% Mizar ND problem: t12_borsuk_1,borsuk_1,85,54 fof(dh_c1_6__borsuk_1,definition, ( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(c1_6__borsuk_1)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( k12_mcart_1(c1_6__borsuk_1,A,B,C) != k1_xboole_0 => ( k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,A),c1_6__borsuk_1,k9_funct_3(c1_6__borsuk_1,A),k12_mcart_1(c1_6__borsuk_1,A,B,C)) = B & k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,A),A,k10_funct_3(c1_6__borsuk_1,A),k12_mcart_1(c1_6__borsuk_1,A,B,C)) = C ) ) ) ) => ! [D,E,F] : ( m1_subset_1(F,k1_zfmisc_1(D)) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(E)) => ( k12_mcart_1(D,E,F,G) != k1_xboole_0 => ( k2_funct_2(k2_zfmisc_1(D,E),D,k9_funct_3(D,E),k12_mcart_1(D,E,F,G)) = F & k2_funct_2(k2_zfmisc_1(D,E),E,k10_funct_3(D,E),k12_mcart_1(D,E,F,G)) = G ) ) ) ) ), introduced(definition,[new_symbol(c1_6__borsuk_1),file(borsuk_1,c1_6__borsuk_1)]), [interesting(0.8),axiom,file(borsuk_1,c1_6__borsuk_1)]). fof(dh_c2_6__borsuk_1,definition, ( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(c1_6__borsuk_1)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(c2_6__borsuk_1)) => ( k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,A,B) != k1_xboole_0 => ( k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c1_6__borsuk_1,k9_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,A,B)) = A & k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c2_6__borsuk_1,k10_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,A,B)) = B ) ) ) ) => ! [C,D] : ( m1_subset_1(D,k1_zfmisc_1(c1_6__borsuk_1)) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(C)) => ( k12_mcart_1(c1_6__borsuk_1,C,D,E) != k1_xboole_0 => ( k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,C),c1_6__borsuk_1,k9_funct_3(c1_6__borsuk_1,C),k12_mcart_1(c1_6__borsuk_1,C,D,E)) = D & k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,C),C,k10_funct_3(c1_6__borsuk_1,C),k12_mcart_1(c1_6__borsuk_1,C,D,E)) = E ) ) ) ) ), introduced(definition,[new_symbol(c2_6__borsuk_1),file(borsuk_1,c2_6__borsuk_1)]), [interesting(0.8),axiom,file(borsuk_1,c2_6__borsuk_1)]). fof(dh_c3_6__borsuk_1,definition, ( ( m1_subset_1(c3_6__borsuk_1,k1_zfmisc_1(c1_6__borsuk_1)) => ! [A] : ( m1_subset_1(A,k1_zfmisc_1(c2_6__borsuk_1)) => ( k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,A) != k1_xboole_0 => ( k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c1_6__borsuk_1,k9_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,A)) = c3_6__borsuk_1 & k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c2_6__borsuk_1,k10_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,A)) = A ) ) ) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(c1_6__borsuk_1)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(c2_6__borsuk_1)) => ( k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,B,C) != k1_xboole_0 => ( k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c1_6__borsuk_1,k9_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,B,C)) = B & k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c2_6__borsuk_1,k10_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,B,C)) = C ) ) ) ) ), introduced(definition,[new_symbol(c3_6__borsuk_1),file(borsuk_1,c3_6__borsuk_1)]), [interesting(0.8),axiom,file(borsuk_1,c3_6__borsuk_1)]). fof(dh_c4_6__borsuk_1,definition, ( ( m1_subset_1(c4_6__borsuk_1,k1_zfmisc_1(c2_6__borsuk_1)) => ( k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1) != k1_xboole_0 => ( k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c1_6__borsuk_1,k9_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1)) = c3_6__borsuk_1 & k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c2_6__borsuk_1,k10_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1)) = c4_6__borsuk_1 ) ) ) => ! [A] : ( m1_subset_1(A,k1_zfmisc_1(c2_6__borsuk_1)) => ( k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,A) != k1_xboole_0 => ( k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c1_6__borsuk_1,k9_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,A)) = c3_6__borsuk_1 & k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c2_6__borsuk_1,k10_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,A)) = A ) ) ) ), introduced(definition,[new_symbol(c4_6__borsuk_1),file(borsuk_1,c4_6__borsuk_1)]), [interesting(0.8),axiom,file(borsuk_1,c4_6__borsuk_1)]). fof(cc1_funct_2,theorem,( ! [A,B,C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_partfun1(C,A,B) ) => ( v1_funct_1(C) & v1_funct_2(C,A,B) ) ) ) ), file(funct_2,cc1_funct_2), [interesting(0.9),axiom,file(funct_2,cc1_funct_2)]). fof(cc2_finset_1,theorem,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_finset_1(B) ) ) ), file(finset_1,cc2_finset_1), [interesting(0.9),axiom,file(finset_1,cc2_finset_1)]). fof(fc13_finset_1,theorem,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(B) ) => v1_finset_1(k9_relat_1(A,B)) ) ), file(finset_1,fc13_finset_1), [interesting(0.9),axiom,file(finset_1,fc13_finset_1)]). fof(fc14_finset_1,theorem,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_zfmisc_1(A,B)) ) ), file(finset_1,fc14_finset_1), [interesting(0.9),axiom,file(finset_1,fc14_finset_1)]). fof(rc1_finset_1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) ) ), file(finset_1,rc1_finset_1), [interesting(0.9),axiom,file(finset_1,rc1_finset_1)]). fof(rc1_funct_2,theorem,( ! [A,B] : ? [C] : ( m1_relset_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C) & v1_funct_2(C,A,B) ) ), file(funct_2,rc1_funct_2), [interesting(0.9),axiom,file(funct_2,rc1_funct_2)]). fof(rc2_partfun1,theorem,( ! [A,B] : ? [C] : ( m1_relset_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C) ) ), file(partfun1,rc2_partfun1), [interesting(0.9),axiom,file(partfun1,rc2_partfun1)]). fof(rc3_finset_1,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc3_finset_1), [interesting(0.9),axiom,file(finset_1,rc3_finset_1)]). fof(rc4_finset_1,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc4_finset_1), [interesting(0.9),axiom,file(finset_1,rc4_finset_1)]). 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_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]). fof(dt_k7_funct_3,axiom,( ! [A,B] : ( v1_relat_1(k7_funct_3(A,B)) & v1_funct_1(k7_funct_3(A,B)) ) ), file(funct_3,k7_funct_3), [interesting(0.9),axiom,file(funct_3,k7_funct_3)]). fof(dt_k8_funct_3,axiom,( ! [A,B] : ( v1_relat_1(k8_funct_3(A,B)) & v1_funct_1(k8_funct_3(A,B)) ) ), file(funct_3,k8_funct_3), [interesting(0.9),axiom,file(funct_3,k8_funct_3)]). fof(dt_k9_relat_1,axiom,( $true ), file(relat_1,k9_relat_1), [interesting(0.9),axiom,file(relat_1,k9_relat_1)]). 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_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), [interesting(0.9),axiom,file(subset_1,m1_subset_1)]). 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(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(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(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_finset_1,theorem,( ! [A] : ( v1_xboole_0(A) => v1_finset_1(A) ) ), file(finset_1,cc1_finset_1), [interesting(0.9),axiom,file(finset_1,cc1_finset_1)]). 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(cc5_funct_2,theorem,( ! [A,B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_funct_2(C,A,B) ) => ( v1_funct_1(C) & v1_partfun1(C,A,B) & v1_funct_2(C,A,B) ) ) ) ) ), file(funct_2,cc5_funct_2), [interesting(0.9),axiom,file(funct_2,cc5_funct_2)]). fof(cc6_funct_2,theorem,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ! [C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_funct_2(C,A,B) ) => ( v1_funct_1(C) & ~ v1_xboole_0(C) & v1_partfun1(C,A,B) & v1_funct_2(C,A,B) ) ) ) ) ), file(funct_2,cc6_funct_2), [interesting(0.9),axiom,file(funct_2,cc6_funct_2)]). 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_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(redefinition_k10_funct_3,definition,( ! [A,B] : k10_funct_3(A,B) = k8_funct_3(A,B) ), file(funct_3,k10_funct_3), [interesting(0.9),axiom,file(funct_3,k10_funct_3)]). fof(redefinition_k12_mcart_1,definition,( ! [A,B,C,D] : ( ( m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(D,k1_zfmisc_1(B)) ) => k12_mcart_1(A,B,C,D) = k2_zfmisc_1(C,D) ) ), file(mcart_1,k12_mcart_1), [interesting(0.9),axiom,file(mcart_1,k12_mcart_1)]). fof(redefinition_k2_funct_2,definition,( ! [A,B,C,D] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) ) => k2_funct_2(A,B,C,D) = k9_relat_1(C,D) ) ), file(funct_2,k2_funct_2), [interesting(0.9),axiom,file(funct_2,k2_funct_2)]). fof(redefinition_k9_funct_3,definition,( ! [A,B] : k9_funct_3(A,B) = k7_funct_3(A,B) ), file(funct_3,k9_funct_3), [interesting(0.9),axiom,file(funct_3,k9_funct_3)]). fof(dt_k10_funct_3,axiom,( ! [A,B] : ( v1_funct_1(k10_funct_3(A,B)) & v1_funct_2(k10_funct_3(A,B),k2_zfmisc_1(A,B),B) & m2_relset_1(k10_funct_3(A,B),k2_zfmisc_1(A,B),B) ) ), file(funct_3,k10_funct_3), [interesting(0.9),axiom,file(funct_3,k10_funct_3)]). fof(dt_k12_mcart_1,axiom,( ! [A,B,C,D] : ( ( m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(D,k1_zfmisc_1(B)) ) => m1_subset_1(k12_mcart_1(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ), file(mcart_1,k12_mcart_1), [interesting(0.9),axiom,file(mcart_1,k12_mcart_1)]). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]). fof(dt_k2_funct_2,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) ) => m1_subset_1(k2_funct_2(A,B,C,D),k1_zfmisc_1(B)) ) ), file(funct_2,k2_funct_2), [interesting(0.9),axiom,file(funct_2,k2_funct_2)]). 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_k9_funct_3,axiom,( ! [A,B] : ( v1_funct_1(k9_funct_3(A,B)) & v1_funct_2(k9_funct_3(A,B),k2_zfmisc_1(A,B),A) & m2_relset_1(k9_funct_3(A,B),k2_zfmisc_1(A,B),A) ) ), file(funct_3,k9_funct_3), [interesting(0.9),axiom,file(funct_3,k9_funct_3)]). fof(dt_c1_6__borsuk_1,assumption,( $true ), introduced(assumption,[file(borsuk_1,c1_6__borsuk_1)]), [interesting(0.8),axiom,file(borsuk_1,c1_6__borsuk_1)]). fof(dt_c2_6__borsuk_1,assumption,( $true ), introduced(assumption,[file(borsuk_1,c2_6__borsuk_1)]), [interesting(0.8),axiom,file(borsuk_1,c2_6__borsuk_1)]). fof(dt_c3_6__borsuk_1,assumption,( m1_subset_1(c3_6__borsuk_1,k1_zfmisc_1(c1_6__borsuk_1)) ), introduced(assumption,[file(borsuk_1,c3_6__borsuk_1)]), [interesting(0.8),axiom,file(borsuk_1,c3_6__borsuk_1)]). fof(dt_c4_6__borsuk_1,assumption,( m1_subset_1(c4_6__borsuk_1,k1_zfmisc_1(c2_6__borsuk_1)) ), introduced(assumption,[file(borsuk_1,c4_6__borsuk_1)]), [interesting(0.8),axiom,file(borsuk_1,c4_6__borsuk_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(e1_6__borsuk_1,assumption,( k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1) != k1_xboole_0 ), introduced(assumption,[file(borsuk_1,e1_6__borsuk_1)]), [interesting(0.8),axiom,file(borsuk_1,e1_6__borsuk_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(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_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(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(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(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(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(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(dh_c1_6_1__borsuk_1,definition, ( ( ( r2_hidden(c1_6_1__borsuk_1,k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c1_6__borsuk_1,k9_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1))) => r2_hidden(c1_6_1__borsuk_1,c3_6__borsuk_1) ) & ( r2_hidden(c1_6_1__borsuk_1,c3_6__borsuk_1) => r2_hidden(c1_6_1__borsuk_1,k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c1_6__borsuk_1,k9_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1))) ) ) => ! [A] : ( ( r2_hidden(A,k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c1_6__borsuk_1,k9_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1))) => r2_hidden(A,c3_6__borsuk_1) ) & ( r2_hidden(A,c3_6__borsuk_1) => r2_hidden(A,k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c1_6__borsuk_1,k9_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1))) ) ) ), introduced(definition,[new_symbol(c1_6_1__borsuk_1),file(borsuk_1,c1_6_1__borsuk_1)]), [interesting(0.65),axiom,file(borsuk_1,c1_6_1__borsuk_1)]). fof(dt_c1_6_1__borsuk_1,assumption,( $true ), introduced(assumption,[file(borsuk_1,c1_6_1__borsuk_1)]), [interesting(0.65),axiom,file(borsuk_1,c1_6_1__borsuk_1)]). fof(e1_6_1_1__borsuk_1,assumption,( r2_hidden(c1_6_1__borsuk_1,k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c1_6__borsuk_1,k9_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1))) ), introduced(assumption,[file(borsuk_1,e1_6_1_1__borsuk_1)]), [interesting(0.5),axiom,file(borsuk_1,e1_6_1_1__borsuk_1)]). fof(fc10_membered,theorem,( ! [A] : ( v1_int_1(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) ) ) ), file(membered,fc10_membered), [interesting(0.9),axiom,file(membered,fc10_membered)]). fof(fc11_membered,theorem,( ! [A] : ( v4_ordinal2(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) & v5_membered(k1_tarski(A)) ) ) ), file(membered,fc11_membered), [interesting(0.9),axiom,file(membered,fc11_membered)]). fof(fc12_membered,theorem,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => v1_membered(k2_tarski(A,B)) ) ), file(membered,fc12_membered), [interesting(0.9),axiom,file(membered,fc12_membered)]). fof(fc13_membered,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) ) ) ), file(membered,fc13_membered), [interesting(0.9),axiom,file(membered,fc13_membered)]). fof(fc14_membered,theorem,( ! [A,B] : ( ( v1_rat_1(A) & v1_rat_1(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) ) ) ), file(membered,fc14_membered), [interesting(0.9),axiom,file(membered,fc14_membered)]). fof(fc15_membered,theorem,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) ) ) ), file(membered,fc15_membered), [interesting(0.9),axiom,file(membered,fc15_membered)]). fof(fc16_membered,theorem,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) & v5_membered(k2_tarski(A,B)) ) ) ), file(membered,fc16_membered), [interesting(0.9),axiom,file(membered,fc16_membered)]). fof(fc7_membered,theorem,( ! [A] : ( v1_xcmplx_0(A) => v1_membered(k1_tarski(A)) ) ), file(membered,fc7_membered), [interesting(0.9),axiom,file(membered,fc7_membered)]). fof(fc8_membered,theorem,( ! [A] : ( v1_xreal_0(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) ) ) ), file(membered,fc8_membered), [interesting(0.9),axiom,file(membered,fc8_membered)]). fof(fc9_membered,theorem,( ! [A] : ( v1_rat_1(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) ) ) ), file(membered,fc9_membered), [interesting(0.9),axiom,file(membered,fc9_membered)]). fof(commutativity_k2_tarski,theorem,( ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ), file(tarski,k2_tarski), [interesting(0.9),axiom,file(tarski,k2_tarski)]). fof(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), [interesting(0.9),axiom,file(tarski,k1_tarski)]). fof(dt_k2_tarski,axiom,( $true ), file(tarski,k2_tarski), [interesting(0.9),axiom,file(tarski,k2_tarski)]). fof(fc1_finset_1,theorem,( ! [A] : ( ~ v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)) ) ), file(finset_1,fc1_finset_1), [interesting(0.9),axiom,file(finset_1,fc1_finset_1)]). fof(fc2_finset_1,theorem,( ! [A,B] : ( ~ v1_xboole_0(k2_tarski(A,B)) & v1_finset_1(k2_tarski(A,B)) ) ), file(finset_1,fc2_finset_1), [interesting(0.9),axiom,file(finset_1,fc2_finset_1)]). fof(fc2_subset_1,theorem,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) ), file(subset_1,fc2_subset_1), [interesting(0.9),axiom,file(subset_1,fc2_subset_1)]). fof(fc3_subset_1,theorem,( ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ), file(subset_1,fc3_subset_1), [interesting(0.9),axiom,file(subset_1,fc3_subset_1)]). 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_k1_mcart_1,axiom,( $true ), file(mcart_1,k1_mcart_1), [interesting(0.9),axiom,file(mcart_1,k1_mcart_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_mcart_1,axiom,( $true ), file(mcart_1,k2_mcart_1), [interesting(0.9),axiom,file(mcart_1,k2_mcart_1)]). fof(dt_k4_tarski,axiom,( $true ), file(tarski,k4_tarski), [interesting(0.9),axiom,file(tarski,k4_tarski)]). fof(dh_c1_6_1_1__borsuk_1,definition, ( ? [A] : ( r2_hidden(A,k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1)) & r2_hidden(A,k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1)) & c1_6_1__borsuk_1 = k1_funct_1(k9_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),A) ) => ( r2_hidden(c1_6_1_1__borsuk_1,k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1)) & r2_hidden(c1_6_1_1__borsuk_1,k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1)) & c1_6_1__borsuk_1 = k1_funct_1(k9_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),c1_6_1_1__borsuk_1) ) ), introduced(definition,[new_symbol(c1_6_1_1__borsuk_1),file(borsuk_1,c1_6_1_1__borsuk_1)]), [interesting(0.5),axiom,file(borsuk_1,c1_6_1_1__borsuk_1)]). fof(t115_funct_2,theorem,( ! [A,B,C,D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) ) => ! [E] : ~ ( r2_hidden(E,k2_funct_2(A,B,D,C)) & ! [F] : ~ ( r2_hidden(F,A) & r2_hidden(F,C) & E = k1_funct_1(D,F) ) ) ) ), file(funct_2,t115_funct_2), [interesting(0.9),axiom,file(funct_2,t115_funct_2)]). fof(e2_6_1_1__borsuk_1,plain,( ? [A] : ( r2_hidden(A,k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1)) & r2_hidden(A,k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1)) & c1_6_1__borsuk_1 = k1_funct_1(k9_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),A) ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__borsuk_1,dt_c1_6_1__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6_1_1__borsuk_1])],[reflexivity_r1_tarski,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,fc13_finset_1,fc14_finset_1,fc6_membered,rc1_finset_1,rc1_membered,rc3_finset_1,rc4_finset_1,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k7_funct_3,dt_k9_relat_1,dt_m1_relset_1,dt_m1_subset_1,cc15_membered,cc1_finset_1,cc1_relset_1,cc5_funct_2,cc6_funct_2,fc1_subset_1,fc4_subset_1,rc1_funct_2,rc1_subset_1,rc2_partfun1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_k12_mcart_1,redefinition_k2_funct_2,redefinition_k9_funct_3,redefinition_m2_relset_1,dt_k12_mcart_1,dt_k1_funct_1,dt_k2_funct_2,dt_k2_zfmisc_1,dt_k9_funct_3,dt_m2_relset_1,dt_c1_6__borsuk_1,dt_c1_6_1__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,t1_subset,t7_boole,e1_6_1_1__borsuk_1,t115_funct_2]), [interesting(0.5),file(borsuk_1,e2_6_1_1__borsuk_1),[file(borsuk_1,e2_6_1_1__borsuk_1)]]). fof(dt_c1_6_1_1__borsuk_1,plain,( $true ), inference(consider,[status(thm),assumptions([dt_c1_6__borsuk_1,dt_c1_6_1__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6_1_1__borsuk_1])],[dh_c1_6_1_1__borsuk_1,e2_6_1_1__borsuk_1]), [interesting(0.5),file(borsuk_1,c1_6_1_1__borsuk_1),[file(borsuk_1,c1_6_1_1__borsuk_1)]]). fof(d5_tarski,definition,( ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ), file(tarski,d5_tarski), [interesting(0.9),axiom,file(tarski,d5_tarski)]). fof(e3_6_1_1__borsuk_1,plain, ( r2_hidden(c1_6_1_1__borsuk_1,k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1)) & r2_hidden(c1_6_1_1__borsuk_1,k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1)) & c1_6_1__borsuk_1 = k1_funct_1(k9_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),c1_6_1_1__borsuk_1) ), inference(consider,[status(thm),assumptions([dt_c1_6__borsuk_1,dt_c1_6_1__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6_1_1__borsuk_1])],[cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,fc14_finset_1,rc1_finset_1,rc1_membered,rc3_finset_1,rc4_finset_1,dt_m1_relset_1,cc15_membered,cc1_finset_1,cc5_funct_2,cc6_funct_2,fc4_subset_1,rc1_funct_2,rc1_subset_1,rc2_partfun1,rc2_subset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k7_funct_3,dt_m1_subset_1,dt_m2_relset_1,cc1_relset_1,fc1_subset_1,antisymmetry_r2_hidden,redefinition_k12_mcart_1,redefinition_k9_funct_3,dt_k12_mcart_1,dt_k1_funct_1,dt_k2_zfmisc_1,dt_k9_funct_3,dt_c1_6__borsuk_1,dt_c1_6_1__borsuk_1,dt_c1_6_1_1__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,dh_c1_6_1_1__borsuk_1,e2_6_1_1__borsuk_1]), [interesting(0.5),file(borsuk_1,e3_6_1_1__borsuk_1),[file(borsuk_1,e3_6_1_1__borsuk_1)]]). fof(t10_mcart_1,theorem,( ! [A,B,C] : ( r2_hidden(A,k2_zfmisc_1(B,C)) => ( r2_hidden(k1_mcart_1(A),B) & r2_hidden(k2_mcart_1(A),C) ) ) ), file(mcart_1,t10_mcart_1), [interesting(0.9),axiom,file(mcart_1,t10_mcart_1)]). fof(e6_6_1_1__borsuk_1,plain, ( r2_hidden(k1_mcart_1(c1_6_1_1__borsuk_1),c1_6__borsuk_1) & r2_hidden(k2_mcart_1(c1_6_1_1__borsuk_1),c2_6__borsuk_1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__borsuk_1,dt_c1_6_1__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6_1_1__borsuk_1])],[cc1_funct_2,reflexivity_r1_tarski,existence_m1_relset_1,dt_k1_xboole_0,dt_m1_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,cc5_funct_2,cc6_funct_2,fc14_finset_1,fc6_membered,rc1_finset_1,rc1_funct_2,rc1_membered,rc2_partfun1,rc3_finset_1,rc4_finset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k7_funct_3,dt_m1_subset_1,dt_m2_relset_1,cc15_membered,cc1_finset_1,cc1_relset_1,fc1_subset_1,fc4_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k12_mcart_1,redefinition_k9_funct_3,dt_k12_mcart_1,dt_k1_funct_1,dt_k1_mcart_1,dt_k2_mcart_1,dt_k2_zfmisc_1,dt_k9_funct_3,dt_c1_6__borsuk_1,dt_c1_6_1__borsuk_1,dt_c1_6_1_1__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,t1_subset,t7_boole,e3_6_1_1__borsuk_1,t10_mcart_1]), [interesting(0.5),file(borsuk_1,e6_6_1_1__borsuk_1),[file(borsuk_1,e6_6_1_1__borsuk_1)]]). fof(t23_mcart_1,theorem,( ! [A,B,C] : ( r2_hidden(A,k2_zfmisc_1(B,C)) => A = k4_tarski(k1_mcart_1(A),k2_mcart_1(A)) ) ), file(mcart_1,t23_mcart_1), [interesting(0.9),axiom,file(mcart_1,t23_mcart_1)]). fof(e4_6_1_1__borsuk_1,plain,( c1_6_1_1__borsuk_1 = k4_tarski(k1_mcart_1(c1_6_1_1__borsuk_1),k2_mcart_1(c1_6_1_1__borsuk_1)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__borsuk_1,dt_c1_6_1__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6_1_1__borsuk_1])],[cc1_funct_2,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc7_membered,fc8_membered,fc9_membered,reflexivity_r1_tarski,existence_m1_relset_1,dt_k1_xboole_0,dt_m1_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,cc5_funct_2,cc6_funct_2,fc14_finset_1,fc6_membered,rc1_finset_1,rc1_funct_2,rc1_membered,rc2_partfun1,rc3_finset_1,rc4_finset_1,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_tarski,dt_k7_funct_3,dt_m1_subset_1,dt_m2_relset_1,cc15_membered,cc1_finset_1,cc1_relset_1,fc1_finset_1,fc1_subset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,fc4_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k12_mcart_1,redefinition_k9_funct_3,dt_k12_mcart_1,dt_k1_funct_1,dt_k1_mcart_1,dt_k2_mcart_1,dt_k2_zfmisc_1,dt_k4_tarski,dt_k9_funct_3,dt_c1_6__borsuk_1,dt_c1_6_1__borsuk_1,dt_c1_6_1_1__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,t1_subset,t7_boole,d5_tarski,e3_6_1_1__borsuk_1,t23_mcart_1]), [interesting(0.5),file(borsuk_1,e4_6_1_1__borsuk_1),[file(borsuk_1,e4_6_1_1__borsuk_1)]]). fof(e5_6_1_1__borsuk_1,plain,( r2_hidden(k1_mcart_1(c1_6_1_1__borsuk_1),c3_6__borsuk_1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__borsuk_1,dt_c1_6_1__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6_1_1__borsuk_1])],[cc1_funct_2,reflexivity_r1_tarski,existence_m1_relset_1,dt_k1_xboole_0,dt_m1_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,cc5_funct_2,cc6_funct_2,fc14_finset_1,fc6_membered,rc1_finset_1,rc1_funct_2,rc1_membered,rc2_partfun1,rc3_finset_1,rc4_finset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k7_funct_3,dt_m1_subset_1,dt_m2_relset_1,cc15_membered,cc1_finset_1,cc1_relset_1,fc1_subset_1,fc4_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k12_mcart_1,redefinition_k9_funct_3,dt_k12_mcart_1,dt_k1_funct_1,dt_k1_mcart_1,dt_k2_mcart_1,dt_k2_zfmisc_1,dt_k9_funct_3,dt_c1_6__borsuk_1,dt_c1_6_1__borsuk_1,dt_c1_6_1_1__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,t1_subset,t7_boole,e3_6_1_1__borsuk_1,t10_mcart_1]), [interesting(0.5),file(borsuk_1,e5_6_1_1__borsuk_1),[file(borsuk_1,e5_6_1_1__borsuk_1)]]). fof(d5_funct_3,definition,( ! [A,B,C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( C = k7_funct_3(A,B) <=> ( k1_relat_1(C) = k2_zfmisc_1(A,B) & ! [D,E] : ( ( r2_hidden(D,A) & r2_hidden(E,B) ) => k1_funct_1(C,k4_tarski(D,E)) = D ) ) ) ) ), file(funct_3,d5_funct_3), [interesting(0.9),axiom,file(funct_3,d5_funct_3)]). fof(e7_6_1_1__borsuk_1,plain,( r2_hidden(c1_6_1__borsuk_1,c3_6__borsuk_1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__borsuk_1,dt_c1_6_1__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6_1_1__borsuk_1])],[cc1_funct_2,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc7_membered,fc8_membered,fc9_membered,reflexivity_r1_tarski,existence_m1_relset_1,dt_k1_xboole_0,dt_m1_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,cc5_funct_2,cc6_funct_2,fc14_finset_1,fc6_membered,rc1_finset_1,rc1_funct_2,rc1_membered,rc2_partfun1,rc3_finset_1,rc4_finset_1,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_tarski,dt_m1_subset_1,dt_m2_relset_1,cc15_membered,cc1_finset_1,cc1_relset_1,fc1_finset_1,fc1_subset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,fc4_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k12_mcart_1,redefinition_k9_funct_3,dt_k12_mcart_1,dt_k1_funct_1,dt_k1_mcart_1,dt_k1_relat_1,dt_k2_mcart_1,dt_k2_zfmisc_1,dt_k4_tarski,dt_k7_funct_3,dt_k9_funct_3,dt_c1_6__borsuk_1,dt_c1_6_1__borsuk_1,dt_c1_6_1_1__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,t1_subset,t7_boole,d5_tarski,e6_6_1_1__borsuk_1,e3_6_1_1__borsuk_1,e4_6_1_1__borsuk_1,e5_6_1_1__borsuk_1,d5_funct_3]), [interesting(0.5),file(borsuk_1,e7_6_1_1__borsuk_1),[file(borsuk_1,e7_6_1_1__borsuk_1)]]). fof(i2_6_1_1__borsuk_1,theorem,( $true ), introduced(tautology,[file(borsuk_1,i2_6_1_1__borsuk_1)]), [interesting(0.5),trivial,file(borsuk_1,i2_6_1_1__borsuk_1)]). fof(i1_6_1_1__borsuk_1,plain,( r2_hidden(c1_6_1__borsuk_1,c3_6__borsuk_1) ), inference(conclusion,[status(thm),assumptions([dt_c1_6__borsuk_1,dt_c1_6_1__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6_1_1__borsuk_1])],[e7_6_1_1__borsuk_1,i2_6_1_1__borsuk_1]), [interesting(0.5),file(borsuk_1,i1_6_1_1__borsuk_1),[file(borsuk_1,i1_6_1_1__borsuk_1)]]). fof(i1_6_1_1_tmp__borsuk_1,plain, ( r2_hidden(c1_6_1__borsuk_1,k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c1_6__borsuk_1,k9_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1))) => r2_hidden(c1_6_1__borsuk_1,c3_6__borsuk_1) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_6__borsuk_1,dt_c1_6_1__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1]),discharge_asm(discharge,[e1_6_1_1__borsuk_1])],[e1_6_1_1__borsuk_1,i1_6_1_1__borsuk_1]), [interesting(0.65),e1_6_1__borsuk_1]). fof(e1_6_1__borsuk_1,plain, ( r2_hidden(c1_6_1__borsuk_1,k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c1_6__borsuk_1,k9_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1))) => r2_hidden(c1_6_1__borsuk_1,c3_6__borsuk_1) ), inference(mizar_def_expansion,[status(thm),assumptions([dt_c1_6__borsuk_1,dt_c1_6_1__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1])],[i1_6_1_1_tmp__borsuk_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,fc13_finset_1,fc14_finset_1,rc1_finset_1,rc1_membered,rc3_finset_1,rc4_finset_1,cc15_membered,cc1_finset_1,cc5_funct_2,cc6_funct_2,fc4_subset_1,rc1_funct_2,rc1_subset_1,rc2_partfun1,rc2_subset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k7_funct_3,dt_k9_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc1_relset_1,fc1_subset_1,antisymmetry_r2_hidden,redefinition_k12_mcart_1,redefinition_k2_funct_2,redefinition_k9_funct_3,dt_k12_mcart_1,dt_k2_funct_2,dt_k2_zfmisc_1,dt_k9_funct_3,dt_c1_6__borsuk_1,dt_c1_6_1__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1]), [interesting(0.65),file(borsuk_1,e1_6_1__borsuk_1),[file(borsuk_1,e1_6_1__borsuk_1)]]). fof(e3_6_1__borsuk_1,assumption,( r2_hidden(c1_6_1__borsuk_1,c3_6__borsuk_1) ), introduced(assumption,[file(borsuk_1,e3_6_1__borsuk_1)]), [interesting(0.65),axiom,file(borsuk_1,e3_6_1__borsuk_1)]). fof(dh_c2_6_1__borsuk_1,definition, ( ? [A] : m1_subset_1(A,c4_6__borsuk_1) => m1_subset_1(c2_6_1__borsuk_1,c4_6__borsuk_1) ), introduced(definition,[new_symbol(c2_6_1__borsuk_1),file(borsuk_1,c2_6_1__borsuk_1)]), [interesting(0.65),axiom,file(borsuk_1,c2_6_1__borsuk_1)]). fof(e2_6_1__borsuk_1,plain,( ? [A] : m1_subset_1(A,c4_6__borsuk_1) ), inference(mizar_by,[status(thm),assumptions([dt_c2_6__borsuk_1,dt_c4_6__borsuk_1])],[antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_finset_1,rc1_membered,rc3_finset_1,rc4_finset_1,t1_subset,t4_subset,t5_subset,t8_boole,reflexivity_r1_tarski,cc15_membered,cc1_finset_1,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,dt_k1_zfmisc_1,dt_c2_6__borsuk_1,fc1_subset_1,t3_subset,existence_m1_subset_1,dt_m1_subset_1,dt_c4_6__borsuk_1]), [interesting(0.65),file(borsuk_1,e2_6_1__borsuk_1),[file(borsuk_1,e2_6_1__borsuk_1)]]). fof(dt_c2_6_1__borsuk_1,plain,( m1_subset_1(c2_6_1__borsuk_1,c4_6__borsuk_1) ), inference(consider,[status(thm),assumptions([dt_c2_6__borsuk_1,dt_c4_6__borsuk_1])],[dh_c2_6_1__borsuk_1,e2_6_1__borsuk_1]), [interesting(0.65),file(borsuk_1,c2_6_1__borsuk_1),[file(borsuk_1,c2_6_1__borsuk_1)]]). fof(t113_zfmisc_1,theorem,( ! [A,B] : ( k2_zfmisc_1(A,B) = k1_xboole_0 <=> ( A = k1_xboole_0 | B = k1_xboole_0 ) ) ), file(zfmisc_1,t113_zfmisc_1), [interesting(0.9),axiom,file(zfmisc_1,t113_zfmisc_1)]). fof(e2_6__borsuk_1,plain, ( c3_6__borsuk_1 != k1_xboole_0 & c4_6__borsuk_1 != k1_xboole_0 & r1_tarski(c3_6__borsuk_1,c1_6__borsuk_1) & r1_tarski(c4_6__borsuk_1,c2_6__borsuk_1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6__borsuk_1])],[antisymmetry_r2_hidden,cc2_finset_1,fc14_finset_1,rc1_finset_1,rc3_finset_1,rc4_finset_1,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,dt_k1_zfmisc_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_finset_1,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc1_subset_1,fc4_subset_1,rc1_membered,rc1_subset_1,rc2_subset_1,t2_subset,t7_boole,t8_boole,reflexivity_r1_tarski,redefinition_k12_mcart_1,dt_k12_mcart_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_c1_6__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,fc6_membered,t3_subset,t6_boole,e1_6__borsuk_1,t113_zfmisc_1]), [interesting(0.8),file(borsuk_1,e2_6__borsuk_1),[file(borsuk_1,e2_6__borsuk_1)]]). fof(d3_tarski,definition,( ! [A,B] : ( r1_tarski(A,B) <=> ! [C] : ( r2_hidden(C,A) => r2_hidden(C,B) ) ) ), file(tarski,d3_tarski), [interesting(0.9),axiom,file(tarski,d3_tarski)]). fof(e4_6_1__borsuk_1,plain, ( r2_hidden(c1_6_1__borsuk_1,c1_6__borsuk_1) & r2_hidden(c2_6_1__borsuk_1,c2_6__borsuk_1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6_1__borsuk_1,e3_6_1__borsuk_1,dt_c1_6__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6__borsuk_1])],[cc2_finset_1,rc1_finset_1,rc3_finset_1,rc4_finset_1,existence_m1_subset_1,dt_k1_zfmisc_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_finset_1,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc1_subset_1,rc1_membered,rc1_subset_1,rc2_subset_1,t2_subset,t4_subset,t5_subset,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_c1_6__borsuk_1,dt_c1_6_1__borsuk_1,dt_c2_6__borsuk_1,dt_c2_6_1__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,fc6_membered,t1_subset,t3_subset,t6_boole,t7_boole,e3_6_1__borsuk_1,e2_6__borsuk_1,d3_tarski]), [interesting(0.65),file(borsuk_1,e4_6_1__borsuk_1),[file(borsuk_1,e4_6_1__borsuk_1)]]). fof(e6_6_1__borsuk_1,plain,( c1_6_1__borsuk_1 = k1_funct_1(k9_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k4_tarski(c1_6_1__borsuk_1,c2_6_1__borsuk_1)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6_1__borsuk_1,e3_6_1__borsuk_1,dt_c1_6__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6__borsuk_1])],[reflexivity_r1_tarski,cc1_funct_2,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc7_membered,fc8_membered,fc9_membered,existence_m1_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_m1_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,cc5_funct_2,cc6_funct_2,fc14_finset_1,fc1_subset_1,fc6_membered,rc1_finset_1,rc1_funct_2,rc1_membered,rc1_subset_1,rc2_partfun1,rc2_subset_1,rc3_finset_1,rc4_finset_1,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,dt_m2_relset_1,dt_c4_6__borsuk_1,cc15_membered,cc1_finset_1,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,fc4_subset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k9_funct_3,dt_k1_funct_1,dt_k1_relat_1,dt_k2_zfmisc_1,dt_k4_tarski,dt_k7_funct_3,dt_k9_funct_3,dt_c1_6__borsuk_1,dt_c1_6_1__borsuk_1,dt_c2_6__borsuk_1,dt_c2_6_1__borsuk_1,t1_subset,t7_boole,d5_tarski,e4_6_1__borsuk_1,d5_funct_3]), [interesting(0.65),file(borsuk_1,e6_6_1__borsuk_1),[file(borsuk_1,e6_6_1__borsuk_1)]]). fof(t3_xboole_1,theorem,( ! [A] : ( r1_tarski(A,k1_xboole_0) => A = k1_xboole_0 ) ), file(xboole_1,t3_xboole_1), [interesting(0.9),axiom,file(xboole_1,t3_xboole_1)]). fof(e3_6__borsuk_1,plain, ( c1_6__borsuk_1 != k1_xboole_0 & c2_6__borsuk_1 != k1_xboole_0 ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6__borsuk_1])],[antisymmetry_r2_hidden,cc2_finset_1,rc1_finset_1,rc3_finset_1,rc4_finset_1,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,dt_k1_zfmisc_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_finset_1,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc1_subset_1,rc1_membered,rc1_subset_1,rc2_subset_1,t2_subset,t7_boole,t8_boole,reflexivity_r1_tarski,dt_k1_xboole_0,dt_c1_6__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,fc6_membered,t3_subset,t6_boole,e2_6__borsuk_1,t3_xboole_1]), [interesting(0.8),file(borsuk_1,e3_6__borsuk_1),[file(borsuk_1,e3_6__borsuk_1)]]). fof(t106_zfmisc_1,theorem,( ! [A,B,C,D] : ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D)) <=> ( r2_hidden(A,C) & r2_hidden(B,D) ) ) ), file(zfmisc_1,t106_zfmisc_1), [interesting(0.9),axiom,file(zfmisc_1,t106_zfmisc_1)]). fof(e5_6_1__borsuk_1,plain,( r2_hidden(k4_tarski(c1_6_1__borsuk_1,c2_6_1__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6_1__borsuk_1,dt_c1_6__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6__borsuk_1,e3_6_1__borsuk_1])],[cc2_finset_1,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_finset_1,fc14_membered,fc15_membered,fc16_membered,fc7_membered,fc8_membered,fc9_membered,rc1_finset_1,rc3_finset_1,rc4_finset_1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_tarski,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_finset_1,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc1_finset_1,fc1_subset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,fc4_subset_1,rc1_membered,rc1_subset_1,rc2_subset_1,t2_subset,t4_subset,t5_subset,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k12_mcart_1,dt_k12_mcart_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_k4_tarski,dt_c1_6__borsuk_1,dt_c1_6_1__borsuk_1,dt_c2_6__borsuk_1,dt_c2_6_1__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,fc6_membered,t1_subset,t3_subset,t6_boole,t7_boole,d5_tarski,e2_6__borsuk_1,e3_6_1__borsuk_1,t106_zfmisc_1]), [interesting(0.65),file(borsuk_1,e5_6_1__borsuk_1),[file(borsuk_1,e5_6_1__borsuk_1)]]). fof(t43_funct_2,theorem,( ! [A,B,C,D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) ) => ( B != k1_xboole_0 => ! [E] : ( ? [F] : ( r2_hidden(F,A) & r2_hidden(F,C) & E = k1_funct_1(D,F) ) => r2_hidden(E,k9_relat_1(D,C)) ) ) ) ), file(funct_2,t43_funct_2), [interesting(0.9),axiom,file(funct_2,t43_funct_2)]). fof(e7_6_1__borsuk_1,plain,( r2_hidden(c1_6_1__borsuk_1,k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c1_6__borsuk_1,k9_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6_1__borsuk_1,dt_c1_6__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6__borsuk_1,e3_6_1__borsuk_1])],[reflexivity_r1_tarski,cc1_funct_2,cc2_finset_1,fc10_membered,fc11_membered,fc12_membered,fc13_finset_1,fc13_membered,fc14_finset_1,fc14_membered,fc15_membered,fc16_membered,fc7_membered,fc8_membered,fc9_membered,rc1_finset_1,rc3_finset_1,rc4_finset_1,commutativity_k2_tarski,existence_m1_relset_1,existence_m1_subset_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_tarski,dt_k7_funct_3,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_finset_1,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc5_funct_2,cc6_funct_2,fc1_finset_1,fc1_subset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,fc4_subset_1,rc1_funct_2,rc1_membered,rc1_subset_1,rc2_partfun1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_k12_mcart_1,redefinition_k2_funct_2,redefinition_k9_funct_3,redefinition_m2_relset_1,dt_k12_mcart_1,dt_k1_funct_1,dt_k1_xboole_0,dt_k2_funct_2,dt_k2_zfmisc_1,dt_k4_tarski,dt_k9_funct_3,dt_k9_relat_1,dt_m2_relset_1,dt_c1_6__borsuk_1,dt_c1_6_1__borsuk_1,dt_c2_6__borsuk_1,dt_c2_6_1__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,fc6_membered,t1_subset,t6_boole,t7_boole,d5_tarski,e6_6_1__borsuk_1,e3_6__borsuk_1,e5_6_1__borsuk_1,t43_funct_2]), [interesting(0.65),file(borsuk_1,e7_6_1__borsuk_1),[file(borsuk_1,e7_6_1__borsuk_1)]]). fof(i4_6_1__borsuk_1,theorem,( $true ), introduced(tautology,[file(borsuk_1,i4_6_1__borsuk_1)]), [interesting(0.65),trivial,file(borsuk_1,i4_6_1__borsuk_1)]). fof(i3_6_1__borsuk_1,plain,( r2_hidden(c1_6_1__borsuk_1,k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c1_6__borsuk_1,k9_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1))) ), inference(conclusion,[status(thm),assumptions([dt_c1_6_1__borsuk_1,dt_c1_6__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6__borsuk_1,e3_6_1__borsuk_1])],[cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,fc13_finset_1,fc14_finset_1,rc1_finset_1,rc1_membered,rc3_finset_1,rc4_finset_1,cc15_membered,cc1_finset_1,cc5_funct_2,cc6_funct_2,fc4_subset_1,rc1_funct_2,rc1_subset_1,rc2_partfun1,rc2_subset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k7_funct_3,dt_k9_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc1_relset_1,fc1_subset_1,antisymmetry_r2_hidden,redefinition_k12_mcart_1,redefinition_k2_funct_2,redefinition_k9_funct_3,dt_k12_mcart_1,dt_k2_funct_2,dt_k2_zfmisc_1,dt_k9_funct_3,dt_c1_6__borsuk_1,dt_c1_6_1__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e7_6_1__borsuk_1,i4_6_1__borsuk_1]), [interesting(0.65),file(borsuk_1,i3_6_1__borsuk_1),[file(borsuk_1,i3_6_1__borsuk_1)]]). fof(i3_6_1_tmp__borsuk_1,plain, ( r2_hidden(c1_6_1__borsuk_1,c3_6__borsuk_1) => r2_hidden(c1_6_1__borsuk_1,k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c1_6__borsuk_1,k9_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1))) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_6_1__borsuk_1,dt_c1_6__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6__borsuk_1]),discharge_asm(discharge,[e3_6_1__borsuk_1])],[e3_6_1__borsuk_1,i3_6_1__borsuk_1]), [interesting(0.65),i2_6_1__borsuk_1]). fof(i2_6_1__borsuk_1,plain, ( r2_hidden(c1_6_1__borsuk_1,c3_6__borsuk_1) => r2_hidden(c1_6_1__borsuk_1,k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c1_6__borsuk_1,k9_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1))) ), inference(mizar_def_expansion,[status(thm),assumptions([dt_c1_6_1__borsuk_1,dt_c1_6__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6__borsuk_1])],[i3_6_1_tmp__borsuk_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,fc13_finset_1,fc14_finset_1,rc1_finset_1,rc1_membered,rc3_finset_1,rc4_finset_1,cc15_membered,cc1_finset_1,cc5_funct_2,cc6_funct_2,fc4_subset_1,rc1_funct_2,rc1_subset_1,rc2_partfun1,rc2_subset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k7_funct_3,dt_k9_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc1_relset_1,fc1_subset_1,antisymmetry_r2_hidden,redefinition_k12_mcart_1,redefinition_k2_funct_2,redefinition_k9_funct_3,dt_k12_mcart_1,dt_k2_funct_2,dt_k2_zfmisc_1,dt_k9_funct_3,dt_c1_6__borsuk_1,dt_c1_6_1__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1]), [interesting(0.65),file(borsuk_1,i2_6_1__borsuk_1),[file(borsuk_1,i2_6_1__borsuk_1)]]). fof(i1_6_1__borsuk_1,plain, ( ( r2_hidden(c1_6_1__borsuk_1,k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c1_6__borsuk_1,k9_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1))) => r2_hidden(c1_6_1__borsuk_1,c3_6__borsuk_1) ) & ( r2_hidden(c1_6_1__borsuk_1,c3_6__borsuk_1) => r2_hidden(c1_6_1__borsuk_1,k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c1_6__borsuk_1,k9_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1))) ) ), inference(conclusion,[status(thm),assumptions([dt_c1_6_1__borsuk_1,dt_c1_6__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6__borsuk_1])],[cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,fc13_finset_1,fc14_finset_1,rc1_finset_1,rc1_membered,rc3_finset_1,rc4_finset_1,cc15_membered,cc1_finset_1,cc5_funct_2,cc6_funct_2,fc4_subset_1,rc1_funct_2,rc1_subset_1,rc2_partfun1,rc2_subset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k7_funct_3,dt_k9_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc1_relset_1,fc1_subset_1,antisymmetry_r2_hidden,redefinition_k12_mcart_1,redefinition_k2_funct_2,redefinition_k9_funct_3,dt_k12_mcart_1,dt_k2_funct_2,dt_k2_zfmisc_1,dt_k9_funct_3,dt_c1_6__borsuk_1,dt_c1_6_1__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6_1__borsuk_1,i2_6_1__borsuk_1]), [interesting(0.65),file(borsuk_1,i1_6_1__borsuk_1),[file(borsuk_1,i1_6_1__borsuk_1)]]). fof(i1_6_1_tmp__borsuk_1,plain, ( ( r2_hidden(c1_6_1__borsuk_1,k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c1_6__borsuk_1,k9_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1))) => r2_hidden(c1_6_1__borsuk_1,c3_6__borsuk_1) ) & ( r2_hidden(c1_6_1__borsuk_1,c3_6__borsuk_1) => r2_hidden(c1_6_1__borsuk_1,k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c1_6__borsuk_1,k9_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1))) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_6__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6__borsuk_1]),discharge_asm(discharge,[dt_c1_6_1__borsuk_1])],[dt_c1_6_1__borsuk_1,i1_6_1__borsuk_1]), [interesting(0.8),e4_6__borsuk_1]). fof(e4_6__borsuk_1,plain,( ! [A] : ( ( r2_hidden(A,k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c1_6__borsuk_1,k9_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1))) => r2_hidden(A,c3_6__borsuk_1) ) & ( r2_hidden(A,c3_6__borsuk_1) => r2_hidden(A,k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c1_6__borsuk_1,k9_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1))) ) ) ), inference(let,[status(thm),assumptions([dt_c1_6__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6__borsuk_1])],[i1_6_1_tmp__borsuk_1,dh_c1_6_1__borsuk_1]), [interesting(0.8),file(borsuk_1,e4_6__borsuk_1),[file(borsuk_1,e4_6__borsuk_1)]]). fof(t2_tarski,theorem,( ! [A,B] : ( ! [C] : ( r2_hidden(C,A) <=> r2_hidden(C,B) ) => A = B ) ), file(tarski,t2_tarski), [interesting(0.9),axiom,file(tarski,t2_tarski)]). fof(e5_6__borsuk_1,plain,( k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c1_6__borsuk_1,k9_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1)) = c3_6__borsuk_1 ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6__borsuk_1])],[reflexivity_r1_tarski,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,fc13_finset_1,fc14_finset_1,fc6_membered,rc1_finset_1,rc1_funct_2,rc1_membered,rc2_partfun1,rc3_finset_1,rc4_finset_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k7_funct_3,dt_k9_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc15_membered,cc1_finset_1,cc1_relset_1,cc5_funct_2,cc6_funct_2,fc1_subset_1,fc4_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k12_mcart_1,redefinition_k2_funct_2,redefinition_k9_funct_3,dt_k12_mcart_1,dt_k2_funct_2,dt_k2_zfmisc_1,dt_k9_funct_3,dt_c1_6__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,t1_subset,t7_boole,e4_6__borsuk_1,t2_tarski]), [interesting(0.8),file(borsuk_1,e5_6__borsuk_1),[file(borsuk_1,e5_6__borsuk_1)]]). fof(dh_c1_6_2__borsuk_1,definition, ( ( ( r2_hidden(c1_6_2__borsuk_1,k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c2_6__borsuk_1,k10_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1))) => r2_hidden(c1_6_2__borsuk_1,c4_6__borsuk_1) ) & ( r2_hidden(c1_6_2__borsuk_1,c4_6__borsuk_1) => r2_hidden(c1_6_2__borsuk_1,k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c2_6__borsuk_1,k10_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1))) ) ) => ! [A] : ( ( r2_hidden(A,k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c2_6__borsuk_1,k10_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1))) => r2_hidden(A,c4_6__borsuk_1) ) & ( r2_hidden(A,c4_6__borsuk_1) => r2_hidden(A,k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c2_6__borsuk_1,k10_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1))) ) ) ), introduced(definition,[new_symbol(c1_6_2__borsuk_1),file(borsuk_1,c1_6_2__borsuk_1)]), [interesting(0.65),axiom,file(borsuk_1,c1_6_2__borsuk_1)]). fof(dt_c1_6_2__borsuk_1,assumption,( $true ), introduced(assumption,[file(borsuk_1,c1_6_2__borsuk_1)]), [interesting(0.65),axiom,file(borsuk_1,c1_6_2__borsuk_1)]). fof(e1_6_2_1__borsuk_1,assumption,( r2_hidden(c1_6_2__borsuk_1,k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c2_6__borsuk_1,k10_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1))) ), introduced(assumption,[file(borsuk_1,e1_6_2_1__borsuk_1)]), [interesting(0.5),axiom,file(borsuk_1,e1_6_2_1__borsuk_1)]). fof(dh_c1_6_2_1__borsuk_1,definition, ( ? [A] : ( r2_hidden(A,k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1)) & r2_hidden(A,k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1)) & c1_6_2__borsuk_1 = k1_funct_1(k10_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),A) ) => ( r2_hidden(c1_6_2_1__borsuk_1,k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1)) & r2_hidden(c1_6_2_1__borsuk_1,k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1)) & c1_6_2__borsuk_1 = k1_funct_1(k10_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),c1_6_2_1__borsuk_1) ) ), introduced(definition,[new_symbol(c1_6_2_1__borsuk_1),file(borsuk_1,c1_6_2_1__borsuk_1)]), [interesting(0.5),axiom,file(borsuk_1,c1_6_2_1__borsuk_1)]). fof(e2_6_2_1__borsuk_1,plain,( ? [A] : ( r2_hidden(A,k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1)) & r2_hidden(A,k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1)) & c1_6_2__borsuk_1 = k1_funct_1(k10_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),A) ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__borsuk_1,dt_c1_6_2__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6_2_1__borsuk_1])],[reflexivity_r1_tarski,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,fc13_finset_1,fc14_finset_1,fc6_membered,rc1_finset_1,rc1_membered,rc3_finset_1,rc4_finset_1,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k8_funct_3,dt_k9_relat_1,dt_m1_relset_1,dt_m1_subset_1,cc15_membered,cc1_finset_1,cc1_relset_1,cc5_funct_2,cc6_funct_2,fc1_subset_1,fc4_subset_1,rc1_funct_2,rc1_subset_1,rc2_partfun1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_k10_funct_3,redefinition_k12_mcart_1,redefinition_k2_funct_2,redefinition_m2_relset_1,dt_k10_funct_3,dt_k12_mcart_1,dt_k1_funct_1,dt_k2_funct_2,dt_k2_zfmisc_1,dt_m2_relset_1,dt_c1_6__borsuk_1,dt_c1_6_2__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,t1_subset,t7_boole,e1_6_2_1__borsuk_1,t115_funct_2]), [interesting(0.5),file(borsuk_1,e2_6_2_1__borsuk_1),[file(borsuk_1,e2_6_2_1__borsuk_1)]]). fof(dt_c1_6_2_1__borsuk_1,plain,( $true ), inference(consider,[status(thm),assumptions([dt_c1_6__borsuk_1,dt_c1_6_2__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6_2_1__borsuk_1])],[dh_c1_6_2_1__borsuk_1,e2_6_2_1__borsuk_1]), [interesting(0.5),file(borsuk_1,c1_6_2_1__borsuk_1),[file(borsuk_1,c1_6_2_1__borsuk_1)]]). fof(e3_6_2_1__borsuk_1,plain, ( r2_hidden(c1_6_2_1__borsuk_1,k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1)) & r2_hidden(c1_6_2_1__borsuk_1,k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1)) & c1_6_2__borsuk_1 = k1_funct_1(k10_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),c1_6_2_1__borsuk_1) ), inference(consider,[status(thm),assumptions([dt_c1_6__borsuk_1,dt_c1_6_2__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6_2_1__borsuk_1])],[cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,fc14_finset_1,rc1_finset_1,rc1_membered,rc3_finset_1,rc4_finset_1,dt_m1_relset_1,cc15_membered,cc1_finset_1,cc5_funct_2,cc6_funct_2,fc4_subset_1,rc1_funct_2,rc1_subset_1,rc2_partfun1,rc2_subset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k8_funct_3,dt_m1_subset_1,dt_m2_relset_1,cc1_relset_1,fc1_subset_1,antisymmetry_r2_hidden,redefinition_k10_funct_3,redefinition_k12_mcart_1,dt_k10_funct_3,dt_k12_mcart_1,dt_k1_funct_1,dt_k2_zfmisc_1,dt_c1_6__borsuk_1,dt_c1_6_2__borsuk_1,dt_c1_6_2_1__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,dh_c1_6_2_1__borsuk_1,e2_6_2_1__borsuk_1]), [interesting(0.5),file(borsuk_1,e3_6_2_1__borsuk_1),[file(borsuk_1,e3_6_2_1__borsuk_1)]]). fof(e6_6_2_1__borsuk_1,plain, ( r2_hidden(k1_mcart_1(c1_6_2_1__borsuk_1),c1_6__borsuk_1) & r2_hidden(k2_mcart_1(c1_6_2_1__borsuk_1),c2_6__borsuk_1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__borsuk_1,dt_c1_6_2__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6_2_1__borsuk_1])],[cc1_funct_2,reflexivity_r1_tarski,existence_m1_relset_1,dt_k1_xboole_0,dt_m1_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,cc5_funct_2,cc6_funct_2,fc14_finset_1,fc6_membered,rc1_finset_1,rc1_funct_2,rc1_membered,rc2_partfun1,rc3_finset_1,rc4_finset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k8_funct_3,dt_m1_subset_1,dt_m2_relset_1,cc15_membered,cc1_finset_1,cc1_relset_1,fc1_subset_1,fc4_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k10_funct_3,redefinition_k12_mcart_1,dt_k10_funct_3,dt_k12_mcart_1,dt_k1_funct_1,dt_k1_mcart_1,dt_k2_mcart_1,dt_k2_zfmisc_1,dt_c1_6__borsuk_1,dt_c1_6_2__borsuk_1,dt_c1_6_2_1__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,t1_subset,t7_boole,e3_6_2_1__borsuk_1,t10_mcart_1]), [interesting(0.5),file(borsuk_1,e6_6_2_1__borsuk_1),[file(borsuk_1,e6_6_2_1__borsuk_1)]]). fof(e4_6_2_1__borsuk_1,plain,( c1_6_2_1__borsuk_1 = k4_tarski(k1_mcart_1(c1_6_2_1__borsuk_1),k2_mcart_1(c1_6_2_1__borsuk_1)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__borsuk_1,dt_c1_6_2__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6_2_1__borsuk_1])],[cc1_funct_2,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc7_membered,fc8_membered,fc9_membered,reflexivity_r1_tarski,existence_m1_relset_1,dt_k1_xboole_0,dt_m1_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,cc5_funct_2,cc6_funct_2,fc14_finset_1,fc6_membered,rc1_finset_1,rc1_funct_2,rc1_membered,rc2_partfun1,rc3_finset_1,rc4_finset_1,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_tarski,dt_k8_funct_3,dt_m1_subset_1,dt_m2_relset_1,cc15_membered,cc1_finset_1,cc1_relset_1,fc1_finset_1,fc1_subset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,fc4_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k10_funct_3,redefinition_k12_mcart_1,dt_k10_funct_3,dt_k12_mcart_1,dt_k1_funct_1,dt_k1_mcart_1,dt_k2_mcart_1,dt_k2_zfmisc_1,dt_k4_tarski,dt_c1_6__borsuk_1,dt_c1_6_2__borsuk_1,dt_c1_6_2_1__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,t1_subset,t7_boole,d5_tarski,e3_6_2_1__borsuk_1,t23_mcart_1]), [interesting(0.5),file(borsuk_1,e4_6_2_1__borsuk_1),[file(borsuk_1,e4_6_2_1__borsuk_1)]]). fof(e5_6_2_1__borsuk_1,plain,( r2_hidden(k2_mcart_1(c1_6_2_1__borsuk_1),c4_6__borsuk_1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__borsuk_1,dt_c1_6_2__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6_2_1__borsuk_1])],[cc1_funct_2,reflexivity_r1_tarski,existence_m1_relset_1,dt_k1_xboole_0,dt_m1_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,cc5_funct_2,cc6_funct_2,fc14_finset_1,fc6_membered,rc1_finset_1,rc1_funct_2,rc1_membered,rc2_partfun1,rc3_finset_1,rc4_finset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k8_funct_3,dt_m1_subset_1,dt_m2_relset_1,cc15_membered,cc1_finset_1,cc1_relset_1,fc1_subset_1,fc4_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k10_funct_3,redefinition_k12_mcart_1,dt_k10_funct_3,dt_k12_mcart_1,dt_k1_funct_1,dt_k1_mcart_1,dt_k2_mcart_1,dt_k2_zfmisc_1,dt_c1_6__borsuk_1,dt_c1_6_2__borsuk_1,dt_c1_6_2_1__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,t1_subset,t7_boole,e3_6_2_1__borsuk_1,t10_mcart_1]), [interesting(0.5),file(borsuk_1,e5_6_2_1__borsuk_1),[file(borsuk_1,e5_6_2_1__borsuk_1)]]). fof(d6_funct_3,definition,( ! [A,B,C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( C = k8_funct_3(A,B) <=> ( k1_relat_1(C) = k2_zfmisc_1(A,B) & ! [D,E] : ( ( r2_hidden(D,A) & r2_hidden(E,B) ) => k1_funct_1(C,k4_tarski(D,E)) = E ) ) ) ) ), file(funct_3,d6_funct_3), [interesting(0.9),axiom,file(funct_3,d6_funct_3)]). fof(e7_6_2_1__borsuk_1,plain,( r2_hidden(c1_6_2__borsuk_1,c4_6__borsuk_1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__borsuk_1,dt_c1_6_2__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6_2_1__borsuk_1])],[cc1_funct_2,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc7_membered,fc8_membered,fc9_membered,reflexivity_r1_tarski,existence_m1_relset_1,dt_k1_xboole_0,dt_m1_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,cc5_funct_2,cc6_funct_2,fc14_finset_1,fc6_membered,rc1_finset_1,rc1_funct_2,rc1_membered,rc2_partfun1,rc3_finset_1,rc4_finset_1,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_tarski,dt_m1_subset_1,dt_m2_relset_1,cc15_membered,cc1_finset_1,cc1_relset_1,fc1_finset_1,fc1_subset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,fc4_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k10_funct_3,redefinition_k12_mcart_1,dt_k10_funct_3,dt_k12_mcart_1,dt_k1_funct_1,dt_k1_mcart_1,dt_k1_relat_1,dt_k2_mcart_1,dt_k2_zfmisc_1,dt_k4_tarski,dt_k8_funct_3,dt_c1_6__borsuk_1,dt_c1_6_2__borsuk_1,dt_c1_6_2_1__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,t1_subset,t7_boole,d5_tarski,e6_6_2_1__borsuk_1,e3_6_2_1__borsuk_1,e4_6_2_1__borsuk_1,e5_6_2_1__borsuk_1,d6_funct_3]), [interesting(0.5),file(borsuk_1,e7_6_2_1__borsuk_1),[file(borsuk_1,e7_6_2_1__borsuk_1)]]). fof(i2_6_2_1__borsuk_1,theorem,( $true ), introduced(tautology,[file(borsuk_1,i2_6_2_1__borsuk_1)]), [interesting(0.5),trivial,file(borsuk_1,i2_6_2_1__borsuk_1)]). fof(i1_6_2_1__borsuk_1,plain,( r2_hidden(c1_6_2__borsuk_1,c4_6__borsuk_1) ), inference(conclusion,[status(thm),assumptions([dt_c1_6__borsuk_1,dt_c1_6_2__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6_2_1__borsuk_1])],[e7_6_2_1__borsuk_1,i2_6_2_1__borsuk_1]), [interesting(0.5),file(borsuk_1,i1_6_2_1__borsuk_1),[file(borsuk_1,i1_6_2_1__borsuk_1)]]). fof(i1_6_2_1_tmp__borsuk_1,plain, ( r2_hidden(c1_6_2__borsuk_1,k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c2_6__borsuk_1,k10_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1))) => r2_hidden(c1_6_2__borsuk_1,c4_6__borsuk_1) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_6__borsuk_1,dt_c1_6_2__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1]),discharge_asm(discharge,[e1_6_2_1__borsuk_1])],[e1_6_2_1__borsuk_1,i1_6_2_1__borsuk_1]), [interesting(0.65),e1_6_2__borsuk_1]). fof(e1_6_2__borsuk_1,plain, ( r2_hidden(c1_6_2__borsuk_1,k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c2_6__borsuk_1,k10_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1))) => r2_hidden(c1_6_2__borsuk_1,c4_6__borsuk_1) ), inference(mizar_def_expansion,[status(thm),assumptions([dt_c1_6__borsuk_1,dt_c1_6_2__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1])],[i1_6_2_1_tmp__borsuk_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,fc13_finset_1,fc14_finset_1,rc1_finset_1,rc1_membered,rc3_finset_1,rc4_finset_1,cc15_membered,cc1_finset_1,cc5_funct_2,cc6_funct_2,fc4_subset_1,rc1_funct_2,rc1_subset_1,rc2_partfun1,rc2_subset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k8_funct_3,dt_k9_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc1_relset_1,fc1_subset_1,antisymmetry_r2_hidden,redefinition_k10_funct_3,redefinition_k12_mcart_1,redefinition_k2_funct_2,dt_k10_funct_3,dt_k12_mcart_1,dt_k2_funct_2,dt_k2_zfmisc_1,dt_c1_6__borsuk_1,dt_c1_6_2__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1]), [interesting(0.65),file(borsuk_1,e1_6_2__borsuk_1),[file(borsuk_1,e1_6_2__borsuk_1)]]). fof(e3_6_2__borsuk_1,assumption,( r2_hidden(c1_6_2__borsuk_1,c4_6__borsuk_1) ), introduced(assumption,[file(borsuk_1,e3_6_2__borsuk_1)]), [interesting(0.65),axiom,file(borsuk_1,e3_6_2__borsuk_1)]). fof(dh_c2_6_2__borsuk_1,definition, ( ? [A] : m1_subset_1(A,c3_6__borsuk_1) => m1_subset_1(c2_6_2__borsuk_1,c3_6__borsuk_1) ), introduced(definition,[new_symbol(c2_6_2__borsuk_1),file(borsuk_1,c2_6_2__borsuk_1)]), [interesting(0.65),axiom,file(borsuk_1,c2_6_2__borsuk_1)]). fof(e2_6_2__borsuk_1,plain,( ? [A] : m1_subset_1(A,c3_6__borsuk_1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__borsuk_1,dt_c3_6__borsuk_1])],[antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_finset_1,rc1_membered,rc3_finset_1,rc4_finset_1,t1_subset,t4_subset,t5_subset,t8_boole,reflexivity_r1_tarski,cc15_membered,cc1_finset_1,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,dt_k1_zfmisc_1,dt_c1_6__borsuk_1,fc1_subset_1,t3_subset,existence_m1_subset_1,dt_m1_subset_1,dt_c3_6__borsuk_1]), [interesting(0.65),file(borsuk_1,e2_6_2__borsuk_1),[file(borsuk_1,e2_6_2__borsuk_1)]]). fof(dt_c2_6_2__borsuk_1,plain,( m1_subset_1(c2_6_2__borsuk_1,c3_6__borsuk_1) ), inference(consider,[status(thm),assumptions([dt_c1_6__borsuk_1,dt_c3_6__borsuk_1])],[dh_c2_6_2__borsuk_1,e2_6_2__borsuk_1]), [interesting(0.65),file(borsuk_1,c2_6_2__borsuk_1),[file(borsuk_1,c2_6_2__borsuk_1)]]). fof(e4_6_2__borsuk_1,plain, ( r2_hidden(c2_6_2__borsuk_1,c1_6__borsuk_1) & r2_hidden(c1_6_2__borsuk_1,c2_6__borsuk_1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6_2__borsuk_1,e3_6_2__borsuk_1,dt_c1_6__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6__borsuk_1])],[cc2_finset_1,rc1_finset_1,rc3_finset_1,rc4_finset_1,existence_m1_subset_1,dt_k1_zfmisc_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_finset_1,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc1_subset_1,rc1_membered,rc1_subset_1,rc2_subset_1,t2_subset,t4_subset,t5_subset,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_c1_6__borsuk_1,dt_c1_6_2__borsuk_1,dt_c2_6__borsuk_1,dt_c2_6_2__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,fc6_membered,t1_subset,t3_subset,t6_boole,t7_boole,e3_6_2__borsuk_1,e2_6__borsuk_1,d3_tarski]), [interesting(0.65),file(borsuk_1,e4_6_2__borsuk_1),[file(borsuk_1,e4_6_2__borsuk_1)]]). fof(e6_6_2__borsuk_1,plain,( c1_6_2__borsuk_1 = k1_funct_1(k10_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k4_tarski(c2_6_2__borsuk_1,c1_6_2__borsuk_1)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6_2__borsuk_1,e3_6_2__borsuk_1,dt_c1_6__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6__borsuk_1])],[reflexivity_r1_tarski,cc1_funct_2,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc7_membered,fc8_membered,fc9_membered,existence_m1_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_m1_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,cc5_funct_2,cc6_funct_2,fc14_finset_1,fc1_subset_1,fc6_membered,rc1_finset_1,rc1_funct_2,rc1_membered,rc1_subset_1,rc2_partfun1,rc2_subset_1,rc3_finset_1,rc4_finset_1,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,dt_m2_relset_1,dt_c3_6__borsuk_1,cc15_membered,cc1_finset_1,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,fc4_subset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k10_funct_3,dt_k10_funct_3,dt_k1_funct_1,dt_k1_relat_1,dt_k2_zfmisc_1,dt_k4_tarski,dt_k8_funct_3,dt_c1_6__borsuk_1,dt_c1_6_2__borsuk_1,dt_c2_6__borsuk_1,dt_c2_6_2__borsuk_1,t1_subset,t7_boole,d5_tarski,e4_6_2__borsuk_1,d6_funct_3]), [interesting(0.65),file(borsuk_1,e6_6_2__borsuk_1),[file(borsuk_1,e6_6_2__borsuk_1)]]). fof(e5_6_2__borsuk_1,plain,( r2_hidden(k4_tarski(c2_6_2__borsuk_1,c1_6_2__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6_2__borsuk_1,dt_c1_6__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6__borsuk_1,e3_6_2__borsuk_1])],[cc2_finset_1,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_finset_1,fc14_membered,fc15_membered,fc16_membered,fc7_membered,fc8_membered,fc9_membered,rc1_finset_1,rc3_finset_1,rc4_finset_1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_tarski,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_finset_1,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc1_finset_1,fc1_subset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,fc4_subset_1,rc1_membered,rc1_subset_1,rc2_subset_1,t2_subset,t4_subset,t5_subset,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k12_mcart_1,dt_k12_mcart_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_k4_tarski,dt_c1_6__borsuk_1,dt_c1_6_2__borsuk_1,dt_c2_6__borsuk_1,dt_c2_6_2__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,fc6_membered,t1_subset,t3_subset,t6_boole,t7_boole,d5_tarski,e2_6__borsuk_1,e3_6_2__borsuk_1,t106_zfmisc_1]), [interesting(0.65),file(borsuk_1,e5_6_2__borsuk_1),[file(borsuk_1,e5_6_2__borsuk_1)]]). fof(e7_6_2__borsuk_1,plain,( r2_hidden(c1_6_2__borsuk_1,k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c2_6__borsuk_1,k10_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6_2__borsuk_1,dt_c1_6__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6__borsuk_1,e3_6_2__borsuk_1])],[reflexivity_r1_tarski,cc1_funct_2,cc2_finset_1,fc10_membered,fc11_membered,fc12_membered,fc13_finset_1,fc13_membered,fc14_finset_1,fc14_membered,fc15_membered,fc16_membered,fc7_membered,fc8_membered,fc9_membered,rc1_finset_1,rc3_finset_1,rc4_finset_1,commutativity_k2_tarski,existence_m1_relset_1,existence_m1_subset_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_tarski,dt_k8_funct_3,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_finset_1,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc5_funct_2,cc6_funct_2,fc1_finset_1,fc1_subset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,fc4_subset_1,rc1_funct_2,rc1_membered,rc1_subset_1,rc2_partfun1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_k10_funct_3,redefinition_k12_mcart_1,redefinition_k2_funct_2,redefinition_m2_relset_1,dt_k10_funct_3,dt_k12_mcart_1,dt_k1_funct_1,dt_k1_xboole_0,dt_k2_funct_2,dt_k2_zfmisc_1,dt_k4_tarski,dt_k9_relat_1,dt_m2_relset_1,dt_c1_6__borsuk_1,dt_c1_6_2__borsuk_1,dt_c2_6__borsuk_1,dt_c2_6_2__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,fc6_membered,t1_subset,t6_boole,t7_boole,d5_tarski,e6_6_2__borsuk_1,e3_6__borsuk_1,e5_6_2__borsuk_1,t43_funct_2]), [interesting(0.65),file(borsuk_1,e7_6_2__borsuk_1),[file(borsuk_1,e7_6_2__borsuk_1)]]). fof(i4_6_2__borsuk_1,theorem,( $true ), introduced(tautology,[file(borsuk_1,i4_6_2__borsuk_1)]), [interesting(0.65),trivial,file(borsuk_1,i4_6_2__borsuk_1)]). fof(i3_6_2__borsuk_1,plain,( r2_hidden(c1_6_2__borsuk_1,k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c2_6__borsuk_1,k10_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1))) ), inference(conclusion,[status(thm),assumptions([dt_c1_6_2__borsuk_1,dt_c1_6__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6__borsuk_1,e3_6_2__borsuk_1])],[cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,fc13_finset_1,fc14_finset_1,rc1_finset_1,rc1_membered,rc3_finset_1,rc4_finset_1,cc15_membered,cc1_finset_1,cc5_funct_2,cc6_funct_2,fc4_subset_1,rc1_funct_2,rc1_subset_1,rc2_partfun1,rc2_subset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k8_funct_3,dt_k9_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc1_relset_1,fc1_subset_1,antisymmetry_r2_hidden,redefinition_k10_funct_3,redefinition_k12_mcart_1,redefinition_k2_funct_2,dt_k10_funct_3,dt_k12_mcart_1,dt_k2_funct_2,dt_k2_zfmisc_1,dt_c1_6__borsuk_1,dt_c1_6_2__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e7_6_2__borsuk_1,i4_6_2__borsuk_1]), [interesting(0.65),file(borsuk_1,i3_6_2__borsuk_1),[file(borsuk_1,i3_6_2__borsuk_1)]]). fof(i3_6_2_tmp__borsuk_1,plain, ( r2_hidden(c1_6_2__borsuk_1,c4_6__borsuk_1) => r2_hidden(c1_6_2__borsuk_1,k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c2_6__borsuk_1,k10_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1))) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_6_2__borsuk_1,dt_c1_6__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6__borsuk_1]),discharge_asm(discharge,[e3_6_2__borsuk_1])],[e3_6_2__borsuk_1,i3_6_2__borsuk_1]), [interesting(0.65),i2_6_2__borsuk_1]). fof(i2_6_2__borsuk_1,plain, ( r2_hidden(c1_6_2__borsuk_1,c4_6__borsuk_1) => r2_hidden(c1_6_2__borsuk_1,k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c2_6__borsuk_1,k10_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1))) ), inference(mizar_def_expansion,[status(thm),assumptions([dt_c1_6_2__borsuk_1,dt_c1_6__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6__borsuk_1])],[i3_6_2_tmp__borsuk_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,fc13_finset_1,fc14_finset_1,rc1_finset_1,rc1_membered,rc3_finset_1,rc4_finset_1,cc15_membered,cc1_finset_1,cc5_funct_2,cc6_funct_2,fc4_subset_1,rc1_funct_2,rc1_subset_1,rc2_partfun1,rc2_subset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k8_funct_3,dt_k9_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc1_relset_1,fc1_subset_1,antisymmetry_r2_hidden,redefinition_k10_funct_3,redefinition_k12_mcart_1,redefinition_k2_funct_2,dt_k10_funct_3,dt_k12_mcart_1,dt_k2_funct_2,dt_k2_zfmisc_1,dt_c1_6__borsuk_1,dt_c1_6_2__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1]), [interesting(0.65),file(borsuk_1,i2_6_2__borsuk_1),[file(borsuk_1,i2_6_2__borsuk_1)]]). fof(i1_6_2__borsuk_1,plain, ( ( r2_hidden(c1_6_2__borsuk_1,k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c2_6__borsuk_1,k10_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1))) => r2_hidden(c1_6_2__borsuk_1,c4_6__borsuk_1) ) & ( r2_hidden(c1_6_2__borsuk_1,c4_6__borsuk_1) => r2_hidden(c1_6_2__borsuk_1,k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c2_6__borsuk_1,k10_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1))) ) ), inference(conclusion,[status(thm),assumptions([dt_c1_6_2__borsuk_1,dt_c1_6__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6__borsuk_1])],[cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,fc13_finset_1,fc14_finset_1,rc1_finset_1,rc1_membered,rc3_finset_1,rc4_finset_1,cc15_membered,cc1_finset_1,cc5_funct_2,cc6_funct_2,fc4_subset_1,rc1_funct_2,rc1_subset_1,rc2_partfun1,rc2_subset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k8_funct_3,dt_k9_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc1_relset_1,fc1_subset_1,antisymmetry_r2_hidden,redefinition_k10_funct_3,redefinition_k12_mcart_1,redefinition_k2_funct_2,dt_k10_funct_3,dt_k12_mcart_1,dt_k2_funct_2,dt_k2_zfmisc_1,dt_c1_6__borsuk_1,dt_c1_6_2__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6_2__borsuk_1,i2_6_2__borsuk_1]), [interesting(0.65),file(borsuk_1,i1_6_2__borsuk_1),[file(borsuk_1,i1_6_2__borsuk_1)]]). fof(i1_6_2_tmp__borsuk_1,plain, ( ( r2_hidden(c1_6_2__borsuk_1,k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c2_6__borsuk_1,k10_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1))) => r2_hidden(c1_6_2__borsuk_1,c4_6__borsuk_1) ) & ( r2_hidden(c1_6_2__borsuk_1,c4_6__borsuk_1) => r2_hidden(c1_6_2__borsuk_1,k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c2_6__borsuk_1,k10_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1))) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_6__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6__borsuk_1]),discharge_asm(discharge,[dt_c1_6_2__borsuk_1])],[dt_c1_6_2__borsuk_1,i1_6_2__borsuk_1]), [interesting(0.8),e6_6__borsuk_1]). fof(e6_6__borsuk_1,plain,( ! [A] : ( ( r2_hidden(A,k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c2_6__borsuk_1,k10_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1))) => r2_hidden(A,c4_6__borsuk_1) ) & ( r2_hidden(A,c4_6__borsuk_1) => r2_hidden(A,k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c2_6__borsuk_1,k10_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1))) ) ) ), inference(let,[status(thm),assumptions([dt_c1_6__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6__borsuk_1])],[i1_6_2_tmp__borsuk_1,dh_c1_6_2__borsuk_1]), [interesting(0.8),file(borsuk_1,e6_6__borsuk_1),[file(borsuk_1,e6_6__borsuk_1)]]). fof(e7_6__borsuk_1,plain,( k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c2_6__borsuk_1,k10_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1)) = c4_6__borsuk_1 ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6__borsuk_1])],[reflexivity_r1_tarski,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,fc13_finset_1,fc14_finset_1,fc6_membered,rc1_finset_1,rc1_funct_2,rc1_membered,rc2_partfun1,rc3_finset_1,rc4_finset_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k8_funct_3,dt_k9_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc15_membered,cc1_finset_1,cc1_relset_1,cc5_funct_2,cc6_funct_2,fc1_subset_1,fc4_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k10_funct_3,redefinition_k12_mcart_1,redefinition_k2_funct_2,dt_k10_funct_3,dt_k12_mcart_1,dt_k2_funct_2,dt_k2_zfmisc_1,dt_c1_6__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,t1_subset,t7_boole,e6_6__borsuk_1,t2_tarski]), [interesting(0.8),file(borsuk_1,e7_6__borsuk_1),[file(borsuk_1,e7_6__borsuk_1)]]). fof(i7_6__borsuk_1,theorem,( $true ), introduced(tautology,[file(borsuk_1,i7_6__borsuk_1)]), [interesting(0.8),trivial,file(borsuk_1,i7_6__borsuk_1)]). fof(i6_6__borsuk_1,plain,( k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c2_6__borsuk_1,k10_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1)) = c4_6__borsuk_1 ), inference(conclusion,[status(thm),assumptions([dt_c1_6__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6__borsuk_1])],[cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,fc13_finset_1,fc14_finset_1,rc1_finset_1,rc1_membered,rc3_finset_1,rc4_finset_1,cc15_membered,cc1_finset_1,cc5_funct_2,cc6_funct_2,fc4_subset_1,rc1_funct_2,rc1_subset_1,rc2_partfun1,rc2_subset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k8_funct_3,dt_k9_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc1_relset_1,fc1_subset_1,redefinition_k10_funct_3,redefinition_k12_mcart_1,redefinition_k2_funct_2,dt_k10_funct_3,dt_k12_mcart_1,dt_k2_funct_2,dt_k2_zfmisc_1,dt_c1_6__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e7_6__borsuk_1,i7_6__borsuk_1]), [interesting(0.8),file(borsuk_1,i6_6__borsuk_1),[file(borsuk_1,i6_6__borsuk_1)]]). fof(i5_6__borsuk_1,plain, ( k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c1_6__borsuk_1,k9_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1)) = c3_6__borsuk_1 & k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c2_6__borsuk_1,k10_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1)) = c4_6__borsuk_1 ), inference(conclusion,[status(thm),assumptions([dt_c1_6__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e1_6__borsuk_1])],[cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,fc13_finset_1,fc14_finset_1,rc1_finset_1,rc1_membered,rc3_finset_1,rc4_finset_1,cc15_membered,cc1_finset_1,cc5_funct_2,cc6_funct_2,fc4_subset_1,rc1_funct_2,rc1_subset_1,rc2_partfun1,rc2_subset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k7_funct_3,dt_k8_funct_3,dt_k9_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc1_relset_1,fc1_subset_1,redefinition_k10_funct_3,redefinition_k12_mcart_1,redefinition_k2_funct_2,redefinition_k9_funct_3,dt_k10_funct_3,dt_k12_mcart_1,dt_k2_funct_2,dt_k2_zfmisc_1,dt_k9_funct_3,dt_c1_6__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,e5_6__borsuk_1,i6_6__borsuk_1]), [interesting(0.8),file(borsuk_1,i5_6__borsuk_1),[file(borsuk_1,i5_6__borsuk_1)]]). fof(i5_6_tmp__borsuk_1,plain, ( k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1) != k1_xboole_0 => ( k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c1_6__borsuk_1,k9_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1)) = c3_6__borsuk_1 & k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c2_6__borsuk_1,k10_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1)) = c4_6__borsuk_1 ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_6__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1]),discharge_asm(discharge,[e1_6__borsuk_1])],[e1_6__borsuk_1,i5_6__borsuk_1]), [interesting(0.8),i4_6__borsuk_1]). fof(i4_6__borsuk_1,plain, ( k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1) != k1_xboole_0 => ( k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c1_6__borsuk_1,k9_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1)) = c3_6__borsuk_1 & k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c2_6__borsuk_1,k10_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1)) = c4_6__borsuk_1 ) ), inference(mizar_def_expansion,[status(thm),assumptions([dt_c1_6__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1])],[i5_6_tmp__borsuk_1,cc1_funct_2,cc2_finset_1,fc13_finset_1,fc14_finset_1,rc1_finset_1,rc1_funct_2,rc2_partfun1,rc3_finset_1,rc4_finset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k7_funct_3,dt_k8_funct_3,dt_k9_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finset_1,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc5_funct_2,cc6_funct_2,fc1_subset_1,fc4_subset_1,rc1_membered,rc1_subset_1,rc2_subset_1,redefinition_k10_funct_3,redefinition_k12_mcart_1,redefinition_k2_funct_2,redefinition_k9_funct_3,dt_k10_funct_3,dt_k12_mcart_1,dt_k1_xboole_0,dt_k2_funct_2,dt_k2_zfmisc_1,dt_k9_funct_3,dt_c1_6__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1,dt_c4_6__borsuk_1,fc6_membered]), [interesting(0.8),file(borsuk_1,i4_6__borsuk_1),[file(borsuk_1,i4_6__borsuk_1)]]). fof(i4_6_tmp__borsuk_1,plain, ( m1_subset_1(c4_6__borsuk_1,k1_zfmisc_1(c2_6__borsuk_1)) => ( k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1) != k1_xboole_0 => ( k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c1_6__borsuk_1,k9_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1)) = c3_6__borsuk_1 & k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c2_6__borsuk_1,k10_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,c4_6__borsuk_1)) = c4_6__borsuk_1 ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_6__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1]),discharge_asm(discharge,[dt_c4_6__borsuk_1])],[dt_c4_6__borsuk_1,i4_6__borsuk_1]), [interesting(0.8),i3_6__borsuk_1]). fof(i3_6__borsuk_1,plain,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(c2_6__borsuk_1)) => ( k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,A) != k1_xboole_0 => ( k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c1_6__borsuk_1,k9_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,A)) = c3_6__borsuk_1 & k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c2_6__borsuk_1,k10_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,A)) = A ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_6__borsuk_1,dt_c2_6__borsuk_1,dt_c3_6__borsuk_1])],[i4_6_tmp__borsuk_1,dh_c4_6__borsuk_1]), [interesting(0.8),file(borsuk_1,i3_6__borsuk_1),[file(borsuk_1,i3_6__borsuk_1)]]). fof(i3_6_tmp__borsuk_1,plain, ( m1_subset_1(c3_6__borsuk_1,k1_zfmisc_1(c1_6__borsuk_1)) => ! [A] : ( m1_subset_1(A,k1_zfmisc_1(c2_6__borsuk_1)) => ( k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,A) != k1_xboole_0 => ( k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c1_6__borsuk_1,k9_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,A)) = c3_6__borsuk_1 & k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c2_6__borsuk_1,k10_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,c3_6__borsuk_1,A)) = A ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_6__borsuk_1,dt_c2_6__borsuk_1]),discharge_asm(discharge,[dt_c3_6__borsuk_1])],[dt_c3_6__borsuk_1,i3_6__borsuk_1]), [interesting(0.8),i2_6__borsuk_1]). fof(i2_6__borsuk_1,plain,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(c1_6__borsuk_1)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(c2_6__borsuk_1)) => ( k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,A,B) != k1_xboole_0 => ( k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c1_6__borsuk_1,k9_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,A,B)) = A & k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c2_6__borsuk_1,k10_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,A,B)) = B ) ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_6__borsuk_1,dt_c2_6__borsuk_1])],[i3_6_tmp__borsuk_1,dh_c3_6__borsuk_1]), [interesting(0.8),file(borsuk_1,i2_6__borsuk_1),[file(borsuk_1,i2_6__borsuk_1)]]). fof(i2_6_tmp__borsuk_1,plain,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(c1_6__borsuk_1)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(c2_6__borsuk_1)) => ( k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,A,B) != k1_xboole_0 => ( k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c1_6__borsuk_1,k9_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,A,B)) = A & k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,c2_6__borsuk_1),c2_6__borsuk_1,k10_funct_3(c1_6__borsuk_1,c2_6__borsuk_1),k12_mcart_1(c1_6__borsuk_1,c2_6__borsuk_1,A,B)) = B ) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_6__borsuk_1]),discharge_asm(discharge,[dt_c2_6__borsuk_1])],[dt_c2_6__borsuk_1,i2_6__borsuk_1]), [interesting(0.8),i1_6__borsuk_1]). fof(i1_6__borsuk_1,plain,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(c1_6__borsuk_1)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( k12_mcart_1(c1_6__borsuk_1,A,B,C) != k1_xboole_0 => ( k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,A),c1_6__borsuk_1,k9_funct_3(c1_6__borsuk_1,A),k12_mcart_1(c1_6__borsuk_1,A,B,C)) = B & k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,A),A,k10_funct_3(c1_6__borsuk_1,A),k12_mcart_1(c1_6__borsuk_1,A,B,C)) = C ) ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_6__borsuk_1])],[i2_6_tmp__borsuk_1,dh_c2_6__borsuk_1]), [interesting(0.8),file(borsuk_1,i1_6__borsuk_1),[file(borsuk_1,i1_6__borsuk_1)]]). fof(i1_6_tmp__borsuk_1,plain,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(c1_6__borsuk_1)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( k12_mcart_1(c1_6__borsuk_1,A,B,C) != k1_xboole_0 => ( k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,A),c1_6__borsuk_1,k9_funct_3(c1_6__borsuk_1,A),k12_mcart_1(c1_6__borsuk_1,A,B,C)) = B & k2_funct_2(k2_zfmisc_1(c1_6__borsuk_1,A),A,k10_funct_3(c1_6__borsuk_1,A),k12_mcart_1(c1_6__borsuk_1,A,B,C)) = C ) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_6__borsuk_1])],[dt_c1_6__borsuk_1,i1_6__borsuk_1]), [interesting(1),t12_borsuk_1]). fof(t12_borsuk_1,theorem,( ! [A,B,C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) => ( k12_mcart_1(A,B,C,D) != k1_xboole_0 => ( k2_funct_2(k2_zfmisc_1(A,B),A,k9_funct_3(A,B),k12_mcart_1(A,B,C,D)) = C & k2_funct_2(k2_zfmisc_1(A,B),B,k10_funct_3(A,B),k12_mcart_1(A,B,C,D)) = D ) ) ) ) ), inference(let,[status(thm),assumptions([])],[i1_6_tmp__borsuk_1,dh_c1_6__borsuk_1]), [interesting(1),file(borsuk_1,t12_borsuk_1),[file(borsuk_1,t12_borsuk_1)]]).