% Mizar ND problem: t6_anproj_1,anproj_1,57,49 fof(dh_c1_4__anproj_1,definition, ( ( ( ~ v3_struct_0(c1_4__anproj_1) & v3_rlvect_1(c1_4__anproj_1) & v4_rlvect_1(c1_4__anproj_1) & v5_rlvect_1(c1_4__anproj_1) & v6_rlvect_1(c1_4__anproj_1) & v7_rlvect_1(c1_4__anproj_1) & l2_rlvect_1(c1_4__anproj_1) ) => ! [A] : ( m1_subset_1(A,u1_struct_0(c1_4__anproj_1)) => ! [B] : ( m1_subset_1(B,u1_struct_0(c1_4__anproj_1)) => ! [C] : ( m1_subset_1(C,u1_struct_0(c1_4__anproj_1)) => ( ( r1_anproj_1(c1_4__anproj_1,A,B) & r1_anproj_1(c1_4__anproj_1,B,C) ) => r1_anproj_1(c1_4__anproj_1,A,C) ) ) ) ) ) => ! [D] : ( ( ~ v3_struct_0(D) & v3_rlvect_1(D) & v4_rlvect_1(D) & v5_rlvect_1(D) & v6_rlvect_1(D) & v7_rlvect_1(D) & l2_rlvect_1(D) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(D)) => ! [F] : ( m1_subset_1(F,u1_struct_0(D)) => ! [G] : ( m1_subset_1(G,u1_struct_0(D)) => ( ( r1_anproj_1(D,E,F) & r1_anproj_1(D,F,G) ) => r1_anproj_1(D,E,G) ) ) ) ) ) ), introduced(definition,[new_symbol(c1_4__anproj_1),file(anproj_1,c1_4__anproj_1)]), [interesting(0.8),axiom,file(anproj_1,c1_4__anproj_1)]). fof(dh_c2_4__anproj_1,definition, ( ( m1_subset_1(c2_4__anproj_1,u1_struct_0(c1_4__anproj_1)) => ! [A] : ( m1_subset_1(A,u1_struct_0(c1_4__anproj_1)) => ! [B] : ( m1_subset_1(B,u1_struct_0(c1_4__anproj_1)) => ( ( r1_anproj_1(c1_4__anproj_1,c2_4__anproj_1,A) & r1_anproj_1(c1_4__anproj_1,A,B) ) => r1_anproj_1(c1_4__anproj_1,c2_4__anproj_1,B) ) ) ) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(c1_4__anproj_1)) => ! [D] : ( m1_subset_1(D,u1_struct_0(c1_4__anproj_1)) => ! [E] : ( m1_subset_1(E,u1_struct_0(c1_4__anproj_1)) => ( ( r1_anproj_1(c1_4__anproj_1,C,D) & r1_anproj_1(c1_4__anproj_1,D,E) ) => r1_anproj_1(c1_4__anproj_1,C,E) ) ) ) ) ), introduced(definition,[new_symbol(c2_4__anproj_1),file(anproj_1,c2_4__anproj_1)]), [interesting(0.8),axiom,file(anproj_1,c2_4__anproj_1)]). fof(dh_c3_4__anproj_1,definition, ( ( m1_subset_1(c3_4__anproj_1,u1_struct_0(c1_4__anproj_1)) => ! [A] : ( m1_subset_1(A,u1_struct_0(c1_4__anproj_1)) => ( ( r1_anproj_1(c1_4__anproj_1,c2_4__anproj_1,c3_4__anproj_1) & r1_anproj_1(c1_4__anproj_1,c3_4__anproj_1,A) ) => r1_anproj_1(c1_4__anproj_1,c2_4__anproj_1,A) ) ) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(c1_4__anproj_1)) => ! [C] : ( m1_subset_1(C,u1_struct_0(c1_4__anproj_1)) => ( ( r1_anproj_1(c1_4__anproj_1,c2_4__anproj_1,B) & r1_anproj_1(c1_4__anproj_1,B,C) ) => r1_anproj_1(c1_4__anproj_1,c2_4__anproj_1,C) ) ) ) ), introduced(definition,[new_symbol(c3_4__anproj_1),file(anproj_1,c3_4__anproj_1)]), [interesting(0.8),axiom,file(anproj_1,c3_4__anproj_1)]). fof(dh_c4_4__anproj_1,definition, ( ( m1_subset_1(c4_4__anproj_1,u1_struct_0(c1_4__anproj_1)) => ( ( r1_anproj_1(c1_4__anproj_1,c2_4__anproj_1,c3_4__anproj_1) & r1_anproj_1(c1_4__anproj_1,c3_4__anproj_1,c4_4__anproj_1) ) => r1_anproj_1(c1_4__anproj_1,c2_4__anproj_1,c4_4__anproj_1) ) ) => ! [A] : ( m1_subset_1(A,u1_struct_0(c1_4__anproj_1)) => ( ( r1_anproj_1(c1_4__anproj_1,c2_4__anproj_1,c3_4__anproj_1) & r1_anproj_1(c1_4__anproj_1,c3_4__anproj_1,A) ) => r1_anproj_1(c1_4__anproj_1,c2_4__anproj_1,A) ) ) ), introduced(definition,[new_symbol(c4_4__anproj_1),file(anproj_1,c4_4__anproj_1)]), [interesting(0.8),axiom,file(anproj_1,c4_4__anproj_1)]). fof(e1_4__anproj_1,assumption,( r1_anproj_1(c1_4__anproj_1,c2_4__anproj_1,c3_4__anproj_1) ), introduced(assumption,[file(anproj_1,e1_4__anproj_1)]), [interesting(0.8),axiom,file(anproj_1,e1_4__anproj_1)]). fof(e2_4__anproj_1,assumption,( r1_anproj_1(c1_4__anproj_1,c3_4__anproj_1,c4_4__anproj_1) ), introduced(assumption,[file(anproj_1,e2_4__anproj_1)]), [interesting(0.8),axiom,file(anproj_1,e2_4__anproj_1)]). fof(reflexivity_r1_tarski,theorem,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), [interesting(0.9),axiom,file(tarski,r1_tarski)]). 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_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_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_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(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(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(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(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(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(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(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(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_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_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(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(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(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(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(cc4_membered,theorem,( ! [A] : ( v2_membered(A) => v1_membered(A) ) ), file(membered,cc4_membered), [interesting(0.9),axiom,file(membered,cc4_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(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(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(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(t1_numerals,theorem,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), [interesting(0.9),axiom,file(numerals,t1_numerals)]). 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(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(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(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(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(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_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(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_numbers,axiom,( $true ), file(numbers,k1_numbers), [interesting(0.9),axiom,file(numbers,k1_numbers)]). 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_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_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_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_4__anproj_1,assumption, ( ~ v3_struct_0(c1_4__anproj_1) & v3_rlvect_1(c1_4__anproj_1) & v4_rlvect_1(c1_4__anproj_1) & v5_rlvect_1(c1_4__anproj_1) & v6_rlvect_1(c1_4__anproj_1) & v7_rlvect_1(c1_4__anproj_1) & l2_rlvect_1(c1_4__anproj_1) ), introduced(assumption,[file(anproj_1,c1_4__anproj_1)]), [interesting(0.8),axiom,file(anproj_1,c1_4__anproj_1)]). fof(dt_c2_4__anproj_1,assumption,( m1_subset_1(c2_4__anproj_1,u1_struct_0(c1_4__anproj_1)) ), introduced(assumption,[file(anproj_1,c2_4__anproj_1)]), [interesting(0.8),axiom,file(anproj_1,c2_4__anproj_1)]). fof(dt_c3_4__anproj_1,assumption,( m1_subset_1(c3_4__anproj_1,u1_struct_0(c1_4__anproj_1)) ), introduced(assumption,[file(anproj_1,c3_4__anproj_1)]), [interesting(0.8),axiom,file(anproj_1,c3_4__anproj_1)]). fof(dt_c4_4__anproj_1,assumption,( m1_subset_1(c4_4__anproj_1,u1_struct_0(c1_4__anproj_1)) ), introduced(assumption,[file(anproj_1,c4_4__anproj_1)]), [interesting(0.8),axiom,file(anproj_1,c4_4__anproj_1)]). fof(dh_c5_4__anproj_1,definition, ( ? [A] : ( m1_subset_1(A,k1_numbers) & ? [B] : ( m1_subset_1(B,k1_numbers) & k3_rlvect_1(c1_4__anproj_1,c2_4__anproj_1,A) = k3_rlvect_1(c1_4__anproj_1,c3_4__anproj_1,B) & A != 0 & B != 0 ) ) => ( m1_subset_1(c5_4__anproj_1,k1_numbers) & ? [C] : ( m1_subset_1(C,k1_numbers) & k3_rlvect_1(c1_4__anproj_1,c2_4__anproj_1,c5_4__anproj_1) = k3_rlvect_1(c1_4__anproj_1,c3_4__anproj_1,C) & c5_4__anproj_1 != 0 & C != 0 ) ) ), introduced(definition,[new_symbol(c5_4__anproj_1),file(anproj_1,c5_4__anproj_1)]), [interesting(0.8),axiom,file(anproj_1,c5_4__anproj_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(rc3_rlvect_1,theorem,( ? [A] : ( l2_rlvect_1(A) & ~ v3_struct_0(A) ) ), file(rlvect_1,rc3_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,rc3_rlvect_1)]). 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(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(e3_4__anproj_1,plain,( ? [A] : ( m1_subset_1(A,k1_numbers) & ? [B] : ( m1_subset_1(B,k1_numbers) & k3_rlvect_1(c1_4__anproj_1,c2_4__anproj_1,A) = k3_rlvect_1(c1_4__anproj_1,c3_4__anproj_1,B) & A != 0 & B != 0 ) ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_4__anproj_1,dt_c2_4__anproj_1,dt_c3_4__anproj_1,e1_4__anproj_1])],[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,fc5_membered,fc6_membered,rc1_membered,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_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,symmetry_r1_anproj_1,reflexivity_r1_anproj_1,existence_l2_rlvect_1,existence_m1_subset_1,dt_k1_numbers,dt_k3_rlvect_1,dt_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_4__anproj_1,dt_c2_4__anproj_1,dt_c3_4__anproj_1,fc2_membered,rc3_rlvect_1,spc0_numerals,spc0_boole,e1_4__anproj_1,d2_anproj_1]), [interesting(0.8),file(anproj_1,e3_4__anproj_1),[file(anproj_1,e3_4__anproj_1)]]). fof(dt_c5_4__anproj_1,plain,( m1_subset_1(c5_4__anproj_1,k1_numbers) ), inference(consider,[status(thm),assumptions([dt_c1_4__anproj_1,dt_c2_4__anproj_1,dt_c3_4__anproj_1,e1_4__anproj_1])],[dh_c5_4__anproj_1,e3_4__anproj_1]), [interesting(0.8),file(anproj_1,c5_4__anproj_1),[file(anproj_1,c5_4__anproj_1)]]). fof(dh_c6_4__anproj_1,definition, ( ? [A] : ( m1_subset_1(A,k1_numbers) & k3_rlvect_1(c1_4__anproj_1,c2_4__anproj_1,c5_4__anproj_1) = k3_rlvect_1(c1_4__anproj_1,c3_4__anproj_1,A) & c5_4__anproj_1 != 0 & A != 0 ) => ( m1_subset_1(c6_4__anproj_1,k1_numbers) & k3_rlvect_1(c1_4__anproj_1,c2_4__anproj_1,c5_4__anproj_1) = k3_rlvect_1(c1_4__anproj_1,c3_4__anproj_1,c6_4__anproj_1) & c5_4__anproj_1 != 0 & c6_4__anproj_1 != 0 ) ), introduced(definition,[new_symbol(c6_4__anproj_1),file(anproj_1,c6_4__anproj_1)]), [interesting(0.8),axiom,file(anproj_1,c6_4__anproj_1)]). fof(dt_c6_4__anproj_1,plain,( m1_subset_1(c6_4__anproj_1,k1_numbers) ), inference(consider,[status(thm),assumptions([dt_c1_4__anproj_1,dt_c2_4__anproj_1,dt_c3_4__anproj_1,e1_4__anproj_1])],[dh_c5_4__anproj_1,dh_c6_4__anproj_1,e3_4__anproj_1]), [interesting(0.8),file(anproj_1,c6_4__anproj_1),[file(anproj_1,c6_4__anproj_1)]]). fof(dh_c7_4__anproj_1,definition, ( ? [A] : ( m1_subset_1(A,k1_numbers) & ? [B] : ( m1_subset_1(B,k1_numbers) & k3_rlvect_1(c1_4__anproj_1,c3_4__anproj_1,A) = k3_rlvect_1(c1_4__anproj_1,c4_4__anproj_1,B) & A != 0 & B != 0 ) ) => ( m1_subset_1(c7_4__anproj_1,k1_numbers) & ? [C] : ( m1_subset_1(C,k1_numbers) & k3_rlvect_1(c1_4__anproj_1,c3_4__anproj_1,c7_4__anproj_1) = k3_rlvect_1(c1_4__anproj_1,c4_4__anproj_1,C) & c7_4__anproj_1 != 0 & C != 0 ) ) ), introduced(definition,[new_symbol(c7_4__anproj_1),file(anproj_1,c7_4__anproj_1)]), [interesting(0.8),axiom,file(anproj_1,c7_4__anproj_1)]). fof(e5_4__anproj_1,plain,( ? [A] : ( m1_subset_1(A,k1_numbers) & ? [B] : ( m1_subset_1(B,k1_numbers) & k3_rlvect_1(c1_4__anproj_1,c3_4__anproj_1,A) = k3_rlvect_1(c1_4__anproj_1,c4_4__anproj_1,B) & A != 0 & B != 0 ) ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_4__anproj_1,dt_c3_4__anproj_1,dt_c4_4__anproj_1,e2_4__anproj_1])],[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,fc5_membered,fc6_membered,rc1_membered,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_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,symmetry_r1_anproj_1,reflexivity_r1_anproj_1,existence_l2_rlvect_1,existence_m1_subset_1,dt_k1_numbers,dt_k3_rlvect_1,dt_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_4__anproj_1,dt_c3_4__anproj_1,dt_c4_4__anproj_1,fc2_membered,rc3_rlvect_1,spc0_numerals,spc0_boole,e2_4__anproj_1,d2_anproj_1]), [interesting(0.8),file(anproj_1,e5_4__anproj_1),[file(anproj_1,e5_4__anproj_1)]]). fof(dt_c7_4__anproj_1,plain,( m1_subset_1(c7_4__anproj_1,k1_numbers) ), inference(consider,[status(thm),assumptions([dt_c1_4__anproj_1,dt_c3_4__anproj_1,dt_c4_4__anproj_1,e2_4__anproj_1])],[dh_c7_4__anproj_1,e5_4__anproj_1]), [interesting(0.8),file(anproj_1,c7_4__anproj_1),[file(anproj_1,c7_4__anproj_1)]]). fof(dh_c8_4__anproj_1,definition, ( ? [A] : ( m1_subset_1(A,k1_numbers) & k3_rlvect_1(c1_4__anproj_1,c3_4__anproj_1,c7_4__anproj_1) = k3_rlvect_1(c1_4__anproj_1,c4_4__anproj_1,A) & c7_4__anproj_1 != 0 & A != 0 ) => ( m1_subset_1(c8_4__anproj_1,k1_numbers) & k3_rlvect_1(c1_4__anproj_1,c3_4__anproj_1,c7_4__anproj_1) = k3_rlvect_1(c1_4__anproj_1,c4_4__anproj_1,c8_4__anproj_1) & c7_4__anproj_1 != 0 & c8_4__anproj_1 != 0 ) ), introduced(definition,[new_symbol(c8_4__anproj_1),file(anproj_1,c8_4__anproj_1)]), [interesting(0.8),axiom,file(anproj_1,c8_4__anproj_1)]). fof(dt_c8_4__anproj_1,plain,( m1_subset_1(c8_4__anproj_1,k1_numbers) ), inference(consider,[status(thm),assumptions([dt_c1_4__anproj_1,dt_c3_4__anproj_1,dt_c4_4__anproj_1,e2_4__anproj_1])],[dh_c7_4__anproj_1,dh_c8_4__anproj_1,e5_4__anproj_1]), [interesting(0.8),file(anproj_1,c8_4__anproj_1),[file(anproj_1,c8_4__anproj_1)]]). 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(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(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(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(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(e4_4__anproj_1,plain, ( k3_rlvect_1(c1_4__anproj_1,c2_4__anproj_1,c5_4__anproj_1) = k3_rlvect_1(c1_4__anproj_1,c3_4__anproj_1,c6_4__anproj_1) & c5_4__anproj_1 != 0 & c6_4__anproj_1 != 0 ), inference(consider,[status(thm),assumptions([dt_c1_4__anproj_1,dt_c2_4__anproj_1,dt_c3_4__anproj_1,e1_4__anproj_1])],[dh_c5_4__anproj_1,dh_c6_4__anproj_1,e3_4__anproj_1]), [interesting(0.8),file(anproj_1,e4_4__anproj_1),[file(anproj_1,e4_4__anproj_1)]]). 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(e9_4__anproj_1,plain,( k2_real_1(c6_4__anproj_1) != 0 ), inference(mizar_by,[status(thm),assumptions([dt_c1_4__anproj_1,dt_c2_4__anproj_1,dt_c3_4__anproj_1,e1_4__anproj_1])],[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,fc5_membered,fc6_membered,rc1_membered,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,rc3_rlvect_1,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_k3_rlvect_1,dt_k5_xcmplx_0,dt_c1_4__anproj_1,dt_c2_4__anproj_1,dt_c3_4__anproj_1,dt_c5_4__anproj_1,dt_c6_4__anproj_1,spc0_numerals,spc0_boole,e4_4__anproj_1,t203_xcmplx_1]), [interesting(0.8),file(anproj_1,e9_4__anproj_1),[file(anproj_1,e9_4__anproj_1)]]). 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(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(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(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(e10_4__anproj_1,plain,( k4_real_1(k2_real_1(c6_4__anproj_1),c5_4__anproj_1) != 0 ), inference(mizar_by,[status(thm),assumptions([dt_c1_4__anproj_1,dt_c2_4__anproj_1,dt_c3_4__anproj_1,e1_4__anproj_1])],[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,fc5_membered,fc6_membered,rc1_membered,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,rc3_rlvect_1,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,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_k4_xcmplx_0,dt_c1_4__anproj_1,dt_c2_4__anproj_1,dt_c3_4__anproj_1,dt_c5_4__anproj_1,dt_c6_4__anproj_1,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,e9_4__anproj_1,e4_4__anproj_1,t6_xcmplx_1,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealNeg__k4_xcmplx_0__r1_rm1]), [interesting(0.8),file(anproj_1,e10_4__anproj_1),[file(anproj_1,e10_4__anproj_1)]]). fof(e6_4__anproj_1,plain, ( k3_rlvect_1(c1_4__anproj_1,c3_4__anproj_1,c7_4__anproj_1) = k3_rlvect_1(c1_4__anproj_1,c4_4__anproj_1,c8_4__anproj_1) & c7_4__anproj_1 != 0 & c8_4__anproj_1 != 0 ), inference(consider,[status(thm),assumptions([dt_c1_4__anproj_1,dt_c3_4__anproj_1,dt_c4_4__anproj_1,e2_4__anproj_1])],[dh_c7_4__anproj_1,dh_c8_4__anproj_1,e5_4__anproj_1]), [interesting(0.8),file(anproj_1,e6_4__anproj_1),[file(anproj_1,e6_4__anproj_1)]]). fof(e11_4__anproj_1,plain,( k4_real_1(c7_4__anproj_1,k4_real_1(k2_real_1(c6_4__anproj_1),c5_4__anproj_1)) != 0 ), inference(mizar_by,[status(thm),assumptions([dt_c2_4__anproj_1,e1_4__anproj_1,dt_c1_4__anproj_1,dt_c3_4__anproj_1,dt_c4_4__anproj_1,e2_4__anproj_1])],[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,fc5_membered,fc6_membered,rc1_membered,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,rc3_rlvect_1,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,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_k4_xcmplx_0,dt_c1_4__anproj_1,dt_c3_4__anproj_1,dt_c4_4__anproj_1,dt_c5_4__anproj_1,dt_c6_4__anproj_1,dt_c7_4__anproj_1,dt_c8_4__anproj_1,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,e10_4__anproj_1,e6_4__anproj_1,t6_xcmplx_1,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealNeg__k4_xcmplx_0__r1_rm1]), [interesting(0.8),file(anproj_1,e11_4__anproj_1),[file(anproj_1,e11_4__anproj_1)]]). 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(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__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(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(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(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_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_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(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(e1_4_1__anproj_1,plain,( k3_rlvect_1(c1_4__anproj_1,c2_4__anproj_1,k4_real_1(k2_real_1(c6_4__anproj_1),c5_4__anproj_1)) = k3_rlvect_1(c1_4__anproj_1,k3_rlvect_1(c1_4__anproj_1,c3_4__anproj_1,c6_4__anproj_1),k2_real_1(c6_4__anproj_1)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_4__anproj_1,dt_c2_4__anproj_1,dt_c3_4__anproj_1,e1_4__anproj_1])],[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,fc5_membered,fc6_membered,rc1_membered,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_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,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,spc10_arithm,spc5_arithm,spc6_arithm,spc7_arithm,t1_arithm,t1_numerals,t2_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,involutiveness_k2_real_1,commutativity_k3_real_1,commutativity_k3_xcmplx_0,commutativity_k4_real_1,existence_l2_rlvect_1,existence_m1_subset_1,redefinition_k2_real_1,redefinition_k3_real_1,redefinition_k4_real_1,dt_k1_numbers,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_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_4__anproj_1,dt_c2_4__anproj_1,dt_c3_4__anproj_1,dt_c5_4__anproj_1,dt_c6_4__anproj_1,fc2_membered,rc3_rlvect_1,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_4__anproj_1,d9_rlvect_1,rqRealMult__k3_xcmplx_0__r1_r1_r1]), [interesting(0.65),file(anproj_1,e1_4_1__anproj_1),[file(anproj_1,e1_4_1__anproj_1)]]). fof(e2_4_1__anproj_1,plain,( k3_rlvect_1(c1_4__anproj_1,k3_rlvect_1(c1_4__anproj_1,c3_4__anproj_1,c6_4__anproj_1),k2_real_1(c6_4__anproj_1)) = k3_rlvect_1(c1_4__anproj_1,c3_4__anproj_1,k4_real_1(k2_real_1(c6_4__anproj_1),c6_4__anproj_1)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_4__anproj_1,dt_c2_4__anproj_1,dt_c3_4__anproj_1,e1_4__anproj_1])],[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,fc5_membered,fc6_membered,rc1_membered,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_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,spc5_arithm,spc6_arithm,spc7_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,involutiveness_k2_real_1,commutativity_k3_real_1,commutativity_k3_xcmplx_0,commutativity_k4_real_1,existence_l2_rlvect_1,existence_m1_subset_1,redefinition_k2_real_1,redefinition_k3_real_1,redefinition_k4_real_1,dt_k1_numbers,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_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_4__anproj_1,dt_c3_4__anproj_1,dt_c6_4__anproj_1,fc2_membered,rc3_rlvect_1,spc1_numerals,spc1_boole,d9_rlvect_1,rqRealMult__k3_xcmplx_0__r1_r1_r1]), [interesting(0.65),file(anproj_1,e2_4_1__anproj_1),[file(anproj_1,e2_4_1__anproj_1)]]). 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(e3_4_1__anproj_1,plain,( k3_rlvect_1(c1_4__anproj_1,c3_4__anproj_1,k4_real_1(k2_real_1(c6_4__anproj_1),c6_4__anproj_1)) = k3_rlvect_1(c1_4__anproj_1,c3_4__anproj_1,1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_4__anproj_1,dt_c2_4__anproj_1,dt_c3_4__anproj_1,e1_4__anproj_1])],[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,fc5_membered,fc6_membered,rc1_membered,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,rc3_rlvect_1,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,involutiveness_k2_real_1,commutativity_k3_xcmplx_0,commutativity_k4_real_1,involutiveness_k5_xcmplx_0,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_xcmplx_0,dt_c1_4__anproj_1,dt_c2_4__anproj_1,dt_c3_4__anproj_1,dt_c5_4__anproj_1,dt_c6_4__anproj_1,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,spc10_arithm,spc7_arithm,t2_arithm,t3_arithm,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e4_4__anproj_1,d7_xcmplx_0,rqRealMult__k3_xcmplx_0__r1_r1_r1]), [interesting(0.65),file(anproj_1,e3_4_1__anproj_1),[file(anproj_1,e3_4_1__anproj_1)]]). fof(e4_4_1__anproj_1,plain,( k3_rlvect_1(c1_4__anproj_1,c3_4__anproj_1,1) = c3_4__anproj_1 ), inference(mizar_by,[status(thm),assumptions([dt_c1_4__anproj_1,dt_c3_4__anproj_1])],[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,fc5_membered,fc6_membered,rc1_membered,rc4_struct_0,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_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,rqRealMult__k3_xcmplx_0__r1_r1_r1,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k3_real_1,commutativity_k4_real_1,existence_l2_rlvect_1,existence_m1_subset_1,redefinition_k3_real_1,redefinition_k4_real_1,dt_k1_numbers,dt_k2_rlvect_1,dt_k3_real_1,dt_k3_rlvect_1,dt_k4_real_1,dt_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_4__anproj_1,dt_c3_4__anproj_1,fc2_membered,rc3_rlvect_1,spc1_numerals,spc1_boole,d9_rlvect_1]), [interesting(0.65),file(anproj_1,e4_4_1__anproj_1),[file(anproj_1,e4_4_1__anproj_1)]]). fof(e7_4__anproj_1,plain,( k3_rlvect_1(c1_4__anproj_1,c2_4__anproj_1,k4_real_1(k2_real_1(c6_4__anproj_1),c5_4__anproj_1)) = c3_4__anproj_1 ), inference(iterative_eq,[status(thm),assumptions([dt_c2_4__anproj_1,e1_4__anproj_1,dt_c1_4__anproj_1,dt_c3_4__anproj_1])],[e1_4_1__anproj_1,e2_4_1__anproj_1,e3_4_1__anproj_1,e4_4_1__anproj_1]), [interesting(0.8),file(anproj_1,e7_4__anproj_1),[file(anproj_1,e7_4__anproj_1)]]). fof(e8_4__anproj_1,plain,( k3_rlvect_1(c1_4__anproj_1,c4_4__anproj_1,c8_4__anproj_1) = k3_rlvect_1(c1_4__anproj_1,c2_4__anproj_1,k4_real_1(c7_4__anproj_1,k4_real_1(k2_real_1(c6_4__anproj_1),c5_4__anproj_1))) ), inference(mizar_by,[status(thm),assumptions([dt_c2_4__anproj_1,e1_4__anproj_1,dt_c1_4__anproj_1,dt_c3_4__anproj_1,dt_c4_4__anproj_1,e2_4__anproj_1])],[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,fc5_membered,fc6_membered,rc1_membered,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_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,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,spc10_arithm,spc5_arithm,spc6_arithm,spc7_arithm,t1_arithm,t1_numerals,t2_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,involutiveness_k2_real_1,commutativity_k3_real_1,commutativity_k3_xcmplx_0,commutativity_k4_real_1,existence_l2_rlvect_1,existence_m1_subset_1,redefinition_k2_real_1,redefinition_k3_real_1,redefinition_k4_real_1,dt_k1_numbers,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_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_4__anproj_1,dt_c2_4__anproj_1,dt_c3_4__anproj_1,dt_c4_4__anproj_1,dt_c5_4__anproj_1,dt_c6_4__anproj_1,dt_c7_4__anproj_1,dt_c8_4__anproj_1,fc2_membered,rc3_rlvect_1,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,e7_4__anproj_1,e6_4__anproj_1,d9_rlvect_1,rqRealMult__k3_xcmplx_0__r1_r1_r1]), [interesting(0.8),file(anproj_1,e8_4__anproj_1),[file(anproj_1,e8_4__anproj_1)]]). fof(e12_4__anproj_1,plain,( r1_anproj_1(c1_4__anproj_1,c2_4__anproj_1,c4_4__anproj_1) ), inference(mizar_by,[status(thm),assumptions([dt_c2_4__anproj_1,e1_4__anproj_1,dt_c1_4__anproj_1,dt_c3_4__anproj_1,dt_c4_4__anproj_1,e2_4__anproj_1])],[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,fc5_membered,fc6_membered,rc1_membered,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_c1_4__anproj_1,dt_c2_4__anproj_1,dt_c3_4__anproj_1,dt_c4_4__anproj_1,dt_c5_4__anproj_1,dt_c6_4__anproj_1,dt_c7_4__anproj_1,dt_c8_4__anproj_1,fc2_membered,rc3_rlvect_1,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,e11_4__anproj_1,e6_4__anproj_1,e8_4__anproj_1,d2_anproj_1,rqRealMult__k3_xcmplx_0__r1_r1_r1]), [interesting(0.8),file(anproj_1,e12_4__anproj_1),[file(anproj_1,e12_4__anproj_1)]]). fof(i6_4__anproj_1,theorem,( $true ), introduced(tautology,[file(anproj_1,i6_4__anproj_1)]), [interesting(0.8),trivial,file(anproj_1,i6_4__anproj_1)]). fof(i5_4__anproj_1,plain,( r1_anproj_1(c1_4__anproj_1,c2_4__anproj_1,c4_4__anproj_1) ), inference(conclusion,[status(thm),assumptions([dt_c2_4__anproj_1,e1_4__anproj_1,dt_c1_4__anproj_1,dt_c3_4__anproj_1,dt_c4_4__anproj_1,e2_4__anproj_1])],[e12_4__anproj_1,i6_4__anproj_1]), [interesting(0.8),file(anproj_1,i5_4__anproj_1),[file(anproj_1,i5_4__anproj_1)]]). fof(i4_4__anproj_1,plain, ( ( r1_anproj_1(c1_4__anproj_1,c2_4__anproj_1,c3_4__anproj_1) & r1_anproj_1(c1_4__anproj_1,c3_4__anproj_1,c4_4__anproj_1) ) => r1_anproj_1(c1_4__anproj_1,c2_4__anproj_1,c4_4__anproj_1) ), inference(discharge_asm,[status(thm),assumptions([dt_c2_4__anproj_1,dt_c1_4__anproj_1,dt_c3_4__anproj_1,dt_c4_4__anproj_1]),discharge_asm(discharge,[e1_4__anproj_1,e2_4__anproj_1])],[e1_4__anproj_1,e2_4__anproj_1,i5_4__anproj_1]), [interesting(0.8),file(anproj_1,i4_4__anproj_1),[file(anproj_1,i4_4__anproj_1)]]). fof(i4_4_tmp__anproj_1,plain, ( m1_subset_1(c4_4__anproj_1,u1_struct_0(c1_4__anproj_1)) => ( ( r1_anproj_1(c1_4__anproj_1,c2_4__anproj_1,c3_4__anproj_1) & r1_anproj_1(c1_4__anproj_1,c3_4__anproj_1,c4_4__anproj_1) ) => r1_anproj_1(c1_4__anproj_1,c2_4__anproj_1,c4_4__anproj_1) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c2_4__anproj_1,dt_c1_4__anproj_1,dt_c3_4__anproj_1]),discharge_asm(discharge,[dt_c4_4__anproj_1])],[dt_c4_4__anproj_1,i4_4__anproj_1]), [interesting(0.8),i3_4__anproj_1]). fof(i3_4__anproj_1,plain,( ! [A] : ( m1_subset_1(A,u1_struct_0(c1_4__anproj_1)) => ( ( r1_anproj_1(c1_4__anproj_1,c2_4__anproj_1,c3_4__anproj_1) & r1_anproj_1(c1_4__anproj_1,c3_4__anproj_1,A) ) => r1_anproj_1(c1_4__anproj_1,c2_4__anproj_1,A) ) ) ), inference(let,[status(thm),assumptions([dt_c2_4__anproj_1,dt_c1_4__anproj_1,dt_c3_4__anproj_1])],[i4_4_tmp__anproj_1,dh_c4_4__anproj_1]), [interesting(0.8),file(anproj_1,i3_4__anproj_1),[file(anproj_1,i3_4__anproj_1)]]). fof(i3_4_tmp__anproj_1,plain, ( m1_subset_1(c3_4__anproj_1,u1_struct_0(c1_4__anproj_1)) => ! [A] : ( m1_subset_1(A,u1_struct_0(c1_4__anproj_1)) => ( ( r1_anproj_1(c1_4__anproj_1,c2_4__anproj_1,c3_4__anproj_1) & r1_anproj_1(c1_4__anproj_1,c3_4__anproj_1,A) ) => r1_anproj_1(c1_4__anproj_1,c2_4__anproj_1,A) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c2_4__anproj_1,dt_c1_4__anproj_1]),discharge_asm(discharge,[dt_c3_4__anproj_1])],[dt_c3_4__anproj_1,i3_4__anproj_1]), [interesting(0.8),i2_4__anproj_1]). fof(i2_4__anproj_1,plain,( ! [A] : ( m1_subset_1(A,u1_struct_0(c1_4__anproj_1)) => ! [B] : ( m1_subset_1(B,u1_struct_0(c1_4__anproj_1)) => ( ( r1_anproj_1(c1_4__anproj_1,c2_4__anproj_1,A) & r1_anproj_1(c1_4__anproj_1,A,B) ) => r1_anproj_1(c1_4__anproj_1,c2_4__anproj_1,B) ) ) ) ), inference(let,[status(thm),assumptions([dt_c2_4__anproj_1,dt_c1_4__anproj_1])],[i3_4_tmp__anproj_1,dh_c3_4__anproj_1]), [interesting(0.8),file(anproj_1,i2_4__anproj_1),[file(anproj_1,i2_4__anproj_1)]]). fof(i2_4_tmp__anproj_1,plain, ( m1_subset_1(c2_4__anproj_1,u1_struct_0(c1_4__anproj_1)) => ! [A] : ( m1_subset_1(A,u1_struct_0(c1_4__anproj_1)) => ! [B] : ( m1_subset_1(B,u1_struct_0(c1_4__anproj_1)) => ( ( r1_anproj_1(c1_4__anproj_1,c2_4__anproj_1,A) & r1_anproj_1(c1_4__anproj_1,A,B) ) => r1_anproj_1(c1_4__anproj_1,c2_4__anproj_1,B) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_4__anproj_1]),discharge_asm(discharge,[dt_c2_4__anproj_1])],[dt_c2_4__anproj_1,i2_4__anproj_1]), [interesting(0.8),i1_4__anproj_1]). fof(i1_4__anproj_1,plain,( ! [A] : ( m1_subset_1(A,u1_struct_0(c1_4__anproj_1)) => ! [B] : ( m1_subset_1(B,u1_struct_0(c1_4__anproj_1)) => ! [C] : ( m1_subset_1(C,u1_struct_0(c1_4__anproj_1)) => ( ( r1_anproj_1(c1_4__anproj_1,A,B) & r1_anproj_1(c1_4__anproj_1,B,C) ) => r1_anproj_1(c1_4__anproj_1,A,C) ) ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_4__anproj_1])],[i2_4_tmp__anproj_1,dh_c2_4__anproj_1]), [interesting(0.8),file(anproj_1,i1_4__anproj_1),[file(anproj_1,i1_4__anproj_1)]]). fof(i1_4_tmp__anproj_1,plain, ( ( ~ v3_struct_0(c1_4__anproj_1) & v3_rlvect_1(c1_4__anproj_1) & v4_rlvect_1(c1_4__anproj_1) & v5_rlvect_1(c1_4__anproj_1) & v6_rlvect_1(c1_4__anproj_1) & v7_rlvect_1(c1_4__anproj_1) & l2_rlvect_1(c1_4__anproj_1) ) => ! [A] : ( m1_subset_1(A,u1_struct_0(c1_4__anproj_1)) => ! [B] : ( m1_subset_1(B,u1_struct_0(c1_4__anproj_1)) => ! [C] : ( m1_subset_1(C,u1_struct_0(c1_4__anproj_1)) => ( ( r1_anproj_1(c1_4__anproj_1,A,B) & r1_anproj_1(c1_4__anproj_1,B,C) ) => r1_anproj_1(c1_4__anproj_1,A,C) ) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_4__anproj_1])],[dt_c1_4__anproj_1,i1_4__anproj_1]), [interesting(1),t6_anproj_1]). fof(t6_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,C,D) ) => r1_anproj_1(A,B,D) ) ) ) ) ) ), inference(let,[status(thm),assumptions([])],[i1_4_tmp__anproj_1,dh_c1_4__anproj_1]), [interesting(1),file(anproj_1,t6_anproj_1),[file(anproj_1,t6_anproj_1)]]).