% Mizar ND problem: t1_msafree,msafree,40,51 fof(dh_c1_1__msafree,definition, ( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,c1_1__msafree,k3_finseq_2(A)) & m2_relset_1(B,c1_1__msafree,k3_finseq_2(A)) ) => ! [C] : ( m1_pboole(C,A) => ! [D] : ( m2_finseq_2(D,A,k3_finseq_2(A)) => ! [E] : ( ( r2_hidden(E,c1_1__msafree) & D = k1_funct_1(B,E) ) => k1_funct_1(k7_pboole(c1_1__msafree,k3_finseq_2(A),B,k6_pboole(A,C)),E) = k4_card_3(k5_relat_1(D,C)) ) ) ) ) ) => ! [F,G] : ( ~ v1_xboole_0(G) => ! [H] : ( ( v1_funct_1(H) & v1_funct_2(H,F,k3_finseq_2(G)) & m2_relset_1(H,F,k3_finseq_2(G)) ) => ! [I] : ( m1_pboole(I,G) => ! [J] : ( m2_finseq_2(J,G,k3_finseq_2(G)) => ! [K] : ( ( r2_hidden(K,F) & J = k1_funct_1(H,K) ) => k1_funct_1(k7_pboole(F,k3_finseq_2(G),H,k6_pboole(G,I)),K) = k4_card_3(k5_relat_1(J,I)) ) ) ) ) ) ), introduced(definition,[new_symbol(c1_1__msafree),file(msafree,c1_1__msafree)]), [interesting(0.8),axiom,file(msafree,c1_1__msafree)]). fof(dh_c2_1__msafree,definition, ( ( ~ v1_xboole_0(c2_1__msafree) => ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,c1_1__msafree,k3_finseq_2(c2_1__msafree)) & m2_relset_1(A,c1_1__msafree,k3_finseq_2(c2_1__msafree)) ) => ! [B] : ( m1_pboole(B,c2_1__msafree) => ! [C] : ( m2_finseq_2(C,c2_1__msafree,k3_finseq_2(c2_1__msafree)) => ! [D] : ( ( r2_hidden(D,c1_1__msafree) & C = k1_funct_1(A,D) ) => k1_funct_1(k7_pboole(c1_1__msafree,k3_finseq_2(c2_1__msafree),A,k6_pboole(c2_1__msafree,B)),D) = k4_card_3(k5_relat_1(C,B)) ) ) ) ) ) => ! [E] : ( ~ v1_xboole_0(E) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,c1_1__msafree,k3_finseq_2(E)) & m2_relset_1(F,c1_1__msafree,k3_finseq_2(E)) ) => ! [G] : ( m1_pboole(G,E) => ! [H] : ( m2_finseq_2(H,E,k3_finseq_2(E)) => ! [I] : ( ( r2_hidden(I,c1_1__msafree) & H = k1_funct_1(F,I) ) => k1_funct_1(k7_pboole(c1_1__msafree,k3_finseq_2(E),F,k6_pboole(E,G)),I) = k4_card_3(k5_relat_1(H,G)) ) ) ) ) ) ), introduced(definition,[new_symbol(c2_1__msafree),file(msafree,c2_1__msafree)]), [interesting(0.8),axiom,file(msafree,c2_1__msafree)]). fof(dh_c3_1__msafree,definition, ( ( ( v1_funct_1(c3_1__msafree) & v1_funct_2(c3_1__msafree,c1_1__msafree,k3_finseq_2(c2_1__msafree)) & m2_relset_1(c3_1__msafree,c1_1__msafree,k3_finseq_2(c2_1__msafree)) ) => ! [A] : ( m1_pboole(A,c2_1__msafree) => ! [B] : ( m2_finseq_2(B,c2_1__msafree,k3_finseq_2(c2_1__msafree)) => ! [C] : ( ( r2_hidden(C,c1_1__msafree) & B = k1_funct_1(c3_1__msafree,C) ) => k1_funct_1(k7_pboole(c1_1__msafree,k3_finseq_2(c2_1__msafree),c3_1__msafree,k6_pboole(c2_1__msafree,A)),C) = k4_card_3(k5_relat_1(B,A)) ) ) ) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,c1_1__msafree,k3_finseq_2(c2_1__msafree)) & m2_relset_1(D,c1_1__msafree,k3_finseq_2(c2_1__msafree)) ) => ! [E] : ( m1_pboole(E,c2_1__msafree) => ! [F] : ( m2_finseq_2(F,c2_1__msafree,k3_finseq_2(c2_1__msafree)) => ! [G] : ( ( r2_hidden(G,c1_1__msafree) & F = k1_funct_1(D,G) ) => k1_funct_1(k7_pboole(c1_1__msafree,k3_finseq_2(c2_1__msafree),D,k6_pboole(c2_1__msafree,E)),G) = k4_card_3(k5_relat_1(F,E)) ) ) ) ) ), introduced(definition,[new_symbol(c3_1__msafree),file(msafree,c3_1__msafree)]), [interesting(0.8),axiom,file(msafree,c3_1__msafree)]). fof(dh_c4_1__msafree,definition, ( ( m1_pboole(c4_1__msafree,c2_1__msafree) => ! [A] : ( m2_finseq_2(A,c2_1__msafree,k3_finseq_2(c2_1__msafree)) => ! [B] : ( ( r2_hidden(B,c1_1__msafree) & A = k1_funct_1(c3_1__msafree,B) ) => k1_funct_1(k7_pboole(c1_1__msafree,k3_finseq_2(c2_1__msafree),c3_1__msafree,k6_pboole(c2_1__msafree,c4_1__msafree)),B) = k4_card_3(k5_relat_1(A,c4_1__msafree)) ) ) ) => ! [C] : ( m1_pboole(C,c2_1__msafree) => ! [D] : ( m2_finseq_2(D,c2_1__msafree,k3_finseq_2(c2_1__msafree)) => ! [E] : ( ( r2_hidden(E,c1_1__msafree) & D = k1_funct_1(c3_1__msafree,E) ) => k1_funct_1(k7_pboole(c1_1__msafree,k3_finseq_2(c2_1__msafree),c3_1__msafree,k6_pboole(c2_1__msafree,C)),E) = k4_card_3(k5_relat_1(D,C)) ) ) ) ), introduced(definition,[new_symbol(c4_1__msafree),file(msafree,c4_1__msafree)]), [interesting(0.8),axiom,file(msafree,c4_1__msafree)]). fof(dh_c5_1__msafree,definition, ( ( m2_finseq_2(c5_1__msafree,c2_1__msafree,k3_finseq_2(c2_1__msafree)) => ! [A] : ( ( r2_hidden(A,c1_1__msafree) & c5_1__msafree = k1_funct_1(c3_1__msafree,A) ) => k1_funct_1(k7_pboole(c1_1__msafree,k3_finseq_2(c2_1__msafree),c3_1__msafree,k6_pboole(c2_1__msafree,c4_1__msafree)),A) = k4_card_3(k5_relat_1(c5_1__msafree,c4_1__msafree)) ) ) => ! [B] : ( m2_finseq_2(B,c2_1__msafree,k3_finseq_2(c2_1__msafree)) => ! [C] : ( ( r2_hidden(C,c1_1__msafree) & B = k1_funct_1(c3_1__msafree,C) ) => k1_funct_1(k7_pboole(c1_1__msafree,k3_finseq_2(c2_1__msafree),c3_1__msafree,k6_pboole(c2_1__msafree,c4_1__msafree)),C) = k4_card_3(k5_relat_1(B,c4_1__msafree)) ) ) ), introduced(definition,[new_symbol(c5_1__msafree),file(msafree,c5_1__msafree)]), [interesting(0.8),axiom,file(msafree,c5_1__msafree)]). fof(dh_c6_1__msafree,definition, ( ( ( r2_hidden(c6_1__msafree,c1_1__msafree) & c5_1__msafree = k1_funct_1(c3_1__msafree,c6_1__msafree) ) => k1_funct_1(k7_pboole(c1_1__msafree,k3_finseq_2(c2_1__msafree),c3_1__msafree,k6_pboole(c2_1__msafree,c4_1__msafree)),c6_1__msafree) = k4_card_3(k5_relat_1(c5_1__msafree,c4_1__msafree)) ) => ! [A] : ( ( r2_hidden(A,c1_1__msafree) & c5_1__msafree = k1_funct_1(c3_1__msafree,A) ) => k1_funct_1(k7_pboole(c1_1__msafree,k3_finseq_2(c2_1__msafree),c3_1__msafree,k6_pboole(c2_1__msafree,c4_1__msafree)),A) = k4_card_3(k5_relat_1(c5_1__msafree,c4_1__msafree)) ) ), introduced(definition,[new_symbol(c6_1__msafree),file(msafree,c6_1__msafree)]), [interesting(0.8),axiom,file(msafree,c6_1__msafree)]). fof(cc1_arytm_3,theorem,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_ordinal1(B) & v2_ordinal1(B) & v3_ordinal1(B) ) ) ) ), file(arytm_3,cc1_arytm_3), [interesting(0.9),axiom,file(arytm_3,cc1_arytm_3)]). fof(cc2_arytm_3,theorem,( ! [A] : ( ( v1_xboole_0(A) & v3_ordinal1(A) ) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ) ), file(arytm_3,cc2_arytm_3), [interesting(0.9),axiom,file(arytm_3,cc2_arytm_3)]). fof(rc1_arytm_3,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ), file(arytm_3,rc1_arytm_3), [interesting(0.9),axiom,file(arytm_3,rc1_arytm_3)]). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), [interesting(0.9),axiom,file(numbers,k1_numbers)]). fof(dt_k5_ordinal2,axiom,( $true ), file(ordinal2,k5_ordinal2), [interesting(0.9),axiom,file(ordinal2,k5_ordinal2)]). fof(cc3_arytm_3,theorem,( ! [A] : ( m1_subset_1(A,k5_ordinal2) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ) ), file(arytm_3,cc3_arytm_3), [interesting(0.9),axiom,file(arytm_3,cc3_arytm_3)]). 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(fc1_ordinal2,theorem, ( v1_ordinal1(k5_ordinal2) & v2_ordinal1(k5_ordinal2) & v3_ordinal1(k5_ordinal2) & ~ v1_xboole_0(k5_ordinal2) ), file(ordinal2,fc1_ordinal2), [interesting(0.9),axiom,file(ordinal2,fc1_ordinal2)]). 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(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(rc2_finseq_1,theorem,( ! [A] : ? [B] : ( m1_relset_1(B,k5_numbers,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc2_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc2_finseq_1)]). fof(rc3_finseq_1,theorem,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc3_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc3_finseq_1)]). fof(rc4_finseq_1,theorem,( ! [A] : ? [B] : ( m1_finseq_1(B,A) & v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc4_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc4_finseq_1)]). fof(rc6_finseq_1,theorem,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc6_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc6_finseq_1)]). fof(rc7_finseq_1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc7_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc7_finseq_1)]). fof(rc8_finseq_1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc8_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc8_finseq_1)]). fof(redefinition_k5_numbers,definition,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), [interesting(0.9),axiom,file(numbers,k5_numbers)]). fof(dt_k5_numbers,axiom,( m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ), file(numbers,k5_numbers), [interesting(0.9),axiom,file(numbers,k5_numbers)]). fof(dt_m1_finseq_1,axiom,( ! [A,B] : ( m1_finseq_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) ) ), file(finseq_1,m1_finseq_1), [interesting(0.9),axiom,file(finseq_1,m1_finseq_1)]). fof(cc1_finseq_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ) ), file(finseq_1,cc1_finseq_1), [interesting(0.9),axiom,file(finseq_1,cc1_finseq_1)]). 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(rc1_finseq_1,theorem,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc1_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc1_finseq_1)]). fof(redefinition_m2_finseq_1,definition,( ! [A,B] : ( m2_finseq_1(B,A) <=> m1_finseq_1(B,A) ) ), file(finseq_1,m2_finseq_1), [interesting(0.9),axiom,file(finseq_1,m2_finseq_1)]). 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_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), [interesting(0.9),axiom,file(zfmisc_1,k2_zfmisc_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_m2_finseq_1,axiom,( ! [A,B] : ( m2_finseq_1(B,A) => ( v1_funct_1(B) & v1_finseq_1(B) & m2_relset_1(B,k5_numbers,A) ) ) ), file(finseq_1,m2_finseq_1), [interesting(0.9),axiom,file(finseq_1,m2_finseq_1)]). fof(cc10_membered,theorem,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,A) => v1_xcmplx_0(B) ) ) ), file(membered,cc10_membered), [interesting(0.9),axiom,file(membered,cc10_membered)]). fof(cc11_membered,theorem,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) ) ) ) ), file(membered,cc11_membered), [interesting(0.9),axiom,file(membered,cc11_membered)]). fof(cc12_membered,theorem,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_rat_1(B) ) ) ) ), file(membered,cc12_membered), [interesting(0.9),axiom,file(membered,cc12_membered)]). fof(cc13_membered,theorem,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc13_membered), [interesting(0.9),axiom,file(membered,cc13_membered)]). fof(cc14_membered,theorem,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v4_ordinal2(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc14_membered), [interesting(0.9),axiom,file(membered,cc14_membered)]). fof(cc16_membered,theorem,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_membered(B) ) ) ), file(membered,cc16_membered), [interesting(0.9),axiom,file(membered,cc16_membered)]). fof(cc17_membered,theorem,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) ) ) ) ), file(membered,cc17_membered), [interesting(0.9),axiom,file(membered,cc17_membered)]). fof(cc18_membered,theorem,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) ) ) ) ), file(membered,cc18_membered), [interesting(0.9),axiom,file(membered,cc18_membered)]). fof(cc19_membered,theorem,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) ) ) ) ), file(membered,cc19_membered), [interesting(0.9),axiom,file(membered,cc19_membered)]). fof(cc1_dtconstr,theorem,( ! [A,B] : ( m1_subset_1(B,k3_finseq_2(A)) => v1_finseq_1(B) ) ), file(dtconstr,cc1_dtconstr), [interesting(0.9),axiom,file(dtconstr,cc1_dtconstr)]). fof(cc1_fraenkel,theorem,( ! [A] : ( v1_fraenkel(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ) ), file(fraenkel,cc1_fraenkel), [interesting(0.9),axiom,file(fraenkel,cc1_fraenkel)]). fof(cc1_membered,theorem,( ! [A] : ( v5_membered(A) => v4_membered(A) ) ), file(membered,cc1_membered), [interesting(0.9),axiom,file(membered,cc1_membered)]). fof(cc1_relset_1,theorem,( ! [A,B,C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => v1_relat_1(C) ) ), file(relset_1,cc1_relset_1), [interesting(0.9),axiom,file(relset_1,cc1_relset_1)]). fof(cc20_membered,theorem,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) ) ) ) ), file(membered,cc20_membered), [interesting(0.9),axiom,file(membered,cc20_membered)]). fof(cc2_membered,theorem,( ! [A] : ( v4_membered(A) => v3_membered(A) ) ), file(membered,cc2_membered), [interesting(0.9),axiom,file(membered,cc2_membered)]). fof(cc3_membered,theorem,( ! [A] : ( v3_membered(A) => v2_membered(A) ) ), file(membered,cc3_membered), [interesting(0.9),axiom,file(membered,cc3_membered)]). fof(cc4_membered,theorem,( ! [A] : ( v2_membered(A) => v1_membered(A) ) ), file(membered,cc4_membered), [interesting(0.9),axiom,file(membered,cc4_membered)]). fof(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(fc4_subset_1,theorem,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ), file(subset_1,fc4_subset_1), [interesting(0.9),axiom,file(subset_1,fc4_subset_1)]). fof(rc1_fraenkel,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_fraenkel(A) ) ), file(fraenkel,rc1_fraenkel), [interesting(0.9),axiom,file(fraenkel,rc1_fraenkel)]). fof(rc1_membered,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ), file(membered,rc1_membered), [interesting(0.9),axiom,file(membered,rc1_membered)]). fof(rc1_subset_1,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) ) ) ), file(subset_1,rc1_subset_1), [interesting(0.9),axiom,file(subset_1,rc1_subset_1)]). fof(rc2_subset_1,theorem,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) ) ), file(subset_1,rc2_subset_1), [interesting(0.9),axiom,file(subset_1,rc2_subset_1)]). fof(rc3_funct_1,theorem,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ), file(funct_1,rc3_funct_1), [interesting(0.9),axiom,file(funct_1,rc3_funct_1)]). fof(redefinition_m2_finseq_2,definition,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) ) => ! [C] : ( m2_finseq_2(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(finseq_2,m2_finseq_2), [interesting(0.9),axiom,file(finseq_2,m2_finseq_2)]). fof(redefinition_m2_relset_1,definition,( ! [A,B,C] : ( m2_relset_1(C,A,B) <=> m1_relset_1(C,A,B) ) ), file(relset_1,m2_relset_1), [interesting(0.9),axiom,file(relset_1,m2_relset_1)]). fof(dt_k13_finseq_1,axiom,( $true ), file(finseq_1,k13_finseq_1), [interesting(0.9),axiom,file(finseq_1,k13_finseq_1)]). fof(dt_m1_finseq_2,axiom,( $true ), file(finseq_2,m1_finseq_2), [interesting(0.9),axiom,file(finseq_2,m1_finseq_2)]). fof(dt_m1_pboole,axiom,( ! [A,B] : ( m1_pboole(B,A) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ), file(pboole,m1_pboole), [interesting(0.9),axiom,file(pboole,m1_pboole)]). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), [interesting(0.9),axiom,file(relset_1,m1_relset_1)]). fof(dt_m2_finseq_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) ) => ! [C] : ( m2_finseq_2(C,A,B) => m2_finseq_1(C,A) ) ) ), file(finseq_2,m2_finseq_2), [interesting(0.9),axiom,file(finseq_2,m2_finseq_2)]). fof(dt_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ), file(relset_1,m2_relset_1), [interesting(0.9),axiom,file(relset_1,m2_relset_1)]). fof(cc15_membered,theorem,( ! [A] : ( v1_xboole_0(A) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc15_membered), [interesting(0.9),axiom,file(membered,cc15_membered)]). fof(cc1_funct_1,theorem,( ! [A] : ( v1_xboole_0(A) => v1_funct_1(A) ) ), file(funct_1,cc1_funct_1), [interesting(0.9),axiom,file(funct_1,cc1_funct_1)]). fof(cc2_funct_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ) ), file(funct_1,cc2_funct_1), [interesting(0.9),axiom,file(funct_1,cc2_funct_1)]). fof(fc16_finseq_1,theorem,( ! [A] : ( ~ v1_xboole_0(k13_finseq_1(A)) & v1_fraenkel(k13_finseq_1(A)) ) ), file(finseq_1,fc16_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc16_finseq_1)]). fof(fc1_funct_1,theorem,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => ( v1_relat_1(k5_relat_1(A,B)) & v1_funct_1(k5_relat_1(A,B)) ) ) ), file(funct_1,fc1_funct_1), [interesting(0.9),axiom,file(funct_1,fc1_funct_1)]). fof(fc9_finseq_1,theorem,( ! [A] : ~ v1_xboole_0(k13_finseq_1(A)) ), file(finseq_1,fc9_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc9_finseq_1)]). fof(rc1_funct_1,theorem,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc1_funct_1), [interesting(0.9),axiom,file(funct_1,rc1_funct_1)]). fof(rc1_xboole_0,theorem,( ? [A] : v1_xboole_0(A) ), file(xboole_0,rc1_xboole_0), [interesting(0.9),axiom,file(xboole_0,rc1_xboole_0)]). fof(rc2_funct_1,theorem,( ? [A] : ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) ), file(funct_1,rc2_funct_1), [interesting(0.9),axiom,file(funct_1,rc2_funct_1)]). fof(rc2_xboole_0,theorem,( ? [A] : ~ v1_xboole_0(A) ), file(xboole_0,rc2_xboole_0), [interesting(0.9),axiom,file(xboole_0,rc2_xboole_0)]). fof(antisymmetry_r2_hidden,theorem,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), [interesting(0.9),axiom,file(hidden,r2_hidden)]). fof(redefinition_k3_finseq_2,definition,( ! [A] : k3_finseq_2(A) = k13_finseq_1(A) ), file(finseq_2,k3_finseq_2), [interesting(0.9),axiom,file(finseq_2,k3_finseq_2)]). fof(redefinition_k7_pboole,definition,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_pboole(D,B) ) => k7_pboole(A,B,C,D) = k5_relat_1(C,D) ) ), file(pboole,k7_pboole), [interesting(0.9),axiom,file(pboole,k7_pboole)]). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), [interesting(0.9),axiom,file(funct_1,k1_funct_1)]). fof(dt_k3_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(k3_finseq_2(A)) & m1_finseq_2(k3_finseq_2(A),A) ) ), file(finseq_2,k3_finseq_2), [interesting(0.9),axiom,file(finseq_2,k3_finseq_2)]). fof(dt_k4_card_3,axiom,( $true ), file(card_3,k4_card_3), [interesting(0.9),axiom,file(card_3,k4_card_3)]). fof(dt_k5_relat_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => v1_relat_1(k5_relat_1(A,B)) ) ), file(relat_1,k5_relat_1), [interesting(0.9),axiom,file(relat_1,k5_relat_1)]). fof(dt_k6_pboole,axiom,( ! [A,B] : ( m1_pboole(B,A) => m1_pboole(k6_pboole(A,B),k3_finseq_2(A)) ) ), file(pboole,k6_pboole), [interesting(0.9),axiom,file(pboole,k6_pboole)]). fof(dt_k7_pboole,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_pboole(D,B) ) => m1_pboole(k7_pboole(A,B,C,D),A) ) ), file(pboole,k7_pboole), [interesting(0.9),axiom,file(pboole,k7_pboole)]). fof(dt_c1_1__msafree,assumption,( $true ), introduced(assumption,[file(msafree,c1_1__msafree)]), [interesting(0.8),axiom,file(msafree,c1_1__msafree)]). fof(dt_c2_1__msafree,assumption,( ~ v1_xboole_0(c2_1__msafree) ), introduced(assumption,[file(msafree,c2_1__msafree)]), [interesting(0.8),axiom,file(msafree,c2_1__msafree)]). fof(dt_c3_1__msafree,assumption, ( v1_funct_1(c3_1__msafree) & v1_funct_2(c3_1__msafree,c1_1__msafree,k3_finseq_2(c2_1__msafree)) & m2_relset_1(c3_1__msafree,c1_1__msafree,k3_finseq_2(c2_1__msafree)) ), introduced(assumption,[file(msafree,c3_1__msafree)]), [interesting(0.8),axiom,file(msafree,c3_1__msafree)]). fof(dt_c4_1__msafree,assumption,( m1_pboole(c4_1__msafree,c2_1__msafree) ), introduced(assumption,[file(msafree,c4_1__msafree)]), [interesting(0.8),axiom,file(msafree,c4_1__msafree)]). fof(dt_c5_1__msafree,assumption,( m2_finseq_2(c5_1__msafree,c2_1__msafree,k3_finseq_2(c2_1__msafree)) ), introduced(assumption,[file(msafree,c5_1__msafree)]), [interesting(0.8),axiom,file(msafree,c5_1__msafree)]). fof(dt_c6_1__msafree,assumption,( $true ), introduced(assumption,[file(msafree,c6_1__msafree)]), [interesting(0.8),axiom,file(msafree,c6_1__msafree)]). fof(e1_1__msafree,assumption, ( r2_hidden(c6_1__msafree,c1_1__msafree) & c5_1__msafree = k1_funct_1(c3_1__msafree,c6_1__msafree) ), introduced(assumption,[file(msafree,e1_1__msafree)]), [interesting(0.8),axiom,file(msafree,e1_1__msafree)]). fof(cc1_pboole,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_pboole(B,A) => ( v2_relat_1(B) => ~ v3_relat_1(B) ) ) ) ), file(pboole,cc1_pboole), [interesting(0.9),axiom,file(pboole,cc1_pboole)]). fof(fc1_pboole,theorem,( ! [A,B] : ( ( v2_relat_1(B) & m1_pboole(B,A) ) => ( v1_relat_1(k6_pboole(A,B)) & v2_relat_1(k6_pboole(A,B)) & ~ v3_relat_1(k6_pboole(A,B)) & v1_funct_1(k6_pboole(A,B)) ) ) ), file(pboole,fc1_pboole), [interesting(0.9),axiom,file(pboole,fc1_pboole)]). fof(fc2_pboole,theorem,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v2_relat_1(B) & m1_pboole(B,A) & m1_subset_1(C,A) ) => ~ v1_xboole_0(k1_funct_1(B,C)) ) ), file(pboole,fc2_pboole), [interesting(0.9),axiom,file(pboole,fc2_pboole)]). fof(fc6_funct_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) ) => v1_setfam_1(k2_relat_1(A)) ) ), file(funct_1,fc6_funct_1), [interesting(0.9),axiom,file(funct_1,fc6_funct_1)]). fof(rc3_pboole,theorem,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v2_relat_1(B) & v1_funct_1(B) ) ), file(pboole,rc3_pboole), [interesting(0.9),axiom,file(pboole,rc3_pboole)]). fof(rc5_funct_1,theorem,( ? [A] : ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc5_funct_1), [interesting(0.9),axiom,file(funct_1,rc5_funct_1)]). fof(existence_m1_finseq_1,axiom,( ! [A] : ? [B] : m1_finseq_1(B,A) ), file(finseq_1,m1_finseq_1), [interesting(0.9),axiom,file(finseq_1,m1_finseq_1)]). fof(cc2_pboole,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_pboole(B,A) => ( v3_relat_1(B) => ~ v2_relat_1(B) ) ) ) ), file(pboole,cc2_pboole), [interesting(0.9),axiom,file(pboole,cc2_pboole)]). fof(fc11_finseq_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_finset_1(A) ) => v1_finset_1(k2_relat_1(A)) ) ), file(finseq_1,fc11_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc11_finseq_1)]). fof(fc17_finseq_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) => v1_finset_1(k1_relat_1(A)) ) ), file(finseq_1,fc17_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc17_finseq_1)]). fof(rc1_pboole,theorem,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A) ) ), file(pboole,rc1_pboole), [interesting(0.9),axiom,file(pboole,rc1_pboole)]). fof(rc2_pboole,theorem,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v3_relat_1(B) & v1_funct_1(B) ) ), file(pboole,rc2_pboole), [interesting(0.9),axiom,file(pboole,rc2_pboole)]). fof(rc4_funct_1,theorem,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc4_funct_1), [interesting(0.9),axiom,file(funct_1,rc4_funct_1)]). fof(existence_m2_finseq_1,axiom,( ! [A] : ? [B] : m2_finseq_1(B,A) ), file(finseq_1,m2_finseq_1), [interesting(0.9),axiom,file(finseq_1,m2_finseq_1)]). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]). fof(fc1_xboole_0,theorem,( v1_xboole_0(k1_xboole_0) ), file(xboole_0,fc1_xboole_0), [interesting(0.9),axiom,file(xboole_0,fc1_xboole_0)]). fof(fc2_finseq_1,theorem, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) & v1_funct_1(k1_xboole_0) & v2_funct_1(k1_xboole_0) & v1_finset_1(k1_xboole_0) & v1_finseq_1(k1_xboole_0) ), file(finseq_1,fc2_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc2_finseq_1)]). 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(existence_m1_finseq_2,axiom,( ! [A] : ? [B] : m1_finseq_2(B,A) ), file(finseq_2,m1_finseq_2), [interesting(0.9),axiom,file(finseq_2,m1_finseq_2)]). fof(existence_m1_pboole,axiom,( ! [A] : ? [B] : m1_pboole(B,A) ), file(pboole,m1_pboole), [interesting(0.9),axiom,file(pboole,m1_pboole)]). fof(existence_m1_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), [interesting(0.9),axiom,file(relset_1,m1_relset_1)]). fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), [interesting(0.9),axiom,file(subset_1,m1_subset_1)]). fof(existence_m2_finseq_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) ) => ? [C] : m2_finseq_2(C,A,B) ) ), file(finseq_2,m2_finseq_2), [interesting(0.9),axiom,file(finseq_2,m2_finseq_2)]). fof(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), [interesting(0.9),axiom,file(relset_1,m2_relset_1)]). 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(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(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(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(reflexivity_r1_tarski,theorem,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), [interesting(0.9),axiom,file(tarski,r1_tarski)]). fof(redefinition_k4_relset_1,definition,( ! [A,B,C] : ( m1_relset_1(C,A,B) => k4_relset_1(A,B,C) = k1_relat_1(C) ) ), file(relset_1,k4_relset_1), [interesting(0.9),axiom,file(relset_1,k4_relset_1)]). fof(dt_k1_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), [interesting(0.9),axiom,file(relat_1,k1_relat_1)]). fof(dt_k2_relat_1,axiom,( $true ), file(relat_1,k2_relat_1), [interesting(0.9),axiom,file(relat_1,k2_relat_1)]). fof(dt_k4_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(relset_1,k4_relset_1), [interesting(0.9),axiom,file(relset_1,k4_relset_1)]). 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(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(d1_funct_2,definition,( ! [A,B,C] : ( m2_relset_1(C,A,B) => ( ( ( B = k1_xboole_0 => A = k1_xboole_0 ) => ( v1_funct_2(C,A,B) <=> A = k4_relset_1(A,B,C) ) ) & ( B = k1_xboole_0 => ( A = k1_xboole_0 | ( v1_funct_2(C,A,B) <=> C = k1_xboole_0 ) ) ) ) ) ), file(funct_2,d1_funct_2), [interesting(0.9),axiom,file(funct_2,d1_funct_2)]). fof(t12_relset_1,theorem,( ! [A,B,C] : ( m2_relset_1(C,A,B) => ( r1_tarski(k1_relat_1(C),A) & r1_tarski(k2_relat_1(C),B) ) ) ), file(relset_1,t12_relset_1), [interesting(0.9),axiom,file(relset_1,t12_relset_1)]). fof(e2_1__msafree,plain, ( k4_relset_1(c1_1__msafree,k3_finseq_2(c2_1__msafree),c3_1__msafree) = c1_1__msafree & r1_tarski(k2_relat_1(c3_1__msafree),k3_finseq_2(c2_1__msafree)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_1__msafree,dt_c2_1__msafree,dt_c3_1__msafree])],[antisymmetry_r2_hidden,cc1_fraenkel,rc1_fraenkel,t1_subset,t4_subset,t5_subset,existence_m1_finseq_2,existence_m1_relset_1,existence_m1_subset_1,dt_k13_finseq_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_finseq_2,dt_m1_relset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_dtconstr,cc1_finseq_1,cc1_funct_1,cc1_membered,cc1_relset_1,cc20_membered,cc2_funct_1,cc2_membered,cc3_membered,cc4_membered,fc11_finseq_1,fc16_finseq_1,fc17_finseq_1,fc1_subset_1,fc4_subset_1,fc9_finseq_1,rc1_finseq_1,rc1_funct_1,rc1_membered,rc1_pboole,rc1_subset_1,rc1_xboole_0,rc2_funct_1,rc2_subset_1,rc2_xboole_0,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t7_boole,t8_boole,reflexivity_r1_tarski,existence_m2_relset_1,redefinition_k3_finseq_2,redefinition_k4_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k2_relat_1,dt_k3_finseq_2,dt_k4_relset_1,dt_m2_relset_1,dt_c1_1__msafree,dt_c2_1__msafree,dt_c3_1__msafree,fc1_xboole_0,fc2_finseq_1,fc6_membered,t3_subset,t6_boole,d1_funct_2,t12_relset_1]), [interesting(0.8),file(msafree,e2_1__msafree),[file(msafree,e2_1__msafree)]]). fof(d3_pboole,definition,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( m1_pboole(B,A) <=> k1_relat_1(B) = A ) ) ), file(pboole,d3_pboole), [interesting(0.9),axiom,file(pboole,d3_pboole)]). fof(e3_1__msafree,plain,( k1_relat_1(k7_pboole(c1_1__msafree,k3_finseq_2(c2_1__msafree),c3_1__msafree,k6_pboole(c2_1__msafree,c4_1__msafree))) = k4_relset_1(c1_1__msafree,k3_finseq_2(c2_1__msafree),c3_1__msafree) ), inference(mizar_by,[status(thm),assumptions([dt_c4_1__msafree,dt_c1_1__msafree,dt_c2_1__msafree,dt_c3_1__msafree])],[cc1_pboole,fc1_pboole,fc6_funct_1,rc3_pboole,rc5_funct_1,cc2_pboole,fc11_finseq_1,fc17_finseq_1,rc1_pboole,rc2_pboole,rc3_finseq_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k2_zfmisc_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finseq_1,cc1_fraenkel,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc1_xboole_0,fc2_finseq_1,fc4_subset_1,fc6_membered,rc1_finseq_1,rc1_fraenkel,rc1_membered,rc3_funct_1,t1_subset,t4_subset,t5_subset,existence_m1_finseq_2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k13_finseq_1,dt_k1_zfmisc_1,dt_k5_relat_1,dt_m1_finseq_2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc15_membered,cc1_dtconstr,cc1_funct_1,cc2_funct_1,fc16_finseq_1,fc1_funct_1,fc1_subset_1,fc9_finseq_1,rc1_subset_1,rc1_xboole_0,rc2_funct_1,rc2_subset_1,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,reflexivity_r1_tarski,existence_m1_pboole,redefinition_k3_finseq_2,redefinition_k4_relset_1,redefinition_k7_pboole,dt_k1_relat_1,dt_k2_relat_1,dt_k3_finseq_2,dt_k4_relset_1,dt_k6_pboole,dt_k7_pboole,dt_m1_pboole,dt_c1_1__msafree,dt_c2_1__msafree,dt_c3_1__msafree,dt_c4_1__msafree,rc1_funct_1,t3_subset,e2_1__msafree,d3_pboole]), [interesting(0.8),file(msafree,e3_1__msafree),[file(msafree,e3_1__msafree)]]). fof(t22_funct_1,theorem,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(A,k1_relat_1(k5_relat_1(C,B))) => k1_funct_1(k5_relat_1(C,B),A) = k1_funct_1(B,k1_funct_1(C,A)) ) ) ) ), file(funct_1,t22_funct_1), [interesting(0.9),axiom,file(funct_1,t22_funct_1)]). fof(e1_1_1__msafree,plain,( k1_funct_1(k7_pboole(c1_1__msafree,k3_finseq_2(c2_1__msafree),c3_1__msafree,k6_pboole(c2_1__msafree,c4_1__msafree)),c6_1__msafree) = k1_funct_1(k6_pboole(c2_1__msafree,c4_1__msafree),c5_1__msafree) ), inference(mizar_by,[status(thm),assumptions([dt_c5_1__msafree,dt_c6_1__msafree,dt_c4_1__msafree,e1_1__msafree,dt_c1_1__msafree,dt_c2_1__msafree,dt_c3_1__msafree])],[cc1_arytm_3,cc2_arytm_3,rc1_arytm_3,dt_k1_numbers,dt_k5_ordinal2,cc1_pboole,cc3_arytm_3,cc6_membered,fc1_ordinal2,fc1_pboole,fc2_membered,fc2_pboole,fc5_membered,fc6_funct_1,rc3_pboole,rc5_funct_1,existence_m1_finseq_1,redefinition_k5_numbers,dt_k5_numbers,dt_m1_finseq_1,cc2_pboole,cc9_membered,fc11_finseq_1,fc17_finseq_1,rc1_pboole,rc2_finseq_1,rc2_pboole,rc3_finseq_1,rc4_finseq_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m2_finseq_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finseq_1,cc1_fraenkel,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc1_xboole_0,fc2_finseq_1,fc4_subset_1,fc6_membered,rc1_finseq_1,rc1_fraenkel,rc1_membered,rc3_funct_1,existence_m1_finseq_2,existence_m1_pboole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_2,existence_m2_relset_1,redefinition_m2_finseq_2,redefinition_m2_relset_1,dt_k13_finseq_1,dt_k1_zfmisc_1,dt_m1_finseq_2,dt_m1_pboole,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_2,dt_m2_relset_1,cc15_membered,cc1_dtconstr,cc1_funct_1,cc2_funct_1,fc16_finseq_1,fc1_subset_1,fc9_finseq_1,rc1_subset_1,rc1_xboole_0,rc2_funct_1,rc2_subset_1,rc2_xboole_0,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k3_finseq_2,redefinition_k4_relset_1,redefinition_k7_pboole,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_k3_finseq_2,dt_k4_relset_1,dt_k5_relat_1,dt_k6_pboole,dt_k7_pboole,dt_c1_1__msafree,dt_c2_1__msafree,dt_c3_1__msafree,dt_c4_1__msafree,dt_c5_1__msafree,dt_c6_1__msafree,fc1_funct_1,rc1_funct_1,t1_subset,t3_subset,t7_boole,e3_1__msafree,e1_1__msafree,e2_1__msafree,t22_funct_1]), [interesting(0.65),file(msafree,e1_1_1__msafree),[file(msafree,e1_1_1__msafree)]]). fof(d19_pboole,definition,( ! [A,B] : ( m1_pboole(B,A) => ! [C] : ( m1_pboole(C,k3_finseq_2(A)) => ( C = k6_pboole(A,B) <=> ! [D] : ( m2_finseq_2(D,A,k3_finseq_2(A)) => k1_funct_1(C,D) = k4_card_3(k5_relat_1(D,B)) ) ) ) ) ), file(pboole,d19_pboole), [interesting(0.9),axiom,file(pboole,d19_pboole)]). fof(e2_1_1__msafree,plain,( k1_funct_1(k6_pboole(c2_1__msafree,c4_1__msafree),c5_1__msafree) = k4_card_3(k5_relat_1(c5_1__msafree,c4_1__msafree)) ), inference(mizar_by,[status(thm),assumptions([dt_c2_1__msafree,dt_c4_1__msafree,dt_c5_1__msafree])],[reflexivity_r1_tarski,cc1_arytm_3,cc1_pboole,cc2_arytm_3,fc1_pboole,fc2_pboole,rc1_arytm_3,rc3_pboole,rc5_funct_1,existence_m1_relset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_m1_relset_1,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_relset_1,cc20_membered,cc2_pboole,cc3_arytm_3,cc6_membered,cc9_membered,fc1_ordinal2,fc1_subset_1,fc2_membered,fc4_subset_1,fc5_membered,rc1_pboole,rc1_subset_1,rc2_finseq_1,rc2_pboole,rc2_subset_1,rc3_finseq_1,rc4_finseq_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t3_subset,t4_subset,t5_subset,antisymmetry_r2_hidden,existence_m1_finseq_1,existence_m2_relset_1,redefinition_k5_numbers,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k5_numbers,dt_m1_finseq_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_finseq_1,cc1_fraenkel,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc1_xboole_0,fc2_finseq_1,fc6_membered,rc1_finseq_1,rc1_fraenkel,rc1_membered,rc3_funct_1,t1_subset,existence_m1_finseq_2,existence_m1_subset_1,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_m1_finseq_2,dt_m1_subset_1,dt_m2_finseq_1,cc15_membered,cc1_dtconstr,cc1_funct_1,cc2_funct_1,fc16_finseq_1,fc1_funct_1,fc9_finseq_1,rc1_funct_1,rc1_xboole_0,rc2_funct_1,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_pboole,existence_m2_finseq_2,redefinition_k3_finseq_2,redefinition_m2_finseq_2,dt_k1_funct_1,dt_k3_finseq_2,dt_k4_card_3,dt_k5_relat_1,dt_k6_pboole,dt_m1_pboole,dt_m2_finseq_2,dt_c2_1__msafree,dt_c4_1__msafree,dt_c5_1__msafree,d19_pboole]), [interesting(0.65),file(msafree,e2_1_1__msafree),[file(msafree,e2_1_1__msafree)]]). fof(e4_1__msafree,plain,( k1_funct_1(k7_pboole(c1_1__msafree,k3_finseq_2(c2_1__msafree),c3_1__msafree,k6_pboole(c2_1__msafree,c4_1__msafree)),c6_1__msafree) = k4_card_3(k5_relat_1(c5_1__msafree,c4_1__msafree)) ), inference(iterative_eq,[status(thm),assumptions([dt_c6_1__msafree,e1_1__msafree,dt_c1_1__msafree,dt_c3_1__msafree,dt_c2_1__msafree,dt_c4_1__msafree,dt_c5_1__msafree])],[cc1_arytm_3,cc2_arytm_3,rc1_arytm_3,dt_k1_numbers,dt_k5_ordinal2,cc3_arytm_3,cc6_membered,fc1_ordinal2,fc2_membered,fc5_membered,rc2_finseq_1,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,redefinition_k5_numbers,dt_k5_numbers,dt_m1_finseq_1,cc1_finseq_1,cc9_membered,rc1_finseq_1,redefinition_m2_finseq_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_subset_1,dt_m2_finseq_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_dtconstr,cc1_fraenkel,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc1_subset_1,fc4_subset_1,rc1_fraenkel,rc1_membered,rc1_subset_1,rc2_subset_1,rc3_funct_1,redefinition_m2_finseq_2,redefinition_m2_relset_1,dt_k13_finseq_1,dt_m1_finseq_2,dt_m1_pboole,dt_m1_relset_1,dt_m2_finseq_2,dt_m2_relset_1,cc15_membered,cc1_funct_1,cc2_funct_1,fc16_finseq_1,fc1_funct_1,fc9_finseq_1,rc1_funct_1,rc1_xboole_0,rc2_funct_1,rc2_xboole_0,redefinition_k3_finseq_2,redefinition_k7_pboole,dt_k1_funct_1,dt_k3_finseq_2,dt_k4_card_3,dt_k5_relat_1,dt_k6_pboole,dt_k7_pboole,dt_c1_1__msafree,dt_c2_1__msafree,dt_c3_1__msafree,dt_c4_1__msafree,dt_c5_1__msafree,dt_c6_1__msafree,e1_1_1__msafree,e2_1_1__msafree]), [interesting(0.8),file(msafree,e4_1__msafree),[file(msafree,e4_1__msafree)]]). fof(i8_1__msafree,theorem,( $true ), introduced(tautology,[file(msafree,i8_1__msafree)]), [interesting(0.8),trivial,file(msafree,i8_1__msafree)]). fof(i7_1__msafree,plain,( k1_funct_1(k7_pboole(c1_1__msafree,k3_finseq_2(c2_1__msafree),c3_1__msafree,k6_pboole(c2_1__msafree,c4_1__msafree)),c6_1__msafree) = k4_card_3(k5_relat_1(c5_1__msafree,c4_1__msafree)) ), inference(conclusion,[status(thm),assumptions([dt_c6_1__msafree,e1_1__msafree,dt_c1_1__msafree,dt_c3_1__msafree,dt_c2_1__msafree,dt_c4_1__msafree,dt_c5_1__msafree])],[cc1_arytm_3,cc2_arytm_3,rc1_arytm_3,dt_k1_numbers,dt_k5_ordinal2,cc3_arytm_3,cc6_membered,fc1_ordinal2,fc2_membered,fc5_membered,rc2_finseq_1,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,redefinition_k5_numbers,dt_k5_numbers,dt_m1_finseq_1,cc1_finseq_1,cc9_membered,rc1_finseq_1,redefinition_m2_finseq_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_subset_1,dt_m2_finseq_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_dtconstr,cc1_fraenkel,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc1_subset_1,fc4_subset_1,rc1_fraenkel,rc1_membered,rc1_subset_1,rc2_subset_1,rc3_funct_1,redefinition_m2_finseq_2,redefinition_m2_relset_1,dt_k13_finseq_1,dt_m1_finseq_2,dt_m1_pboole,dt_m1_relset_1,dt_m2_finseq_2,dt_m2_relset_1,cc15_membered,cc1_funct_1,cc2_funct_1,fc16_finseq_1,fc1_funct_1,fc9_finseq_1,rc1_funct_1,rc1_xboole_0,rc2_funct_1,rc2_xboole_0,redefinition_k3_finseq_2,redefinition_k7_pboole,dt_k1_funct_1,dt_k3_finseq_2,dt_k4_card_3,dt_k5_relat_1,dt_k6_pboole,dt_k7_pboole,dt_c1_1__msafree,dt_c2_1__msafree,dt_c3_1__msafree,dt_c4_1__msafree,dt_c5_1__msafree,dt_c6_1__msafree,e4_1__msafree,i8_1__msafree]), [interesting(0.8),file(msafree,i7_1__msafree),[file(msafree,i7_1__msafree)]]). fof(i7_1_tmp__msafree,plain, ( ( r2_hidden(c6_1__msafree,c1_1__msafree) & c5_1__msafree = k1_funct_1(c3_1__msafree,c6_1__msafree) ) => k1_funct_1(k7_pboole(c1_1__msafree,k3_finseq_2(c2_1__msafree),c3_1__msafree,k6_pboole(c2_1__msafree,c4_1__msafree)),c6_1__msafree) = k4_card_3(k5_relat_1(c5_1__msafree,c4_1__msafree)) ), inference(discharge_asm,[status(thm),assumptions([dt_c6_1__msafree,dt_c1_1__msafree,dt_c3_1__msafree,dt_c2_1__msafree,dt_c4_1__msafree,dt_c5_1__msafree]),discharge_asm(discharge,[e1_1__msafree])],[e1_1__msafree,i7_1__msafree]), [interesting(0.8),i6_1__msafree]). fof(i6_1__msafree,plain, ( ( r2_hidden(c6_1__msafree,c1_1__msafree) & c5_1__msafree = k1_funct_1(c3_1__msafree,c6_1__msafree) ) => k1_funct_1(k7_pboole(c1_1__msafree,k3_finseq_2(c2_1__msafree),c3_1__msafree,k6_pboole(c2_1__msafree,c4_1__msafree)),c6_1__msafree) = k4_card_3(k5_relat_1(c5_1__msafree,c4_1__msafree)) ), inference(mizar_def_expansion,[status(thm),assumptions([dt_c6_1__msafree,dt_c1_1__msafree,dt_c3_1__msafree,dt_c2_1__msafree,dt_c4_1__msafree,dt_c5_1__msafree])],[i7_1_tmp__msafree,cc1_arytm_3,cc2_arytm_3,rc1_arytm_3,dt_k1_numbers,dt_k5_ordinal2,cc3_arytm_3,cc6_membered,fc1_ordinal2,fc2_membered,fc5_membered,rc2_finseq_1,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,redefinition_k5_numbers,dt_k5_numbers,dt_m1_finseq_1,cc1_finseq_1,cc9_membered,rc1_finseq_1,redefinition_m2_finseq_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_subset_1,dt_m2_finseq_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_dtconstr,cc1_fraenkel,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc1_subset_1,fc4_subset_1,rc1_fraenkel,rc1_membered,rc1_subset_1,rc2_subset_1,rc3_funct_1,redefinition_m2_finseq_2,redefinition_m2_relset_1,dt_k13_finseq_1,dt_m1_finseq_2,dt_m1_pboole,dt_m1_relset_1,dt_m2_finseq_2,dt_m2_relset_1,cc15_membered,cc1_funct_1,cc2_funct_1,fc16_finseq_1,fc1_funct_1,fc9_finseq_1,rc1_funct_1,rc1_xboole_0,rc2_funct_1,rc2_xboole_0,antisymmetry_r2_hidden,redefinition_k3_finseq_2,redefinition_k7_pboole,dt_k1_funct_1,dt_k3_finseq_2,dt_k4_card_3,dt_k5_relat_1,dt_k6_pboole,dt_k7_pboole,dt_c1_1__msafree,dt_c2_1__msafree,dt_c3_1__msafree,dt_c4_1__msafree,dt_c5_1__msafree,dt_c6_1__msafree]), [interesting(0.8),file(msafree,i6_1__msafree),[file(msafree,i6_1__msafree)]]). fof(i6_1_tmp__msafree,plain, ( ( r2_hidden(c6_1__msafree,c1_1__msafree) & c5_1__msafree = k1_funct_1(c3_1__msafree,c6_1__msafree) ) => k1_funct_1(k7_pboole(c1_1__msafree,k3_finseq_2(c2_1__msafree),c3_1__msafree,k6_pboole(c2_1__msafree,c4_1__msafree)),c6_1__msafree) = k4_card_3(k5_relat_1(c5_1__msafree,c4_1__msafree)) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_1__msafree,dt_c3_1__msafree,dt_c2_1__msafree,dt_c4_1__msafree,dt_c5_1__msafree]),discharge_asm(discharge,[dt_c6_1__msafree])],[dt_c6_1__msafree,i6_1__msafree]), [interesting(0.8),i5_1__msafree]). fof(i5_1__msafree,plain,( ! [A] : ( ( r2_hidden(A,c1_1__msafree) & c5_1__msafree = k1_funct_1(c3_1__msafree,A) ) => k1_funct_1(k7_pboole(c1_1__msafree,k3_finseq_2(c2_1__msafree),c3_1__msafree,k6_pboole(c2_1__msafree,c4_1__msafree)),A) = k4_card_3(k5_relat_1(c5_1__msafree,c4_1__msafree)) ) ), inference(let,[status(thm),assumptions([dt_c1_1__msafree,dt_c3_1__msafree,dt_c2_1__msafree,dt_c4_1__msafree,dt_c5_1__msafree])],[i6_1_tmp__msafree,dh_c6_1__msafree]), [interesting(0.8),file(msafree,i5_1__msafree),[file(msafree,i5_1__msafree)]]). fof(i5_1_tmp__msafree,plain, ( m2_finseq_2(c5_1__msafree,c2_1__msafree,k3_finseq_2(c2_1__msafree)) => ! [A] : ( ( r2_hidden(A,c1_1__msafree) & c5_1__msafree = k1_funct_1(c3_1__msafree,A) ) => k1_funct_1(k7_pboole(c1_1__msafree,k3_finseq_2(c2_1__msafree),c3_1__msafree,k6_pboole(c2_1__msafree,c4_1__msafree)),A) = k4_card_3(k5_relat_1(c5_1__msafree,c4_1__msafree)) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_1__msafree,dt_c3_1__msafree,dt_c2_1__msafree,dt_c4_1__msafree]),discharge_asm(discharge,[dt_c5_1__msafree])],[dt_c5_1__msafree,i5_1__msafree]), [interesting(0.8),i4_1__msafree]). fof(i4_1__msafree,plain,( ! [A] : ( m2_finseq_2(A,c2_1__msafree,k3_finseq_2(c2_1__msafree)) => ! [B] : ( ( r2_hidden(B,c1_1__msafree) & A = k1_funct_1(c3_1__msafree,B) ) => k1_funct_1(k7_pboole(c1_1__msafree,k3_finseq_2(c2_1__msafree),c3_1__msafree,k6_pboole(c2_1__msafree,c4_1__msafree)),B) = k4_card_3(k5_relat_1(A,c4_1__msafree)) ) ) ), inference(let,[status(thm),assumptions([dt_c1_1__msafree,dt_c3_1__msafree,dt_c2_1__msafree,dt_c4_1__msafree])],[i5_1_tmp__msafree,dh_c5_1__msafree]), [interesting(0.8),file(msafree,i4_1__msafree),[file(msafree,i4_1__msafree)]]). fof(i4_1_tmp__msafree,plain, ( m1_pboole(c4_1__msafree,c2_1__msafree) => ! [A] : ( m2_finseq_2(A,c2_1__msafree,k3_finseq_2(c2_1__msafree)) => ! [B] : ( ( r2_hidden(B,c1_1__msafree) & A = k1_funct_1(c3_1__msafree,B) ) => k1_funct_1(k7_pboole(c1_1__msafree,k3_finseq_2(c2_1__msafree),c3_1__msafree,k6_pboole(c2_1__msafree,c4_1__msafree)),B) = k4_card_3(k5_relat_1(A,c4_1__msafree)) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_1__msafree,dt_c3_1__msafree,dt_c2_1__msafree]),discharge_asm(discharge,[dt_c4_1__msafree])],[dt_c4_1__msafree,i4_1__msafree]), [interesting(0.8),i3_1__msafree]). fof(i3_1__msafree,plain,( ! [A] : ( m1_pboole(A,c2_1__msafree) => ! [B] : ( m2_finseq_2(B,c2_1__msafree,k3_finseq_2(c2_1__msafree)) => ! [C] : ( ( r2_hidden(C,c1_1__msafree) & B = k1_funct_1(c3_1__msafree,C) ) => k1_funct_1(k7_pboole(c1_1__msafree,k3_finseq_2(c2_1__msafree),c3_1__msafree,k6_pboole(c2_1__msafree,A)),C) = k4_card_3(k5_relat_1(B,A)) ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_1__msafree,dt_c3_1__msafree,dt_c2_1__msafree])],[i4_1_tmp__msafree,dh_c4_1__msafree]), [interesting(0.8),file(msafree,i3_1__msafree),[file(msafree,i3_1__msafree)]]). fof(i3_1_tmp__msafree,plain, ( ( v1_funct_1(c3_1__msafree) & v1_funct_2(c3_1__msafree,c1_1__msafree,k3_finseq_2(c2_1__msafree)) & m2_relset_1(c3_1__msafree,c1_1__msafree,k3_finseq_2(c2_1__msafree)) ) => ! [A] : ( m1_pboole(A,c2_1__msafree) => ! [B] : ( m2_finseq_2(B,c2_1__msafree,k3_finseq_2(c2_1__msafree)) => ! [C] : ( ( r2_hidden(C,c1_1__msafree) & B = k1_funct_1(c3_1__msafree,C) ) => k1_funct_1(k7_pboole(c1_1__msafree,k3_finseq_2(c2_1__msafree),c3_1__msafree,k6_pboole(c2_1__msafree,A)),C) = k4_card_3(k5_relat_1(B,A)) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_1__msafree,dt_c2_1__msafree]),discharge_asm(discharge,[dt_c3_1__msafree])],[dt_c3_1__msafree,i3_1__msafree]), [interesting(0.8),i2_1__msafree]). fof(i2_1__msafree,plain,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,c1_1__msafree,k3_finseq_2(c2_1__msafree)) & m2_relset_1(A,c1_1__msafree,k3_finseq_2(c2_1__msafree)) ) => ! [B] : ( m1_pboole(B,c2_1__msafree) => ! [C] : ( m2_finseq_2(C,c2_1__msafree,k3_finseq_2(c2_1__msafree)) => ! [D] : ( ( r2_hidden(D,c1_1__msafree) & C = k1_funct_1(A,D) ) => k1_funct_1(k7_pboole(c1_1__msafree,k3_finseq_2(c2_1__msafree),A,k6_pboole(c2_1__msafree,B)),D) = k4_card_3(k5_relat_1(C,B)) ) ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_1__msafree,dt_c2_1__msafree])],[i3_1_tmp__msafree,dh_c3_1__msafree]), [interesting(0.8),file(msafree,i2_1__msafree),[file(msafree,i2_1__msafree)]]). fof(i2_1_tmp__msafree,plain, ( ~ v1_xboole_0(c2_1__msafree) => ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,c1_1__msafree,k3_finseq_2(c2_1__msafree)) & m2_relset_1(A,c1_1__msafree,k3_finseq_2(c2_1__msafree)) ) => ! [B] : ( m1_pboole(B,c2_1__msafree) => ! [C] : ( m2_finseq_2(C,c2_1__msafree,k3_finseq_2(c2_1__msafree)) => ! [D] : ( ( r2_hidden(D,c1_1__msafree) & C = k1_funct_1(A,D) ) => k1_funct_1(k7_pboole(c1_1__msafree,k3_finseq_2(c2_1__msafree),A,k6_pboole(c2_1__msafree,B)),D) = k4_card_3(k5_relat_1(C,B)) ) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_1__msafree]),discharge_asm(discharge,[dt_c2_1__msafree])],[dt_c2_1__msafree,i2_1__msafree]), [interesting(0.8),i1_1__msafree]). fof(i1_1__msafree,plain,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,c1_1__msafree,k3_finseq_2(A)) & m2_relset_1(B,c1_1__msafree,k3_finseq_2(A)) ) => ! [C] : ( m1_pboole(C,A) => ! [D] : ( m2_finseq_2(D,A,k3_finseq_2(A)) => ! [E] : ( ( r2_hidden(E,c1_1__msafree) & D = k1_funct_1(B,E) ) => k1_funct_1(k7_pboole(c1_1__msafree,k3_finseq_2(A),B,k6_pboole(A,C)),E) = k4_card_3(k5_relat_1(D,C)) ) ) ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_1__msafree])],[i2_1_tmp__msafree,dh_c2_1__msafree]), [interesting(0.8),file(msafree,i1_1__msafree),[file(msafree,i1_1__msafree)]]). fof(i1_1_tmp__msafree,plain,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,c1_1__msafree,k3_finseq_2(A)) & m2_relset_1(B,c1_1__msafree,k3_finseq_2(A)) ) => ! [C] : ( m1_pboole(C,A) => ! [D] : ( m2_finseq_2(D,A,k3_finseq_2(A)) => ! [E] : ( ( r2_hidden(E,c1_1__msafree) & D = k1_funct_1(B,E) ) => k1_funct_1(k7_pboole(c1_1__msafree,k3_finseq_2(A),B,k6_pboole(A,C)),E) = k4_card_3(k5_relat_1(D,C)) ) ) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_1__msafree])],[dt_c1_1__msafree,i1_1__msafree]), [interesting(1),t1_msafree]). fof(t1_msafree,theorem,( ! [A,B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,k3_finseq_2(B)) & m2_relset_1(C,A,k3_finseq_2(B)) ) => ! [D] : ( m1_pboole(D,B) => ! [E] : ( m2_finseq_2(E,B,k3_finseq_2(B)) => ! [F] : ( ( r2_hidden(F,A) & E = k1_funct_1(C,F) ) => k1_funct_1(k7_pboole(A,k3_finseq_2(B),C,k6_pboole(B,D)),F) = k4_card_3(k5_relat_1(E,D)) ) ) ) ) ) ), inference(let,[status(thm),assumptions([])],[i1_1_tmp__msafree,dh_c1_1__msafree]), [interesting(1),file(msafree,t1_msafree),[file(msafree,t1_msafree)]]).