcmplx_0__r1_r2_rm1,theorem,( k6_xcmplx_0(1,2) = k4_xcmplx_0(1) ), file(arithm,rqRealDiff__k6_xcmplx_0__r1_r2_rm1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_r2_rm1)]). fof(rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2,theorem,( k6_xcmplx_0(1,k7_xcmplx_0(1,2)) = k7_xcmplx_0(1,2) ), file(arithm,rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2)]). fof(rqRealDiff__k6_xcmplx_0__r2_r0_r2,theorem,( k6_xcmplx_0(2,0) = 2 ), file(arithm,rqRealDiff__k6_xcmplx_0__r2_r0_r2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r2_r0_r2)]). fof(rqRealDiff__k6_xcmplx_0__r2_r1_r1,theorem,( k6_xcmplx_0(2,1) = 1 ), file(arithm,rqRealDiff__k6_xcmplx_0__r2_r1_r1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r2_r1_r1)]). fof(rqRealDiff__k6_xcmplx_0__r2_r2_r0,theorem,( k6_xcmplx_0(2,2) = 0 ), file(arithm,rqRealDiff__k6_xcmplx_0__r2_r2_r0), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r2_r2_r0)]). fof(rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,theorem,( k6_xcmplx_0(k4_xcmplx_0(1),0) = k4_xcmplx_0(1) ), file(arithm,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1)]). fof(rqRealDiff__k6_xcmplx_0__rm1_rm2_r1,theorem,( k6_xcmplx_0(k4_xcmplx_0(1),k4_xcmplx_0(2)) = 1 ), file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm2_r1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm2_r1)]). fof(rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2,theorem,( k6_xcmplx_0(k4_xcmplx_0(1),k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ), file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2)]). fof(rqRealDiff__k6_xcmplx_0__rm2_r0_rm2,theorem,( k6_xcmplx_0(k4_xcmplx_0(2),0) = k4_xcmplx_0(2) ), file(arithm,rqRealDiff__k6_xcmplx_0__rm2_r0_rm2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm2_r0_rm2)]). fof(rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1,theorem,( k6_xcmplx_0(k4_xcmplx_0(2),k4_xcmplx_0(1)) = k4_xcmplx_0(1) ), file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1)]). fof(rqRealDiff__k6_xcmplx_0__rm2_rm2_r0,theorem,( k6_xcmplx_0(k4_xcmplx_0(2),k4_xcmplx_0(2)) = 0 ), file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rm2_r0), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rm2_r0)]). fof(rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2,theorem,( k6_xcmplx_0(k7_xcmplx_0(1,2),0) = k7_xcmplx_0(1,2) ), file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2)]). fof(rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2,theorem,( k6_xcmplx_0(k7_xcmplx_0(1,2),1) = k7_xcmplx_0(k4_xcmplx_0(1),2) ), file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2)]). fof(rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0,theorem,( k6_xcmplx_0(k7_xcmplx_0(1,2),k7_xcmplx_0(1,2)) = 0 ), file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0)]). fof(rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1,theorem,( k6_xcmplx_0(k7_xcmplx_0(1,2),k7_xcmplx_0(k4_xcmplx_0(1),2)) = 1 ), file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1)]). fof(rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2,theorem,( k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),0) = k7_xcmplx_0(k4_xcmplx_0(1),2) ), file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2)]). fof(rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2,theorem,( k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k4_xcmplx_0(1)) = k7_xcmplx_0(1,2) ), file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2)]). fof(rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1,theorem,( k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(1,2)) = k4_xcmplx_0(1) ), file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1)]). fof(rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0,theorem,( k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(k4_xcmplx_0(1),2)) = 0 ), file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0)]). fof(rqRealDiv__k7_xcmplx_0__r0_r1_r0,theorem,( k7_xcmplx_0(0,1) = 0 ), file(arithm,rqRealDiv__k7_xcmplx_0__r0_r1_r0), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r0_r1_r0)]). fof(rqRealDiv__k7_xcmplx_0__r0_r2_r0,theorem,( k7_xcmplx_0(0,2) = 0 ), file(arithm,rqRealDiv__k7_xcmplx_0__r0_r2_r0), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r0_r2_r0)]). fof(rqRealDiv__k7_xcmplx_0__r0_rn1d2_r0,theorem,( k7_xcmplx_0(0,k7_xcmplx_0(1,2)) = 0 ), file(arithm,rqRealDiv__k7_xcmplx_0__r0_rn1d2_r0), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r0_rn1d2_r0)]). fof(rqRealDiv__k7_xcmplx_0__r1_r1_r1,theorem,( k7_xcmplx_0(1,1) = 1 ), file(arithm,rqRealDiv__k7_xcmplx_0__r1_r1_r1), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_r1_r1)]). fof(rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2,theorem,( k7_xcmplx_0(1,2) = k7_xcmplx_0(1,2) ), file(arithm,rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2)]). fof(rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2,theorem,( k7_xcmplx_0(1,k4_xcmplx_0(2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ), file(arithm,rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2)]). fof(rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2,theorem,( k7_xcmplx_0(1,k7_xcmplx_0(1,2)) = 2 ), file(arithm,rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2)]). fof(rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2,theorem,( k7_xcmplx_0(1,k7_xcmplx_0(k4_xcmplx_0(1),2)) = k4_xcmplx_0(2) ), file(arithm,rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2)]). fof(rqRealDiv__k7_xcmplx_0__r2_r1_r2,theorem,( k7_xcmplx_0(2,1) = 2 ), file(arithm,rqRealDiv__k7_xcmplx_0__r2_r1_r2), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r2_r1_r2)]). fof(rqRealDiv__k7_xcmplx_0__r2_r2_r1,theorem,( k7_xcmplx_0(2,2) = 1 ), file(arithm,rqRealDiv__k7_xcmplx_0__r2_r2_r1), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r2_r2_r1)]). fof(rqRealDiv__k7_xcmplx_0__rm1_r1_rm1,theorem,( k7_xcmplx_0(k4_xcmplx_0(1),1) = k4_xcmplx_0(1) ), file(arithm,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1)]). fof(rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2,theorem,( k7_xcmplx_0(k4_xcmplx_0(1),2) = k7_xcmplx_0(k4_xcmplx_0(1),2) ), file(arithm,rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2)]). fof(rqRealDiv__k7_xcmplx_0__rnm1d2_rn1d2_rm1,theorem,( k7_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(1,2)) = k4_xcmplx_0(1) ), file(arithm,rqRealDiv__k7_xcmplx_0__rnm1d2_rn1d2_rm1), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__rnm1d2_rn1d2_rm1)]). fof(rqRealMult__k3_xcmplx_0__r0_r2_r0,theorem,( k3_xcmplx_0(0,2) = 0 ), file(arithm,rqRealMult__k3_xcmplx_0__r0_r2_r0), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r0_r2_r0)]). fof(rqRealMult__k3_xcmplx_0__r0_rm2_r0,theorem,( k3_xcmplx_0(0,k4_xcmplx_0(2)) = 0 ), file(arithm,rqRealMult__k3_xcmplx_0__r0_rm2_r0), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r0_rm2_r0)]). fof(rqRealMult__k3_xcmplx_0__r0_rn1d2_r0,theorem,( k3_xcmplx_0(0,k7_xcmplx_0(1,2)) = 0 ), file(arithm,rqRealMult__k3_xcmplx_0__r0_rn1d2_r0), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r0_rn1d2_r0)]). fof(rqRealMult__k3_xcmplx_0__r1_r2_r2,theorem,( k3_xcmplx_0(1,2) = 2 ), file(arithm,rqRealMult__k3_xcmplx_0__r1_r2_r2), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_r2_r2)]). fof(rqRealMult__k3_xcmplx_0__r1_rm2_rm2,theorem,( k3_xcmplx_0(1,k4_xcmplx_0(2)) = k4_xcmplx_0(2) ), file(arithm,rqRealMult__k3_xcmplx_0__r1_rm2_rm2), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_rm2_rm2)]). fof(rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2,theorem,( k3_xcmplx_0(1,k7_xcmplx_0(1,2)) = k7_xcmplx_0(1,2) ), file(arithm,rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2)]). fof(rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2,theorem,( k3_xcmplx_0(1,k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ), file(arithm,rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2)]). fof(rqRealMult__k3_xcmplx_0__r2_r0_r0,theorem,( k3_xcmplx_0(2,0) = 0 ), file(arithm,rqRealMult__k3_xcmplx_0__r2_r0_r0), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r2_r0_r0)]). fof(rqRealMult__k3_xcmplx_0__r2_r1_r2,theorem,( k3_xcmplx_0(2,1) = 2 ), file(arithm,rqRealMult__k3_xcmplx_0__r2_r1_r2), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r2_r1_r2)]). fof(rqRealMult__k3_xcmplx_0__r2_rn1d2_r1,theorem,( k3_xcmplx_0(2,k7_xcmplx_0(1,2)) = 1 ), file(arithm,rqRealMult__k3_xcmplx_0__r2_rn1d2_r1), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r2_rn1d2_r1)]). fof(rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1,theorem,( k3_xcmplx_0(2,k7_xcmplx_0(k4_xcmplx_0(1),2)) = k4_xcmplx_0(1) ), file(arithm,rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1)]). fof(rqRealMult__k3_xcmplx_0__rm2_r0_r0,theorem,( k3_xcmplx_0(k4_xcmplx_0(2),0) = 0 ), file(arithm,rqRealMult__k3_xcmplx_0__rm2_r0_r0), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm2_r0_r0)]). fof(rqRealMult__k3_xcmplx_0__rm2_r1_rm2,theorem,( k3_xcmplx_0(k4_xcmplx_0(2),1) = k4_xcmplx_0(2) ), file(arithm,rqRealMult__k3_xcmplx_0__rm2_r1_rm2), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm2_r1_rm2)]). fof(rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1,theorem,( k3_xcmplx_0(k4_xcmplx_0(2),k7_xcmplx_0(1,2)) = k4_xcmplx_0(1) ), file(arithm,rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1)]). fof(rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1,theorem,( k3_xcmplx_0(k4_xcmplx_0(2),k7_xcmplx_0(k4_xcmplx_0(1),2)) = 1 ), file(arithm,rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1)]). fof(rqRealMult__k3_xcmplx_0__rn1d2_r0_r0,theorem,( k3_xcmplx_0(k7_xcmplx_0(1,2),0) = 0 ), file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_r0_r0), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_r0_r0)]). fof(rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2,theorem,( k3_xcmplx_0(k7_xcmplx_0(1,2),1) = k7_xcmplx_0(1,2) ), file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2)]). fof(rqRealMult__k3_xcmplx_0__rn1d2_r2_r1,theorem,( k3_xcmplx_0(k7_xcmplx_0(1,2),2) = 1 ), file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_r2_r1), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_r2_r1)]). fof(rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1,theorem,( k3_xcmplx_0(k7_xcmplx_0(1,2),k4_xcmplx_0(2)) = k4_xcmplx_0(1) ), file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1)]). fof(rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2,theorem,( k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),1) = k7_xcmplx_0(k4_xcmplx_0(1),2) ), file(arithm,rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2)]). fof(rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1,theorem,( k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),2) = k4_xcmplx_0(1) ), file(arithm,rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1)]). fof(rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1,theorem,( k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k4_xcmplx_0(2)) = 1 ), file(arithm,rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1)]). fof(rqRealNeg__k4_xcmplx_0__r2_rm2,theorem,( k4_xcmplx_0(2) = k4_xcmplx_0(2) ), file(arithm,rqRealNeg__k4_xcmplx_0__r2_rm2), [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__r2_rm2)]). fof(rqRealNeg__k4_xcmplx_0__rm2_r2,theorem,( k4_xcmplx_0(k4_xcmplx_0(2)) = 2 ), file(arithm,rqRealNeg__k4_xcmplx_0__rm2_r2), [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rm2_r2)]). fof(rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2,theorem,( k4_xcmplx_0(k7_xcmplx_0(1,2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ), file(arithm,rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2), [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2)]). fof(rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2,theorem,( k4_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(1,2) ), file(arithm,rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2), [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2)]). fof(spc2_numerals,theorem, ( v2_xreal_0(2) & m2_subset_1(2,k1_numbers,k5_numbers) & m1_subset_1(2,k5_numbers) & m1_subset_1(2,k1_numbers) ), file(numerals,spc2_numerals), [interesting(0.9),axiom,file(numerals,spc2_numerals)]). fof(spc2_boole,theorem,( ~ v1_xboole_0(2) ), file(boole,spc2_boole), [interesting(0.9),axiom,file(boole,spc2_boole)]). fof(e1_6_4_2_2__anproj_2,plain,( k3_real_1(k4_real_1(1,c9_6__anproj_2),k4_real_1(k1_real_1(k4_real_1(c9_6__anproj_2,k2_real_1(c12_6__anproj_2))),c12_6__anproj_2)) = k3_real_1(c9_6__anproj_2,k4_real_1(k1_real_1(c9_6__anproj_2),k4_real_1(k2_real_1(c12_6__anproj_2),c12_6__anproj_2))) ), inference(mizar_by,[status(thm),assumptions([dt_c6_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,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,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,t1_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,involutiveness_k5_xcmplx_0,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_xcmplx_0,dt_k5_numbers,dt_k5_xcmplx_0,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,fc2_membered,spc10_arithm,spc2_arithm,spc5_arithm,spc6_arithm,spc7_arithm,spc8_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,involutiveness_k1_real_1,involutiveness_k2_real_1,commutativity_k3_real_1,commutativity_k3_xcmplx_0,commutativity_k4_real_1,involutiveness_k4_xcmplx_0,redefinition_k1_real_1,redefinition_k2_real_1,redefinition_k3_real_1,redefinition_k4_real_1,dt_k1_real_1,dt_k2_real_1,dt_k3_real_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_k4_xcmplx_0,dt_c12_6__anproj_2,dt_c9_6__anproj_2,rqRealNeg__k4_xcmplx_0__rm1_r1,spc1_numerals,spc1_boole,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealNeg__k4_xcmplx_0__r1_rm1]), [interesting(0.35),file(anproj_2,e1_6_4_2_2__anproj_2),[file(anproj_2,e1_6_4_2_2__anproj_2)]]). fof(d7_xcmplx_0,definition,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( ( A != 0 => ( B = k5_xcmplx_0(A) <=> k3_xcmplx_0(A,B) = 1 ) ) & ( A = 0 => ( B = k5_xcmplx_0(A) <=> B = 0 ) ) ) ) ) ), file(xcmplx_0,d7_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,d7_xcmplx_0)]). fof(e2_6_4_2_2__anproj_2,plain,( k3_real_1(c9_6__anproj_2,k4_real_1(k1_real_1(c9_6__anproj_2),k4_real_1(k2_real_1(c12_6__anproj_2),c12_6__anproj_2))) = k3_real_1(c9_6__anproj_2,k4_real_1(k1_real_1(c9_6__anproj_2),1)) ), inference(mizar_by,[status(thm),assumptions([dt_c6_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2,e1_6_4_2__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,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,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,fc2_membered,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,involutiveness_k1_real_1,involutiveness_k2_real_1,commutativity_k2_xcmplx_0,commutativity_k3_real_1,commutativity_k3_xcmplx_0,commutativity_k4_real_1,involutiveness_k4_xcmplx_0,involutiveness_k5_xcmplx_0,redefinition_k1_real_1,redefinition_k2_real_1,redefinition_k3_real_1,redefinition_k4_real_1,dt_k1_real_1,dt_k2_real_1,dt_k2_xcmplx_0,dt_k3_real_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_k4_xcmplx_0,dt_k5_xcmplx_0,dt_c12_6__anproj_2,dt_c9_6__anproj_2,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_rm1_r0,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealNeg__k4_xcmplx_0__rm1_r1,spc10_arithm,spc2_arithm,spc5_arithm,spc6_arithm,spc7_arithm,spc8_arithm,t1_arithm,t2_arithm,t3_arithm,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e1_6_4_2__anproj_2,d7_xcmplx_0,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealAdd__k2_xcmplx_0__rm1_r1_r0]), [interesting(0.35),file(anproj_2,e2_6_4_2_2__anproj_2),[file(anproj_2,e2_6_4_2_2__anproj_2)]]). fof(e3_6_4_2_2__anproj_2,plain,( k3_real_1(c9_6__anproj_2,k4_real_1(k1_real_1(c9_6__anproj_2),1)) = 0 ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,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,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,fc2_membered,spc2_arithm,spc5_arithm,spc6_arithm,spc7_arithm,spc8_arithm,t1_arithm,t1_numerals,t2_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,involutiveness_k1_real_1,commutativity_k2_xcmplx_0,commutativity_k3_real_1,commutativity_k3_xcmplx_0,commutativity_k4_real_1,involutiveness_k4_xcmplx_0,redefinition_k1_real_1,redefinition_k3_real_1,redefinition_k4_real_1,dt_k1_real_1,dt_k2_xcmplx_0,dt_k3_real_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_k4_xcmplx_0,dt_c9_6__anproj_2,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,rqRealAdd__k2_xcmplx_0__rm1_r1_r0,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealNeg__k4_xcmplx_0__rm1_r1,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealAdd__k2_xcmplx_0__r1_rm1_r0]), [interesting(0.35),file(anproj_2,e3_6_4_2_2__anproj_2),[file(anproj_2,e3_6_4_2_2__anproj_2)]]). fof(e5_6_4_2__anproj_2,plain,( k3_real_1(k4_real_1(1,c9_6__anproj_2),k4_real_1(k1_real_1(k4_real_1(c9_6__anproj_2,k2_real_1(c12_6__anproj_2))),c12_6__anproj_2)) = 0 ), inference(iterative_eq,[status(thm),assumptions([dt_c6_6__anproj_2,e1_6_4_2__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2])],[e1_6_4_2_2__anproj_2,e2_6_4_2_2__anproj_2,e3_6_4_2_2__anproj_2]), [interesting(0.5),file(anproj_2,e5_6_4_2__anproj_2),[file(anproj_2,e5_6_4_2__anproj_2)]]). fof(dh_c1_6_1__anproj_2,definition, ( ( m1_subset_1(c1_6_1__anproj_2,k1_numbers) => ! [A] : ( m1_subset_1(A,k1_numbers) => k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,c1_6_1__anproj_2),k3_rlvect_1(c1_6__anproj_2,c6_6__anproj_2,A)) = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,k3_real_1(k4_real_1(c1_6_1__anproj_2,c7_6__anproj_2),k4_real_1(A,c10_6__anproj_2))),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k3_real_1(k4_real_1(c1_6_1__anproj_2,c8_6__anproj_2),k4_real_1(A,c11_6__anproj_2)))),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,k3_real_1(k4_real_1(c1_6_1__anproj_2,c9_6__anproj_2),k4_real_1(A,c12_6__anproj_2)))) ) ) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,k1_numbers) => k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,B),k3_rlvect_1(c1_6__anproj_2,c6_6__anproj_2,C)) = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,k3_real_1(k4_real_1(B,c7_6__anproj_2),k4_real_1(C,c10_6__anproj_2))),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k3_real_1(k4_real_1(B,c8_6__anproj_2),k4_real_1(C,c11_6__anproj_2)))),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,k3_real_1(k4_real_1(B,c9_6__anproj_2),k4_real_1(C,c12_6__anproj_2)))) ) ) ), introduced(definition,[new_symbol(c1_6_1__anproj_2),file(anproj_2,c1_6_1__anproj_2)]), [interesting(0.65),axiom,file(anproj_2,c1_6_1__anproj_2)]). fof(dh_c2_6_1__anproj_2,definition, ( ( m1_subset_1(c2_6_1__anproj_2,k1_numbers) => k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,c1_6_1__anproj_2),k3_rlvect_1(c1_6__anproj_2,c6_6__anproj_2,c2_6_1__anproj_2)) = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,k3_real_1(k4_real_1(c1_6_1__anproj_2,c7_6__anproj_2),k4_real_1(c2_6_1__anproj_2,c10_6__anproj_2))),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k3_real_1(k4_real_1(c1_6_1__anproj_2,c8_6__anproj_2),k4_real_1(c2_6_1__anproj_2,c11_6__anproj_2)))),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,k3_real_1(k4_real_1(c1_6_1__anproj_2,c9_6__anproj_2),k4_real_1(c2_6_1__anproj_2,c12_6__anproj_2)))) ) => ! [A] : ( m1_subset_1(A,k1_numbers) => k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,c1_6_1__anproj_2),k3_rlvect_1(c1_6__anproj_2,c6_6__anproj_2,A)) = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,k3_real_1(k4_real_1(c1_6_1__anproj_2,c7_6__anproj_2),k4_real_1(A,c10_6__anproj_2))),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k3_real_1(k4_real_1(c1_6_1__anproj_2,c8_6__anproj_2),k4_real_1(A,c11_6__anproj_2)))),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,k3_real_1(k4_real_1(c1_6_1__anproj_2,c9_6__anproj_2),k4_real_1(A,c12_6__anproj_2)))) ) ), introduced(definition,[new_symbol(c2_6_1__anproj_2),file(anproj_2,c2_6_1__anproj_2)]), [interesting(0.65),axiom,file(anproj_2,c2_6_1__anproj_2)]). fof(dt_c1_6_1__anproj_2,assumption,( m1_subset_1(c1_6_1__anproj_2,k1_numbers) ), introduced(assumption,[file(anproj_2,c1_6_1__anproj_2)]), [interesting(0.65),axiom,file(anproj_2,c1_6_1__anproj_2)]). fof(dt_c2_6_1__anproj_2,assumption,( m1_subset_1(c2_6_1__anproj_2,k1_numbers) ), introduced(assumption,[file(anproj_2,c2_6_1__anproj_2)]), [interesting(0.65),axiom,file(anproj_2,c2_6_1__anproj_2)]). fof(e4_6__anproj_2,plain,( c5_6__anproj_2 = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,c7_6__anproj_2),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,c8_6__anproj_2)),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,c9_6__anproj_2)) ), inference(consider,[status(thm),assumptions([dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2])],[dh_c7_6__anproj_2,dh_c8_6__anproj_2,dh_c9_6__anproj_2,e3_6__anproj_2]), [interesting(0.8),file(anproj_2,e4_6__anproj_2),[file(anproj_2,e4_6__anproj_2)]]). fof(l4_anproj_2,plain,( ! [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,k1_numbers) => ! [F] : ( m1_subset_1(F,k1_numbers) => ! [G] : ( m1_subset_1(G,k1_numbers) => ! [H] : ( m1_subset_1(H,k1_numbers) => k3_rlvect_1(A,k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,F),k3_rlvect_1(A,C,G)),k3_rlvect_1(A,D,H)),E) = k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,k4_real_1(E,F)),k3_rlvect_1(A,C,k4_real_1(E,G))),k3_rlvect_1(A,D,k4_real_1(E,H))) ) ) ) ) ) ) ) ) ), file(anproj_2,l4_anproj_2), [interesting(0.9),axiom,file(anproj_2,l4_anproj_2)]). fof(e1_6_1__anproj_2,plain,( k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,c1_6_1__anproj_2) = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,k4_real_1(c1_6_1__anproj_2,c7_6__anproj_2)),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k4_real_1(c1_6_1__anproj_2,c8_6__anproj_2))),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,k4_real_1(c1_6_1__anproj_2,c9_6__anproj_2))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6_1__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l2_struct_0,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l2_struct_0,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc4_struct_0,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_l1_rlvect_1,existence_l1_struct_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k2_rlvect_1,dt_k5_numbers,dt_l1_rlvect_1,dt_l1_struct_0,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc4_membered,fc1_struct_0,rc3_struct_0,spc7_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_real_1,commutativity_k4_rlvect_1,existence_l2_rlvect_1,existence_m1_subset_1,redefinition_k4_real_1,redefinition_k4_rlvect_1,dt_k1_numbers,dt_k3_rlvect_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_k4_rlvect_1,dt_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_6__anproj_2,dt_c1_6_1__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,dt_c7_6__anproj_2,dt_c8_6__anproj_2,dt_c9_6__anproj_2,fc2_membered,spc1_numerals,spc1_boole,e4_6__anproj_2,l4_anproj_2,rqRealMult__k3_xcmplx_0__r1_r1_r1]), [interesting(0.65),file(anproj_2,e1_6_1__anproj_2),[file(anproj_2,e1_6_1__anproj_2)]]). fof(e6_6__anproj_2,plain,( c6_6__anproj_2 = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,c10_6__anproj_2),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,c11_6__anproj_2)),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,c12_6__anproj_2)) ), inference(consider,[status(thm),assumptions([dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c6_6__anproj_2,e1_6__anproj_2])],[dh_c10_6__anproj_2,dh_c11_6__anproj_2,dh_c12_6__anproj_2,e5_6__anproj_2]), [interesting(0.8),file(anproj_2,e6_6__anproj_2),[file(anproj_2,e6_6__anproj_2)]]). fof(e1_6_1_1__anproj_2,plain,( k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,c1_6_1__anproj_2),k3_rlvect_1(c1_6__anproj_2,c6_6__anproj_2,c2_6_1__anproj_2)) = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,k4_real_1(c1_6_1__anproj_2,c7_6__anproj_2)),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k4_real_1(c1_6_1__anproj_2,c8_6__anproj_2))),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,k4_real_1(c1_6_1__anproj_2,c9_6__anproj_2))),k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,k4_real_1(c2_6_1__anproj_2,c10_6__anproj_2)),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k4_real_1(c2_6_1__anproj_2,c11_6__anproj_2))),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,k4_real_1(c2_6_1__anproj_2,c12_6__anproj_2)))) ), inference(mizar_by,[status(thm),assumptions([dt_c2_6_1__anproj_2,dt_c1_6_1__anproj_2,dt_c5_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c6_6__anproj_2,e1_6__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l2_struct_0,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l2_struct_0,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc4_struct_0,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_l1_rlvect_1,existence_l1_struct_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k2_rlvect_1,dt_k5_numbers,dt_l1_rlvect_1,dt_l1_struct_0,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc4_membered,fc1_struct_0,rc3_struct_0,spc7_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_real_1,commutativity_k4_rlvect_1,existence_l2_rlvect_1,existence_m1_subset_1,redefinition_k4_real_1,redefinition_k4_rlvect_1,dt_k1_numbers,dt_k3_rlvect_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_k4_rlvect_1,dt_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c10_6__anproj_2,dt_c11_6__anproj_2,dt_c12_6__anproj_2,dt_c1_6__anproj_2,dt_c1_6_1__anproj_2,dt_c2_6__anproj_2,dt_c2_6_1__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,dt_c6_6__anproj_2,dt_c7_6__anproj_2,dt_c8_6__anproj_2,dt_c9_6__anproj_2,fc2_membered,spc1_numerals,spc1_boole,e1_6_1__anproj_2,e6_6__anproj_2,l4_anproj_2,rqRealMult__k3_xcmplx_0__r1_r1_r1]), [interesting(0.5),file(anproj_2,e1_6_1_1__anproj_2),[file(anproj_2,e1_6_1_1__anproj_2)]]). fof(l5_anproj_2,plain,( ! [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)) => k4_rlvect_1(A,k4_rlvect_1(A,k4_rlvect_1(A,B,C),D),k4_rlvect_1(A,k4_rlvect_1(A,E,F),G)) = k4_rlvect_1(A,k4_rlvect_1(A,k4_rlvect_1(A,B,E),k4_rlvect_1(A,C,F)),k4_rlvect_1(A,D,G)) ) ) ) ) ) ) ) ), file(anproj_2,l5_anproj_2), [interesting(0.9),axiom,file(anproj_2,l5_anproj_2)]). fof(e2_6_1_1__anproj_2,plain,( k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,k4_real_1(c1_6_1__anproj_2,c7_6__anproj_2)),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k4_real_1(c1_6_1__anproj_2,c8_6__anproj_2))),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,k4_real_1(c1_6_1__anproj_2,c9_6__anproj_2))),k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,k4_real_1(c2_6_1__anproj_2,c10_6__anproj_2)),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k4_real_1(c2_6_1__anproj_2,c11_6__anproj_2))),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,k4_real_1(c2_6_1__anproj_2,c12_6__anproj_2)))) = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,k4_real_1(c1_6_1__anproj_2,c7_6__anproj_2)),k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,k4_real_1(c2_6_1__anproj_2,c10_6__anproj_2))),k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k4_real_1(c1_6_1__anproj_2,c8_6__anproj_2)),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k4_real_1(c2_6_1__anproj_2,c11_6__anproj_2)))),k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,k4_real_1(c1_6_1__anproj_2,c9_6__anproj_2)),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,k4_real_1(c2_6_1__anproj_2,c12_6__anproj_2)))) ), inference(mizar_by,[status(thm),assumptions([dt_c6_6__anproj_2,dt_c1_6_1__anproj_2,dt_c2_6_1__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l2_struct_0,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l2_struct_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,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc4_struct_0,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_l1_rlvect_1,existence_l1_struct_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_rlvect_1,dt_k5_numbers,dt_l1_rlvect_1,dt_l1_struct_0,dt_m2_subset_1,cc15_membered,fc1_struct_0,fc2_membered,rc3_struct_0,spc7_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_real_1,commutativity_k4_rlvect_1,existence_l2_rlvect_1,existence_m1_subset_1,redefinition_k4_real_1,redefinition_k4_rlvect_1,dt_k3_rlvect_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_k4_rlvect_1,dt_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c10_6__anproj_2,dt_c11_6__anproj_2,dt_c12_6__anproj_2,dt_c1_6__anproj_2,dt_c1_6_1__anproj_2,dt_c2_6__anproj_2,dt_c2_6_1__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c7_6__anproj_2,dt_c8_6__anproj_2,dt_c9_6__anproj_2,spc1_numerals,spc1_boole,l5_anproj_2,rqRealMult__k3_xcmplx_0__r1_r1_r1]), [interesting(0.5),file(anproj_2,e2_6_1_1__anproj_2),[file(anproj_2,e2_6_1_1__anproj_2)]]). fof(d9_rlvect_1,definition,( ! [A] : ( ( ~ v3_struct_0(A) & l2_rlvect_1(A) ) => ( v7_rlvect_1(A) <=> ( ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k3_rlvect_1(A,k2_rlvect_1(A,C,D),B) = k2_rlvect_1(A,k3_rlvect_1(A,C,B),k3_rlvect_1(A,D,B)) ) ) ) & ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,k1_numbers) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k3_rlvect_1(A,D,k3_real_1(B,C)) = k2_rlvect_1(A,k3_rlvect_1(A,D,B),k3_rlvect_1(A,D,C)) ) ) ) & ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,k1_numbers) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k3_rlvect_1(A,D,k4_real_1(B,C)) = k3_rlvect_1(A,k3_rlvect_1(A,D,C),B) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k3_rlvect_1(A,B,1) = B ) ) ) ) ), file(rlvect_1,d9_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,d9_rlvect_1)]). fof(e3_6_1_1__anproj_2,plain,( k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,k4_real_1(c1_6_1__anproj_2,c7_6__anproj_2)),k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,k4_real_1(c2_6_1__anproj_2,c10_6__anproj_2))),k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k4_real_1(c1_6_1__anproj_2,c8_6__anproj_2)),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k4_real_1(c2_6_1__anproj_2,c11_6__anproj_2)))),k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,k4_real_1(c1_6_1__anproj_2,c9_6__anproj_2)),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,k4_real_1(c2_6_1__anproj_2,c12_6__anproj_2)))) = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,k3_real_1(k4_real_1(c1_6_1__anproj_2,c7_6__anproj_2),k4_real_1(c2_6_1__anproj_2,c10_6__anproj_2))),k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k4_real_1(c1_6_1__anproj_2,c8_6__anproj_2)),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k4_real_1(c2_6_1__anproj_2,c11_6__anproj_2)))),k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,k4_real_1(c1_6_1__anproj_2,c9_6__anproj_2)),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,k4_real_1(c2_6_1__anproj_2,c12_6__anproj_2)))) ), inference(mizar_by,[status(thm),assumptions([dt_c6_6__anproj_2,dt_c1_6_1__anproj_2,dt_c2_6_1__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l2_struct_0,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l2_struct_0,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc4_struct_0,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_l1_rlvect_1,existence_l1_struct_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k2_xcmplx_0,dt_k5_numbers,dt_l1_rlvect_1,dt_l1_struct_0,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc4_membered,fc1_struct_0,rc3_struct_0,spc5_arithm,spc6_arithm,spc7_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,commutativity_k3_real_1,commutativity_k3_xcmplx_0,commutativity_k4_real_1,commutativity_k4_rlvect_1,existence_l2_rlvect_1,existence_m1_subset_1,redefinition_k3_real_1,redefinition_k4_real_1,redefinition_k4_rlvect_1,dt_k1_numbers,dt_k2_rlvect_1,dt_k3_real_1,dt_k3_rlvect_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_k4_rlvect_1,dt_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c10_6__anproj_2,dt_c11_6__anproj_2,dt_c12_6__anproj_2,dt_c1_6__anproj_2,dt_c1_6_1__anproj_2,dt_c2_6__anproj_2,dt_c2_6_1__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c7_6__anproj_2,dt_c8_6__anproj_2,dt_c9_6__anproj_2,fc2_membered,spc1_numerals,spc1_boole,d9_rlvect_1,rqRealMult__k3_xcmplx_0__r1_r1_r1]), [interesting(0.5),file(anproj_2,e3_6_1_1__anproj_2),[file(anproj_2,e3_6_1_1__anproj_2)]]). fof(e4_6_1_1__anproj_2,plain,( k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,k3_real_1(k4_real_1(c1_6_1__anproj_2,c7_6__anproj_2),k4_real_1(c2_6_1__anproj_2,c10_6__anproj_2))),k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k4_real_1(c1_6_1__anproj_2,c8_6__anproj_2)),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k4_real_1(c2_6_1__anproj_2,c11_6__anproj_2)))),k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,k4_real_1(c1_6_1__anproj_2,c9_6__anproj_2)),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,k4_real_1(c2_6_1__anproj_2,c12_6__anproj_2)))) = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,k3_real_1(k4_real_1(c1_6_1__anproj_2,c7_6__anproj_2),k4_real_1(c2_6_1__anproj_2,c10_6__anproj_2))),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k3_real_1(k4_real_1(c1_6_1__anproj_2,c8_6__anproj_2),k4_real_1(c2_6_1__anproj_2,c11_6__anproj_2)))),k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,k4_real_1(c1_6_1__anproj_2,c9_6__anproj_2)),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,k4_real_1(c2_6_1__anproj_2,c12_6__anproj_2)))) ), inference(mizar_by,[status(thm),assumptions([dt_c6_6__anproj_2,dt_c1_6_1__anproj_2,dt_c2_6_1__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l2_struct_0,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l2_struct_0,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc4_struct_0,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_l1_rlvect_1,existence_l1_struct_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k2_xcmplx_0,dt_k5_numbers,dt_l1_rlvect_1,dt_l1_struct_0,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc4_membered,fc1_struct_0,rc3_struct_0,spc5_arithm,spc6_arithm,spc7_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,commutativity_k3_real_1,commutativity_k3_xcmplx_0,commutativity_k4_real_1,commutativity_k4_rlvect_1,existence_l2_rlvect_1,existence_m1_subset_1,redefinition_k3_real_1,redefinition_k4_real_1,redefinition_k4_rlvect_1,dt_k1_numbers,dt_k2_rlvect_1,dt_k3_real_1,dt_k3_rlvect_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_k4_rlvect_1,dt_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c10_6__anproj_2,dt_c11_6__anproj_2,dt_c12_6__anproj_2,dt_c1_6__anproj_2,dt_c1_6_1__anproj_2,dt_c2_6__anproj_2,dt_c2_6_1__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c7_6__anproj_2,dt_c8_6__anproj_2,dt_c9_6__anproj_2,fc2_membered,spc1_numerals,spc1_boole,d9_rlvect_1,rqRealMult__k3_xcmplx_0__r1_r1_r1]), [interesting(0.5),file(anproj_2,e4_6_1_1__anproj_2),[file(anproj_2,e4_6_1_1__anproj_2)]]). fof(e5_6_1_1__anproj_2,plain,( k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,k3_real_1(k4_real_1(c1_6_1__anproj_2,c7_6__anproj_2),k4_real_1(c2_6_1__anproj_2,c10_6__anproj_2))),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k3_real_1(k4_real_1(c1_6_1__anproj_2,c8_6__anproj_2),k4_real_1(c2_6_1__anproj_2,c11_6__anproj_2)))),k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,k4_real_1(c1_6_1__anproj_2,c9_6__anproj_2)),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,k4_real_1(c2_6_1__anproj_2,c12_6__anproj_2)))) = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,k3_real_1(k4_real_1(c1_6_1__anproj_2,c7_6__anproj_2),k4_real_1(c2_6_1__anproj_2,c10_6__anproj_2))),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k3_real_1(k4_real_1(c1_6_1__anproj_2,c8_6__anproj_2),k4_real_1(c2_6_1__anproj_2,c11_6__anproj_2)))),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,k3_real_1(k4_real_1(c1_6_1__anproj_2,c9_6__anproj_2),k4_real_1(c2_6_1__anproj_2,c12_6__anproj_2)))) ), inference(mizar_by,[status(thm),assumptions([dt_c6_6__anproj_2,dt_c1_6_1__anproj_2,dt_c2_6_1__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l2_struct_0,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l2_struct_0,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc4_struct_0,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_l1_rlvect_1,existence_l1_struct_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k2_xcmplx_0,dt_k5_numbers,dt_l1_rlvect_1,dt_l1_struct_0,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc4_membered,fc1_struct_0,rc3_struct_0,spc5_arithm,spc6_arithm,spc7_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,commutativity_k3_real_1,commutativity_k3_xcmplx_0,commutativity_k4_real_1,commutativity_k4_rlvect_1,existence_l2_rlvect_1,existence_m1_subset_1,redefinition_k3_real_1,redefinition_k4_real_1,redefinition_k4_rlvect_1,dt_k1_numbers,dt_k2_rlvect_1,dt_k3_real_1,dt_k3_rlvect_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_k4_rlvect_1,dt_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c10_6__anproj_2,dt_c11_6__anproj_2,dt_c12_6__anproj_2,dt_c1_6__anproj_2,dt_c1_6_1__anproj_2,dt_c2_6__anproj_2,dt_c2_6_1__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c7_6__anproj_2,dt_c8_6__anproj_2,dt_c9_6__anproj_2,fc2_membered,spc1_numerals,spc1_boole,d9_rlvect_1,rqRealMult__k3_xcmplx_0__r1_r1_r1]), [interesting(0.5),file(anproj_2,e5_6_1_1__anproj_2),[file(anproj_2,e5_6_1_1__anproj_2)]]). fof(e2_6_1__anproj_2,plain,( k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,c1_6_1__anproj_2),k3_rlvect_1(c1_6__anproj_2,c6_6__anproj_2,c2_6_1__anproj_2)) = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,k3_real_1(k4_real_1(c1_6_1__anproj_2,c7_6__anproj_2),k4_real_1(c2_6_1__anproj_2,c10_6__anproj_2))),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k3_real_1(k4_real_1(c1_6_1__anproj_2,c8_6__anproj_2),k4_real_1(c2_6_1__anproj_2,c11_6__anproj_2)))),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,k3_real_1(k4_real_1(c1_6_1__anproj_2,c9_6__anproj_2),k4_real_1(c2_6_1__anproj_2,c12_6__anproj_2)))) ), inference(iterative_eq,[status(thm),assumptions([dt_c6_6__anproj_2,dt_c1_6_1__anproj_2,dt_c2_6_1__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2])],[e1_6_1_1__anproj_2,e2_6_1_1__anproj_2,e3_6_1_1__anproj_2,e4_6_1_1__anproj_2,e5_6_1_1__anproj_2]), [interesting(0.65),file(anproj_2,e2_6_1__anproj_2),[file(anproj_2,e2_6_1__anproj_2)]]). fof(i3_6_1__anproj_2,theorem,( $true ), introduced(tautology,[file(anproj_2,i3_6_1__anproj_2)]), [interesting(0.65),trivial,file(anproj_2,i3_6_1__anproj_2)]). fof(i2_6_1__anproj_2,plain,( k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,c1_6_1__anproj_2),k3_rlvect_1(c1_6__anproj_2,c6_6__anproj_2,c2_6_1__anproj_2)) = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,k3_real_1(k4_real_1(c1_6_1__anproj_2,c7_6__anproj_2),k4_real_1(c2_6_1__anproj_2,c10_6__anproj_2))),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k3_real_1(k4_real_1(c1_6_1__anproj_2,c8_6__anproj_2),k4_real_1(c2_6_1__anproj_2,c11_6__anproj_2)))),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,k3_real_1(k4_real_1(c1_6_1__anproj_2,c9_6__anproj_2),k4_real_1(c2_6_1__anproj_2,c12_6__anproj_2)))) ), inference(conclusion,[status(thm),assumptions([dt_c6_6__anproj_2,dt_c1_6_1__anproj_2,dt_c2_6_1__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2])],[e2_6_1__anproj_2,i3_6_1__anproj_2]), [interesting(0.65),file(anproj_2,i2_6_1__anproj_2),[file(anproj_2,i2_6_1__anproj_2)]]). fof(i2_6_1_tmp__anproj_2,plain, ( m1_subset_1(c2_6_1__anproj_2,k1_numbers) => k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,c1_6_1__anproj_2),k3_rlvect_1(c1_6__anproj_2,c6_6__anproj_2,c2_6_1__anproj_2)) = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,k3_real_1(k4_real_1(c1_6_1__anproj_2,c7_6__anproj_2),k4_real_1(c2_6_1__anproj_2,c10_6__anproj_2))),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k3_real_1(k4_real_1(c1_6_1__anproj_2,c8_6__anproj_2),k4_real_1(c2_6_1__anproj_2,c11_6__anproj_2)))),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,k3_real_1(k4_real_1(c1_6_1__anproj_2,c9_6__anproj_2),k4_real_1(c2_6_1__anproj_2,c12_6__anproj_2)))) ), inference(discharge_asm,[status(thm),assumptions([dt_c6_6__anproj_2,dt_c1_6_1__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2]),discharge_asm(discharge,[dt_c2_6_1__anproj_2])],[dt_c2_6_1__anproj_2,i2_6_1__anproj_2]), [interesting(0.65),i1_6_1__anproj_2]). fof(i1_6_1__anproj_2,plain,( ! [A] : ( m1_subset_1(A,k1_numbers) => k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,c1_6_1__anproj_2),k3_rlvect_1(c1_6__anproj_2,c6_6__anproj_2,A)) = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,k3_real_1(k4_real_1(c1_6_1__anproj_2,c7_6__anproj_2),k4_real_1(A,c10_6__anproj_2))),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k3_real_1(k4_real_1(c1_6_1__anproj_2,c8_6__anproj_2),k4_real_1(A,c11_6__anproj_2)))),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,k3_real_1(k4_real_1(c1_6_1__anproj_2,c9_6__anproj_2),k4_real_1(A,c12_6__anproj_2)))) ) ), inference(let,[status(thm),assumptions([dt_c6_6__anproj_2,dt_c1_6_1__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2])],[i2_6_1_tmp__anproj_2,dh_c2_6_1__anproj_2]), [interesting(0.65),file(anproj_2,i1_6_1__anproj_2),[file(anproj_2,i1_6_1__anproj_2)]]). fof(i1_6_1_tmp__anproj_2,plain, ( m1_subset_1(c1_6_1__anproj_2,k1_numbers) => ! [A] : ( m1_subset_1(A,k1_numbers) => k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,c1_6_1__anproj_2),k3_rlvect_1(c1_6__anproj_2,c6_6__anproj_2,A)) = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,k3_real_1(k4_real_1(c1_6_1__anproj_2,c7_6__anproj_2),k4_real_1(A,c10_6__anproj_2))),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k3_real_1(k4_real_1(c1_6_1__anproj_2,c8_6__anproj_2),k4_real_1(A,c11_6__anproj_2)))),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,k3_real_1(k4_real_1(c1_6_1__anproj_2,c9_6__anproj_2),k4_real_1(A,c12_6__anproj_2)))) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c6_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2]),discharge_asm(discharge,[dt_c1_6_1__anproj_2])],[dt_c1_6_1__anproj_2,i1_6_1__anproj_2]), [interesting(0.8),e8_6__anproj_2]). fof(e8_6__anproj_2,plain,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,A),k3_rlvect_1(c1_6__anproj_2,c6_6__anproj_2,B)) = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,k3_real_1(k4_real_1(A,c7_6__anproj_2),k4_real_1(B,c10_6__anproj_2))),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k3_real_1(k4_real_1(A,c8_6__anproj_2),k4_real_1(B,c11_6__anproj_2)))),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,k3_real_1(k4_real_1(A,c9_6__anproj_2),k4_real_1(B,c12_6__anproj_2)))) ) ) ), inference(let,[status(thm),assumptions([dt_c6_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2])],[i1_6_1_tmp__anproj_2,dh_c1_6_1__anproj_2]), [interesting(0.8),file(anproj_2,e8_6__anproj_2),[file(anproj_2,e8_6__anproj_2)]]). fof(rqRealDiv__k7_xcmplx_0__r1_rm1_rm1,theorem,( k7_xcmplx_0(1,k4_xcmplx_0(1)) = k4_xcmplx_0(1) ), file(arithm,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1)]). fof(rqRealDiff__k6_xcmplx_0__r1_r1_r0,theorem,( k6_xcmplx_0(1,1) = 0 ), file(arithm,rqRealDiff__k6_xcmplx_0__r1_r1_r0), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_r1_r0)]). fof(rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,theorem,( k6_xcmplx_0(k4_xcmplx_0(1),k4_xcmplx_0(1)) = 0 ), file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0)]). fof(rqRealDiff__k6_xcmplx_0__r0_r1_rm1,theorem,( k6_xcmplx_0(0,1) = k4_xcmplx_0(1) ), file(arithm,rqRealDiff__k6_xcmplx_0__r0_r1_rm1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_r1_rm1)]). fof(rqRealDiff__k6_xcmplx_0__r1_rm1_r2,theorem,( k6_xcmplx_0(1,k4_xcmplx_0(1)) = 2 ), file(arithm,rqRealDiff__k6_xcmplx_0__r1_rm1_r2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_rm1_r2)]). fof(rqRealDiff__k6_xcmplx_0__rm1_r1_rm2,theorem,( k6_xcmplx_0(k4_xcmplx_0(1),1) = k4_xcmplx_0(2) ), file(arithm,rqRealDiff__k6_xcmplx_0__rm1_r1_rm2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_r1_rm2)]). fof(e1_6_4_2_3__anproj_2,plain,( k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,1),k3_rlvect_1(c1_6__anproj_2,c6_6__anproj_2,k1_real_1(k4_real_1(c9_6__anproj_2,k2_real_1(c12_6__anproj_2))))) = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,k3_real_1(k4_real_1(1,c7_6__anproj_2),k4_real_1(k1_real_1(k4_real_1(c9_6__anproj_2,k2_real_1(c12_6__anproj_2))),c10_6__anproj_2))),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k3_real_1(k4_real_1(1,c8_6__anproj_2),k4_real_1(k1_real_1(k4_real_1(c9_6__anproj_2,k2_real_1(c12_6__anproj_2))),c11_6__anproj_2)))),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,0)) ), inference(mizar_by,[status(thm),assumptions([e1_6_4_2__anproj_2,dt_c6_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l1_struct_0,existence_l2_struct_0,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l1_struct_0,dt_l2_struct_0,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc6_membered,cc9_membered,fc1_struct_0,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc4_struct_0,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,involutiveness_k5_xcmplx_0,existence_l1_rlvect_1,existence_l2_rlvect_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k2_rlvect_1,dt_k2_xcmplx_0,dt_k5_numbers,dt_k5_xcmplx_0,dt_l1_rlvect_1,dt_l2_rlvect_1,dt_m2_subset_1,dt_u1_struct_0,cc10_membered,cc11_membered,cc15_membered,cc4_membered,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_r2_r2,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r0_rm2_rm2,rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2,rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_r1_r2,rqRealAdd__k2_xcmplx_0__r1_rm1_r0,rqRealAdd__k2_xcmplx_0__r1_rm2_rm1,rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2,rqRealAdd__k2_xcmplx_0__r2_r0_r2,rqRealAdd__k2_xcmplx_0__r2_rm1_r1,rqRealAdd__k2_xcmplx_0__r2_rm2_r0,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,rqRealAdd__k2_xcmplx_0__rm1_r1_r0,rqRealAdd__k2_xcmplx_0__rm1_r2_r1,rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2,rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2,rqRealAdd__k2_xcmplx_0__rm2_r0_rm2,rqRealAdd__k2_xcmplx_0__rm2_r1_rm1,rqRealAdd__k2_xcmplx_0__rm2_r2_r0,rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2,rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2,rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1,rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0,rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2,rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0,rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1,spc10_arithm,spc11_arithm,spc12_arithm,spc1_arithm,spc2_arithm,spc3_arithm,spc4_arithm,spc5_arithm,spc6_arithm,spc7_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_numerals,t2_arithm,t2_subset,t3_arithm,t4_arithm,t5_arithm,t6_arithm,t6_boole,t7_boole,t8_boole,involutiveness_k1_real_1,involutiveness_k2_real_1,commutativity_k3_real_1,commutativity_k3_xcmplx_0,commutativity_k4_real_1,commutativity_k4_rlvect_1,involutiveness_k4_xcmplx_0,existence_m1_subset_1,redefinition_k1_real_1,redefinition_k2_real_1,redefinition_k3_real_1,redefinition_k4_real_1,redefinition_k4_rlvect_1,dt_k1_numbers,dt_k1_real_1,dt_k2_real_1,dt_k3_real_1,dt_k3_rlvect_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_k4_rlvect_1,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_k7_xcmplx_0,dt_m1_subset_1,dt_c10_6__anproj_2,dt_c11_6__anproj_2,dt_c12_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,dt_c6_6__anproj_2,dt_c7_6__anproj_2,dt_c8_6__anproj_2,dt_c9_6__anproj_2,fc2_membered,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_r2_rm2,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r0_rm2_r2,rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2,rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__r1_r2_rm1,rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2,rqRealDiff__k6_xcmplx_0__r2_r0_r2,rqRealDiff__k6_xcmplx_0__r2_r1_r1,rqRealDiff__k6_xcmplx_0__r2_r2_r0,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealDiff__k6_xcmplx_0__rm1_rm2_r1,rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2,rqRealDiff__k6_xcmplx_0__rm2_r0_rm2,rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1,rqRealDiff__k6_xcmplx_0__rm2_rm2_r0,rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2,rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2,rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0,rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1,rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2,rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2,rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1,rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0,rqRealDiv__k7_xcmplx_0__r0_r1_r0,rqRealDiv__k7_xcmplx_0__r0_r2_r0,rqRealDiv__k7_xcmplx_0__r0_rn1d2_r0,rqRealDiv__k7_xcmplx_0__r1_r1_r1,rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2,rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2,rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2,rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2,rqRealDiv__k7_xcmplx_0__r2_r1_r2,rqRealDiv__k7_xcmplx_0__r2_r2_r1,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1,rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2,rqRealDiv__k7_xcmplx_0__rnm1d2_rn1d2_rm1,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r0_r2_r0,rqRealMult__k3_xcmplx_0__r0_rm2_r0,rqRealMult__k3_xcmplx_0__r0_rn1d2_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,rqRealMult__k3_xcmplx_0__r1_r2_r2,rqRealMult__k3_xcmplx_0__r1_rm2_rm2,rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2,rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2,rqRealMult__k3_xcmplx_0__r2_r0_r0,rqRealMult__k3_xcmplx_0__r2_r1_r2,rqRealMult__k3_xcmplx_0__r2_rn1d2_r1,rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1,rqRealMult__k3_xcmplx_0__rm2_r0_r0,rqRealMult__k3_xcmplx_0__rm2_r1_rm2,rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1,rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1,rqRealMult__k3_xcmplx_0__rn1d2_r0_r0,rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2,rqRealMult__k3_xcmplx_0__rn1d2_r2_r1,rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1,rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2,rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1,rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1,rqRealNeg__k4_xcmplx_0__r2_rm2,rqRealNeg__k4_xcmplx_0__rm2_r2,rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2,rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2,spc0_numerals,spc1_numerals,spc2_numerals,spc0_boole,spc1_boole,spc2_boole,e5_6_4_2__anproj_2,e8_6__anproj_2,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__r1_rm1_r2,rqRealDiff__k6_xcmplx_0__rm1_r1_rm2]), [interesting(0.35),file(anproj_2,e1_6_4_2_3__anproj_2),[file(anproj_2,e1_6_4_2_3__anproj_2)]]). fof(t23_rlvect_1,theorem,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( ( ~ v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & l2_rlvect_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ( ( A = 0 | C = k1_rlvect_1(B) ) => k3_rlvect_1(B,C,A) = k1_rlvect_1(B) ) ) ) ) ), file(rlvect_1,t23_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,t23_rlvect_1)]). fof(e2_6_4_2_3__anproj_2,plain,( k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,k3_real_1(k4_real_1(1,c7_6__anproj_2),k4_real_1(k1_real_1(k4_real_1(c9_6__anproj_2,k2_real_1(c12_6__anproj_2))),c10_6__anproj_2))),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k3_real_1(k4_real_1(1,c8_6__anproj_2),k4_real_1(k1_real_1(k4_real_1(c9_6__anproj_2,k2_real_1(c12_6__anproj_2))),c11_6__anproj_2)))),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,0)) = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,k3_real_1(k4_real_1(1,c7_6__anproj_2),k4_real_1(k1_real_1(k4_real_1(c9_6__anproj_2,k2_real_1(c12_6__anproj_2))),c10_6__anproj_2))),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k3_real_1(k4_real_1(1,c8_6__anproj_2),k4_real_1(k1_real_1(k4_real_1(c9_6__anproj_2,k2_real_1(c12_6__anproj_2))),c11_6__anproj_2)))),k1_rlvect_1(c1_6__anproj_2)) ), inference(mizar_by,[status(thm),assumptions([dt_c6_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,involutiveness_k5_xcmplx_0,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_struct_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k2_rlvect_1,dt_k2_xcmplx_0,dt_k5_numbers,dt_k5_xcmplx_0,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_struct_0,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc4_membered,fc1_struct_0,rc3_struct_0,rc4_struct_0,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_rm1_r0,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,rqRealAdd__k2_xcmplx_0__rm1_r1_r0,spc10_arithm,spc2_arithm,spc5_arithm,spc6_arithm,spc7_arithm,spc8_arithm,t1_arithm,t1_numerals,t2_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,involutiveness_k1_real_1,involutiveness_k2_real_1,commutativity_k3_real_1,commutativity_k3_xcmplx_0,commutativity_k4_real_1,commutativity_k4_rlvect_1,involutiveness_k4_xcmplx_0,existence_l2_rlvect_1,existence_m1_subset_1,redefinition_k1_real_1,redefinition_k2_real_1,redefinition_k3_real_1,redefinition_k4_real_1,redefinition_k4_rlvect_1,dt_k1_numbers,dt_k1_real_1,dt_k1_rlvect_1,dt_k2_real_1,dt_k3_real_1,dt_k3_rlvect_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_k4_rlvect_1,dt_k4_xcmplx_0,dt_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c10_6__anproj_2,dt_c11_6__anproj_2,dt_c12_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c7_6__anproj_2,dt_c8_6__anproj_2,dt_c9_6__anproj_2,fc2_membered,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealNeg__k4_xcmplx_0__rm1_r1,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,t23_rlvect_1,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealNeg__k4_xcmplx_0__r1_rm1]), [interesting(0.35),file(anproj_2,e2_6_4_2_3__anproj_2),[file(anproj_2,e2_6_4_2_3__anproj_2)]]). fof(t10_rlvect_1,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( k2_rlvect_1(A,B,k1_rlvect_1(A)) = B & k2_rlvect_1(A,k1_rlvect_1(A),B) = B ) ) ) ), file(rlvect_1,t10_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,t10_rlvect_1)]). fof(e3_6_4_2_3__anproj_2,plain,( k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,k3_real_1(k4_real_1(1,c7_6__anproj_2),k4_real_1(k1_real_1(k4_real_1(c9_6__anproj_2,k2_real_1(c12_6__anproj_2))),c10_6__anproj_2))),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k3_real_1(k4_real_1(1,c8_6__anproj_2),k4_real_1(k1_real_1(k4_real_1(c9_6__anproj_2,k2_real_1(c12_6__anproj_2))),c11_6__anproj_2)))),k1_rlvect_1(c1_6__anproj_2)) = k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,k3_real_1(k4_real_1(1,c7_6__anproj_2),k4_real_1(k1_real_1(k4_real_1(c9_6__anproj_2,k2_real_1(c12_6__anproj_2))),c10_6__anproj_2))),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k3_real_1(k4_real_1(1,c8_6__anproj_2),k4_real_1(k1_real_1(k4_real_1(c9_6__anproj_2,k2_real_1(c12_6__anproj_2))),c11_6__anproj_2)))) ), inference(mizar_by,[status(thm),assumptions([dt_c6_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,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,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,involutiveness_k5_xcmplx_0,existence_l1_struct_0,existence_l2_rlvect_1,existence_l2_struct_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_xcmplx_0,dt_k5_numbers,dt_k5_xcmplx_0,dt_l1_struct_0,dt_l2_rlvect_1,dt_l2_struct_0,dt_m2_subset_1,cc15_membered,fc1_struct_0,fc2_membered,rc3_struct_0,rc4_struct_0,spc10_arithm,spc2_arithm,spc5_arithm,spc6_arithm,spc7_arithm,spc8_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,involutiveness_k1_real_1,involutiveness_k2_real_1,commutativity_k3_real_1,commutativity_k3_xcmplx_0,commutativity_k4_real_1,commutativity_k4_rlvect_1,involutiveness_k4_xcmplx_0,existence_l1_rlvect_1,existence_m1_subset_1,redefinition_k1_real_1,redefinition_k2_real_1,redefinition_k3_real_1,redefinition_k4_real_1,redefinition_k4_rlvect_1,dt_k1_real_1,dt_k1_rlvect_1,dt_k2_real_1,dt_k2_rlvect_1,dt_k3_real_1,dt_k3_rlvect_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_k4_rlvect_1,dt_k4_xcmplx_0,dt_l1_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c10_6__anproj_2,dt_c11_6__anproj_2,dt_c12_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c7_6__anproj_2,dt_c8_6__anproj_2,dt_c9_6__anproj_2,rqRealNeg__k4_xcmplx_0__rm1_r1,spc1_numerals,spc1_boole,t10_rlvect_1,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealNeg__k4_xcmplx_0__r1_rm1]), [interesting(0.35),file(anproj_2,e3_6_4_2_3__anproj_2),[file(anproj_2,e3_6_4_2_3__anproj_2)]]). fof(e6_6_4_2__anproj_2,plain,( k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,1),k3_rlvect_1(c1_6__anproj_2,c6_6__anproj_2,k1_real_1(k4_real_1(c9_6__anproj_2,k2_real_1(c12_6__anproj_2))))) = k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,k3_real_1(k4_real_1(1,c7_6__anproj_2),k4_real_1(k1_real_1(k4_real_1(c9_6__anproj_2,k2_real_1(c12_6__anproj_2))),c10_6__anproj_2))),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k3_real_1(k4_real_1(1,c8_6__anproj_2),k4_real_1(k1_real_1(k4_real_1(c9_6__anproj_2,k2_real_1(c12_6__anproj_2))),c11_6__anproj_2)))) ), inference(iterative_eq,[status(thm),assumptions([e1_6_4_2__anproj_2,dt_c6_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2])],[e1_6_4_2_3__anproj_2,e2_6_4_2_3__anproj_2,e3_6_4_2_3__anproj_2]), [interesting(0.5),file(anproj_2,e6_6_4_2__anproj_2),[file(anproj_2,e6_6_4_2__anproj_2)]]). fof(t1_anproj_2,theorem,( ! [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,k1_numbers) => ! [F] : ( m1_subset_1(F,k1_numbers) => ! [G] : ( m1_subset_1(G,k1_numbers) => ( k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,C,F)),k3_rlvect_1(A,D,G)) = k1_rlvect_1(A) => ( E = 0 & F = 0 & G = 0 ) ) ) ) ) => ( v8_rlvect_1(B,A) & v8_rlvect_1(C,A) & v8_rlvect_1(D,A) & ~ r2_anproj_1(A,B,C,D) & ~ r1_anproj_1(A,B,C) ) ) ) ) ) ) ), file(anproj_2,t1_anproj_2), [interesting(0.9),axiom,file(anproj_2,t1_anproj_2)]). fof(e7_6__anproj_2,plain, ( v8_rlvect_1(c2_6__anproj_2,c1_6__anproj_2) & v8_rlvect_1(c3_6__anproj_2,c1_6__anproj_2) & v8_rlvect_1(c4_6__anproj_2,c1_6__anproj_2) & ~ r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,c4_6__anproj_2) & ~ r1_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,e2_6__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_struct_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k2_rlvect_1,dt_k5_numbers,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_struct_0,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc4_membered,fc1_struct_0,rc3_struct_0,rc4_struct_0,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k4_rlvect_1,symmetry_r1_anproj_1,reflexivity_r1_anproj_1,existence_l2_rlvect_1,existence_m1_subset_1,redefinition_k4_rlvect_1,dt_k1_numbers,dt_k1_rlvect_1,dt_k3_rlvect_1,dt_k4_rlvect_1,dt_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,fc2_membered,spc0_numerals,spc0_boole,e2_6__anproj_2,t1_anproj_2]), [interesting(0.8),file(anproj_2,e7_6__anproj_2),[file(anproj_2,e7_6__anproj_2)]]). fof(e7_6_4_2__anproj_2,plain,( r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,1),k3_rlvect_1(c1_6__anproj_2,c6_6__anproj_2,k1_real_1(k4_real_1(c9_6__anproj_2,k2_real_1(c12_6__anproj_2)))))) ), inference(mizar_by,[status(thm),assumptions([e1_6_4_2__anproj_2,dt_c6_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,e2_6__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l2_struct_0,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l2_struct_0,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc4_struct_0,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,involutiveness_k5_xcmplx_0,existence_l1_rlvect_1,existence_l1_struct_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k2_rlvect_1,dt_k2_xcmplx_0,dt_k5_numbers,dt_k5_xcmplx_0,dt_l1_rlvect_1,dt_l1_struct_0,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc4_membered,fc1_struct_0,rc3_struct_0,spc10_arithm,spc2_arithm,spc5_arithm,spc6_arithm,spc7_arithm,spc8_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,involutiveness_k1_real_1,involutiveness_k2_real_1,commutativity_k3_real_1,commutativity_k3_xcmplx_0,commutativity_k4_real_1,commutativity_k4_rlvect_1,involutiveness_k4_xcmplx_0,symmetry_r1_anproj_1,reflexivity_r1_anproj_1,existence_l2_rlvect_1,existence_m1_subset_1,redefinition_k1_real_1,redefinition_k2_real_1,redefinition_k3_real_1,redefinition_k4_real_1,redefinition_k4_rlvect_1,dt_k1_numbers,dt_k1_real_1,dt_k2_real_1,dt_k3_real_1,dt_k3_rlvect_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_k4_rlvect_1,dt_k4_xcmplx_0,dt_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c10_6__anproj_2,dt_c11_6__anproj_2,dt_c12_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,dt_c6_6__anproj_2,dt_c7_6__anproj_2,dt_c8_6__anproj_2,dt_c9_6__anproj_2,fc2_membered,rqRealNeg__k4_xcmplx_0__rm1_r1,spc1_numerals,spc1_boole,e6_6_4_2__anproj_2,e7_6__anproj_2,t11_anproj_1,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealMult__k3_xcmplx_0__r1_r1_r1]), [interesting(0.5),file(anproj_2,e7_6_4_2__anproj_2),[file(anproj_2,e7_6_4_2__anproj_2)]]). fof(e9_6_4_2__anproj_2,plain,( ? [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) & r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,A) & r2_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2,A) & v8_rlvect_1(A,c1_6__anproj_2) ) ), inference(mizar_by,[status(thm),assumptions([e1_6_4__anproj_2,e1_6_4_2__anproj_2,dt_c6_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,e2_6__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l2_struct_0,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l2_struct_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,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc4_struct_0,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,involutiveness_k5_xcmplx_0,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_rlvect_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_rlvect_1,dt_k5_numbers,dt_k5_xcmplx_0,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_rlvect_1,dt_m2_subset_1,cc15_membered,fc1_struct_0,fc2_membered,rc3_struct_0,spc10_arithm,spc2_arithm,spc7_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,involutiveness_k1_real_1,involutiveness_k2_real_1,commutativity_k3_xcmplx_0,commutativity_k4_real_1,commutativity_k4_rlvect_1,involutiveness_k4_xcmplx_0,existence_m1_subset_1,redefinition_k1_real_1,redefinition_k2_real_1,redefinition_k4_real_1,redefinition_k4_rlvect_1,dt_k1_real_1,dt_k2_real_1,dt_k3_rlvect_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_k4_rlvect_1,dt_k4_xcmplx_0,dt_m1_subset_1,dt_u1_struct_0,dt_c12_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c5_6__anproj_2,dt_c6_6__anproj_2,dt_c9_6__anproj_2,rqRealNeg__k4_xcmplx_0__rm1_r1,spc1_numerals,spc1_boole,e8_6_4_2__anproj_2,e4_6_4_2__anproj_2,e7_6_4_2__anproj_2,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealMult__k3_xcmplx_0__r1_r1_r1]), [interesting(0.5),file(anproj_2,e9_6_4_2__anproj_2),[file(anproj_2,e9_6_4_2__anproj_2)]]). fof(i2_6_4_2__anproj_2,theorem,( $true ), introduced(tautology,[file(anproj_2,i2_6_4_2__anproj_2)]), [interesting(0.5),trivial,file(anproj_2,i2_6_4_2__anproj_2)]). fof(i1_6_4_2__anproj_2,plain,( ? [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) & r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,A) & r2_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2,A) & v8_rlvect_1(A,c1_6__anproj_2) ) ), inference(conclusion,[status(thm),assumptions([e1_6_4__anproj_2,e1_6_4_2__anproj_2,dt_c6_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,e2_6__anproj_2])],[e9_6_4_2__anproj_2,i2_6_4_2__anproj_2]), [interesting(0.5),file(anproj_2,i1_6_4_2__anproj_2),[file(anproj_2,i1_6_4_2__anproj_2)]]). fof(e3_6_4__anproj_2,plain,( ~ ( c12_6__anproj_2 != 0 & ! [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) => ~ ( r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,A) & r2_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2,A) & v8_rlvect_1(A,c1_6__anproj_2) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([e1_6_4__anproj_2,dt_c6_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,e2_6__anproj_2]),discharge_asm(discharge,[e1_6_4_2__anproj_2])],[e1_6_4_2__anproj_2,i1_6_4_2__anproj_2]), [interesting(0.65),file(anproj_2,e3_6_4__anproj_2),[file(anproj_2,e3_6_4__anproj_2)]]). fof(e1_6_4_1__anproj_2,assumption,( c12_6__anproj_2 = 0 ), introduced(assumption,[file(anproj_2,e1_6_4_1__anproj_2)]), [interesting(0.5),axiom,file(anproj_2,e1_6_4_1__anproj_2)]). fof(e6_6_4_1__anproj_2,plain,( r2_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,0),k3_rlvect_1(c1_6__anproj_2,c6_6__anproj_2,1))) ), inference(mizar_by,[status(thm),assumptions([dt_c6_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2,e1_6_4__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l2_struct_0,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l2_struct_0,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc4_struct_0,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_l1_rlvect_1,existence_l1_struct_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k2_rlvect_1,dt_k5_numbers,dt_l1_rlvect_1,dt_l1_struct_0,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc4_membered,fc1_struct_0,rc3_struct_0,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k4_rlvect_1,symmetry_r1_anproj_1,reflexivity_r1_anproj_1,existence_l2_rlvect_1,existence_m1_subset_1,redefinition_k4_rlvect_1,dt_k1_numbers,dt_k3_rlvect_1,dt_k4_rlvect_1,dt_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_6__anproj_2,dt_c5_6__anproj_2,dt_c6_6__anproj_2,dt_c9_6__anproj_2,fc2_membered,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e1_6_4__anproj_2,t11_anproj_1]), [interesting(0.5),file(anproj_2,e6_6_4_1__anproj_2),[file(anproj_2,e6_6_4_1__anproj_2)]]). fof(e1_6_4_1_1_1__anproj_2,plain,( k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,0),k3_rlvect_1(c1_6__anproj_2,c6_6__anproj_2,1)) = k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,0),c6_6__anproj_2) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__anproj_2,dt_c5_6__anproj_2,dt_c6_6__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l2_struct_0,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l2_struct_0,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc4_struct_0,rc5_struct_0,spc5_arithm,spc6_arithm,spc7_arithm,t1_arithm,t1_subset,t2_arithm,t3_arithm,t3_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,commutativity_k3_xcmplx_0,existence_l1_rlvect_1,existence_l1_struct_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k2_xcmplx_0,dt_k3_xcmplx_0,dt_k5_numbers,dt_l1_rlvect_1,dt_l1_struct_0,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc4_membered,fc1_struct_0,rc3_struct_0,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,rqRealMult__k3_xcmplx_0__r1_r1_r1,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k3_real_1,commutativity_k4_real_1,commutativity_k4_rlvect_1,existence_l2_rlvect_1,existence_m1_subset_1,redefinition_k3_real_1,redefinition_k4_real_1,redefinition_k4_rlvect_1,dt_k1_numbers,dt_k2_rlvect_1,dt_k3_real_1,dt_k3_rlvect_1,dt_k4_real_1,dt_k4_rlvect_1,dt_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_6__anproj_2,dt_c5_6__anproj_2,dt_c6_6__anproj_2,fc2_membered,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,d9_rlvect_1]), [interesting(0.2),file(anproj_2,e1_6_4_1_1_1__anproj_2),[file(anproj_2,e1_6_4_1_1_1__anproj_2)]]). fof(e2_6_4_1_1_1__anproj_2,plain,( k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,0),c6_6__anproj_2) = k4_rlvect_1(c1_6__anproj_2,k1_rlvect_1(c1_6__anproj_2),c6_6__anproj_2) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__anproj_2,dt_c5_6__anproj_2,dt_c6_6__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_struct_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k2_rlvect_1,dt_k5_numbers,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_struct_0,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc4_membered,fc1_struct_0,rc3_struct_0,rc4_struct_0,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k4_rlvect_1,existence_l2_rlvect_1,existence_m1_subset_1,redefinition_k4_rlvect_1,dt_k1_numbers,dt_k1_rlvect_1,dt_k3_rlvect_1,dt_k4_rlvect_1,dt_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_6__anproj_2,dt_c5_6__anproj_2,dt_c6_6__anproj_2,fc2_membered,spc0_numerals,spc0_boole,t23_rlvect_1]), [interesting(0.2),file(anproj_2,e2_6_4_1_1_1__anproj_2),[file(anproj_2,e2_6_4_1_1_1__anproj_2)]]). fof(e3_6_4_1_1_1__anproj_2,plain,( k4_rlvect_1(c1_6__anproj_2,k1_rlvect_1(c1_6__anproj_2),c6_6__anproj_2) = c6_6__anproj_2 ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__anproj_2,dt_c6_6__anproj_2])],[antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,t1_subset,cc15_membered,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_struct_0,existence_l2_rlvect_1,existence_l2_struct_0,dt_l1_struct_0,dt_l2_rlvect_1,dt_l2_struct_0,fc1_struct_0,rc3_struct_0,rc4_struct_0,commutativity_k4_rlvect_1,existence_l1_rlvect_1,existence_m1_subset_1,redefinition_k4_rlvect_1,dt_k1_rlvect_1,dt_k2_rlvect_1,dt_k4_rlvect_1,dt_l1_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_6__anproj_2,dt_c6_6__anproj_2,t10_rlvect_1]), [interesting(0.2),file(anproj_2,e3_6_4_1_1_1__anproj_2),[file(anproj_2,e3_6_4_1_1_1__anproj_2)]]). fof(e1_6_4_1_1__anproj_2,plain,( k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,0),k3_rlvect_1(c1_6__anproj_2,c6_6__anproj_2,1)) = c6_6__anproj_2 ), inference(iterative_eq,[status(thm),assumptions([dt_c5_6__anproj_2,dt_c1_6__anproj_2,dt_c6_6__anproj_2])],[e1_6_4_1_1_1__anproj_2,e2_6_4_1_1_1__anproj_2,e3_6_4_1_1_1__anproj_2]), [interesting(0.35),file(anproj_2,e1_6_4_1_1__anproj_2),[file(anproj_2,e1_6_4_1_1__anproj_2)]]). fof(e2_6_4_1_1__anproj_2,plain,( v8_rlvect_1(k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,0),k3_rlvect_1(c1_6__anproj_2,c6_6__anproj_2,1)),c1_6__anproj_2) ), inference(mizar_by,[status(thm),assumptions([dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,e1_6__anproj_2,dt_c5_6__anproj_2,dt_c1_6__anproj_2,dt_c6_6__anproj_2,e1_6_4__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l1_struct_0,existence_l2_struct_0,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l1_struct_0,dt_l2_struct_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,cc6_membered,cc9_membered,fc1_struct_0,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc4_struct_0,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_l1_rlvect_1,existence_l2_rlvect_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_rlvect_1,dt_k5_numbers,dt_l1_rlvect_1,dt_l2_rlvect_1,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,cc15_membered,fc2_membered,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k4_rlvect_1,symmetry_r1_anproj_1,reflexivity_r1_anproj_1,redefinition_k4_rlvect_1,dt_k3_rlvect_1,dt_k4_rlvect_1,dt_c1_6__anproj_2,dt_c5_6__anproj_2,dt_c6_6__anproj_2,dt_c9_6__anproj_2,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e1_6_4_1_1__anproj_2,e1_6_4__anproj_2]), [interesting(0.35),file(anproj_2,e2_6_4_1_1__anproj_2),[file(anproj_2,e2_6_4_1_1__anproj_2)]]). fof(i1_6_4_1_1__anproj_2,theorem,( $true ), introduced(tautology,[file(anproj_2,i1_6_4_1_1__anproj_2)]), [interesting(0.35),trivial,file(anproj_2,i1_6_4_1_1__anproj_2)]). fof(e2_6_4_1__anproj_2,plain,( v8_rlvect_1(k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,0),k3_rlvect_1(c1_6__anproj_2,c6_6__anproj_2,1)),c1_6__anproj_2) ), inference(conclusion,[status(thm),assumptions([dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,e1_6__anproj_2,dt_c5_6__anproj_2,dt_c1_6__anproj_2,dt_c6_6__anproj_2,e1_6_4__anproj_2])],[e2_6_4_1_1__anproj_2,i1_6_4_1_1__anproj_2]), [interesting(0.5),file(anproj_2,e2_6_4_1__anproj_2),[file(anproj_2,e2_6_4_1__anproj_2)]]). fof(e3_6_4_1__anproj_2,plain,( k3_real_1(k4_real_1(0,c9_6__anproj_2),k4_real_1(1,c12_6__anproj_2)) = 0 ), inference(mizar_by,[status(thm),assumptions([dt_c6_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2,e1_6_4_1__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,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,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,fc2_membered,spc5_arithm,spc6_arithm,spc7_arithm,t1_arithm,t1_numerals,t2_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,commutativity_k2_xcmplx_0,commutativity_k3_real_1,commutativity_k3_xcmplx_0,commutativity_k4_real_1,redefinition_k3_real_1,redefinition_k4_real_1,dt_k2_xcmplx_0,dt_k3_real_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_c12_6__anproj_2,dt_c9_6__anproj_2,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealMult__k3_xcmplx_0__r0_r0_r0,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e1_6_4_1__anproj_2,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0]), [interesting(0.5),file(anproj_2,e3_6_4_1__anproj_2),[file(anproj_2,e3_6_4_1__anproj_2)]]). fof(e1_6_4_1_2__anproj_2,plain,( k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,0),k3_rlvect_1(c1_6__anproj_2,c6_6__anproj_2,1)) = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,k3_real_1(k4_real_1(0,c7_6__anproj_2),k4_real_1(1,c10_6__anproj_2))),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k3_real_1(k4_real_1(0,c8_6__anproj_2),k4_real_1(1,c11_6__anproj_2)))),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,0)) ), inference(mizar_by,[status(thm),assumptions([e1_6_4_1__anproj_2,dt_c6_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l1_struct_0,existence_l2_struct_0,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l1_struct_0,dt_l2_struct_0,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc6_membered,cc9_membered,fc1_struct_0,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc4_struct_0,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_l1_rlvect_1,existence_l2_rlvect_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k2_rlvect_1,dt_k5_numbers,dt_l1_rlvect_1,dt_l2_rlvect_1,dt_m2_subset_1,dt_u1_struct_0,cc10_membered,cc11_membered,cc15_membered,cc4_membered,spc5_arithm,spc6_arithm,spc7_arithm,t1_arithm,t1_numerals,t2_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,commutativity_k2_xcmplx_0,commutativity_k3_real_1,commutativity_k3_xcmplx_0,commutativity_k4_real_1,commutativity_k4_rlvect_1,existence_m1_subset_1,redefinition_k3_real_1,redefinition_k4_real_1,redefinition_k4_rlvect_1,dt_k1_numbers,dt_k2_xcmplx_0,dt_k3_real_1,dt_k3_rlvect_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_k4_rlvect_1,dt_m1_subset_1,dt_c10_6__anproj_2,dt_c11_6__anproj_2,dt_c12_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,dt_c6_6__anproj_2,dt_c7_6__anproj_2,dt_c8_6__anproj_2,dt_c9_6__anproj_2,fc2_membered,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealMult__k3_xcmplx_0__r0_r0_r0,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e3_6_4_1__anproj_2,e8_6__anproj_2,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0]), [interesting(0.35),file(anproj_2,e1_6_4_1_2__anproj_2),[file(anproj_2,e1_6_4_1_2__anproj_2)]]). fof(e2_6_4_1_2__anproj_2,plain,( k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,k3_real_1(k4_real_1(0,c7_6__anproj_2),k4_real_1(1,c10_6__anproj_2))),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k3_real_1(k4_real_1(0,c8_6__anproj_2),k4_real_1(1,c11_6__anproj_2)))),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,0)) = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,k3_real_1(k4_real_1(0,c7_6__anproj_2),k4_real_1(1,c10_6__anproj_2))),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k3_real_1(k4_real_1(0,c8_6__anproj_2),k4_real_1(1,c11_6__anproj_2)))),k1_rlvect_1(c1_6__anproj_2)) ), inference(mizar_by,[status(thm),assumptions([dt_c6_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_struct_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k2_rlvect_1,dt_k2_xcmplx_0,dt_k5_numbers,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_struct_0,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc4_membered,fc1_struct_0,rc3_struct_0,rc4_struct_0,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,spc5_arithm,spc6_arithm,spc7_arithm,t1_arithm,t1_numerals,t2_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,commutativity_k3_real_1,commutativity_k3_xcmplx_0,commutativity_k4_real_1,commutativity_k4_rlvect_1,existence_l2_rlvect_1,existence_m1_subset_1,redefinition_k3_real_1,redefinition_k4_real_1,redefinition_k4_rlvect_1,dt_k1_numbers,dt_k1_rlvect_1,dt_k3_real_1,dt_k3_rlvect_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_k4_rlvect_1,dt_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c10_6__anproj_2,dt_c11_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c7_6__anproj_2,dt_c8_6__anproj_2,fc2_membered,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,t23_rlvect_1,rqRealMult__k3_xcmplx_0__r1_r1_r1]), [interesting(0.35),file(anproj_2,e2_6_4_1_2__anproj_2),[file(anproj_2,e2_6_4_1_2__anproj_2)]]). fof(e3_6_4_1_2__anproj_2,plain,( k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,k3_real_1(k4_real_1(0,c7_6__anproj_2),k4_real_1(1,c10_6__anproj_2))),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k3_real_1(k4_real_1(0,c8_6__anproj_2),k4_real_1(1,c11_6__anproj_2)))),k1_rlvect_1(c1_6__anproj_2)) = k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,k3_real_1(k4_real_1(0,c7_6__anproj_2),k4_real_1(1,c10_6__anproj_2))),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k3_real_1(k4_real_1(0,c8_6__anproj_2),k4_real_1(1,c11_6__anproj_2)))) ), inference(mizar_by,[status(thm),assumptions([dt_c6_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,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,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_l1_struct_0,existence_l2_rlvect_1,existence_l2_struct_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_xcmplx_0,dt_k5_numbers,dt_l1_struct_0,dt_l2_rlvect_1,dt_l2_struct_0,dt_m2_subset_1,cc15_membered,fc1_struct_0,fc2_membered,rc3_struct_0,rc4_struct_0,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,spc5_arithm,spc6_arithm,spc7_arithm,t1_arithm,t1_numerals,t2_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,commutativity_k3_real_1,commutativity_k3_xcmplx_0,commutativity_k4_real_1,commutativity_k4_rlvect_1,existence_l1_rlvect_1,existence_m1_subset_1,redefinition_k3_real_1,redefinition_k4_real_1,redefinition_k4_rlvect_1,dt_k1_rlvect_1,dt_k2_rlvect_1,dt_k3_real_1,dt_k3_rlvect_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_k4_rlvect_1,dt_l1_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c10_6__anproj_2,dt_c11_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c7_6__anproj_2,dt_c8_6__anproj_2,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,t10_rlvect_1,rqRealMult__k3_xcmplx_0__r1_r1_r1]), [interesting(0.35),file(anproj_2,e3_6_4_1_2__anproj_2),[file(anproj_2,e3_6_4_1_2__anproj_2)]]). fof(e4_6_4_1__anproj_2,plain,( k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,0),k3_rlvect_1(c1_6__anproj_2,c6_6__anproj_2,1)) = k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,k3_real_1(k4_real_1(0,c7_6__anproj_2),k4_real_1(1,c10_6__anproj_2))),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k3_real_1(k4_real_1(0,c8_6__anproj_2),k4_real_1(1,c11_6__anproj_2)))) ), inference(iterative_eq,[status(thm),assumptions([e1_6_4_1__anproj_2,dt_c6_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2])],[e1_6_4_1_2__anproj_2,e2_6_4_1_2__anproj_2,e3_6_4_1_2__anproj_2]), [interesting(0.5),file(anproj_2,e4_6_4_1__anproj_2),[file(anproj_2,e4_6_4_1__anproj_2)]]). fof(e5_6_4_1__anproj_2,plain,( r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,0),k3_rlvect_1(c1_6__anproj_2,c6_6__anproj_2,1))) ), inference(mizar_by,[status(thm),assumptions([e1_6_4_1__anproj_2,dt_c6_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,e2_6__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l2_struct_0,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l2_struct_0,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc4_struct_0,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_l1_rlvect_1,existence_l1_struct_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k2_rlvect_1,dt_k2_xcmplx_0,dt_k5_numbers,dt_l1_rlvect_1,dt_l1_struct_0,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc4_membered,fc1_struct_0,rc3_struct_0,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,spc5_arithm,spc6_arithm,spc7_arithm,t1_arithm,t1_numerals,t2_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,commutativity_k3_real_1,commutativity_k3_xcmplx_0,commutativity_k4_real_1,commutativity_k4_rlvect_1,symmetry_r1_anproj_1,reflexivity_r1_anproj_1,existence_l2_rlvect_1,existence_m1_subset_1,redefinition_k3_real_1,redefinition_k4_real_1,redefinition_k4_rlvect_1,dt_k1_numbers,dt_k3_real_1,dt_k3_rlvect_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_k4_rlvect_1,dt_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c10_6__anproj_2,dt_c11_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,dt_c6_6__anproj_2,dt_c7_6__anproj_2,dt_c8_6__anproj_2,fc2_membered,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e4_6_4_1__anproj_2,e7_6__anproj_2,t11_anproj_1,rqRealMult__k3_xcmplx_0__r1_r1_r1]), [interesting(0.5),file(anproj_2,e5_6_4_1__anproj_2),[file(anproj_2,e5_6_4_1__anproj_2)]]). fof(e7_6_4_1__anproj_2,plain,( ? [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) & r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,A) & r2_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2,A) & v8_rlvect_1(A,c1_6__anproj_2) ) ), inference(mizar_by,[status(thm),assumptions([e1_6_4__anproj_2,e1_6_4_1__anproj_2,dt_c6_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,e2_6__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l2_struct_0,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l2_struct_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,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc4_struct_0,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_rlvect_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_rlvect_1,dt_k5_numbers,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_rlvect_1,dt_m2_subset_1,cc15_membered,fc1_struct_0,fc2_membered,rc3_struct_0,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k4_rlvect_1,existence_m1_subset_1,redefinition_k4_rlvect_1,dt_k3_rlvect_1,dt_k4_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c5_6__anproj_2,dt_c6_6__anproj_2,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e6_6_4_1__anproj_2,e2_6_4_1__anproj_2,e5_6_4_1__anproj_2]), [interesting(0.5),file(anproj_2,e7_6_4_1__anproj_2),[file(anproj_2,e7_6_4_1__anproj_2)]]). fof(i2_6_4_1__anproj_2,theorem,( $true ), introduced(tautology,[file(anproj_2,i2_6_4_1__anproj_2)]), [interesting(0.5),trivial,file(anproj_2,i2_6_4_1__anproj_2)]). fof(i1_6_4_1__anproj_2,plain,( ? [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) & r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,A) & r2_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2,A) & v8_rlvect_1(A,c1_6__anproj_2) ) ), inference(conclusion,[status(thm),assumptions([e1_6_4__anproj_2,e1_6_4_1__anproj_2,dt_c6_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,e2_6__anproj_2])],[e7_6_4_1__anproj_2,i2_6_4_1__anproj_2]), [interesting(0.5),file(anproj_2,i1_6_4_1__anproj_2),[file(anproj_2,i1_6_4_1__anproj_2)]]). fof(e2_6_4__anproj_2,plain,( ~ ( c12_6__anproj_2 = 0 & ! [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) => ~ ( r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,A) & r2_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2,A) & v8_rlvect_1(A,c1_6__anproj_2) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([e1_6_4__anproj_2,dt_c6_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,e2_6__anproj_2]),discharge_asm(discharge,[e1_6_4_1__anproj_2])],[e1_6_4_1__anproj_2,i1_6_4_1__anproj_2]), [interesting(0.65),file(anproj_2,e2_6_4__anproj_2),[file(anproj_2,e2_6_4__anproj_2)]]). fof(e4_6_4__anproj_2,plain,( ? [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) & r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,A) & r2_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2,A) & v8_rlvect_1(A,c1_6__anproj_2) ) ), inference(mizar_by,[status(thm),assumptions([e1_6_4__anproj_2,dt_c6_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,e2_6__anproj_2])],[reflexivity_r1_tarski,existence_l2_struct_0,dt_l2_struct_0,rc4_struct_0,antisymmetry_r2_hidden,existence_l1_rlvect_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l1_rlvect_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,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_l1_struct_0,existence_l2_rlvect_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_l1_struct_0,dt_l2_rlvect_1,dt_m2_subset_1,cc15_membered,fc1_struct_0,fc2_membered,rc3_struct_0,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_m1_subset_1,dt_u1_struct_0,dt_c12_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c5_6__anproj_2,dt_c6_6__anproj_2,spc0_numerals,spc0_boole,e3_6_4__anproj_2,e2_6_4__anproj_2]), [interesting(0.65),file(anproj_2,e4_6_4__anproj_2),[file(anproj_2,e4_6_4__anproj_2)]]). fof(i2_6_4__anproj_2,theorem,( $true ), introduced(tautology,[file(anproj_2,i2_6_4__anproj_2)]), [interesting(0.65),trivial,file(anproj_2,i2_6_4__anproj_2)]). fof(i1_6_4__anproj_2,plain,( ? [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) & r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,A) & r2_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2,A) & v8_rlvect_1(A,c1_6__anproj_2) ) ), inference(conclusion,[status(thm),assumptions([e1_6_4__anproj_2,dt_c6_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,e2_6__anproj_2])],[e4_6_4__anproj_2,i2_6_4__anproj_2]), [interesting(0.65),file(anproj_2,i1_6_4__anproj_2),[file(anproj_2,i1_6_4__anproj_2)]]). fof(e11_6__anproj_2,plain,( ~ ( ~ r1_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2) & v8_rlvect_1(c5_6__anproj_2,c1_6__anproj_2) & v8_rlvect_1(c6_6__anproj_2,c1_6__anproj_2) & c9_6__anproj_2 != 0 & ! [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) => ~ ( r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,A) & r2_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2,A) & v8_rlvect_1(A,c1_6__anproj_2) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c6_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,e2_6__anproj_2]),discharge_asm(discharge,[e1_6_4__anproj_2])],[e1_6_4__anproj_2,i1_6_4__anproj_2]), [interesting(0.8),file(anproj_2,e11_6__anproj_2),[file(anproj_2,e11_6__anproj_2)]]). fof(e1_6_2__anproj_2,assumption,( ~ ( ~ r1_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2) & v8_rlvect_1(c5_6__anproj_2,c1_6__anproj_2) & v8_rlvect_1(c6_6__anproj_2,c1_6__anproj_2) ) ), introduced(assumption,[file(anproj_2,e1_6_2__anproj_2)]), [interesting(0.65),axiom,file(anproj_2,e1_6_2__anproj_2)]). fof(e1_6_2_3__anproj_2,assumption,( ~ v8_rlvect_1(c6_6__anproj_2,c1_6__anproj_2) ), introduced(assumption,[file(anproj_2,e1_6_2_3__anproj_2)]), [interesting(0.5),axiom,file(anproj_2,e1_6_2_3__anproj_2)]). fof(e2_6_2_3__anproj_2,plain,( c6_6__anproj_2 = k1_rlvect_1(c1_6__anproj_2) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__anproj_2,dt_c6_6__anproj_2,e1_6_2_3__anproj_2])],[antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,t1_subset,existence_l1_rlvect_1,dt_l1_rlvect_1,cc15_membered,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_struct_0,existence_l2_rlvect_1,dt_l1_struct_0,dt_l2_rlvect_1,fc1_struct_0,rc3_struct_0,existence_l2_struct_0,existence_m1_subset_1,dt_k1_rlvect_1,dt_l2_struct_0,dt_m1_subset_1,dt_u1_struct_0,dt_c1_6__anproj_2,dt_c6_6__anproj_2,rc4_struct_0,e1_6_2_3__anproj_2,d13_rlvect_1]), [interesting(0.5),file(anproj_2,e2_6_2_3__anproj_2),[file(anproj_2,e2_6_2_3__anproj_2)]]). fof(t15_anproj_1,theorem,( ! [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)) => ( ~ ( B != k1_rlvect_1(A) & C != k1_rlvect_1(A) & D != k1_rlvect_1(A) ) => r2_anproj_1(A,B,C,D) ) ) ) ) ) ), file(anproj_1,t15_anproj_1), [interesting(0.9),axiom,file(anproj_1,t15_anproj_1)]). fof(e4_6_2_3__anproj_2,plain,( r2_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2,c3_6__anproj_2) ), inference(mizar_by,[status(thm),assumptions([dt_c3_6__anproj_2,dt_c5_6__anproj_2,dt_c1_6__anproj_2,dt_c6_6__anproj_2,e1_6_2_3__anproj_2])],[antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,t1_subset,cc15_membered,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_struct_0,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_struct_0,fc1_struct_0,rc3_struct_0,rc4_struct_0,existence_l2_rlvect_1,existence_m1_subset_1,dt_k1_rlvect_1,dt_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_6__anproj_2,dt_c3_6__anproj_2,dt_c5_6__anproj_2,dt_c6_6__anproj_2,e2_6_2_3__anproj_2,t15_anproj_1]), [interesting(0.5),file(anproj_2,e4_6_2_3__anproj_2),[file(anproj_2,e4_6_2_3__anproj_2)]]). fof(t16_anproj_1,theorem,( ! [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)) => ( ~ ( ~ r1_anproj_1(A,B,C) & ~ r1_anproj_1(A,D,B) & ~ r1_anproj_1(A,C,D) ) => r2_anproj_1(A,D,B,C) ) ) ) ) ) ), file(anproj_1,t16_anproj_1), [interesting(0.9),axiom,file(anproj_1,t16_anproj_1)]). fof(e3_6_2_3__anproj_2,plain,( r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,c3_6__anproj_2) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2])],[antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,t1_subset,t8_boole,existence_l2_struct_0,dt_l2_struct_0,cc15_membered,rc4_struct_0,t2_subset,t6_boole,t7_boole,existence_l1_rlvect_1,existence_l1_struct_0,dt_l1_rlvect_1,dt_l1_struct_0,fc1_struct_0,rc3_struct_0,symmetry_r1_anproj_1,reflexivity_r1_anproj_1,existence_l2_rlvect_1,existence_m1_subset_1,dt_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,t16_anproj_1]), [interesting(0.5),file(anproj_2,e3_6_2_3__anproj_2),[file(anproj_2,e3_6_2_3__anproj_2)]]). fof(e5_6_2_3__anproj_2,plain,( ? [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) & r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,A) & r2_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2,A) & v8_rlvect_1(A,c1_6__anproj_2) ) ), inference(mizar_by,[status(thm),assumptions([dt_c5_6__anproj_2,dt_c6_6__anproj_2,e1_6_2_3__anproj_2,dt_c4_6__anproj_2,e2_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2])],[antisymmetry_r2_hidden,existence_l2_struct_0,dt_k1_xboole_0,dt_l2_struct_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,rc4_struct_0,t1_subset,t8_boole,existence_l1_rlvect_1,dt_l1_rlvect_1,cc15_membered,t2_subset,t6_boole,t7_boole,existence_l1_struct_0,existence_l2_rlvect_1,dt_l1_struct_0,dt_l2_rlvect_1,fc1_struct_0,rc3_struct_0,symmetry_r1_anproj_1,reflexivity_r1_anproj_1,existence_m1_subset_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,dt_c6_6__anproj_2,e4_6_2_3__anproj_2,e7_6__anproj_2,e3_6_2_3__anproj_2]), [interesting(0.5),file(anproj_2,e5_6_2_3__anproj_2),[file(anproj_2,e5_6_2_3__anproj_2)]]). fof(i2_6_2_3__anproj_2,theorem,( $true ), introduced(tautology,[file(anproj_2,i2_6_2_3__anproj_2)]), [interesting(0.5),trivial,file(anproj_2,i2_6_2_3__anproj_2)]). fof(i1_6_2_3__anproj_2,plain,( ? [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) & r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,A) & r2_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2,A) & v8_rlvect_1(A,c1_6__anproj_2) ) ), inference(conclusion,[status(thm),assumptions([dt_c5_6__anproj_2,dt_c6_6__anproj_2,e1_6_2_3__anproj_2,dt_c4_6__anproj_2,e2_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2])],[e5_6_2_3__anproj_2,i2_6_2_3__anproj_2]), [interesting(0.5),file(anproj_2,i1_6_2_3__anproj_2),[file(anproj_2,i1_6_2_3__anproj_2)]]). fof(e4_6_2__anproj_2,plain,( ~ ( ~ v8_rlvect_1(c6_6__anproj_2,c1_6__anproj_2) & ! [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) => ~ ( r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,A) & r2_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2,A) & v8_rlvect_1(A,c1_6__anproj_2) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c5_6__anproj_2,dt_c6_6__anproj_2,dt_c4_6__anproj_2,e2_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2]),discharge_asm(discharge,[e1_6_2_3__anproj_2])],[e1_6_2_3__anproj_2,i1_6_2_3__anproj_2]), [interesting(0.65),file(anproj_2,e4_6_2__anproj_2),[file(anproj_2,e4_6_2__anproj_2)]]). fof(e1_6_2_1__anproj_2,assumption,( r1_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2) ), introduced(assumption,[file(anproj_2,e1_6_2_1__anproj_2)]), [interesting(0.5),axiom,file(anproj_2,e1_6_2_1__anproj_2)]). fof(e3_6_2_1__anproj_2,plain,( r2_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2,c3_6__anproj_2) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__anproj_2,dt_c3_6__anproj_2,dt_c5_6__anproj_2,dt_c6_6__anproj_2,e1_6_2_1__anproj_2])],[antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,t1_subset,t8_boole,existence_l2_struct_0,dt_l2_struct_0,cc15_membered,rc4_struct_0,t2_subset,t6_boole,t7_boole,existence_l1_rlvect_1,existence_l1_struct_0,dt_l1_rlvect_1,dt_l1_struct_0,fc1_struct_0,rc3_struct_0,symmetry_r1_anproj_1,reflexivity_r1_anproj_1,existence_l2_rlvect_1,existence_m1_subset_1,dt_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_6__anproj_2,dt_c3_6__anproj_2,dt_c5_6__anproj_2,dt_c6_6__anproj_2,e1_6_2_1__anproj_2,t16_anproj_1]), [interesting(0.5),file(anproj_2,e3_6_2_1__anproj_2),[file(anproj_2,e3_6_2_1__anproj_2)]]). fof(e2_6_2_1__anproj_2,plain,( r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,c3_6__anproj_2) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2])],[antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,t1_subset,t8_boole,existence_l2_struct_0,dt_l2_struct_0,cc15_membered,rc4_struct_0,t2_subset,t6_boole,t7_boole,existence_l1_rlvect_1,existence_l1_struct_0,dt_l1_rlvect_1,dt_l1_struct_0,fc1_struct_0,rc3_struct_0,symmetry_r1_anproj_1,reflexivity_r1_anproj_1,existence_l2_rlvect_1,existence_m1_subset_1,dt_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,t16_anproj_1]), [interesting(0.5),file(anproj_2,e2_6_2_1__anproj_2),[file(anproj_2,e2_6_2_1__anproj_2)]]). fof(e4_6_2_1__anproj_2,plain,( ? [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) & r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,A) & r2_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2,A) & v8_rlvect_1(A,c1_6__anproj_2) ) ), inference(mizar_by,[status(thm),assumptions([dt_c5_6__anproj_2,dt_c6_6__anproj_2,e1_6_2_1__anproj_2,dt_c4_6__anproj_2,e2_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2])],[antisymmetry_r2_hidden,existence_l2_struct_0,dt_k1_xboole_0,dt_l2_struct_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,rc4_struct_0,t1_subset,t8_boole,existence_l1_rlvect_1,dt_l1_rlvect_1,cc15_membered,t2_subset,t6_boole,t7_boole,existence_l1_struct_0,existence_l2_rlvect_1,dt_l1_struct_0,dt_l2_rlvect_1,fc1_struct_0,rc3_struct_0,symmetry_r1_anproj_1,reflexivity_r1_anproj_1,existence_m1_subset_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,dt_c6_6__anproj_2,e3_6_2_1__anproj_2,e7_6__anproj_2,e2_6_2_1__anproj_2]), [interesting(0.5),file(anproj_2,e4_6_2_1__anproj_2),[file(anproj_2,e4_6_2_1__anproj_2)]]). fof(i2_6_2_1__anproj_2,theorem,( $true ), introduced(tautology,[file(anproj_2,i2_6_2_1__anproj_2)]), [interesting(0.5),trivial,file(anproj_2,i2_6_2_1__anproj_2)]). fof(i1_6_2_1__anproj_2,plain,( ? [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) & r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,A) & r2_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2,A) & v8_rlvect_1(A,c1_6__anproj_2) ) ), inference(conclusion,[status(thm),assumptions([dt_c5_6__anproj_2,dt_c6_6__anproj_2,e1_6_2_1__anproj_2,dt_c4_6__anproj_2,e2_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2])],[e4_6_2_1__anproj_2,i2_6_2_1__anproj_2]), [interesting(0.5),file(anproj_2,i1_6_2_1__anproj_2),[file(anproj_2,i1_6_2_1__anproj_2)]]). fof(e2_6_2__anproj_2,plain,( ~ ( r1_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2) & ! [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) => ~ ( r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,A) & r2_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2,A) & v8_rlvect_1(A,c1_6__anproj_2) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c5_6__anproj_2,dt_c6_6__anproj_2,dt_c4_6__anproj_2,e2_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2]),discharge_asm(discharge,[e1_6_2_1__anproj_2])],[e1_6_2_1__anproj_2,i1_6_2_1__anproj_2]), [interesting(0.65),file(anproj_2,e2_6_2__anproj_2),[file(anproj_2,e2_6_2__anproj_2)]]). fof(e1_6_2_2__anproj_2,assumption,( ~ v8_rlvect_1(c5_6__anproj_2,c1_6__anproj_2) ), introduced(assumption,[file(anproj_2,e1_6_2_2__anproj_2)]), [interesting(0.5),axiom,file(anproj_2,e1_6_2_2__anproj_2)]). fof(e2_6_2_2__anproj_2,plain,( c5_6__anproj_2 = k1_rlvect_1(c1_6__anproj_2) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__anproj_2,dt_c5_6__anproj_2,e1_6_2_2__anproj_2])],[antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,t1_subset,existence_l1_rlvect_1,dt_l1_rlvect_1,cc15_membered,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_struct_0,existence_l2_rlvect_1,dt_l1_struct_0,dt_l2_rlvect_1,fc1_struct_0,rc3_struct_0,existence_l2_struct_0,existence_m1_subset_1,dt_k1_rlvect_1,dt_l2_struct_0,dt_m1_subset_1,dt_u1_struct_0,dt_c1_6__anproj_2,dt_c5_6__anproj_2,rc4_struct_0,e1_6_2_2__anproj_2,d13_rlvect_1]), [interesting(0.5),file(anproj_2,e2_6_2_2__anproj_2),[file(anproj_2,e2_6_2_2__anproj_2)]]). fof(e4_6_2_2__anproj_2,plain,( r2_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2,c3_6__anproj_2) ), inference(mizar_by,[status(thm),assumptions([dt_c3_6__anproj_2,dt_c6_6__anproj_2,dt_c1_6__anproj_2,dt_c5_6__anproj_2,e1_6_2_2__anproj_2])],[antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,t1_subset,cc15_membered,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_struct_0,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_struct_0,fc1_struct_0,rc3_struct_0,rc4_struct_0,existence_l2_rlvect_1,existence_m1_subset_1,dt_k1_rlvect_1,dt_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_6__anproj_2,dt_c3_6__anproj_2,dt_c5_6__anproj_2,dt_c6_6__anproj_2,e2_6_2_2__anproj_2,t15_anproj_1]), [interesting(0.5),file(anproj_2,e4_6_2_2__anproj_2),[file(anproj_2,e4_6_2_2__anproj_2)]]). fof(e3_6_2_2__anproj_2,plain,( r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,c3_6__anproj_2) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2])],[antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,t1_subset,t8_boole,existence_l2_struct_0,dt_l2_struct_0,cc15_membered,rc4_struct_0,t2_subset,t6_boole,t7_boole,existence_l1_rlvect_1,existence_l1_struct_0,dt_l1_rlvect_1,dt_l1_struct_0,fc1_struct_0,rc3_struct_0,symmetry_r1_anproj_1,reflexivity_r1_anproj_1,existence_l2_rlvect_1,existence_m1_subset_1,dt_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,t16_anproj_1]), [interesting(0.5),file(anproj_2,e3_6_2_2__anproj_2),[file(anproj_2,e3_6_2_2__anproj_2)]]). fof(e5_6_2_2__anproj_2,plain,( ? [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) & r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,A) & r2_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2,A) & v8_rlvect_1(A,c1_6__anproj_2) ) ), inference(mizar_by,[status(thm),assumptions([dt_c6_6__anproj_2,dt_c5_6__anproj_2,e1_6_2_2__anproj_2,dt_c4_6__anproj_2,e2_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2])],[antisymmetry_r2_hidden,existence_l2_struct_0,dt_k1_xboole_0,dt_l2_struct_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,rc4_struct_0,t1_subset,t8_boole,existence_l1_rlvect_1,dt_l1_rlvect_1,cc15_membered,t2_subset,t6_boole,t7_boole,existence_l1_struct_0,existence_l2_rlvect_1,dt_l1_struct_0,dt_l2_rlvect_1,fc1_struct_0,rc3_struct_0,symmetry_r1_anproj_1,reflexivity_r1_anproj_1,existence_m1_subset_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,dt_c6_6__anproj_2,e4_6_2_2__anproj_2,e7_6__anproj_2,e3_6_2_2__anproj_2]), [interesting(0.5),file(anproj_2,e5_6_2_2__anproj_2),[file(anproj_2,e5_6_2_2__anproj_2)]]). fof(i2_6_2_2__anproj_2,theorem,( $true ), introduced(tautology,[file(anproj_2,i2_6_2_2__anproj_2)]), [interesting(0.5),trivial,file(anproj_2,i2_6_2_2__anproj_2)]). fof(i1_6_2_2__anproj_2,plain,( ? [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) & r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,A) & r2_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2,A) & v8_rlvect_1(A,c1_6__anproj_2) ) ), inference(conclusion,[status(thm),assumptions([dt_c6_6__anproj_2,dt_c5_6__anproj_2,e1_6_2_2__anproj_2,dt_c4_6__anproj_2,e2_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2])],[e5_6_2_2__anproj_2,i2_6_2_2__anproj_2]), [interesting(0.5),file(anproj_2,i1_6_2_2__anproj_2),[file(anproj_2,i1_6_2_2__anproj_2)]]). fof(e3_6_2__anproj_2,plain,( ~ ( ~ v8_rlvect_1(c5_6__anproj_2,c1_6__anproj_2) & ! [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) => ~ ( r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,A) & r2_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2,A) & v8_rlvect_1(A,c1_6__anproj_2) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c6_6__anproj_2,dt_c5_6__anproj_2,dt_c4_6__anproj_2,e2_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2]),discharge_asm(discharge,[e1_6_2_2__anproj_2])],[e1_6_2_2__anproj_2,i1_6_2_2__anproj_2]), [interesting(0.65),file(anproj_2,e3_6_2__anproj_2),[file(anproj_2,e3_6_2__anproj_2)]]). fof(e5_6_2__anproj_2,plain,( ? [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) & r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,A) & r2_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2,A) & v8_rlvect_1(A,c1_6__anproj_2) ) ), inference(mizar_by,[status(thm),assumptions([e1_6_2__anproj_2,dt_c6_6__anproj_2,dt_c5_6__anproj_2,dt_c4_6__anproj_2,e2_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2])],[antisymmetry_r2_hidden,existence_l2_struct_0,dt_k1_xboole_0,dt_l2_struct_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,rc4_struct_0,t1_subset,t8_boole,existence_l1_rlvect_1,dt_l1_rlvect_1,cc15_membered,t2_subset,t6_boole,t7_boole,existence_l1_struct_0,existence_l2_rlvect_1,dt_l1_struct_0,dt_l2_rlvect_1,fc1_struct_0,rc3_struct_0,symmetry_r1_anproj_1,reflexivity_r1_anproj_1,existence_m1_subset_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c5_6__anproj_2,dt_c6_6__anproj_2,e4_6_2__anproj_2,e1_6_2__anproj_2,e2_6_2__anproj_2,e3_6_2__anproj_2]), [interesting(0.65),file(anproj_2,e5_6_2__anproj_2),[file(anproj_2,e5_6_2__anproj_2)]]). fof(i2_6_2__anproj_2,theorem,( $true ), introduced(tautology,[file(anproj_2,i2_6_2__anproj_2)]), [interesting(0.65),trivial,file(anproj_2,i2_6_2__anproj_2)]). fof(i1_6_2__anproj_2,plain,( ? [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) & r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,A) & r2_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2,A) & v8_rlvect_1(A,c1_6__anproj_2) ) ), inference(conclusion,[status(thm),assumptions([e1_6_2__anproj_2,dt_c6_6__anproj_2,dt_c5_6__anproj_2,dt_c4_6__anproj_2,e2_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2])],[e5_6_2__anproj_2,i2_6_2__anproj_2]), [interesting(0.65),file(anproj_2,i1_6_2__anproj_2),[file(anproj_2,i1_6_2__anproj_2)]]). fof(e9_6__anproj_2,plain,( ~ ( ~ ( ~ r1_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2) & v8_rlvect_1(c5_6__anproj_2,c1_6__anproj_2) & v8_rlvect_1(c6_6__anproj_2,c1_6__anproj_2) ) & ! [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) => ~ ( r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,A) & r2_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2,A) & v8_rlvect_1(A,c1_6__anproj_2) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c6_6__anproj_2,dt_c5_6__anproj_2,dt_c4_6__anproj_2,e2_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2]),discharge_asm(discharge,[e1_6_2__anproj_2])],[e1_6_2__anproj_2,i1_6_2__anproj_2]), [interesting(0.8),file(anproj_2,e9_6__anproj_2),[file(anproj_2,e9_6__anproj_2)]]). fof(e1_6_3__anproj_2,assumption, ( ~ r1_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2) & v8_rlvect_1(c5_6__anproj_2,c1_6__anproj_2) & v8_rlvect_1(c6_6__anproj_2,c1_6__anproj_2) & c9_6__anproj_2 = 0 ), introduced(assumption,[file(anproj_2,e1_6_3__anproj_2)]), [interesting(0.65),axiom,file(anproj_2,e1_6_3__anproj_2)]). fof(e5_6_3_1__anproj_2,plain,( r2_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,1),k3_rlvect_1(c1_6__anproj_2,c6_6__anproj_2,0))) ), inference(mizar_by,[status(thm),assumptions([dt_c6_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2,e1_6_3__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l2_struct_0,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l2_struct_0,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc4_struct_0,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_l1_rlvect_1,existence_l1_struct_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k2_rlvect_1,dt_k5_numbers,dt_l1_rlvect_1,dt_l1_struct_0,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc4_membered,fc1_struct_0,rc3_struct_0,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k4_rlvect_1,symmetry_r1_anproj_1,reflexivity_r1_anproj_1,existence_l2_rlvect_1,existence_m1_subset_1,redefinition_k4_rlvect_1,dt_k1_numbers,dt_k3_rlvect_1,dt_k4_rlvect_1,dt_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_6__anproj_2,dt_c5_6__anproj_2,dt_c6_6__anproj_2,dt_c9_6__anproj_2,fc2_membered,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e1_6_3__anproj_2,t11_anproj_1]), [interesting(0.5),file(anproj_2,e5_6_3_1__anproj_2),[file(anproj_2,e5_6_3_1__anproj_2)]]). fof(e1_6_3_1_1_1__anproj_2,plain,( k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,1),k3_rlvect_1(c1_6__anproj_2,c6_6__anproj_2,0)) = k4_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c6_6__anproj_2,0)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__anproj_2,dt_c5_6__anproj_2,dt_c6_6__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l2_struct_0,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l2_struct_0,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc4_struct_0,rc5_struct_0,spc5_arithm,spc6_arithm,spc7_arithm,t1_arithm,t1_subset,t2_arithm,t3_arithm,t3_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,commutativity_k3_xcmplx_0,existence_l1_rlvect_1,existence_l1_struct_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k2_xcmplx_0,dt_k3_xcmplx_0,dt_k5_numbers,dt_l1_rlvect_1,dt_l1_struct_0,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc4_membered,fc1_struct_0,rc3_struct_0,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,rqRealMult__k3_xcmplx_0__r1_r1_r1,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k3_real_1,commutativity_k4_real_1,commutativity_k4_rlvect_1,existence_l2_rlvect_1,existence_m1_subset_1,redefinition_k3_real_1,redefinition_k4_real_1,redefinition_k4_rlvect_1,dt_k1_numbers,dt_k2_rlvect_1,dt_k3_real_1,dt_k3_rlvect_1,dt_k4_real_1,dt_k4_rlvect_1,dt_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_6__anproj_2,dt_c5_6__anproj_2,dt_c6_6__anproj_2,fc2_membered,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,d9_rlvect_1]), [interesting(0.2),file(anproj_2,e1_6_3_1_1_1__anproj_2),[file(anproj_2,e1_6_3_1_1_1__anproj_2)]]). fof(e2_6_3_1_1_1__anproj_2,plain,( k4_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c6_6__anproj_2,0)) = k4_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,k1_rlvect_1(c1_6__anproj_2)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__anproj_2,dt_c5_6__anproj_2,dt_c6_6__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_struct_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k2_rlvect_1,dt_k5_numbers,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_struct_0,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc4_membered,fc1_struct_0,rc3_struct_0,rc4_struct_0,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k4_rlvect_1,existence_l2_rlvect_1,existence_m1_subset_1,redefinition_k4_rlvect_1,dt_k1_numbers,dt_k1_rlvect_1,dt_k3_rlvect_1,dt_k4_rlvect_1,dt_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_6__anproj_2,dt_c5_6__anproj_2,dt_c6_6__anproj_2,fc2_membered,spc0_numerals,spc0_boole,t23_rlvect_1]), [interesting(0.2),file(anproj_2,e2_6_3_1_1_1__anproj_2),[file(anproj_2,e2_6_3_1_1_1__anproj_2)]]). fof(e3_6_3_1_1_1__anproj_2,plain,( k4_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,k1_rlvect_1(c1_6__anproj_2)) = c5_6__anproj_2 ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__anproj_2,dt_c5_6__anproj_2])],[antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,t1_subset,cc15_membered,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_struct_0,existence_l2_rlvect_1,existence_l2_struct_0,dt_l1_struct_0,dt_l2_rlvect_1,dt_l2_struct_0,fc1_struct_0,rc3_struct_0,rc4_struct_0,commutativity_k4_rlvect_1,existence_l1_rlvect_1,existence_m1_subset_1,redefinition_k4_rlvect_1,dt_k1_rlvect_1,dt_k2_rlvect_1,dt_k4_rlvect_1,dt_l1_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_6__anproj_2,dt_c5_6__anproj_2,t10_rlvect_1]), [interesting(0.2),file(anproj_2,e3_6_3_1_1_1__anproj_2),[file(anproj_2,e3_6_3_1_1_1__anproj_2)]]). fof(e1_6_3_1_1__anproj_2,plain,( k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,1),k3_rlvect_1(c1_6__anproj_2,c6_6__anproj_2,0)) = c5_6__anproj_2 ), inference(iterative_eq,[status(thm),assumptions([dt_c6_6__anproj_2,dt_c1_6__anproj_2,dt_c5_6__anproj_2])],[e1_6_3_1_1_1__anproj_2,e2_6_3_1_1_1__anproj_2,e3_6_3_1_1_1__anproj_2]), [interesting(0.35),file(anproj_2,e1_6_3_1_1__anproj_2),[file(anproj_2,e1_6_3_1_1__anproj_2)]]). fof(e2_6_3_1_1__anproj_2,plain,( v8_rlvect_1(k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,1),k3_rlvect_1(c1_6__anproj_2,c6_6__anproj_2,0)),c1_6__anproj_2) ), inference(mizar_by,[status(thm),assumptions([dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,e1_6__anproj_2,dt_c6_6__anproj_2,dt_c1_6__anproj_2,dt_c5_6__anproj_2,e1_6_3__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l1_struct_0,existence_l2_struct_0,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l1_struct_0,dt_l2_struct_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,cc6_membered,cc9_membered,fc1_struct_0,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc4_struct_0,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_l1_rlvect_1,existence_l2_rlvect_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_rlvect_1,dt_k5_numbers,dt_l1_rlvect_1,dt_l2_rlvect_1,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,cc15_membered,fc2_membered,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k4_rlvect_1,symmetry_r1_anproj_1,reflexivity_r1_anproj_1,redefinition_k4_rlvect_1,dt_k3_rlvect_1,dt_k4_rlvect_1,dt_c1_6__anproj_2,dt_c5_6__anproj_2,dt_c6_6__anproj_2,dt_c9_6__anproj_2,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e1_6_3_1_1__anproj_2,e1_6_3__anproj_2]), [interesting(0.35),file(anproj_2,e2_6_3_1_1__anproj_2),[file(anproj_2,e2_6_3_1_1__anproj_2)]]). fof(i1_6_3_1_1__anproj_2,theorem,( $true ), introduced(tautology,[file(anproj_2,i1_6_3_1_1__anproj_2)]), [interesting(0.35),trivial,file(anproj_2,i1_6_3_1_1__anproj_2)]). fof(e1_6_3_1__anproj_2,plain,( v8_rlvect_1(k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,1),k3_rlvect_1(c1_6__anproj_2,c6_6__anproj_2,0)),c1_6__anproj_2) ), inference(conclusion,[status(thm),assumptions([dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,e1_6__anproj_2,dt_c6_6__anproj_2,dt_c1_6__anproj_2,dt_c5_6__anproj_2,e1_6_3__anproj_2])],[e2_6_3_1_1__anproj_2,i1_6_3_1_1__anproj_2]), [interesting(0.5),file(anproj_2,e1_6_3_1__anproj_2),[file(anproj_2,e1_6_3_1__anproj_2)]]). fof(e2_6_3_1__anproj_2,plain,( k3_real_1(k4_real_1(1,c9_6__anproj_2),k4_real_1(0,c12_6__anproj_2)) = 0 ), inference(mizar_by,[status(thm),assumptions([dt_c6_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2,e1_6_3__anproj_2])],[reflexivity_r1_tarski,existence_l2_struct_0,dt_l2_struct_0,rc4_struct_0,antisymmetry_r2_hidden,existence_l1_rlvect_1,existence_l1_struct_0,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l1_rlvect_1,dt_l1_struct_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,cc6_membered,cc9_membered,fc1_struct_0,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_l2_rlvect_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_l2_rlvect_1,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,cc15_membered,fc2_membered,spc5_arithm,spc6_arithm,spc7_arithm,t1_arithm,t1_numerals,t2_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,commutativity_k2_xcmplx_0,commutativity_k3_real_1,commutativity_k3_xcmplx_0,commutativity_k4_real_1,symmetry_r1_anproj_1,reflexivity_r1_anproj_1,redefinition_k3_real_1,redefinition_k4_real_1,dt_k2_xcmplx_0,dt_k3_real_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_c12_6__anproj_2,dt_c1_6__anproj_2,dt_c5_6__anproj_2,dt_c6_6__anproj_2,dt_c9_6__anproj_2,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealMult__k3_xcmplx_0__r0_r0_r0,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e1_6_3__anproj_2,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0]), [interesting(0.5),file(anproj_2,e2_6_3_1__anproj_2),[file(anproj_2,e2_6_3_1__anproj_2)]]). fof(e1_6_3_1_2__anproj_2,plain,( k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,1),k3_rlvect_1(c1_6__anproj_2,c6_6__anproj_2,0)) = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,k3_real_1(k4_real_1(1,c7_6__anproj_2),k4_real_1(0,c10_6__anproj_2))),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k3_real_1(k4_real_1(1,c8_6__anproj_2),k4_real_1(0,c11_6__anproj_2)))),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,0)) ), inference(mizar_by,[status(thm),assumptions([e1_6_3__anproj_2,dt_c6_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l1_struct_0,existence_l2_struct_0,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l1_struct_0,dt_l2_struct_0,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc6_membered,cc9_membered,fc1_struct_0,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc4_struct_0,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_l1_rlvect_1,existence_l2_rlvect_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k2_rlvect_1,dt_k5_numbers,dt_l1_rlvect_1,dt_l2_rlvect_1,dt_m2_subset_1,dt_u1_struct_0,cc10_membered,cc11_membered,cc15_membered,cc4_membered,spc5_arithm,spc6_arithm,spc7_arithm,t1_arithm,t1_numerals,t2_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,commutativity_k2_xcmplx_0,commutativity_k3_real_1,commutativity_k3_xcmplx_0,commutativity_k4_real_1,commutativity_k4_rlvect_1,existence_m1_subset_1,redefinition_k3_real_1,redefinition_k4_real_1,redefinition_k4_rlvect_1,dt_k1_numbers,dt_k2_xcmplx_0,dt_k3_real_1,dt_k3_rlvect_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_k4_rlvect_1,dt_m1_subset_1,dt_c10_6__anproj_2,dt_c11_6__anproj_2,dt_c12_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,dt_c6_6__anproj_2,dt_c7_6__anproj_2,dt_c8_6__anproj_2,dt_c9_6__anproj_2,fc2_membered,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealMult__k3_xcmplx_0__r0_r0_r0,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e2_6_3_1__anproj_2,e8_6__anproj_2,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0]), [interesting(0.35),file(anproj_2,e1_6_3_1_2__anproj_2),[file(anproj_2,e1_6_3_1_2__anproj_2)]]). fof(e2_6_3_1_2__anproj_2,plain,( k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,k3_real_1(k4_real_1(1,c7_6__anproj_2),k4_real_1(0,c10_6__anproj_2))),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k3_real_1(k4_real_1(1,c8_6__anproj_2),k4_real_1(0,c11_6__anproj_2)))),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,0)) = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,k3_real_1(k4_real_1(1,c7_6__anproj_2),k4_real_1(0,c10_6__anproj_2))),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k3_real_1(k4_real_1(1,c8_6__anproj_2),k4_real_1(0,c11_6__anproj_2)))),k1_rlvect_1(c1_6__anproj_2)) ), inference(mizar_by,[status(thm),assumptions([dt_c6_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_struct_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k2_rlvect_1,dt_k2_xcmplx_0,dt_k5_numbers,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_struct_0,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc4_membered,fc1_struct_0,rc3_struct_0,rc4_struct_0,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,spc5_arithm,spc6_arithm,spc7_arithm,t1_arithm,t1_numerals,t2_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,commutativity_k3_real_1,commutativity_k3_xcmplx_0,commutativity_k4_real_1,commutativity_k4_rlvect_1,existence_l2_rlvect_1,existence_m1_subset_1,redefinition_k3_real_1,redefinition_k4_real_1,redefinition_k4_rlvect_1,dt_k1_numbers,dt_k1_rlvect_1,dt_k3_real_1,dt_k3_rlvect_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_k4_rlvect_1,dt_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c10_6__anproj_2,dt_c11_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c7_6__anproj_2,dt_c8_6__anproj_2,fc2_membered,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,t23_rlvect_1,rqRealMult__k3_xcmplx_0__r1_r1_r1]), [interesting(0.35),file(anproj_2,e2_6_3_1_2__anproj_2),[file(anproj_2,e2_6_3_1_2__anproj_2)]]). fof(e3_6_3_1_2__anproj_2,plain,( k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,k3_real_1(k4_real_1(1,c7_6__anproj_2),k4_real_1(0,c10_6__anproj_2))),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k3_real_1(k4_real_1(1,c8_6__anproj_2),k4_real_1(0,c11_6__anproj_2)))),k1_rlvect_1(c1_6__anproj_2)) = k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,k3_real_1(k4_real_1(1,c7_6__anproj_2),k4_real_1(0,c10_6__anproj_2))),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k3_real_1(k4_real_1(1,c8_6__anproj_2),k4_real_1(0,c11_6__anproj_2)))) ), inference(mizar_by,[status(thm),assumptions([dt_c6_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,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,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_l1_struct_0,existence_l2_rlvect_1,existence_l2_struct_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_xcmplx_0,dt_k5_numbers,dt_l1_struct_0,dt_l2_rlvect_1,dt_l2_struct_0,dt_m2_subset_1,cc15_membered,fc1_struct_0,fc2_membered,rc3_struct_0,rc4_struct_0,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,spc5_arithm,spc6_arithm,spc7_arithm,t1_arithm,t1_numerals,t2_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,commutativity_k3_real_1,commutativity_k3_xcmplx_0,commutativity_k4_real_1,commutativity_k4_rlvect_1,existence_l1_rlvect_1,existence_m1_subset_1,redefinition_k3_real_1,redefinition_k4_real_1,redefinition_k4_rlvect_1,dt_k1_rlvect_1,dt_k2_rlvect_1,dt_k3_real_1,dt_k3_rlvect_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_k4_rlvect_1,dt_l1_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c10_6__anproj_2,dt_c11_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c7_6__anproj_2,dt_c8_6__anproj_2,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,t10_rlvect_1,rqRealMult__k3_xcmplx_0__r1_r1_r1]), [interesting(0.35),file(anproj_2,e3_6_3_1_2__anproj_2),[file(anproj_2,e3_6_3_1_2__anproj_2)]]). fof(e3_6_3_1__anproj_2,plain,( k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,1),k3_rlvect_1(c1_6__anproj_2,c6_6__anproj_2,0)) = k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,k3_real_1(k4_real_1(1,c7_6__anproj_2),k4_real_1(0,c10_6__anproj_2))),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,k3_real_1(k4_real_1(1,c8_6__anproj_2),k4_real_1(0,c11_6__anproj_2)))) ), inference(iterative_eq,[status(thm),assumptions([e1_6_3__anproj_2,dt_c6_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2])],[e1_6_3_1_2__anproj_2,e2_6_3_1_2__anproj_2,e3_6_3_1_2__anproj_2]), [interesting(0.5),file(anproj_2,e3_6_3_1__anproj_2),[file(anproj_2,e3_6_3_1__anproj_2)]]). fof(e4_6_3_1__anproj_2,plain,( r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c5_6__anproj_2,1),k3_rlvect_1(c1_6__anproj_2,c6_6__anproj_2,0))) ), inference(mizar_by,[status(thm),assumptions([e1_6_3__anproj_2,dt_c6_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,e2_6__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l2_struct_0,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l2_struct_0,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc4_struct_0,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_l1_rlvect_1,existence_l1_struct_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k2_rlvect_1,dt_k2_xcmplx_0,dt_k5_numbers,dt_l1_rlvect_1,dt_l1_struct_0,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc4_membered,fc1_struct_0,rc3_struct_0,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,spc5_arithm,spc6_arithm,spc7_arithm,t1_arithm,t1_numerals,t2_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,commutativity_k3_real_1,commutativity_k3_xcmplx_0,commutativity_k4_real_1,commutativity_k4_rlvect_1,symmetry_r1_anproj_1,reflexivity_r1_anproj_1,existence_l2_rlvect_1,existence_m1_subset_1,redefinition_k3_real_1,redefinition_k4_real_1,redefinition_k4_rlvect_1,dt_k1_numbers,dt_k3_real_1,dt_k3_rlvect_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_k4_rlvect_1,dt_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c10_6__anproj_2,dt_c11_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,dt_c5_6__anproj_2,dt_c6_6__anproj_2,dt_c7_6__anproj_2,dt_c8_6__anproj_2,fc2_membered,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e3_6_3_1__anproj_2,e7_6__anproj_2,t11_anproj_1,rqRealMult__k3_xcmplx_0__r1_r1_r1]), [interesting(0.5),file(anproj_2,e4_6_3_1__anproj_2),[file(anproj_2,e4_6_3_1__anproj_2)]]). fof(e6_6_3_1__anproj_2,plain,( ? [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) & r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,A) & r2_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2,A) & v8_rlvect_1(A,c1_6__anproj_2) ) ), inference(mizar_by,[status(thm),assumptions([e1_6_3__anproj_2,dt_c6_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,e2_6__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l2_struct_0,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l2_struct_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,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc4_struct_0,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_rlvect_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_rlvect_1,dt_k5_numbers,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_rlvect_1,dt_m2_subset_1,cc15_membered,fc1_struct_0,fc2_membered,rc3_struct_0,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k4_rlvect_1,existence_m1_subset_1,redefinition_k4_rlvect_1,dt_k3_rlvect_1,dt_k4_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c5_6__anproj_2,dt_c6_6__anproj_2,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e5_6_3_1__anproj_2,e1_6_3_1__anproj_2,e4_6_3_1__anproj_2]), [interesting(0.5),file(anproj_2,e6_6_3_1__anproj_2),[file(anproj_2,e6_6_3_1__anproj_2)]]). fof(i1_6_3_1__anproj_2,theorem,( $true ), introduced(tautology,[file(anproj_2,i1_6_3_1__anproj_2)]), [interesting(0.5),trivial,file(anproj_2,i1_6_3_1__anproj_2)]). fof(e2_6_3__anproj_2,plain,( ? [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) & r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,A) & r2_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2,A) & v8_rlvect_1(A,c1_6__anproj_2) ) ), inference(conclusion,[status(thm),assumptions([e1_6_3__anproj_2,dt_c6_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,e2_6__anproj_2])],[e6_6_3_1__anproj_2,i1_6_3_1__anproj_2]), [interesting(0.65),file(anproj_2,e2_6_3__anproj_2),[file(anproj_2,e2_6_3__anproj_2)]]). fof(e3_6_3__anproj_2,plain,( ? [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) & r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,A) & r2_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2,A) & v8_rlvect_1(A,c1_6__anproj_2) ) ), inference(mizar_by,[status(thm),assumptions([e1_6_3__anproj_2,dt_c6_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,e2_6__anproj_2])],[antisymmetry_r2_hidden,existence_l2_struct_0,dt_k1_xboole_0,dt_l2_struct_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,rc4_struct_0,t1_subset,t8_boole,existence_l1_rlvect_1,dt_l1_rlvect_1,cc15_membered,t2_subset,t6_boole,t7_boole,existence_l1_struct_0,existence_l2_rlvect_1,dt_l1_struct_0,dt_l2_rlvect_1,fc1_struct_0,rc3_struct_0,existence_m1_subset_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c5_6__anproj_2,dt_c6_6__anproj_2,e2_6_3__anproj_2]), [interesting(0.65),file(anproj_2,e3_6_3__anproj_2),[file(anproj_2,e3_6_3__anproj_2)]]). fof(i2_6_3__anproj_2,theorem,( $true ), introduced(tautology,[file(anproj_2,i2_6_3__anproj_2)]), [interesting(0.65),trivial,file(anproj_2,i2_6_3__anproj_2)]). fof(i1_6_3__anproj_2,plain,( ? [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) & r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,A) & r2_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2,A) & v8_rlvect_1(A,c1_6__anproj_2) ) ), inference(conclusion,[status(thm),assumptions([e1_6_3__anproj_2,dt_c6_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,e2_6__anproj_2])],[e3_6_3__anproj_2,i2_6_3__anproj_2]), [interesting(0.65),file(anproj_2,i1_6_3__anproj_2),[file(anproj_2,i1_6_3__anproj_2)]]). fof(e10_6__anproj_2,plain,( ~ ( ~ r1_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2) & v8_rlvect_1(c5_6__anproj_2,c1_6__anproj_2) & v8_rlvect_1(c6_6__anproj_2,c1_6__anproj_2) & c9_6__anproj_2 = 0 & ! [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) => ~ ( r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,A) & r2_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2,A) & v8_rlvect_1(A,c1_6__anproj_2) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c6_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,e2_6__anproj_2]),discharge_asm(discharge,[e1_6_3__anproj_2])],[e1_6_3__anproj_2,i1_6_3__anproj_2]), [interesting(0.8),file(anproj_2,e10_6__anproj_2),[file(anproj_2,e10_6__anproj_2)]]). fof(e12_6__anproj_2,plain,( ? [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) & r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,A) & r2_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2,A) & v8_rlvect_1(A,c1_6__anproj_2) ) ), inference(mizar_by,[status(thm),assumptions([dt_c6_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,e2_6__anproj_2])],[reflexivity_r1_tarski,existence_l2_struct_0,dt_l2_struct_0,rc4_struct_0,antisymmetry_r2_hidden,existence_l1_rlvect_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l1_rlvect_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,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_l1_struct_0,existence_l2_rlvect_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_l1_struct_0,dt_l2_rlvect_1,dt_m2_subset_1,cc15_membered,fc1_struct_0,fc2_membered,rc3_struct_0,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,symmetry_r1_anproj_1,reflexivity_r1_anproj_1,existence_m1_subset_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c5_6__anproj_2,dt_c6_6__anproj_2,dt_c9_6__anproj_2,spc0_numerals,spc0_boole,e11_6__anproj_2,e9_6__anproj_2,e10_6__anproj_2]), [interesting(0.8),file(anproj_2,e12_6__anproj_2),[file(anproj_2,e12_6__anproj_2)]]). fof(i8_6__anproj_2,theorem,( $true ), introduced(tautology,[file(anproj_2,i8_6__anproj_2)]), [interesting(0.8),trivial,file(anproj_2,i8_6__anproj_2)]). fof(i7_6__anproj_2,plain,( ? [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) & r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,A) & r2_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2,A) & v8_rlvect_1(A,c1_6__anproj_2) ) ), inference(conclusion,[status(thm),assumptions([dt_c6_6__anproj_2,dt_c5_6__anproj_2,e1_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,e2_6__anproj_2])],[e12_6__anproj_2,i8_6__anproj_2]), [interesting(0.8),file(anproj_2,i7_6__anproj_2),[file(anproj_2,i7_6__anproj_2)]]). fof(i7_6_tmp__anproj_2,plain, ( m1_subset_1(c6_6__anproj_2,u1_struct_0(c1_6__anproj_2)) => ? [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) & r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,A) & r2_anproj_1(c1_6__anproj_2,c5_6__anproj_2,c6_6__anproj_2,A) & v8_rlvect_1(A,c1_6__anproj_2) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c5_6__anproj_2,e1_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,e2_6__anproj_2]),discharge_asm(discharge,[dt_c6_6__anproj_2])],[dt_c6_6__anproj_2,i7_6__anproj_2]), [interesting(0.8),i6_6__anproj_2]). fof(i6_6__anproj_2,plain,( ! [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) => ? [B] : ( m1_subset_1(B,u1_struct_0(c1_6__anproj_2)) & r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,B) & r2_anproj_1(c1_6__anproj_2,c5_6__anproj_2,A,B) & v8_rlvect_1(B,c1_6__anproj_2) ) ) ), inference(let,[status(thm),assumptions([dt_c5_6__anproj_2,e1_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,e2_6__anproj_2])],[i7_6_tmp__anproj_2,dh_c6_6__anproj_2]), [interesting(0.8),file(anproj_2,i6_6__anproj_2),[file(anproj_2,i6_6__anproj_2)]]). fof(i6_6_tmp__anproj_2,plain, ( m1_subset_1(c5_6__anproj_2,u1_struct_0(c1_6__anproj_2)) => ! [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) => ? [B] : ( m1_subset_1(B,u1_struct_0(c1_6__anproj_2)) & r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,B) & r2_anproj_1(c1_6__anproj_2,c5_6__anproj_2,A,B) & v8_rlvect_1(B,c1_6__anproj_2) ) ) ), inference(discharge_asm,[status(thm),assumptions([e1_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,e2_6__anproj_2]),discharge_asm(discharge,[dt_c5_6__anproj_2])],[dt_c5_6__anproj_2,i6_6__anproj_2]), [interesting(0.8),i5_6__anproj_2]). fof(i5_6__anproj_2,plain,( ! [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) => ! [B] : ( m1_subset_1(B,u1_struct_0(c1_6__anproj_2)) => ? [C] : ( m1_subset_1(C,u1_struct_0(c1_6__anproj_2)) & r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,C) & r2_anproj_1(c1_6__anproj_2,A,B,C) & v8_rlvect_1(C,c1_6__anproj_2) ) ) ) ), inference(let,[status(thm),assumptions([e1_6__anproj_2,dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2,e2_6__anproj_2])],[i6_6_tmp__anproj_2,dh_c5_6__anproj_2]), [interesting(0.8),file(anproj_2,i5_6__anproj_2),[file(anproj_2,i5_6__anproj_2)]]). fof(i4_6__anproj_2,plain, ( ( ! [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) => ? [B] : ( m1_subset_1(B,k1_numbers) & ? [C] : ( m1_subset_1(C,k1_numbers) & ? [D] : ( m1_subset_1(D,k1_numbers) & A = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,B),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,C)),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,D)) ) ) ) ) & ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,k1_numbers) => ( k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,A),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,B)),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,C)) = k1_rlvect_1(c1_6__anproj_2) => ( A = 0 & B = 0 & C = 0 ) ) ) ) ) ) => ! [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) => ! [B] : ( m1_subset_1(B,u1_struct_0(c1_6__anproj_2)) => ? [C] : ( m1_subset_1(C,u1_struct_0(c1_6__anproj_2)) & r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,C) & r2_anproj_1(c1_6__anproj_2,A,B,C) & v8_rlvect_1(C,c1_6__anproj_2) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2,dt_c4_6__anproj_2]),discharge_asm(discharge,[e1_6__anproj_2,e2_6__anproj_2])],[e1_6__anproj_2,e2_6__anproj_2,i5_6__anproj_2]), [interesting(0.8),file(anproj_2,i4_6__anproj_2),[file(anproj_2,i4_6__anproj_2)]]). fof(i4_6_tmp__anproj_2,plain, ( m1_subset_1(c4_6__anproj_2,u1_struct_0(c1_6__anproj_2)) => ( ( ! [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) => ? [B] : ( m1_subset_1(B,k1_numbers) & ? [C] : ( m1_subset_1(C,k1_numbers) & ? [D] : ( m1_subset_1(D,k1_numbers) & A = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,B),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,C)),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,D)) ) ) ) ) & ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,k1_numbers) => ( k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,A),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,B)),k3_rlvect_1(c1_6__anproj_2,c4_6__anproj_2,C)) = k1_rlvect_1(c1_6__anproj_2) => ( A = 0 & B = 0 & C = 0 ) ) ) ) ) ) => ! [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) => ! [B] : ( m1_subset_1(B,u1_struct_0(c1_6__anproj_2)) => ? [C] : ( m1_subset_1(C,u1_struct_0(c1_6__anproj_2)) & r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,C) & r2_anproj_1(c1_6__anproj_2,A,B,C) & v8_rlvect_1(C,c1_6__anproj_2) ) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2]),discharge_asm(discharge,[dt_c4_6__anproj_2])],[dt_c4_6__anproj_2,i4_6__anproj_2]), [interesting(0.8),i3_6__anproj_2]). fof(i3_6__anproj_2,plain,( ! [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) => ( ( ! [B] : ( m1_subset_1(B,u1_struct_0(c1_6__anproj_2)) => ? [C] : ( m1_subset_1(C,k1_numbers) & ? [D] : ( m1_subset_1(D,k1_numbers) & ? [E] : ( m1_subset_1(E,k1_numbers) & B = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,C),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,D)),k3_rlvect_1(c1_6__anproj_2,A,E)) ) ) ) ) & ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,k1_numbers) => ! [D] : ( m1_subset_1(D,k1_numbers) => ( k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,B),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,C)),k3_rlvect_1(c1_6__anproj_2,A,D)) = k1_rlvect_1(c1_6__anproj_2) => ( B = 0 & C = 0 & D = 0 ) ) ) ) ) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(c1_6__anproj_2)) => ! [C] : ( m1_subset_1(C,u1_struct_0(c1_6__anproj_2)) => ? [D] : ( m1_subset_1(D,u1_struct_0(c1_6__anproj_2)) & r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,D) & r2_anproj_1(c1_6__anproj_2,B,C,D) & v8_rlvect_1(D,c1_6__anproj_2) ) ) ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_6__anproj_2,dt_c2_6__anproj_2,dt_c3_6__anproj_2])],[i4_6_tmp__anproj_2,dh_c4_6__anproj_2]), [interesting(0.8),file(anproj_2,i3_6__anproj_2),[file(anproj_2,i3_6__anproj_2)]]). fof(i3_6_tmp__anproj_2,plain, ( m1_subset_1(c3_6__anproj_2,u1_struct_0(c1_6__anproj_2)) => ! [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) => ( ( ! [B] : ( m1_subset_1(B,u1_struct_0(c1_6__anproj_2)) => ? [C] : ( m1_subset_1(C,k1_numbers) & ? [D] : ( m1_subset_1(D,k1_numbers) & ? [E] : ( m1_subset_1(E,k1_numbers) & B = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,C),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,D)),k3_rlvect_1(c1_6__anproj_2,A,E)) ) ) ) ) & ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,k1_numbers) => ! [D] : ( m1_subset_1(D,k1_numbers) => ( k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,B),k3_rlvect_1(c1_6__anproj_2,c3_6__anproj_2,C)),k3_rlvect_1(c1_6__anproj_2,A,D)) = k1_rlvect_1(c1_6__anproj_2) => ( B = 0 & C = 0 & D = 0 ) ) ) ) ) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(c1_6__anproj_2)) => ! [C] : ( m1_subset_1(C,u1_struct_0(c1_6__anproj_2)) => ? [D] : ( m1_subset_1(D,u1_struct_0(c1_6__anproj_2)) & r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,c3_6__anproj_2,D) & r2_anproj_1(c1_6__anproj_2,B,C,D) & v8_rlvect_1(D,c1_6__anproj_2) ) ) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_6__anproj_2,dt_c2_6__anproj_2]),discharge_asm(discharge,[dt_c3_6__anproj_2])],[dt_c3_6__anproj_2,i3_6__anproj_2]), [interesting(0.8),i2_6__anproj_2]). fof(i2_6__anproj_2,plain,( ! [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) => ! [B] : ( m1_subset_1(B,u1_struct_0(c1_6__anproj_2)) => ( ( ! [C] : ( m1_subset_1(C,u1_struct_0(c1_6__anproj_2)) => ? [D] : ( m1_subset_1(D,k1_numbers) & ? [E] : ( m1_subset_1(E,k1_numbers) & ? [F] : ( m1_subset_1(F,k1_numbers) & C = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,D),k3_rlvect_1(c1_6__anproj_2,A,E)),k3_rlvect_1(c1_6__anproj_2,B,F)) ) ) ) ) & ! [C] : ( m1_subset_1(C,k1_numbers) => ! [D] : ( m1_subset_1(D,k1_numbers) => ! [E] : ( m1_subset_1(E,k1_numbers) => ( k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,C),k3_rlvect_1(c1_6__anproj_2,A,D)),k3_rlvect_1(c1_6__anproj_2,B,E)) = k1_rlvect_1(c1_6__anproj_2) => ( C = 0 & D = 0 & E = 0 ) ) ) ) ) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(c1_6__anproj_2)) => ! [D] : ( m1_subset_1(D,u1_struct_0(c1_6__anproj_2)) => ? [E] : ( m1_subset_1(E,u1_struct_0(c1_6__anproj_2)) & r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,A,E) & r2_anproj_1(c1_6__anproj_2,C,D,E) & v8_rlvect_1(E,c1_6__anproj_2) ) ) ) ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_6__anproj_2,dt_c2_6__anproj_2])],[i3_6_tmp__anproj_2,dh_c3_6__anproj_2]), [interesting(0.8),file(anproj_2,i2_6__anproj_2),[file(anproj_2,i2_6__anproj_2)]]). fof(i2_6_tmp__anproj_2,plain, ( m1_subset_1(c2_6__anproj_2,u1_struct_0(c1_6__anproj_2)) => ! [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) => ! [B] : ( m1_subset_1(B,u1_struct_0(c1_6__anproj_2)) => ( ( ! [C] : ( m1_subset_1(C,u1_struct_0(c1_6__anproj_2)) => ? [D] : ( m1_subset_1(D,k1_numbers) & ? [E] : ( m1_subset_1(E,k1_numbers) & ? [F] : ( m1_subset_1(F,k1_numbers) & C = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,D),k3_rlvect_1(c1_6__anproj_2,A,E)),k3_rlvect_1(c1_6__anproj_2,B,F)) ) ) ) ) & ! [C] : ( m1_subset_1(C,k1_numbers) => ! [D] : ( m1_subset_1(D,k1_numbers) => ! [E] : ( m1_subset_1(E,k1_numbers) => ( k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,c2_6__anproj_2,C),k3_rlvect_1(c1_6__anproj_2,A,D)),k3_rlvect_1(c1_6__anproj_2,B,E)) = k1_rlvect_1(c1_6__anproj_2) => ( C = 0 & D = 0 & E = 0 ) ) ) ) ) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(c1_6__anproj_2)) => ! [D] : ( m1_subset_1(D,u1_struct_0(c1_6__anproj_2)) => ? [E] : ( m1_subset_1(E,u1_struct_0(c1_6__anproj_2)) & r2_anproj_1(c1_6__anproj_2,c2_6__anproj_2,A,E) & r2_anproj_1(c1_6__anproj_2,C,D,E) & v8_rlvect_1(E,c1_6__anproj_2) ) ) ) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_6__anproj_2]),discharge_asm(discharge,[dt_c2_6__anproj_2])],[dt_c2_6__anproj_2,i2_6__anproj_2]), [interesting(0.8),i1_6__anproj_2]). fof(i1_6__anproj_2,plain,( ! [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) => ! [B] : ( m1_subset_1(B,u1_struct_0(c1_6__anproj_2)) => ! [C] : ( m1_subset_1(C,u1_struct_0(c1_6__anproj_2)) => ( ( ! [D] : ( m1_subset_1(D,u1_struct_0(c1_6__anproj_2)) => ? [E] : ( m1_subset_1(E,k1_numbers) & ? [F] : ( m1_subset_1(F,k1_numbers) & ? [G] : ( m1_subset_1(G,k1_numbers) & D = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,A,E),k3_rlvect_1(c1_6__anproj_2,B,F)),k3_rlvect_1(c1_6__anproj_2,C,G)) ) ) ) ) & ! [D] : ( m1_subset_1(D,k1_numbers) => ! [E] : ( m1_subset_1(E,k1_numbers) => ! [F] : ( m1_subset_1(F,k1_numbers) => ( k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,A,D),k3_rlvect_1(c1_6__anproj_2,B,E)),k3_rlvect_1(c1_6__anproj_2,C,F)) = k1_rlvect_1(c1_6__anproj_2) => ( D = 0 & E = 0 & F = 0 ) ) ) ) ) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(c1_6__anproj_2)) => ! [E] : ( m1_subset_1(E,u1_struct_0(c1_6__anproj_2)) => ? [F] : ( m1_subset_1(F,u1_struct_0(c1_6__anproj_2)) & r2_anproj_1(c1_6__anproj_2,A,B,F) & r2_anproj_1(c1_6__anproj_2,D,E,F) & v8_rlvect_1(F,c1_6__anproj_2) ) ) ) ) ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_6__anproj_2])],[i2_6_tmp__anproj_2,dh_c2_6__anproj_2]), [interesting(0.8),file(anproj_2,i1_6__anproj_2),[file(anproj_2,i1_6__anproj_2)]]). fof(i1_6_tmp__anproj_2,plain, ( ( ~ v3_struct_0(c1_6__anproj_2) & v3_rlvect_1(c1_6__anproj_2) & v4_rlvect_1(c1_6__anproj_2) & v5_rlvect_1(c1_6__anproj_2) & v6_rlvect_1(c1_6__anproj_2) & v7_rlvect_1(c1_6__anproj_2) & l2_rlvect_1(c1_6__anproj_2) ) => ! [A] : ( m1_subset_1(A,u1_struct_0(c1_6__anproj_2)) => ! [B] : ( m1_subset_1(B,u1_struct_0(c1_6__anproj_2)) => ! [C] : ( m1_subset_1(C,u1_struct_0(c1_6__anproj_2)) => ( ( ! [D] : ( m1_subset_1(D,u1_struct_0(c1_6__anproj_2)) => ? [E] : ( m1_subset_1(E,k1_numbers) & ? [F] : ( m1_subset_1(F,k1_numbers) & ? [G] : ( m1_subset_1(G,k1_numbers) & D = k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,A,E),k3_rlvect_1(c1_6__anproj_2,B,F)),k3_rlvect_1(c1_6__anproj_2,C,G)) ) ) ) ) & ! [D] : ( m1_subset_1(D,k1_numbers) => ! [E] : ( m1_subset_1(E,k1_numbers) => ! [F] : ( m1_subset_1(F,k1_numbers) => ( k4_rlvect_1(c1_6__anproj_2,k4_rlvect_1(c1_6__anproj_2,k3_rlvect_1(c1_6__anproj_2,A,D),k3_rlvect_1(c1_6__anproj_2,B,E)),k3_rlvect_1(c1_6__anproj_2,C,F)) = k1_rlvect_1(c1_6__anproj_2) => ( D = 0 & E = 0 & F = 0 ) ) ) ) ) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(c1_6__anproj_2)) => ! [E] : ( m1_subset_1(E,u1_struct_0(c1_6__anproj_2)) => ? [F] : ( m1_subset_1(F,u1_struct_0(c1_6__anproj_2)) & r2_anproj_1(c1_6__anproj_2,A,B,F) & r2_anproj_1(c1_6__anproj_2,D,E,F) & v8_rlvect_1(F,c1_6__anproj_2) ) ) ) ) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_6__anproj_2])],[dt_c1_6__anproj_2,i1_6__anproj_2]), [interesting(1),t3_anproj_2]). fof(t3_anproj_2,theorem,( ! [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,k1_numbers) & ? [G] : ( m1_subset_1(G,k1_numbers) & ? [H] : ( m1_subset_1(H,k1_numbers) & E = k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,F),k3_rlvect_1(A,C,G)),k3_rlvect_1(A,D,H)) ) ) ) ) & ! [E] : ( m1_subset_1(E,k1_numbers) => ! [F] : ( m1_subset_1(F,k1_numbers) => ! [G] : ( m1_subset_1(G,k1_numbers) => ( k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,C,F)),k3_rlvect_1(A,D,G)) = k1_rlvect_1(A) => ( E = 0 & F = 0 & G = 0 ) ) ) ) ) ) => ! [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_anproj_1(A,B,C,G) & r2_anproj_1(A,E,F,G) & v8_rlvect_1(G,A) ) ) ) ) ) ) ) ) ), inference(let,[status(thm),assumptions([])],[i1_6_tmp__anproj_2,dh_c1_6__anproj_2]), [interesting(1),file(anproj_2,t3_anproj_2),[file(anproj_2,t3_anproj_2)]]).