% Mizar ND problem: t1_anproj_2,anproj_2,32,38 fof(dh_c1_1__anproj_2,definition, ( ( ( ~ v3_struct_0(c1_1__anproj_2) & v3_rlvect_1(c1_1__anproj_2) & v4_rlvect_1(c1_1__anproj_2) & v5_rlvect_1(c1_1__anproj_2) & v6_rlvect_1(c1_1__anproj_2) & v7_rlvect_1(c1_1__anproj_2) & l2_rlvect_1(c1_1__anproj_2) ) => ! [A] : ( m1_subset_1(A,u1_struct_0(c1_1__anproj_2)) => ! [B] : ( m1_subset_1(B,u1_struct_0(c1_1__anproj_2)) => ! [C] : ( m1_subset_1(C,u1_struct_0(c1_1__anproj_2)) => ( ! [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_1__anproj_2,k4_rlvect_1(c1_1__anproj_2,k3_rlvect_1(c1_1__anproj_2,A,D),k3_rlvect_1(c1_1__anproj_2,B,E)),k3_rlvect_1(c1_1__anproj_2,C,F)) = k1_rlvect_1(c1_1__anproj_2) => ( D = 0 & E = 0 & F = 0 ) ) ) ) ) => ( v8_rlvect_1(A,c1_1__anproj_2) & v8_rlvect_1(B,c1_1__anproj_2) & v8_rlvect_1(C,c1_1__anproj_2) & ~ r2_anproj_1(c1_1__anproj_2,A,B,C) & ~ r1_anproj_1(c1_1__anproj_2,A,B) ) ) ) ) ) ) => ! [G] : ( ( ~ v3_struct_0(G) & v3_rlvect_1(G) & v4_rlvect_1(G) & v5_rlvect_1(G) & v6_rlvect_1(G) & v7_rlvect_1(G) & l2_rlvect_1(G) ) => ! [H] : ( m1_subset_1(H,u1_struct_0(G)) => ! [I] : ( m1_subset_1(I,u1_struct_0(G)) => ! [J] : ( m1_subset_1(J,u1_struct_0(G)) => ( ! [K] : ( m1_subset_1(K,k1_numbers) => ! [L] : ( m1_subset_1(L,k1_numbers) => ! [M] : ( m1_subset_1(M,k1_numbers) => ( k4_rlvect_1(G,k4_rlvect_1(G,k3_rlvect_1(G,H,K),k3_rlvect_1(G,I,L)),k3_rlvect_1(G,J,M)) = k1_rlvect_1(G) => ( K = 0 & L = 0 & M = 0 ) ) ) ) ) => ( v8_rlvect_1(H,G) & v8_rlvect_1(I,G) & v8_rlvect_1(J,G) & ~ r2_anproj_1(G,H,I,J) & ~ r1_anproj_1(G,H,I) ) ) ) ) ) ) ), introduced(definition,[new_symbol(c1_1__anproj_2),file(anproj_2,c1_1__anproj_2)]), [interesting(0.8),axiom,file(anproj_2,c1_1__anproj_2)]). fof(dh_c2_1__anproj_2,definition, ( ( m1_subset_1(c2_1__anproj_2,u1_struct_0(c1_1__anproj_2)) => ! [A] : ( m1_subset_1(A,u1_struct_0(c1_1__anproj_2)) => ! [B] : ( m1_subset_1(B,u1_struct_0(c1_1__anproj_2)) => ( ! [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_1__anproj_2,k4_rlvect_1(c1_1__anproj_2,k3_rlvect_1(c1_1__anproj_2,c2_1__anproj_2,C),k3_rlvect_1(c1_1__anproj_2,A,D)),k3_rlvect_1(c1_1__anproj_2,B,E)) = k1_rlvect_1(c1_1__anproj_2) => ( C = 0 & D = 0 & E = 0 ) ) ) ) ) => ( v8_rlvect_1(c2_1__anproj_2,c1_1__anproj_2) & v8_rlvect_1(A,c1_1__anproj_2) & v8_rlvect_1(B,c1_1__anproj_2) & ~ r2_anproj_1(c1_1__anproj_2,c2_1__anproj_2,A,B) & ~ r1_anproj_1(c1_1__anproj_2,c2_1__anproj_2,A) ) ) ) ) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(c1_1__anproj_2)) => ! [G] : ( m1_subset_1(G,u1_struct_0(c1_1__anproj_2)) => ! [H] : ( m1_subset_1(H,u1_struct_0(c1_1__anproj_2)) => ( ! [I] : ( m1_subset_1(I,k1_numbers) => ! [J] : ( m1_subset_1(J,k1_numbers) => ! [K] : ( m1_subset_1(K,k1_numbers) => ( k4_rlvect_1(c1_1__anproj_2,k4_rlvect_1(c1_1__anproj_2,k3_rlvect_1(c1_1__anproj_2,F,I),k3_rlvect_1(c1_1__anproj_2,G,J)),k3_rlvect_1(c1_1__anproj_2,H,K)) = k1_rlvect_1(c1_1__anproj_2) => ( I = 0 & J = 0 & K = 0 ) ) ) ) ) => ( v8_rlvect_1(F,c1_1__anproj_2) & v8_rlvect_1(G,c1_1__anproj_2) & v8_rlvect_1(H,c1_1__anproj_2) & ~ r2_anproj_1(c1_1__anproj_2,F,G,H) & ~ r1_anproj_1(c1_1__anproj_2,F,G) ) ) ) ) ) ), introduced(definition,[new_symbol(c2_1__anproj_2),file(anproj_2,c2_1__anproj_2)]), [interesting(0.8),axiom,file(anproj_2,c2_1__anproj_2)]). fof(dh_c3_1__anproj_2,definition, ( ( m1_subset_1(c3_1__anproj_2,u1_struct_0(c1_1__anproj_2)) => ! [A] : ( m1_subset_1(A,u1_struct_0(c1_1__anproj_2)) => ( ! [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_1__anproj_2,k4_rlvect_1(c1_1__anproj_2,k3_rlvect_1(c1_1__anproj_2,c2_1__anproj_2,B),k3_rlvect_1(c1_1__anproj_2,c3_1__anproj_2,C)),k3_rlvect_1(c1_1__anproj_2,A,D)) = k1_rlvect_1(c1_1__anproj_2) => ( B = 0 & C = 0 & D = 0 ) ) ) ) ) => ( v8_rlvect_1(c2_1__anproj_2,c1_1__anproj_2) & v8_rlvect_1(c3_1__anproj_2,c1_1__anproj_2) & v8_rlvect_1(A,c1_1__anproj_2) & ~ r2_anproj_1(c1_1__anproj_2,c2_1__anproj_2,c3_1__anproj_2,A) & ~ r1_anproj_1(c1_1__anproj_2,c2_1__anproj_2,c3_1__anproj_2) ) ) ) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(c1_1__anproj_2)) => ! [F] : ( m1_subset_1(F,u1_struct_0(c1_1__anproj_2)) => ( ! [G] : ( m1_subset_1(G,k1_numbers) => ! [H] : ( m1_subset_1(H,k1_numbers) => ! [I] : ( m1_subset_1(I,k1_numbers) => ( k4_rlvect_1(c1_1__anproj_2,k4_rlvect_1(c1_1__anproj_2,k3_rlvect_1(c1_1__anproj_2,c2_1__anproj_2,G),k3_rlvect_1(c1_1__anproj_2,E,H)),k3_rlvect_1(c1_1__anproj_2,F,I)) = k1_rlvect_1(c1_1__anproj_2) => ( G = 0 & H = 0 & I = 0 ) ) ) ) ) => ( v8_rlvect_1(c2_1__anproj_2,c1_1__anproj_2) & v8_rlvect_1(E,c1_1__anproj_2) & v8_rlvect_1(F,c1_1__anproj_2) & ~ r2_anproj_1(c1_1__anproj_2,c2_1__anproj_2,E,F) & ~ r1_anproj_1(c1_1__anproj_2,c2_1__anproj_2,E) ) ) ) ) ), introduced(definition,[new_symbol(c3_1__anproj_2),file(anproj_2,c3_1__anproj_2)]), [interesting(0.8),axiom,file(anproj_2,c3_1__anproj_2)]). fof(dh_c4_1__anproj_2,definition, ( ( m1_subset_1(c4_1__anproj_2,u1_struct_0(c1_1__anproj_2)) => ( ! [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_1__anproj_2,k4_rlvect_1(c1_1__anproj_2,k3_rlvect_1(c1_1__anproj_2,c2_1__anproj_2,A),k3_rlvect_1(c1_1__anproj_2,c3_1__anproj_2,B)),k3_rlvect_1(c1_1__anproj_2,c4_1__anproj_2,C)) = k1_rlvect_1(c1_1__anproj_2) => ( A = 0 & B = 0 & C = 0 ) ) ) ) ) => ( v8_rlvect_1(c2_1__anproj_2,c1_1__anproj_2) & v8_rlvect_1(c3_1__anproj_2,c1_1__anproj_2) & v8_rlvect_1(c4_1__anproj_2,c1_1__anproj_2) & ~ r2_anproj_1(c1_1__anproj_2,c2_1__anproj_2,c3_1__anproj_2,c4_1__anproj_2) & ~ r1_anproj_1(c1_1__anproj_2,c2_1__anproj_2,c3_1__anproj_2) ) ) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(c1_1__anproj_2)) => ( ! [E] : ( m1_subset_1(E,k1_numbers) => ! [F] : ( m1_subset_1(F,k1_numbers) => ! [G] : ( m1_subset_1(G,k1_numbers) => ( k4_rlvect_1(c1_1__anproj_2,k4_rlvect_1(c1_1__anproj_2,k3_rlvect_1(c1_1__anproj_2,c2_1__anproj_2,E),k3_rlvect_1(c1_1__anproj_2,c3_1__anproj_2,F)),k3_rlvect_1(c1_1__anproj_2,D,G)) = k1_rlvect_1(c1_1__anproj_2) => ( E = 0 & F = 0 & G = 0 ) ) ) ) ) => ( v8_rlvect_1(c2_1__anproj_2,c1_1__anproj_2) & v8_rlvect_1(c3_1__anproj_2,c1_1__anproj_2) & v8_rlvect_1(D,c1_1__anproj_2) & ~ r2_anproj_1(c1_1__anproj_2,c2_1__anproj_2,c3_1__anproj_2,D) & ~ r1_anproj_1(c1_1__anproj_2,c2_1__anproj_2,c3_1__anproj_2) ) ) ) ), introduced(definition,[new_symbol(c4_1__anproj_2),file(anproj_2,c4_1__anproj_2)]), [interesting(0.8),axiom,file(anproj_2,c4_1__anproj_2)]). fof(e1_1__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_1__anproj_2,k4_rlvect_1(c1_1__anproj_2,k3_rlvect_1(c1_1__anproj_2,c2_1__anproj_2,A),k3_rlvect_1(c1_1__anproj_2,c3_1__anproj_2,B)),k3_rlvect_1(c1_1__anproj_2,c4_1__anproj_2,C)) = k1_rlvect_1(c1_1__anproj_2) => ( A = 0 & B = 0 & C = 0 ) ) ) ) ) ), introduced(assumption,[file(anproj_2,e1_1__anproj_2)]), [interesting(0.8),axiom,file(anproj_2,e1_1__anproj_2)]). 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(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]). 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(cc1_membered,theorem,( ! [A] : ( v5_membered(A) => v4_membered(A) ) ), file(membered,cc1_membered), [interesting(0.9),axiom,file(membered,cc1_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(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(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(t8_boole,theorem,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), [interesting(0.9),axiom,file(boole,t8_boole)]). fof(existence_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(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(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(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(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(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(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(dt_l1_struct_0,axiom,( $true ), file(struct_0,l1_struct_0), [interesting(0.9),axiom,file(struct_0,l1_struct_0)]). 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(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(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_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_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_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_1__anproj_2,assumption, ( ~ v3_struct_0(c1_1__anproj_2) & v3_rlvect_1(c1_1__anproj_2) & v4_rlvect_1(c1_1__anproj_2) & v5_rlvect_1(c1_1__anproj_2) & v6_rlvect_1(c1_1__anproj_2) & v7_rlvect_1(c1_1__anproj_2) & l2_rlvect_1(c1_1__anproj_2) ), introduced(assumption,[file(anproj_2,c1_1__anproj_2)]), [interesting(0.8),axiom,file(anproj_2,c1_1__anproj_2)]). fof(dt_c2_1__anproj_2,assumption,( m1_subset_1(c2_1__anproj_2,u1_struct_0(c1_1__anproj_2)) ), introduced(assumption,[file(anproj_2,c2_1__anproj_2)]), [interesting(0.8),axiom,file(anproj_2,c2_1__anproj_2)]). fof(dt_c3_1__anproj_2,assumption,( m1_subset_1(c3_1__anproj_2,u1_struct_0(c1_1__anproj_2)) ), introduced(assumption,[file(anproj_2,c3_1__anproj_2)]), [interesting(0.8),axiom,file(anproj_2,c3_1__anproj_2)]). fof(dt_c4_1__anproj_2,assumption,( m1_subset_1(c4_1__anproj_2,u1_struct_0(c1_1__anproj_2)) ), introduced(assumption,[file(anproj_2,c4_1__anproj_2)]), [interesting(0.8),axiom,file(anproj_2,c4_1__anproj_2)]). fof(e1_1_1_3__anproj_2,assumption,( ~ v8_rlvect_1(c4_1__anproj_2,c1_1__anproj_2) ), introduced(assumption,[file(anproj_2,e1_1_1_3__anproj_2)]), [interesting(0.5),axiom,file(anproj_2,e1_1_1_3__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(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(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(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(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(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(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_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_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(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_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(t1_numerals,theorem,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), [interesting(0.9),axiom,file(numerals,t1_numerals)]). 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_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), [interesting(0.9),axiom,file(numbers,k1_numbers)]). 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(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(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(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(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(spc0_boole,theorem,( v1_xboole_0(0) ), file(boole,spc0_boole), [interesting(0.9),axiom,file(boole,spc0_boole)]). fof(spc1_boole,theorem,( ~ v1_xboole_0(1) ), file(boole,spc1_boole), [interesting(0.9),axiom,file(boole,spc1_boole)]). 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(e1_1_1_3_1__anproj_2,plain,( k1_rlvect_1(c1_1__anproj_2) = k4_rlvect_1(c1_1__anproj_2,k1_rlvect_1(c1_1__anproj_2),k1_rlvect_1(c1_1__anproj_2)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_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,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_1__anproj_2,t10_rlvect_1]), [interesting(0.35),file(anproj_2,e1_1_1_3_1__anproj_2),[file(anproj_2,e1_1_1_3_1__anproj_2)]]). fof(e2_1_1_3_1__anproj_2,plain,( k4_rlvect_1(c1_1__anproj_2,k1_rlvect_1(c1_1__anproj_2),k1_rlvect_1(c1_1__anproj_2)) = k4_rlvect_1(c1_1__anproj_2,k4_rlvect_1(c1_1__anproj_2,k1_rlvect_1(c1_1__anproj_2),k1_rlvect_1(c1_1__anproj_2)),k1_rlvect_1(c1_1__anproj_2)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_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,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_1__anproj_2,t10_rlvect_1]), [interesting(0.35),file(anproj_2,e2_1_1_3_1__anproj_2),[file(anproj_2,e2_1_1_3_1__anproj_2)]]). 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(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(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(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(dt_k2_xcmplx_0,axiom,( $true ), file(xcmplx_0,k2_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k2_xcmplx_0)]). fof(dt_k3_xcmplx_0,axiom,( $true ), file(xcmplx_0,k3_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k3_xcmplx_0)]). 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(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(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(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(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_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_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(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(e2_1_1_3__anproj_2,plain,( c4_1__anproj_2 = k1_rlvect_1(c1_1__anproj_2) ), inference(mizar_by,[status(thm),assumptions([dt_c1_1__anproj_2,dt_c4_1__anproj_2,e1_1_1_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_1__anproj_2,dt_c4_1__anproj_2,rc4_struct_0,e1_1_1_3__anproj_2,d13_rlvect_1]), [interesting(0.5),file(anproj_2,e2_1_1_3__anproj_2),[file(anproj_2,e2_1_1_3__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_1_1_3_1__anproj_2,plain,( k4_rlvect_1(c1_1__anproj_2,k4_rlvect_1(c1_1__anproj_2,k1_rlvect_1(c1_1__anproj_2),k1_rlvect_1(c1_1__anproj_2)),k1_rlvect_1(c1_1__anproj_2)) = k4_rlvect_1(c1_1__anproj_2,k4_rlvect_1(c1_1__anproj_2,k1_rlvect_1(c1_1__anproj_2),k1_rlvect_1(c1_1__anproj_2)),k3_rlvect_1(c1_1__anproj_2,c4_1__anproj_2,1)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_1__anproj_2,dt_c4_1__anproj_2,e1_1_1_3__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,spc5_arithm,spc6_arithm,spc7_arithm,t1_subset,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_l2_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_l2_struct_0,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc4_membered,fc1_struct_0,rc3_struct_0,rc4_struct_0,rqRealMult__k3_xcmplx_0__r1_r1_r1,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_k1_rlvect_1,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_1__anproj_2,dt_c4_1__anproj_2,fc2_membered,spc1_numerals,spc1_boole,e2_1_1_3__anproj_2,d9_rlvect_1]), [interesting(0.35),file(anproj_2,e3_1_1_3_1__anproj_2),[file(anproj_2,e3_1_1_3_1__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(e4_1_1_3_1__anproj_2,plain,( k4_rlvect_1(c1_1__anproj_2,k4_rlvect_1(c1_1__anproj_2,k1_rlvect_1(c1_1__anproj_2),k1_rlvect_1(c1_1__anproj_2)),k3_rlvect_1(c1_1__anproj_2,c4_1__anproj_2,1)) = k4_rlvect_1(c1_1__anproj_2,k4_rlvect_1(c1_1__anproj_2,k3_rlvect_1(c1_1__anproj_2,c2_1__anproj_2,0),k1_rlvect_1(c1_1__anproj_2)),k3_rlvect_1(c1_1__anproj_2,c4_1__anproj_2,1)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_1__anproj_2,dt_c2_1__anproj_2,dt_c4_1__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_1__anproj_2,dt_c2_1__anproj_2,dt_c4_1__anproj_2,fc2_membered,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,t23_rlvect_1]), [interesting(0.35),file(anproj_2,e4_1_1_3_1__anproj_2),[file(anproj_2,e4_1_1_3_1__anproj_2)]]). fof(e5_1_1_3_1__anproj_2,plain,( k4_rlvect_1(c1_1__anproj_2,k4_rlvect_1(c1_1__anproj_2,k3_rlvect_1(c1_1__anproj_2,c2_1__anproj_2,0),k1_rlvect_1(c1_1__anproj_2)),k3_rlvect_1(c1_1__anproj_2,c4_1__anproj_2,1)) = k4_rlvect_1(c1_1__anproj_2,k4_rlvect_1(c1_1__anproj_2,k3_rlvect_1(c1_1__anproj_2,c2_1__anproj_2,0),k3_rlvect_1(c1_1__anproj_2,c3_1__anproj_2,0)),k3_rlvect_1(c1_1__anproj_2,c4_1__anproj_2,1)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_1__anproj_2,dt_c2_1__anproj_2,dt_c3_1__anproj_2,dt_c4_1__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_1__anproj_2,dt_c2_1__anproj_2,dt_c3_1__anproj_2,dt_c4_1__anproj_2,fc2_membered,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,t23_rlvect_1]), [interesting(0.35),file(anproj_2,e5_1_1_3_1__anproj_2),[file(anproj_2,e5_1_1_3_1__anproj_2)]]). fof(e3_1_1_3__anproj_2,plain,( k1_rlvect_1(c1_1__anproj_2) = k4_rlvect_1(c1_1__anproj_2,k4_rlvect_1(c1_1__anproj_2,k3_rlvect_1(c1_1__anproj_2,c2_1__anproj_2,0),k3_rlvect_1(c1_1__anproj_2,c3_1__anproj_2,0)),k3_rlvect_1(c1_1__anproj_2,c4_1__anproj_2,1)) ), inference(iterative_eq,[status(thm),assumptions([e1_1_1_3__anproj_2,dt_c1_1__anproj_2,dt_c2_1__anproj_2,dt_c3_1__anproj_2,dt_c4_1__anproj_2])],[e1_1_1_3_1__anproj_2,e2_1_1_3_1__anproj_2,e3_1_1_3_1__anproj_2,e4_1_1_3_1__anproj_2,e5_1_1_3_1__anproj_2]), [interesting(0.5),file(anproj_2,e3_1_1_3__anproj_2),[file(anproj_2,e3_1_1_3__anproj_2)]]). fof(e4_1_1_3__anproj_2,plain,( ~ $true ), inference(mizar_by,[status(thm),assumptions([e1_1_1_3__anproj_2,dt_c1_1__anproj_2,dt_c2_1__anproj_2,dt_c3_1__anproj_2,dt_c4_1__anproj_2,e1_1__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l1_struct_0,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l1_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,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_l1_rlvect_1,existence_l2_rlvect_1,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_l2_rlvect_1,dt_l2_struct_0,dt_m2_subset_1,dt_u1_struct_0,cc10_membered,cc11_membered,cc15_membered,cc4_membered,rc4_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_k1_numbers,dt_k1_rlvect_1,dt_k3_rlvect_1,dt_k4_rlvect_1,dt_m1_subset_1,dt_c1_1__anproj_2,dt_c2_1__anproj_2,dt_c3_1__anproj_2,dt_c4_1__anproj_2,fc2_membered,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e3_1_1_3__anproj_2,e1_1__anproj_2]), [interesting(0.5),file(anproj_2,e4_1_1_3__anproj_2),[file(anproj_2,e4_1_1_3__anproj_2)]]). fof(i2_1_1_3__anproj_2,theorem,( $true ), introduced(tautology,[file(anproj_2,i2_1_1_3__anproj_2)]), [interesting(0.5),trivial,file(anproj_2,i2_1_1_3__anproj_2)]). fof(i1_1_1_3__anproj_2,plain,( ~ $true ), inference(conclusion,[status(thm),assumptions([e1_1_1_3__anproj_2,dt_c1_1__anproj_2,dt_c2_1__anproj_2,dt_c3_1__anproj_2,dt_c4_1__anproj_2,e1_1__anproj_2])],[e4_1_1_3__anproj_2,i2_1_1_3__anproj_2]), [interesting(0.5),file(anproj_2,i1_1_1_3__anproj_2),[file(anproj_2,i1_1_1_3__anproj_2)]]). fof(e3_1_1__anproj_2,plain,( v8_rlvect_1(c4_1__anproj_2,c1_1__anproj_2) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_1__anproj_2,dt_c2_1__anproj_2,dt_c3_1__anproj_2,dt_c4_1__anproj_2,e1_1__anproj_2]),discharge_asm(discharge,[e1_1_1_3__anproj_2])],[e1_1_1_3__anproj_2,i1_1_1_3__anproj_2]), [interesting(0.65),file(anproj_2,e3_1_1__anproj_2),[file(anproj_2,e3_1_1__anproj_2)]]). fof(e1_1_1_1__anproj_2,assumption,( ~ v8_rlvect_1(c2_1__anproj_2,c1_1__anproj_2) ), introduced(assumption,[file(anproj_2,e1_1_1_1__anproj_2)]), [interesting(0.5),axiom,file(anproj_2,e1_1_1_1__anproj_2)]). fof(e1_1_1_1_1__anproj_2,plain,( k1_rlvect_1(c1_1__anproj_2) = k4_rlvect_1(c1_1__anproj_2,k1_rlvect_1(c1_1__anproj_2),k1_rlvect_1(c1_1__anproj_2)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_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,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_1__anproj_2,t10_rlvect_1]), [interesting(0.35),file(anproj_2,e1_1_1_1_1__anproj_2),[file(anproj_2,e1_1_1_1_1__anproj_2)]]). fof(e2_1_1_1_1__anproj_2,plain,( k4_rlvect_1(c1_1__anproj_2,k1_rlvect_1(c1_1__anproj_2),k1_rlvect_1(c1_1__anproj_2)) = k4_rlvect_1(c1_1__anproj_2,k4_rlvect_1(c1_1__anproj_2,k1_rlvect_1(c1_1__anproj_2),k1_rlvect_1(c1_1__anproj_2)),k1_rlvect_1(c1_1__anproj_2)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_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,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_1__anproj_2,t10_rlvect_1]), [interesting(0.35),file(anproj_2,e2_1_1_1_1__anproj_2),[file(anproj_2,e2_1_1_1_1__anproj_2)]]). fof(e2_1_1_1__anproj_2,plain,( c2_1__anproj_2 = k1_rlvect_1(c1_1__anproj_2) ), inference(mizar_by,[status(thm),assumptions([dt_c1_1__anproj_2,dt_c2_1__anproj_2,e1_1_1_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,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_1__anproj_2,dt_c2_1__anproj_2,rc4_struct_0,e1_1_1_1__anproj_2,d13_rlvect_1]), [interesting(0.5),file(anproj_2,e2_1_1_1__anproj_2),[file(anproj_2,e2_1_1_1__anproj_2)]]). fof(e3_1_1_1_1__anproj_2,plain,( k4_rlvect_1(c1_1__anproj_2,k4_rlvect_1(c1_1__anproj_2,k1_rlvect_1(c1_1__anproj_2),k1_rlvect_1(c1_1__anproj_2)),k1_rlvect_1(c1_1__anproj_2)) = k4_rlvect_1(c1_1__anproj_2,k4_rlvect_1(c1_1__anproj_2,k3_rlvect_1(c1_1__anproj_2,c2_1__anproj_2,1),k1_rlvect_1(c1_1__anproj_2)),k1_rlvect_1(c1_1__anproj_2)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_1__anproj_2,dt_c2_1__anproj_2,e1_1_1_1__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,spc5_arithm,spc6_arithm,spc7_arithm,t1_subset,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_l2_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_l2_struct_0,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc4_membered,fc1_struct_0,rc3_struct_0,rc4_struct_0,rqRealMult__k3_xcmplx_0__r1_r1_r1,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_k1_rlvect_1,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_1__anproj_2,dt_c2_1__anproj_2,fc2_membered,spc1_numerals,spc1_boole,e2_1_1_1__anproj_2,d9_rlvect_1]), [interesting(0.35),file(anproj_2,e3_1_1_1_1__anproj_2),[file(anproj_2,e3_1_1_1_1__anproj_2)]]). fof(e4_1_1_1_1__anproj_2,plain,( k4_rlvect_1(c1_1__anproj_2,k4_rlvect_1(c1_1__anproj_2,k3_rlvect_1(c1_1__anproj_2,c2_1__anproj_2,1),k1_rlvect_1(c1_1__anproj_2)),k1_rlvect_1(c1_1__anproj_2)) = k4_rlvect_1(c1_1__anproj_2,k4_rlvect_1(c1_1__anproj_2,k3_rlvect_1(c1_1__anproj_2,c2_1__anproj_2,1),k3_rlvect_1(c1_1__anproj_2,c3_1__anproj_2,0)),k1_rlvect_1(c1_1__anproj_2)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_1__anproj_2,dt_c2_1__anproj_2,dt_c3_1__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_1__anproj_2,dt_c2_1__anproj_2,dt_c3_1__anproj_2,fc2_membered,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,t23_rlvect_1]), [interesting(0.35),file(anproj_2,e4_1_1_1_1__anproj_2),[file(anproj_2,e4_1_1_1_1__anproj_2)]]). fof(e5_1_1_1_1__anproj_2,plain,( k4_rlvect_1(c1_1__anproj_2,k4_rlvect_1(c1_1__anproj_2,k3_rlvect_1(c1_1__anproj_2,c2_1__anproj_2,1),k3_rlvect_1(c1_1__anproj_2,c3_1__anproj_2,0)),k1_rlvect_1(c1_1__anproj_2)) = k4_rlvect_1(c1_1__anproj_2,k4_rlvect_1(c1_1__anproj_2,k3_rlvect_1(c1_1__anproj_2,c2_1__anproj_2,1),k3_rlvect_1(c1_1__anproj_2,c3_1__anproj_2,0)),k3_rlvect_1(c1_1__anproj_2,c4_1__anproj_2,0)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_1__anproj_2,dt_c2_1__anproj_2,dt_c3_1__anproj_2,dt_c4_1__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_1__anproj_2,dt_c2_1__anproj_2,dt_c3_1__anproj_2,dt_c4_1__anproj_2,fc2_membered,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,t23_rlvect_1]), [interesting(0.35),file(anproj_2,e5_1_1_1_1__anproj_2),[file(anproj_2,e5_1_1_1_1__anproj_2)]]). fof(e3_1_1_1__anproj_2,plain,( k1_rlvect_1(c1_1__anproj_2) = k4_rlvect_1(c1_1__anproj_2,k4_rlvect_1(c1_1__anproj_2,k3_rlvect_1(c1_1__anproj_2,c2_1__anproj_2,1),k3_rlvect_1(c1_1__anproj_2,c3_1__anproj_2,0)),k3_rlvect_1(c1_1__anproj_2,c4_1__anproj_2,0)) ), inference(iterative_eq,[status(thm),assumptions([e1_1_1_1__anproj_2,dt_c1_1__anproj_2,dt_c2_1__anproj_2,dt_c3_1__anproj_2,dt_c4_1__anproj_2])],[e1_1_1_1_1__anproj_2,e2_1_1_1_1__anproj_2,e3_1_1_1_1__anproj_2,e4_1_1_1_1__anproj_2,e5_1_1_1_1__anproj_2]), [interesting(0.5),file(anproj_2,e3_1_1_1__anproj_2),[file(anproj_2,e3_1_1_1__anproj_2)]]). fof(e4_1_1_1__anproj_2,plain,( ~ $true ), inference(mizar_by,[status(thm),assumptions([e1_1_1_1__anproj_2,dt_c1_1__anproj_2,dt_c2_1__anproj_2,dt_c3_1__anproj_2,dt_c4_1__anproj_2,e1_1__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l1_struct_0,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l1_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,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_l1_rlvect_1,existence_l2_rlvect_1,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_l2_rlvect_1,dt_l2_struct_0,dt_m2_subset_1,dt_u1_struct_0,cc10_membered,cc11_membered,cc15_membered,cc4_membered,rc4_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_k1_numbers,dt_k1_rlvect_1,dt_k3_rlvect_1,dt_k4_rlvect_1,dt_m1_subset_1,dt_c1_1__anproj_2,dt_c2_1__anproj_2,dt_c3_1__anproj_2,dt_c4_1__anproj_2,fc2_membered,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e3_1_1_1__anproj_2,e1_1__anproj_2]), [interesting(0.5),file(anproj_2,e4_1_1_1__anproj_2),[file(anproj_2,e4_1_1_1__anproj_2)]]). fof(i2_1_1_1__anproj_2,theorem,( $true ), introduced(tautology,[file(anproj_2,i2_1_1_1__anproj_2)]), [interesting(0.5),trivial,file(anproj_2,i2_1_1_1__anproj_2)]). fof(i1_1_1_1__anproj_2,plain,( ~ $true ), inference(conclusion,[status(thm),assumptions([e1_1_1_1__anproj_2,dt_c1_1__anproj_2,dt_c2_1__anproj_2,dt_c3_1__anproj_2,dt_c4_1__anproj_2,e1_1__anproj_2])],[e4_1_1_1__anproj_2,i2_1_1_1__anproj_2]), [interesting(0.5),file(anproj_2,i1_1_1_1__anproj_2),[file(anproj_2,i1_1_1_1__anproj_2)]]). fof(e1_1_1__anproj_2,plain,( v8_rlvect_1(c2_1__anproj_2,c1_1__anproj_2) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_1__anproj_2,dt_c2_1__anproj_2,dt_c3_1__anproj_2,dt_c4_1__anproj_2,e1_1__anproj_2]),discharge_asm(discharge,[e1_1_1_1__anproj_2])],[e1_1_1_1__anproj_2,i1_1_1_1__anproj_2]), [interesting(0.65),file(anproj_2,e1_1_1__anproj_2),[file(anproj_2,e1_1_1__anproj_2)]]). fof(e1_1_1_2__anproj_2,assumption,( ~ v8_rlvect_1(c3_1__anproj_2,c1_1__anproj_2) ), introduced(assumption,[file(anproj_2,e1_1_1_2__anproj_2)]), [interesting(0.5),axiom,file(anproj_2,e1_1_1_2__anproj_2)]). fof(e1_1_1_2_1__anproj_2,plain,( k1_rlvect_1(c1_1__anproj_2) = k4_rlvect_1(c1_1__anproj_2,k1_rlvect_1(c1_1__anproj_2),k1_rlvect_1(c1_1__anproj_2)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_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,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_1__anproj_2,t10_rlvect_1]), [interesting(0.35),file(anproj_2,e1_1_1_2_1__anproj_2),[file(anproj_2,e1_1_1_2_1__anproj_2)]]). fof(e2_1_1_2_1__anproj_2,plain,( k4_rlvect_1(c1_1__anproj_2,k1_rlvect_1(c1_1__anproj_2),k1_rlvect_1(c1_1__anproj_2)) = k4_rlvect_1(c1_1__anproj_2,k4_rlvect_1(c1_1__anproj_2,k1_rlvect_1(c1_1__anproj_2),k1_rlvect_1(c1_1__anproj_2)),k1_rlvect_1(c1_1__anproj_2)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_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,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_1__anproj_2,t10_rlvect_1]), [interesting(0.35),file(anproj_2,e2_1_1_2_1__anproj_2),[file(anproj_2,e2_1_1_2_1__anproj_2)]]). fof(e2_1_1_2__anproj_2,plain,( c3_1__anproj_2 = k1_rlvect_1(c1_1__anproj_2) ), inference(mizar_by,[status(thm),assumptions([dt_c1_1__anproj_2,dt_c3_1__anproj_2,e1_1_1_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_1__anproj_2,dt_c3_1__anproj_2,rc4_struct_0,e1_1_1_2__anproj_2,d13_rlvect_1]), [interesting(0.5),file(anproj_2,e2_1_1_2__anproj_2),[file(anproj_2,e2_1_1_2__anproj_2)]]). fof(e3_1_1_2_1__anproj_2,plain,( k4_rlvect_1(c1_1__anproj_2,k4_rlvect_1(c1_1__anproj_2,k1_rlvect_1(c1_1__anproj_2),k1_rlvect_1(c1_1__anproj_2)),k1_rlvect_1(c1_1__anproj_2)) = k4_rlvect_1(c1_1__anproj_2,k4_rlvect_1(c1_1__anproj_2,k1_rlvect_1(c1_1__anproj_2),k3_rlvect_1(c1_1__anproj_2,c3_1__anproj_2,1)),k1_rlvect_1(c1_1__anproj_2)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_1__anproj_2,dt_c3_1__anproj_2,e1_1_1_2__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,spc5_arithm,spc6_arithm,spc7_arithm,t1_subset,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_l2_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_l2_struct_0,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc4_membered,fc1_struct_0,rc3_struct_0,rc4_struct_0,rqRealMult__k3_xcmplx_0__r1_r1_r1,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_k1_rlvect_1,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_1__anproj_2,dt_c3_1__anproj_2,fc2_membered,spc1_numerals,spc1_boole,e2_1_1_2__anproj_2,d9_rlvect_1]), [interesting(0.35),file(anproj_2,e3_1_1_2_1__anproj_2),[file(anproj_2,e3_1_1_2_1__anproj_2)]]). fof(e4_1_1_2_1__anproj_2,plain,( k4_rlvect_1(c1_1__anproj_2,k4_rlvect_1(c1_1__anproj_2,k1_rlvect_1(c1_1__anproj_2),k3_rlvect_1(c1_1__anproj_2,c3_1__anproj_2,1)),k1_rlvect_1(c1_1__anproj_2)) = k4_rlvect_1(c1_1__anproj_2,k4_rlvect_1(c1_1__anproj_2,k3_rlvect_1(c1_1__anproj_2,c2_1__anproj_2,0),k3_rlvect_1(c1_1__anproj_2,c3_1__anproj_2,1)),k1_rlvect_1(c1_1__anproj_2)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_1__anproj_2,dt_c2_1__anproj_2,dt_c3_1__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_1__anproj_2,dt_c2_1__anproj_2,dt_c3_1__anproj_2,fc2_membered,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,t23_rlvect_1]), [interesting(0.35),file(anproj_2,e4_1_1_2_1__anproj_2),[file(anproj_2,e4_1_1_2_1__anproj_2)]]). fof(e5_1_1_2_1__anproj_2,plain,( k4_rlvect_1(c1_1__anproj_2,k4_rlvect_1(c1_1__anproj_2,k3_rlvect_1(c1_1__anproj_2,c2_1__anproj_2,0),k3_rlvect_1(c1_1__anproj_2,c3_1__anproj_2,1)),k1_rlvect_1(c1_1__anproj_2)) = k4_rlvect_1(c1_1__anproj_2,k4_rlvect_1(c1_1__anproj_2,k3_rlvect_1(c1_1__anproj_2,c2_1__anproj_2,0),k3_rlvect_1(c1_1__anproj_2,c3_1__anproj_2,1)),k3_rlvect_1(c1_1__anproj_2,c4_1__anproj_2,0)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_1__anproj_2,dt_c2_1__anproj_2,dt_c3_1__anproj_2,dt_c4_1__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_1__anproj_2,dt_c2_1__anproj_2,dt_c3_1__anproj_2,dt_c4_1__anproj_2,fc2_membered,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,t23_rlvect_1]), [interesting(0.35),file(anproj_2,e5_1_1_2_1__anproj_2),[file(anproj_2,e5_1_1_2_1__anproj_2)]]). fof(e3_1_1_2__anproj_2,plain,( k1_rlvect_1(c1_1__anproj_2) = k4_rlvect_1(c1_1__anproj_2,k4_rlvect_1(c1_1__anproj_2,k3_rlvect_1(c1_1__anproj_2,c2_1__anproj_2,0),k3_rlvect_1(c1_1__anproj_2,c3_1__anproj_2,1)),k3_rlvect_1(c1_1__anproj_2,c4_1__anproj_2,0)) ), inference(iterative_eq,[status(thm),assumptions([e1_1_1_2__anproj_2,dt_c1_1__anproj_2,dt_c2_1__anproj_2,dt_c3_1__anproj_2,dt_c4_1__anproj_2])],[e1_1_1_2_1__anproj_2,e2_1_1_2_1__anproj_2,e3_1_1_2_1__anproj_2,e4_1_1_2_1__anproj_2,e5_1_1_2_1__anproj_2]), [interesting(0.5),file(anproj_2,e3_1_1_2__anproj_2),[file(anproj_2,e3_1_1_2__anproj_2)]]). fof(e4_1_1_2__anproj_2,plain,( ~ $true ), inference(mizar_by,[status(thm),assumptions([e1_1_1_2__anproj_2,dt_c1_1__anproj_2,dt_c2_1__anproj_2,dt_c3_1__anproj_2,dt_c4_1__anproj_2,e1_1__anproj_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l1_struct_0,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l1_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,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_l1_rlvect_1,existence_l2_rlvect_1,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_l2_rlvect_1,dt_l2_struct_0,dt_m2_subset_1,dt_u1_struct_0,cc10_membered,cc11_membered,cc15_membered,cc4_membered,rc4_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_k1_numbers,dt_k1_rlvect_1,dt_k3_rlvect_1,dt_k4_rlvect_1,dt_m1_subset_1,dt_c1_1__anproj_2,dt_c2_1__anproj_2,dt_c3_1__anproj_2,dt_c4_1__anproj_2,fc2_membered,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e3_1_1_2__anproj_2,e1_1__anproj_2]), [interesting(0.5),file(anproj_2,e4_1_1_2__anproj_2),[file(anproj_2,e4_1_1_2__anproj_2)]]). fof(i2_1_1_2__anproj_2,theorem,( $true ), introduced(tautology,[file(anproj_2,i2_1_1_2__anproj_2)]), [interesting(0.5),trivial,file(anproj_2,i2_1_1_2__anproj_2)]). fof(i1_1_1_2__anproj_2,plain,( ~ $true ), inference(conclusion,[status(thm),assumptions([e1_1_1_2__anproj_2,dt_c1_1__anproj_2,dt_c2_1__anproj_2,dt_c3_1__anproj_2,dt_c4_1__anproj_2,e1_1__anproj_2])],[e4_1_1_2__anproj_2,i2_1_1_2__anproj_2]), [interesting(0.5),file(anproj_2,i1_1_1_2__anproj_2),[file(anproj_2,i1_1_1_2__anproj_2)]]). fof(e2_1_1__anproj_2,plain,( v8_rlvect_1(c3_1__anproj_2,c1_1__anproj_2) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_1__anproj_2,dt_c2_1__anproj_2,dt_c3_1__anproj_2,dt_c4_1__anproj_2,e1_1__anproj_2]),discharge_asm(discharge,[e1_1_1_2__anproj_2])],[e1_1_1_2__anproj_2,i1_1_1_2__anproj_2]), [interesting(0.65),file(anproj_2,e2_1_1__anproj_2),[file(anproj_2,e2_1_1__anproj_2)]]). fof(e4_1_1__anproj_2,plain, ( v8_rlvect_1(c2_1__anproj_2,c1_1__anproj_2) & v8_rlvect_1(c3_1__anproj_2,c1_1__anproj_2) & v8_rlvect_1(c4_1__anproj_2,c1_1__anproj_2) ), inference(mizar_by,[status(thm),assumptions([dt_c1_1__anproj_2,dt_c2_1__anproj_2,dt_c3_1__anproj_2,dt_c4_1__anproj_2,e1_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,existence_l2_rlvect_1,existence_m1_subset_1,dt_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_1__anproj_2,dt_c2_1__anproj_2,dt_c3_1__anproj_2,dt_c4_1__anproj_2,e3_1_1__anproj_2,e1_1_1__anproj_2,e2_1_1__anproj_2]), [interesting(0.65),file(anproj_2,e4_1_1__anproj_2),[file(anproj_2,e4_1_1__anproj_2)]]). fof(i1_1_1__anproj_2,theorem,( $true ), introduced(tautology,[file(anproj_2,i1_1_1__anproj_2)]), [interesting(0.65),trivial,file(anproj_2,i1_1_1__anproj_2)]). fof(e2_1__anproj_2,plain, ( v8_rlvect_1(c2_1__anproj_2,c1_1__anproj_2) & v8_rlvect_1(c3_1__anproj_2,c1_1__anproj_2) & v8_rlvect_1(c4_1__anproj_2,c1_1__anproj_2) ), inference(conclusion,[status(thm),assumptions([dt_c1_1__anproj_2,dt_c2_1__anproj_2,dt_c3_1__anproj_2,dt_c4_1__anproj_2,e1_1__anproj_2])],[e4_1_1__anproj_2,i1_1_1__anproj_2]), [interesting(0.8),file(anproj_2,e2_1__anproj_2),[file(anproj_2,e2_1__anproj_2)]]). fof(d3_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)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_anproj_1(A,B,C,D) <=> ? [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 ) ) ) ) ) ) ) ) ) ), file(anproj_1,d3_anproj_1), [interesting(0.9),axiom,file(anproj_1,d3_anproj_1)]). fof(e3_1__anproj_2,plain,( ~ r2_anproj_1(c1_1__anproj_2,c2_1__anproj_2,c3_1__anproj_2,c4_1__anproj_2) ), inference(mizar_by,[status(thm),assumptions([dt_c1_1__anproj_2,dt_c2_1__anproj_2,dt_c3_1__anproj_2,dt_c4_1__anproj_2,e1_1__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_1__anproj_2,dt_c2_1__anproj_2,dt_c3_1__anproj_2,dt_c4_1__anproj_2,fc2_membered,spc0_numerals,spc0_boole,e1_1__anproj_2,d3_anproj_1]), [interesting(0.8),file(anproj_2,e3_1__anproj_2),[file(anproj_2,e3_1__anproj_2)]]). 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(t17_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)) => ( ~ r2_anproj_1(A,B,C,D) => ( v8_rlvect_1(B,A) & v8_rlvect_1(C,A) & v8_rlvect_1(D,A) & ~ r1_anproj_1(A,B,C) & ~ r1_anproj_1(A,C,D) & ~ r1_anproj_1(A,D,B) ) ) ) ) ) ) ), file(anproj_1,t17_anproj_1), [interesting(0.9),axiom,file(anproj_1,t17_anproj_1)]). fof(e4_1__anproj_2,plain,( ~ r1_anproj_1(c1_1__anproj_2,c2_1__anproj_2,c3_1__anproj_2) ), inference(mizar_by,[status(thm),assumptions([dt_c1_1__anproj_2,dt_c2_1__anproj_2,dt_c3_1__anproj_2,dt_c4_1__anproj_2,e1_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_1__anproj_2,dt_c2_1__anproj_2,dt_c3_1__anproj_2,dt_c4_1__anproj_2,e3_1__anproj_2,t17_anproj_1]), [interesting(0.8),file(anproj_2,e4_1__anproj_2),[file(anproj_2,e4_1__anproj_2)]]). fof(i8_1__anproj_2,theorem,( $true ), introduced(tautology,[file(anproj_2,i8_1__anproj_2)]), [interesting(0.8),trivial,file(anproj_2,i8_1__anproj_2)]). fof(i7_1__anproj_2,plain,( ~ r1_anproj_1(c1_1__anproj_2,c2_1__anproj_2,c3_1__anproj_2) ), inference(conclusion,[status(thm),assumptions([dt_c1_1__anproj_2,dt_c2_1__anproj_2,dt_c3_1__anproj_2,dt_c4_1__anproj_2,e1_1__anproj_2])],[e4_1__anproj_2,i8_1__anproj_2]), [interesting(0.8),file(anproj_2,i7_1__anproj_2),[file(anproj_2,i7_1__anproj_2)]]). fof(i6_1__anproj_2,plain, ( ~ r2_anproj_1(c1_1__anproj_2,c2_1__anproj_2,c3_1__anproj_2,c4_1__anproj_2) & ~ r1_anproj_1(c1_1__anproj_2,c2_1__anproj_2,c3_1__anproj_2) ), inference(conclusion,[status(thm),assumptions([dt_c1_1__anproj_2,dt_c2_1__anproj_2,dt_c3_1__anproj_2,dt_c4_1__anproj_2,e1_1__anproj_2])],[e3_1__anproj_2,i7_1__anproj_2]), [interesting(0.8),file(anproj_2,i6_1__anproj_2),[file(anproj_2,i6_1__anproj_2)]]). fof(i5_1__anproj_2,plain, ( v8_rlvect_1(c2_1__anproj_2,c1_1__anproj_2) & v8_rlvect_1(c3_1__anproj_2,c1_1__anproj_2) & v8_rlvect_1(c4_1__anproj_2,c1_1__anproj_2) & ~ r2_anproj_1(c1_1__anproj_2,c2_1__anproj_2,c3_1__anproj_2,c4_1__anproj_2) & ~ r1_anproj_1(c1_1__anproj_2,c2_1__anproj_2,c3_1__anproj_2) ), inference(conclusion,[status(thm),assumptions([dt_c1_1__anproj_2,dt_c2_1__anproj_2,dt_c3_1__anproj_2,dt_c4_1__anproj_2,e1_1__anproj_2])],[e2_1__anproj_2,i6_1__anproj_2]), [interesting(0.8),file(anproj_2,i5_1__anproj_2),[file(anproj_2,i5_1__anproj_2)]]). fof(i4_1__anproj_2,plain, ( ! [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_1__anproj_2,k4_rlvect_1(c1_1__anproj_2,k3_rlvect_1(c1_1__anproj_2,c2_1__anproj_2,A),k3_rlvect_1(c1_1__anproj_2,c3_1__anproj_2,B)),k3_rlvect_1(c1_1__anproj_2,c4_1__anproj_2,C)) = k1_rlvect_1(c1_1__anproj_2) => ( A = 0 & B = 0 & C = 0 ) ) ) ) ) => ( v8_rlvect_1(c2_1__anproj_2,c1_1__anproj_2) & v8_rlvect_1(c3_1__anproj_2,c1_1__anproj_2) & v8_rlvect_1(c4_1__anproj_2,c1_1__anproj_2) & ~ r2_anproj_1(c1_1__anproj_2,c2_1__anproj_2,c3_1__anproj_2,c4_1__anproj_2) & ~ r1_anproj_1(c1_1__anproj_2,c2_1__anproj_2,c3_1__anproj_2) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_1__anproj_2,dt_c2_1__anproj_2,dt_c3_1__anproj_2,dt_c4_1__anproj_2]),discharge_asm(discharge,[e1_1__anproj_2])],[e1_1__anproj_2,i5_1__anproj_2]), [interesting(0.8),file(anproj_2,i4_1__anproj_2),[file(anproj_2,i4_1__anproj_2)]]). fof(i4_1_tmp__anproj_2,plain, ( m1_subset_1(c4_1__anproj_2,u1_struct_0(c1_1__anproj_2)) => ( ! [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_1__anproj_2,k4_rlvect_1(c1_1__anproj_2,k3_rlvect_1(c1_1__anproj_2,c2_1__anproj_2,A),k3_rlvect_1(c1_1__anproj_2,c3_1__anproj_2,B)),k3_rlvect_1(c1_1__anproj_2,c4_1__anproj_2,C)) = k1_rlvect_1(c1_1__anproj_2) => ( A = 0 & B = 0 & C = 0 ) ) ) ) ) => ( v8_rlvect_1(c2_1__anproj_2,c1_1__anproj_2) & v8_rlvect_1(c3_1__anproj_2,c1_1__anproj_2) & v8_rlvect_1(c4_1__anproj_2,c1_1__anproj_2) & ~ r2_anproj_1(c1_1__anproj_2,c2_1__anproj_2,c3_1__anproj_2,c4_1__anproj_2) & ~ r1_anproj_1(c1_1__anproj_2,c2_1__anproj_2,c3_1__anproj_2) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_1__anproj_2,dt_c2_1__anproj_2,dt_c3_1__anproj_2]),discharge_asm(discharge,[dt_c4_1__anproj_2])],[dt_c4_1__anproj_2,i4_1__anproj_2]), [interesting(0.8),i3_1__anproj_2]). fof(i3_1__anproj_2,plain,( ! [A] : ( m1_subset_1(A,u1_struct_0(c1_1__anproj_2)) => ( ! [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_1__anproj_2,k4_rlvect_1(c1_1__anproj_2,k3_rlvect_1(c1_1__anproj_2,c2_1__anproj_2,B),k3_rlvect_1(c1_1__anproj_2,c3_1__anproj_2,C)),k3_rlvect_1(c1_1__anproj_2,A,D)) = k1_rlvect_1(c1_1__anproj_2) => ( B = 0 & C = 0 & D = 0 ) ) ) ) ) => ( v8_rlvect_1(c2_1__anproj_2,c1_1__anproj_2) & v8_rlvect_1(c3_1__anproj_2,c1_1__anproj_2) & v8_rlvect_1(A,c1_1__anproj_2) & ~ r2_anproj_1(c1_1__anproj_2,c2_1__anproj_2,c3_1__anproj_2,A) & ~ r1_anproj_1(c1_1__anproj_2,c2_1__anproj_2,c3_1__anproj_2) ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_1__anproj_2,dt_c2_1__anproj_2,dt_c3_1__anproj_2])],[i4_1_tmp__anproj_2,dh_c4_1__anproj_2]), [interesting(0.8),file(anproj_2,i3_1__anproj_2),[file(anproj_2,i3_1__anproj_2)]]). fof(i3_1_tmp__anproj_2,plain, ( m1_subset_1(c3_1__anproj_2,u1_struct_0(c1_1__anproj_2)) => ! [A] : ( m1_subset_1(A,u1_struct_0(c1_1__anproj_2)) => ( ! [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_1__anproj_2,k4_rlvect_1(c1_1__anproj_2,k3_rlvect_1(c1_1__anproj_2,c2_1__anproj_2,B),k3_rlvect_1(c1_1__anproj_2,c3_1__anproj_2,C)),k3_rlvect_1(c1_1__anproj_2,A,D)) = k1_rlvect_1(c1_1__anproj_2) => ( B = 0 & C = 0 & D = 0 ) ) ) ) ) => ( v8_rlvect_1(c2_1__anproj_2,c1_1__anproj_2) & v8_rlvect_1(c3_1__anproj_2,c1_1__anproj_2) & v8_rlvect_1(A,c1_1__anproj_2) & ~ r2_anproj_1(c1_1__anproj_2,c2_1__anproj_2,c3_1__anproj_2,A) & ~ r1_anproj_1(c1_1__anproj_2,c2_1__anproj_2,c3_1__anproj_2) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_1__anproj_2,dt_c2_1__anproj_2]),discharge_asm(discharge,[dt_c3_1__anproj_2])],[dt_c3_1__anproj_2,i3_1__anproj_2]), [interesting(0.8),i2_1__anproj_2]). fof(i2_1__anproj_2,plain,( ! [A] : ( m1_subset_1(A,u1_struct_0(c1_1__anproj_2)) => ! [B] : ( m1_subset_1(B,u1_struct_0(c1_1__anproj_2)) => ( ! [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_1__anproj_2,k4_rlvect_1(c1_1__anproj_2,k3_rlvect_1(c1_1__anproj_2,c2_1__anproj_2,C),k3_rlvect_1(c1_1__anproj_2,A,D)),k3_rlvect_1(c1_1__anproj_2,B,E)) = k1_rlvect_1(c1_1__anproj_2) => ( C = 0 & D = 0 & E = 0 ) ) ) ) ) => ( v8_rlvect_1(c2_1__anproj_2,c1_1__anproj_2) & v8_rlvect_1(A,c1_1__anproj_2) & v8_rlvect_1(B,c1_1__anproj_2) & ~ r2_anproj_1(c1_1__anproj_2,c2_1__anproj_2,A,B) & ~ r1_anproj_1(c1_1__anproj_2,c2_1__anproj_2,A) ) ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_1__anproj_2,dt_c2_1__anproj_2])],[i3_1_tmp__anproj_2,dh_c3_1__anproj_2]), [interesting(0.8),file(anproj_2,i2_1__anproj_2),[file(anproj_2,i2_1__anproj_2)]]). fof(i2_1_tmp__anproj_2,plain, ( m1_subset_1(c2_1__anproj_2,u1_struct_0(c1_1__anproj_2)) => ! [A] : ( m1_subset_1(A,u1_struct_0(c1_1__anproj_2)) => ! [B] : ( m1_subset_1(B,u1_struct_0(c1_1__anproj_2)) => ( ! [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_1__anproj_2,k4_rlvect_1(c1_1__anproj_2,k3_rlvect_1(c1_1__anproj_2,c2_1__anproj_2,C),k3_rlvect_1(c1_1__anproj_2,A,D)),k3_rlvect_1(c1_1__anproj_2,B,E)) = k1_rlvect_1(c1_1__anproj_2) => ( C = 0 & D = 0 & E = 0 ) ) ) ) ) => ( v8_rlvect_1(c2_1__anproj_2,c1_1__anproj_2) & v8_rlvect_1(A,c1_1__anproj_2) & v8_rlvect_1(B,c1_1__anproj_2) & ~ r2_anproj_1(c1_1__anproj_2,c2_1__anproj_2,A,B) & ~ r1_anproj_1(c1_1__anproj_2,c2_1__anproj_2,A) ) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_1__anproj_2]),discharge_asm(discharge,[dt_c2_1__anproj_2])],[dt_c2_1__anproj_2,i2_1__anproj_2]), [interesting(0.8),i1_1__anproj_2]). fof(i1_1__anproj_2,plain,( ! [A] : ( m1_subset_1(A,u1_struct_0(c1_1__anproj_2)) => ! [B] : ( m1_subset_1(B,u1_struct_0(c1_1__anproj_2)) => ! [C] : ( m1_subset_1(C,u1_struct_0(c1_1__anproj_2)) => ( ! [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_1__anproj_2,k4_rlvect_1(c1_1__anproj_2,k3_rlvect_1(c1_1__anproj_2,A,D),k3_rlvect_1(c1_1__anproj_2,B,E)),k3_rlvect_1(c1_1__anproj_2,C,F)) = k1_rlvect_1(c1_1__anproj_2) => ( D = 0 & E = 0 & F = 0 ) ) ) ) ) => ( v8_rlvect_1(A,c1_1__anproj_2) & v8_rlvect_1(B,c1_1__anproj_2) & v8_rlvect_1(C,c1_1__anproj_2) & ~ r2_anproj_1(c1_1__anproj_2,A,B,C) & ~ r1_anproj_1(c1_1__anproj_2,A,B) ) ) ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_1__anproj_2])],[i2_1_tmp__anproj_2,dh_c2_1__anproj_2]), [interesting(0.8),file(anproj_2,i1_1__anproj_2),[file(anproj_2,i1_1__anproj_2)]]). fof(i1_1_tmp__anproj_2,plain, ( ( ~ v3_struct_0(c1_1__anproj_2) & v3_rlvect_1(c1_1__anproj_2) & v4_rlvect_1(c1_1__anproj_2) & v5_rlvect_1(c1_1__anproj_2) & v6_rlvect_1(c1_1__anproj_2) & v7_rlvect_1(c1_1__anproj_2) & l2_rlvect_1(c1_1__anproj_2) ) => ! [A] : ( m1_subset_1(A,u1_struct_0(c1_1__anproj_2)) => ! [B] : ( m1_subset_1(B,u1_struct_0(c1_1__anproj_2)) => ! [C] : ( m1_subset_1(C,u1_struct_0(c1_1__anproj_2)) => ( ! [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_1__anproj_2,k4_rlvect_1(c1_1__anproj_2,k3_rlvect_1(c1_1__anproj_2,A,D),k3_rlvect_1(c1_1__anproj_2,B,E)),k3_rlvect_1(c1_1__anproj_2,C,F)) = k1_rlvect_1(c1_1__anproj_2) => ( D = 0 & E = 0 & F = 0 ) ) ) ) ) => ( v8_rlvect_1(A,c1_1__anproj_2) & v8_rlvect_1(B,c1_1__anproj_2) & v8_rlvect_1(C,c1_1__anproj_2) & ~ r2_anproj_1(c1_1__anproj_2,A,B,C) & ~ r1_anproj_1(c1_1__anproj_2,A,B) ) ) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_1__anproj_2])],[dt_c1_1__anproj_2,i1_1__anproj_2]), [interesting(1),t1_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) ) ) ) ) ) ) ), inference(let,[status(thm),assumptions([])],[i1_1_tmp__anproj_2,dh_c1_1__anproj_2]), [interesting(1),file(anproj_2,t1_anproj_2),[file(anproj_2,t1_anproj_2)]]).