0.12/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s 0.14/0.35 % Computer : n007.cluster.edu 0.14/0.35 % Model : x86_64 x86_64 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.35 % Memory : 8042.1875MB 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.35 % CPULimit : 180 0.14/0.35 % DateTime : Thu Aug 29 14:17:51 EDT 2019 0.14/0.35 % CPUTime : 107.79/107.74 % SZS status Theorem 107.79/107.74 % Mode: mode503:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=4.:SINE_DEPTH=0 107.79/107.74 % Inferences: 338 107.79/107.74 % SZS output start Proof 107.79/107.74 thf(ty_kfst, type, kfst : ($i>$i)). 107.79/107.74 thf(ty_binintersect, type, binintersect : ($i>$i>$i)). 107.79/107.74 thf(ty_singleton, type, singleton : ($i>$o)). 107.79/107.74 thf(ty_if, type, if : ($i>$o>$i>$i>$i)). 107.79/107.74 thf(ty_subset, type, subset : ($i>$i>$o)). 107.79/107.74 thf(ty_eigen__2, type, eigen__2 : $i). 107.79/107.74 thf(ty_setunion, type, setunion : ($i>$i)). 107.79/107.74 thf(ty_iskpair, type, iskpair : ($i>$o)). 107.79/107.74 thf(ty_breln1invset, type, breln1invset : ($i>$i>$i)). 107.79/107.74 thf(ty_eigen__1, type, eigen__1 : ($i>$i)). 107.79/107.74 thf(ty_eigen__0, type, eigen__0 : $i). 107.79/107.74 thf(ty_cartprod, type, cartprod : ($i>$i>$i)). 107.79/107.74 thf(ty_breln, type, breln : ($i>$i>$i>$o)). 107.79/107.74 thf(ty_emptyset, type, emptyset : $i). 107.79/107.74 thf(ty_breln1, type, breln1 : ($i>$i>$o)). 107.79/107.74 thf(ty_setminus, type, setminus : ($i>$i>$i)). 107.79/107.74 thf(ty_kpair, type, kpair : ($i>$i>$i)). 107.79/107.74 thf(ty_eigen__3, type, eigen__3 : $i). 107.79/107.74 thf(ty_descr, type, descr : (($i>$o)>$i)). 107.79/107.74 thf(ty_reflwellordering, type, reflwellordering : ($i>$i>$o)). 107.79/107.74 thf(ty_breln1compset, type, breln1compset : ($i>$i>$i>$i)). 107.79/107.74 thf(ty_breln1Set, type, breln1Set : ($i>$i)). 107.79/107.74 thf(ty_ap, type, ap : ($i>$i>$i>$i>$i)). 107.79/107.74 thf(ty_funcSet, type, funcSet : ($i>$i>$i)). 107.79/107.74 thf(ty_symdiff, type, symdiff : ($i>$i>$i)). 107.79/107.74 thf(ty_dsetconstr, type, dsetconstr : ($i>($i>$o)>$i)). 107.79/107.74 thf(ty_powerset, type, powerset : ($i>$i)). 107.79/107.74 thf(ty_omega, type, omega : $i). 107.79/107.74 thf(ty_ex1, type, ex1 : ($i>($i>$o)>$o)). 107.79/107.74 thf(ty_ksnd, type, ksnd : ($i>$i)). 107.79/107.74 thf(ty_prop2set, type, prop2set : ($o>$i)). 107.79/107.74 thf(ty_set2prop, type, set2prop : ($i>$o)). 107.79/107.74 thf(ty_lam, type, lam : ($i>$i>($i>$i)>$i)). 107.79/107.74 thf(ty_in, type, in : ($i>$i>$o)). 107.79/107.74 thf(ty_func, type, func : ($i>$i>$i>$o)). 107.79/107.74 thf(ty_binunion, type, binunion : ($i>$i>$i)). 107.79/107.74 thf(ty_dpsetconstr, type, dpsetconstr : ($i>$i>($i>$i>$o)>$i)). 107.79/107.74 thf(ty_image1, type, image1 : ($i>($i>$i)>$i)). 107.79/107.74 thf(ty_setadjoin, type, setadjoin : ($i>$i>$i)). 107.79/107.74 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). 107.79/107.74 thf(eigendef_eigen__3, definition, eigen__3 = (eps__0 @ (^[X1:$i]:(~(((eigen__2 = (eigen__1 @ X1)) => (~(((in @ X1) @ eigen__0)))))))), introduced(definition,[new_symbols(definition,[eigen__3])])). 107.79/107.74 thf(h1, assumption, (![X1:($i>$i)>$o]:(![X2:$i>$i]:((X1 @ X2) => (X1 @ (eps__1 @ X1))))),introduced(assumption,[])). 107.79/107.74 thf(eigendef_eigen__1, definition, eigen__1 = (eps__1 @ (^[X1:$i>$i]:(~((![X2:$i]:((~((![X3:$i]:((X2 = (X1 @ X3)) => (~(((in @ X3) @ eigen__0))))))) => ((in @ X2) @ ((image1 @ eigen__0) @ X1)))))))), introduced(definition,[new_symbols(definition,[eigen__1])])). 107.79/107.74 thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:$i]:(~((![X2:$i>$i]:(![X3:$i]:((~((![X4:$i]:((X3 = (X2 @ X4)) => (~(((in @ X4) @ X1))))))) => ((in @ X3) @ ((image1 @ X1) @ X2))))))))), introduced(definition,[new_symbols(definition,[eigen__0])])). 107.79/107.74 thf(eigendef_eigen__2, definition, eigen__2 = (eps__0 @ (^[X1:$i]:(~(((~((![X2:$i]:((X1 = (eigen__1 @ X2)) => (~(((in @ X2) @ eigen__0))))))) => ((in @ X1) @ ((image1 @ eigen__0) @ eigen__1))))))), introduced(definition,[new_symbols(definition,[eigen__2])])). 107.79/107.74 thf(sP1,plain,sP1 <=> ((![X1:$i]:((![X2:$i]:(~(((in @ X2) @ X1)))) => (X1 = emptyset))) => ((![X1:$i]:((![X2:$i]:(~(((in @ X2) @ X1)))) => (X1 = emptyset))) => ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ ((dsetconstr @ X1) @ X2)) = (X2 @ X3)))))) => ((![X1:$i]:((~((X1 = emptyset))) => (~((![X2:$i]:(~(((in @ X2) @ X1)))))))) => ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => (~((((dsetconstr @ X1) @ X2) = emptyset)))))))) => ((![X1:$i]:((~((![X2:$i]:(~(((in @ X2) @ X1)))))) => (~((X1 = emptyset))))) => ((![X1:$i]:(![X2:$i]:((in @ X1) @ ((setadjoin @ X1) @ X2)))) => (((in @ emptyset) @ ((setadjoin @ emptyset) @ emptyset)) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ ((setadjoin @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ X2)) => (![X4:$o]:(((X3 = X1) => X4) => ((((in @ X3) @ X2) => X4) => X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ X2)) => ((~((X3 = X1))) => ((in @ X3) @ X2)))))) => ((![X1:$i]:(((dsetconstr @ X1) @ (^[X2:$i]:(~($false)))) = X1)) => ((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1))) => ((in @ X2) @ (powerset @ X1))))) => ((![X1:$i]:((in @ emptyset) @ (powerset @ X1))) => ((![X1:$i]:((in @ emptyset) @ (powerset @ X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X2) @ (powerset @ X1)) => (((in @ X3) @ X2) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X2) @ X3) => (((in @ X3) @ X1) => ((in @ X2) @ (setunion @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) => (![X3:$o]:((![X4:$i]:(((in @ X2) @ X4) => (((in @ X4) @ X1) => X3))) => X3))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ X1) => ((in @ X2) @ (powerset @ (setunion @ X1)))))) => ((![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (~((![X2:$i]:(~((![X3:$i]:((X1 @ X3) = (X3 = X2)))))))))) => ((![X1:$i]:((~((X1 = emptyset))) => (~((![X2:$i]:(~(((in @ X2) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X1) @ ((setadjoin @ X2) @ emptyset)) => (X1 = X2)))) => ((![X1:$i]:(![X2:$i]:((~((X1 = X2))) => (~(((in @ X2) @ ((setadjoin @ X1) @ emptyset))))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => ((in @ X1) @ ((setadjoin @ X2) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(((in @ X1) @ ((setadjoin @ X2) @ emptyset)) => ((in @ X2) @ ((setadjoin @ X1) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) => ((~((X3 = X1))) => (X3 = X2)))))) => ((![X1:$i]:(![X2:$i]:((in @ X1) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:((in @ X2) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))) => ((![X1:$i]:(![X2:$i>$o]:((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => (~((((dsetconstr @ X1) @ X2) = emptyset)))))) => ((![X1:$i>$o]:(![X2:$i]:(((in @ X2) @ emptyset) => (X1 @ X2)))) => ((![X1:$i]:(![X2:$i>$o]:((~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3))))) => (~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3)))))))) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))) => (![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))) => (![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))) => ((![X1:$i]:(![X2:$i>$o]:((~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3))))) => (~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3)))))))) => ((![X1:$o]:(X1 => ((in @ emptyset) @ (prop2set @ X1)))) => ((![X1:$o]:(X1 => (set2prop @ (prop2set @ X1)))) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))) => (![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))) => ((![X1:$i]:(![X2:$i>$o]:((~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3))))) => (~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3)))))))) => ((![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))))) => ((![X1:$i>$o]:((~((![X2:$i]:(~((X1 @ X2)))))) => ((![X2:$i]:(![X3:$i]:((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))) => (~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3)))))))))))) => ((![X1:$i>$o]:((~((![X2:$i]:(~((![X3:$i]:((X1 @ X3) = (X3 = X2)))))))) => (~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((in @ X3) @ X1) => ((in @ X4) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((in @ X3) @ X1) = ((in @ X4) @ X2)))))))) => ((![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (![X2:$i]:(![X3:$i]:((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))))) => ((![X1:$i>$o]:(![X2:$i>$o]:((![X3:$i]:(![X4:$i]:((X3 = X4) => ((X1 @ X3) = (X2 @ X4))))) => ((~((![X3:$i]:((X1 @ X3) => (~((![X4:$i]:((X1 @ X4) => (X3 = X4))))))))) = (~((![X3:$i]:((X2 @ X3) => (~((![X4:$i]:((X2 @ X4) => (X3 = X4))))))))))))) => ((emptyset = emptyset) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((setadjoin @ X1) @ X3) = ((setadjoin @ X2) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => ((powerset @ X1) = (powerset @ X2))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => ((setunion @ X1) = (setunion @ X2))))) => ((omega = omega) => ((![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (![X2:$i]:(![X3:$i]:((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))))) => ((![X1:$i>$o]:(![X2:$i>$o]:((![X3:$i]:(![X4:$i]:((X3 = X4) => ((X1 @ X3) = (X2 @ X4))))) => ((~((![X3:$i]:((X1 @ X3) => (~((![X4:$i]:((X1 @ X4) => (X3 = X4))))))))) => ((~((![X3:$i]:((X2 @ X3) => (~((![X4:$i]:((X2 @ X4) => (X3 = X4))))))))) => ((descr @ X1) = (descr @ X2))))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i>$o]:(![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => ((X5 = X6) => ((X3 @ X5) = (X4 @ X6))))))) => (((dsetconstr @ X1) @ X3) = ((dsetconstr @ X2) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((subset @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => ((subset @ X2) @ X1)))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => ((subset @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((subset @ X1) @ X2)))) => (((!!) @ (subset @ emptyset)) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X2) => (((in @ X3) @ X1) => ((in @ X3) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X2) => ((~(((in @ X3) @ X2))) => (~(((in @ X3) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => (~(((subset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:((~(((subset @ X1) @ X2))) => (~((X1 = X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => (~((X1 = X2)))))))) => ((![X1:$i]:((subset @ X1) @ X1)) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X2) => (((subset @ X2) @ X3) => ((subset @ X1) @ X3)))))) => ((![X1:$i]:(![X2:$i]:((subset @ X2) @ ((setadjoin @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X3) => ((subset @ X1) @ ((setadjoin @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => ((in @ X1) @ (powerset @ X2))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((subset @ X2) @ X1) => (X1 = X2))))) => ((![X1:$i]:(((subset @ X1) @ emptyset) => (X1 = emptyset))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ X1) => ((in @ X2) @ (powerset @ X1))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ X2) @ X1)))) => ((![X1:$i]:((in @ X1) @ (powerset @ X1))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => ((subset @ (powerset @ X1)) @ (powerset @ X2))))) => ((![X1:$i]:(![X2:$i>$o]:((in @ ((dsetconstr @ X1) @ X2)) @ (powerset @ X1)))) => ((![X1:$i]:(![X2:$i>$o]:((subset @ ((dsetconstr @ X1) @ X2)) @ X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ ((binunion @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:((in @ X2) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ ((binunion @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$o]:(((in @ X3) @ ((binunion @ X1) @ X2)) => ((((in @ X3) @ X1) => X4) => ((((in @ X3) @ X2) => X4) => X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((binunion @ X1) @ X2)) => ((~(((in @ X3) @ X1))) => ((in @ X3) @ X2)))))) => ((![X1:$i]:(![X2:$i]:((subset @ X1) @ ((binunion @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:((subset @ X2) @ ((binunion @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => ((in @ X3) @ ((binintersect @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X3) @ X1) => (((subset @ X3) @ X2) => ((subset @ X3) @ ((binintersect @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((binintersect @ X1) @ X2)) => ((in @ X3) @ X1))))) => ((![X1:$i]:(![X2:$i]:((subset @ ((binintersect @ X1) @ X2)) @ X1))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((binintersect @ X1) @ X2) = X1)))) => ((![X1:$i]:(![X2:$i]:((((binintersect @ X1) @ X2) = X2) => ((subset @ X2) @ X1)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((binintersect @ X1) @ X2)) => ((in @ X3) @ X2))))) => ((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => (~(((in @ X3) @ X2))))) => (((binintersect @ X1) @ X2) = emptyset)))) => ((![X1:$i]:(![X2:$i]:((subset @ ((binintersect @ X1) @ X2)) @ X2))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ X1) => (((binintersect @ X1) @ X2) = X2)))) => ((![X1:$i]:(![X2:$i]:((((binintersect @ X1) @ X2) = X1) => ((subset @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((binintersect @ X1) @ ((binunion @ X2) @ X3)) = ((binunion @ ((binintersect @ X1) @ X2)) @ ((binintersect @ X1) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => ((in @ X3) @ ((setminus @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setminus @ X1) @ X2)) => ((in @ X3) @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setminus @ X1) @ X2)) => (~(((in @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((setminus @ X1) @ X2) = emptyset)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ ((setminus @ X1) @ X2)))) => (((in @ X3) @ X1) => ((in @ X3) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ ((setminus @ X1) @ X2)))) => ((~(((in @ X3) @ X2))) => (~(((in @ X3) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X2) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:((subset @ ((setminus @ X1) @ X2)) @ X1))) => ((![X1:$i]:(![X2:$i]:((((setminus @ X1) @ X2) = emptyset) => ((subset @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((symdiff @ X1) @ X2)) => (![X4:$o]:((((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => X4)) => (((~(((in @ X3) @ X1))) => (((in @ X3) @ X2) => X4)) => X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => ((in @ X3) @ ((symdiff @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => (((in @ X3) @ X2) => ((in @ X3) @ ((symdiff @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => (~(((in @ X3) @ ((symdiff @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => ((~(((in @ X3) @ X2))) => (~(((in @ X3) @ ((symdiff @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:((in @ X2) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:((in @ X1) @ (setunion @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)))))) => ((![X1:$i]:(![X2:$i]:((in @ X2) @ (setunion @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)))))) => ((![X1:$i]:(![X2:$i]:(iskpair @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(iskpair @ ((kpair @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ X1) => ((subset @ ((setadjoin @ X2) @ emptyset)) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ X1) => ((in @ ((setadjoin @ X2) @ emptyset)) @ (powerset @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((in @ ((setadjoin @ X3) @ emptyset)) @ (powerset @ ((binunion @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) => ((~((X3 = X1))) => (X3 = X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((subset @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ ((binunion @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((subset @ ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) @ (powerset @ (powerset @ ((binunion @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ (powerset @ (powerset @ ((binunion @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (~((X3 = ((kpair @ X4) @ X5)))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (iskpair @ X3))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) => (~((![X3:$i]:(((in @ X3) @ X1) => (~(((in @ X2) @ X3)))))))))) => ((![X1:$i]:((subset @ (setunion @ ((setadjoin @ X1) @ emptyset))) @ X1)) => ((![X1:$i]:((subset @ X1) @ (setunion @ ((setadjoin @ X1) @ emptyset)))) => ((![X1:$i]:((setunion @ ((setadjoin @ X1) @ emptyset)) = X1)) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => (singleton @ ((dsetconstr @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))))) => ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X4) => (X4 = X3)))) => ((ex1 @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => ((ex1 @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:((((setadjoin @ X1) @ emptyset) = ((setadjoin @ X2) @ emptyset)) => (X1 = X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) => (X1 = X3))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:((in @ ((setadjoin @ X2) @ emptyset)) @ X1)))))) => ((![X1:$i]:((singleton @ X1) => ((in @ (setunion @ X1)) @ X1))) => ((![X1:$i]:(![X2:$i]:((kfst @ ((kpair @ X1) @ X2)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (kfst @ X3)) @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X1) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => ((X3 = X4) => (X2 = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X3) @ emptyset)) => (X1 = X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X2 = X4)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X2 = X4)))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:(X1 = ((kpair @ (kfst @ X1)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:((ksnd @ ((kpair @ X1) @ X2)) = X2))) => ((![X1:$i]:((iskpair @ X1) => (((kpair @ (kfst @ X1)) @ (ksnd @ X1)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X4) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => (((kpair @ X3) @ X4) = ((kpair @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => 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(![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ X1))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))) => ((![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X3) => ((in @ X4) @ X2)))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))) => ((in @ X2) @ (powerset @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X2) @ (powerset @ X3)) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ ((setminus @ X1) @ X2)))) => ((in @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X2))) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => (((in @ X4) @ X3) => (~(((in @ X4) @ X2)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((subset @ X2) @ X3) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ X2)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ X3) => ((subset @ ((setminus @ X1) @ X3)) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ ((setminus @ X1) @ X3)) @ ((setminus @ X1) @ X2)) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => ((in @ X3) @ ((setminus @ X1) @ ((setminus @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ ((setminus @ X1) @ ((setminus @ 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X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => (~(((in @ X4) @ X2))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$o]:(![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binunion @ X2) @ X3)) => ((((in @ X5) @ X2) => X4) => ((((in @ X5) @ X3) => X4) => X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X2))) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ ((binunion @ X2) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ 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=> (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (((in @ X4) @ ((setminus @ X1) @ X3)) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => ((![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))) => (~((![X4:$i]:((![X5:$i]:(((in @ X5) @ X4) = (~((![X6:$i]:(((in @ X6) @ X1) => (~((X5 = (X2 @ X6)))))))))) => (X3 = X4))))))))))) => ((![X1:$i]:(![X2:$i>$i]:(![X3:$i]:(((in @ X3) @ ((image1 @ X1) @ X2)) = (~((![X4:$i]:(((in @ X4) @ X1) => (~((X3 = (X2 @ X4)))))))))))) => ((![X1:$i]:(![X2:$i>$i]:(![X3:$i]:(((in @ X3) @ ((image1 @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (~((X3 = (X2 @ X4)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(![X3:$i]:((~((![X4:$i]:((X3 = (X2 @ X4)) => (~(((in @ X4) @ X1))))))) => ((in @ X3) @ ((image1 @ X1) @ X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP1])])). 107.79/107.74 thf(sP2,plain,sP2 <=> ((![X1:$i]:(![X2:$i]:((X1 = X2) => ((in @ X1) @ ((setadjoin @ X2) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(((in @ X1) @ ((setadjoin @ X2) @ emptyset)) => ((in @ X2) @ ((setadjoin @ X1) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) => ((~((X3 = X1))) => (X3 = X2)))))) => ((![X1:$i]:(![X2:$i]:((in @ X1) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:((in @ X2) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))) => ((![X1:$i]:(![X2:$i>$o]:((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => (~((((dsetconstr @ X1) @ X2) = emptyset)))))) => ((![X1:$i>$o]:(![X2:$i]:(((in @ X2) @ emptyset) => (X1 @ X2)))) => ((![X1:$i]:(![X2:$i>$o]:((~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3))))) => (~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3)))))))) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))) => (![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))) => (![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))) => ((![X1:$i]:(![X2:$i>$o]:((~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3))))) => (~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3)))))))) => ((![X1:$o]:(X1 => ((in @ emptyset) @ (prop2set @ X1)))) => ((![X1:$o]:(X1 => (set2prop @ (prop2set @ 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X2)))))))) => ((![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (![X2:$i]:(![X3:$i]:((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))))) => ((![X1:$i>$o]:(![X2:$i>$o]:((![X3:$i]:(![X4:$i]:((X3 = X4) => ((X1 @ X3) = (X2 @ X4))))) => ((~((![X3:$i]:((X1 @ X3) => (~((![X4:$i]:((X1 @ X4) => (X3 = X4))))))))) = (~((![X3:$i]:((X2 @ X3) => (~((![X4:$i]:((X2 @ X4) => (X3 = X4))))))))))))) => ((emptyset = emptyset) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((setadjoin @ X1) @ X3) = ((setadjoin @ X2) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => ((powerset @ X1) = (powerset @ X2))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => ((setunion @ X1) = (setunion @ X2))))) => ((omega = omega) => ((![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (![X2:$i]:(![X3:$i]:((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))))) => ((![X1:$i>$o]:(![X2:$i>$o]:((![X3:$i]:(![X4:$i]:((X3 = X4) => ((X1 @ X3) = (X2 @ X4))))) => ((~((![X3:$i]:((X1 @ X3) => (~((![X4:$i]:((X1 @ X4) => (X3 = X4))))))))) => ((~((![X3:$i]:((X2 @ X3) => (~((![X4:$i]:((X2 @ X4) => (X3 = X4))))))))) => ((descr @ X1) = (descr @ X2))))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i>$o]:(![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => ((X5 = X6) => ((X3 @ X5) = (X4 @ X6))))))) => (((dsetconstr @ X1) @ X3) = ((dsetconstr @ X2) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((subset @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => ((subset @ X2) @ X1)))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => ((subset @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((subset @ X1) @ X2)))) => (((!!) @ (subset @ emptyset)) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X2) => (((in @ X3) @ X1) => ((in @ X3) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X2) => ((~(((in @ X3) @ X2))) => (~(((in @ X3) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => (~(((subset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:((~(((subset @ X1) @ X2))) => (~((X1 = X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => (~((X1 = X2)))))))) => ((![X1:$i]:((subset @ X1) @ X1)) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X2) => (((subset @ X2) @ X3) => ((subset @ X1) @ X3)))))) => ((![X1:$i]:(![X2:$i]:((subset @ X2) @ ((setadjoin @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X3) => ((subset @ X1) @ ((setadjoin @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => ((in @ X1) @ (powerset @ X2))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((subset @ X2) @ X1) => (X1 = X2))))) => ((![X1:$i]:(((subset @ X1) @ emptyset) => (X1 = emptyset))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ X1) => ((in @ X2) @ (powerset @ X1))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ X2) @ X1)))) => ((![X1:$i]:((in @ X1) @ (powerset @ X1))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => ((subset @ (powerset @ X1)) @ (powerset @ X2))))) => ((![X1:$i]:(![X2:$i>$o]:((in @ ((dsetconstr @ X1) @ X2)) @ (powerset @ X1)))) => ((![X1:$i]:(![X2:$i>$o]:((subset @ ((dsetconstr @ X1) @ X2)) @ X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ ((binunion @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:((in @ X2) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ ((binunion @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$o]:(((in @ X3) @ ((binunion @ X1) @ X2)) => ((((in @ X3) @ X1) => X4) => ((((in @ X3) @ X2) => X4) => X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((binunion @ X1) @ X2)) => ((~(((in @ X3) @ X1))) => ((in @ X3) @ X2)))))) => ((![X1:$i]:(![X2:$i]:((subset @ X1) @ ((binunion @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:((subset @ X2) @ ((binunion @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => ((in @ X3) @ ((binintersect @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X3) @ X1) => (((subset @ X3) @ X2) => ((subset @ X3) @ ((binintersect @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((binintersect @ X1) @ X2)) => ((in @ X3) @ X1))))) => ((![X1:$i]:(![X2:$i]:((subset @ ((binintersect @ X1) @ X2)) @ X1))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((binintersect @ X1) @ X2) = X1)))) => ((![X1:$i]:(![X2:$i]:((((binintersect @ X1) @ X2) = X2) => ((subset @ X2) @ X1)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((binintersect @ X1) @ X2)) => ((in @ X3) @ X2))))) => ((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => (~(((in @ X3) @ X2))))) => (((binintersect @ X1) @ X2) = emptyset)))) => ((![X1:$i]:(![X2:$i]:((subset @ ((binintersect @ X1) @ X2)) @ X2))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ X1) => (((binintersect @ X1) @ X2) = X2)))) => ((![X1:$i]:(![X2:$i]:((((binintersect @ X1) @ X2) = X1) => ((subset @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((binintersect @ X1) @ ((binunion @ X2) @ X3)) = ((binunion @ ((binintersect @ X1) @ X2)) @ ((binintersect @ X1) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => ((in @ X3) @ ((setminus @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setminus @ X1) @ X2)) => ((in @ X3) @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setminus @ X1) @ X2)) => (~(((in @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((setminus @ X1) @ X2) = emptyset)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ ((setminus @ X1) @ X2)))) => (((in @ X3) @ X1) => ((in @ X3) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ ((setminus @ X1) @ X2)))) => ((~(((in @ X3) @ X2))) => (~(((in @ X3) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X2) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:((subset @ ((setminus @ X1) @ X2)) @ X1))) => ((![X1:$i]:(![X2:$i]:((((setminus @ X1) @ X2) = emptyset) => ((subset @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((symdiff @ X1) @ X2)) => (![X4:$o]:((((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => X4)) => (((~(((in @ X3) @ X1))) => (((in @ X3) @ X2) => X4)) => X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => ((in @ X3) @ ((symdiff @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => (((in @ X3) @ X2) => ((in @ X3) @ ((symdiff @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => (~(((in @ X3) @ ((symdiff @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => ((~(((in @ X3) @ X2))) => (~(((in @ X3) @ ((symdiff @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:((in @ X2) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:((in @ X1) @ (setunion @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)))))) => ((![X1:$i]:(![X2:$i]:((in @ X2) @ (setunion @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)))))) => ((![X1:$i]:(![X2:$i]:(iskpair @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(iskpair @ ((kpair @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ X1) => ((subset @ ((setadjoin @ X2) @ emptyset)) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ X1) => ((in @ ((setadjoin @ X2) @ emptyset)) @ (powerset @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((in @ ((setadjoin @ X3) @ emptyset)) @ (powerset @ ((binunion @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) => ((~((X3 = X1))) => (X3 = X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((subset @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ ((binunion @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((subset @ ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) @ (powerset @ (powerset @ ((binunion @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ (powerset @ (powerset @ ((binunion @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (~((X3 = ((kpair @ X4) @ X5)))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (iskpair @ X3))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) => (~((![X3:$i]:(((in @ X3) @ X1) => (~(((in @ X2) @ X3)))))))))) => ((![X1:$i]:((subset @ (setunion @ ((setadjoin @ X1) @ emptyset))) @ X1)) => ((![X1:$i]:((subset @ X1) @ (setunion @ ((setadjoin @ X1) @ emptyset)))) => ((![X1:$i]:((setunion @ ((setadjoin @ X1) @ emptyset)) = X1)) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => (singleton @ ((dsetconstr @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))))) => ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X4) => (X4 = X3)))) => ((ex1 @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => ((ex1 @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:((((setadjoin @ X1) @ emptyset) = ((setadjoin @ X2) @ emptyset)) => (X1 = X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) => (X1 = X3))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:((in @ ((setadjoin @ X2) @ emptyset)) @ X1)))))) => ((![X1:$i]:((singleton @ X1) => ((in @ (setunion @ X1)) @ X1))) => ((![X1:$i]:(![X2:$i]:((kfst @ ((kpair @ X1) @ X2)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (kfst @ X3)) @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X1) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => ((X3 = X4) => (X2 = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X3) @ emptyset)) => (X1 = X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X2 = X4)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X2 = X4)))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:(X1 = ((kpair @ (kfst @ X1)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:((ksnd @ ((kpair @ X1) @ X2)) = X2))) => ((![X1:$i]:((iskpair @ X1) => (((kpair @ (kfst @ X1)) @ (ksnd @ X1)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X4) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => (((kpair @ X3) @ X4) = ((kpair @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))) => 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X3)) => ((in @ X5) @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => (~(((in @ X4) @ X2))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$o]:(![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binunion @ X2) @ X3)) => ((((in @ X5) @ X2) => X4) => ((((in @ X5) @ X3) => X4) => X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X2))) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ ((binunion @ X2) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))) => ((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ X2) @ X3)) = ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (((in @ X4) @ ((setminus @ X1) @ X3)) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => ((![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))) => (~((![X4:$i]:((![X5:$i]:(((in @ X5) @ X4) = (~((![X6:$i]:(((in @ X6) @ X1) => (~((X5 = (X2 @ X6)))))))))) => (X3 = X4))))))))))) => ((![X1:$i]:(![X2:$i>$i]:(![X3:$i]:(((in @ X3) @ ((image1 @ X1) @ X2)) = (~((![X4:$i]:(((in @ X4) @ X1) => (~((X3 = (X2 @ X4)))))))))))) => ((![X1:$i]:(![X2:$i>$i]:(![X3:$i]:(((in @ X3) @ ((image1 @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (~((X3 = (X2 @ X4)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(![X3:$i]:((~((![X4:$i]:((X3 = (X2 @ X4)) => (~(((in @ X4) @ X1))))))) => ((in @ X3) @ ((image1 @ X1) @ X2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP2])])). 107.79/107.75 thf(sP3,plain,sP3 <=> ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => ((![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))) => (~((![X4:$i]:((![X5:$i]:(((in @ X5) @ X4) = (~((![X6:$i]:(((in @ X6) @ X1) => (~((X5 = (X2 @ X6)))))))))) => (X3 = X4))))))))))) => ((![X1:$i]:(![X2:$i>$i]:(![X3:$i]:(((in @ X3) @ ((image1 @ X1) @ X2)) = (~((![X4:$i]:(((in @ X4) @ X1) => (~((X3 = (X2 @ X4)))))))))))) => ((![X1:$i]:(![X2:$i>$i]:(![X3:$i]:(((in @ X3) @ ((image1 @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (~((X3 = (X2 @ X4)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(![X3:$i]:((~((![X4:$i]:((X3 = (X2 @ X4)) => (~(((in @ X4) @ X1))))))) => ((in @ X3) @ ((image1 @ X1) @ X2))))))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP3])])). 107.79/107.75 thf(sP4,plain,sP4 <=> ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ ((dsetconstr @ X1) @ X2)) => (X2 @ X3))))) => ((![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))))) => ((![X1:$o]:(![X2:$i]:(((in @ X2) @ (prop2set @ X1)) => X1))) => ((![X1:$i]:(((in @ X1) @ emptyset) => (![X2:$o]:X2))) => ((![X1:$i]:(~(((in @ X1) @ emptyset)))) => ((![X1:$i]:(~(((in @ X1) @ emptyset)))) => ((![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (~((![X2:$i]:(~((X1 @ X2)))))))) => ((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1))) => (X1 = X2))))) => sP1)))))))),introduced(definition,[new_symbols(definition,[sP4])])). 107.79/107.75 thf(sP5,plain,sP5 <=> ((![X1:$i]:(![X2:$i]:((subset @ ((setminus @ X1) @ X2)) @ X1))) => ((![X1:$i]:(![X2:$i]:((((setminus @ X1) @ X2) = emptyset) => ((subset @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((symdiff @ X1) @ X2)) => (![X4:$o]:((((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => X4)) => (((~(((in @ X3) @ X1))) => (((in @ X3) @ X2) => X4)) => X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => ((in @ X3) @ ((symdiff @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => (((in @ X3) @ X2) => ((in @ X3) @ ((symdiff @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => (~(((in @ X3) @ ((symdiff @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => ((~(((in @ X3) @ X2))) => (~(((in @ X3) @ ((symdiff @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:((in @ X2) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:((in @ X1) @ (setunion @ ((setadjoin @ ((setadjoin @ X1) @ 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=> ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => 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X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => (~(((in @ X4) @ X2))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$o]:(![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binunion @ X2) @ X3)) => ((((in @ X5) @ X2) => X4) => ((((in @ X5) @ X3) => X4) => X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X2))) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ ((binunion @ X2) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ 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=> (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (((in @ X4) @ ((setminus @ X1) @ X3)) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ 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(![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => sP3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP5])])). 107.79/107.75 thf(sP6,plain,sP6 <=> ((![X1:$i]:(((in @ X1) @ emptyset) => (![X2:$o]:X2))) => ((![X1:$i]:(~(((in @ X1) @ emptyset)))) => ((![X1:$i]:(~(((in @ X1) @ emptyset)))) => ((![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (~((![X2:$i]:(~((X1 @ X2)))))))) => ((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1))) => (X1 = X2))))) => sP1))))),introduced(definition,[new_symbols(definition,[sP6])])). 107.79/107.75 thf(sP7,plain,sP7 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ X1) => ((in @ ((setadjoin @ X2) @ emptyset)) @ (powerset @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((in @ ((setadjoin @ X3) @ emptyset)) @ (powerset @ 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emptyset))) @ emptyset))) @ (powerset @ (powerset @ ((binunion @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ (powerset @ (powerset @ ((binunion @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (~((X3 = ((kpair @ X4) @ X5)))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (iskpair @ X3))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) => (~((![X3:$i]:(((in @ X3) @ X1) => (~(((in @ X2) @ X3)))))))))) => ((![X1:$i]:((subset @ (setunion @ ((setadjoin @ X1) @ emptyset))) @ X1)) => ((![X1:$i]:((subset @ X1) @ (setunion @ ((setadjoin @ X1) @ emptyset)))) => ((![X1:$i]:((setunion @ ((setadjoin @ X1) @ 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((setadjoin @ X2) @ emptyset))) @ emptyset))) => (X1 = X3))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:((in @ ((setadjoin @ X2) @ emptyset)) @ X1)))))) => ((![X1:$i]:((singleton @ X1) => ((in @ (setunion @ X1)) @ X1))) => ((![X1:$i]:(![X2:$i]:((kfst @ ((kpair @ X1) @ X2)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (kfst @ X3)) @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X1) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => ((X3 = X4) => (X2 = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X3) @ emptyset)) => (X1 = X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X2 = X4)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X2 = X4)))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:(X1 = ((kpair @ (kfst @ X1)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:((ksnd @ ((kpair @ X1) @ X2)) = X2))) => ((![X1:$i]:((iskpair @ X1) => (((kpair @ (kfst @ X1)) @ (ksnd @ X1)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X4) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => (((kpair @ X3) @ X4) = ((kpair @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => 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X1) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))) => ((in @ X2) @ (powerset @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X2) @ (powerset @ X3)) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ ((setminus @ X1) @ X2)))) => ((in @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X2))) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => (((in @ X4) @ X3) => (~(((in @ X4) @ X2)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((subset @ X2) @ X3) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ X2)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ X3) => ((subset @ ((setminus @ X1) @ X3)) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ ((setminus @ X1) @ X3)) @ ((setminus @ X1) @ X2)) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => ((in @ X3) @ ((setminus @ X1) @ ((setminus @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ ((setminus @ X1) @ ((setminus @ X1) @ X2))) => ((in @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ X2) @ ((setminus @ X1) @ ((setminus @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ ((setminus @ X1) @ X2))) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (X2 = ((setminus @ X1) @ ((setminus @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X3) => ((in @ X4) @ ((setminus @ X1) @ X2))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ ((binunion @ X2) @ X3)))) => (~(((in @ X4) @ X2))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ ((binunion @ X2) @ X3)))) => (~(((in @ X4) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binintersect @ X2) @ X3)) => ((in @ X5) @ ((binunion @ X2) @ X4)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binintersect @ X2) @ X3)) => ((in @ X5) @ ((binunion @ X3) @ X4)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binintersect @ X2) @ X3)) => ((in @ X5) @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => (~(((in @ X4) @ X2))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$o]:(![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binunion @ X2) @ X3)) => ((((in @ X5) @ X2) => X4) => ((((in @ X5) @ X3) => X4) => X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X2))) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ ((binunion @ X2) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ 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@ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => 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(![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binintersect @ X2) @ X3)) => ((in @ X5) @ ((binunion @ X2) @ X4)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binintersect @ X2) @ X3)) => ((in @ X5) @ ((binunion @ X3) @ X4)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binintersect @ X2) @ X3)) => ((in @ X5) @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => 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=> ((in @ X3) @ X2)))))) => ((![X1:$i]:(((dsetconstr @ X1) @ (^[X2:$i]:(~($false)))) = X1)) => sP10)))))))))),introduced(definition,[new_symbols(definition,[sP11])])). 107.79/107.75 thf(sP12,plain,sP12 <=> ((![X1:$i]:((in @ X1) @ (powerset @ X1))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => ((subset @ (powerset @ X1)) @ (powerset @ X2))))) => ((![X1:$i]:(![X2:$i>$o]:((in @ ((dsetconstr @ X1) @ X2)) @ (powerset @ X1)))) => ((![X1:$i]:(![X2:$i>$o]:((subset @ ((dsetconstr @ X1) @ X2)) @ X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ ((binunion @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:((in @ X2) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ ((binunion @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$o]:(((in @ X3) @ ((binunion @ X1) @ X2)) => ((((in @ X3) @ X1) => X4) => ((((in @ X3) @ X2) => X4) => X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((binunion @ X1) @ X2)) => ((~(((in @ X3) @ X1))) => ((in @ X3) @ X2)))))) => ((![X1:$i]:(![X2:$i]:((subset @ X1) @ ((binunion @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:((subset @ X2) @ ((binunion @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => ((in @ X3) @ ((binintersect @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X3) @ X1) => (((subset @ X3) @ X2) => ((subset @ X3) @ ((binintersect @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((binintersect @ X1) @ X2)) => ((in @ X3) @ X1))))) => ((![X1:$i]:(![X2:$i]:((subset @ ((binintersect @ X1) @ X2)) @ X1))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((binintersect @ X1) @ X2) = X1)))) => ((![X1:$i]:(![X2:$i]:((((binintersect @ X1) @ X2) = X2) => ((subset @ X2) @ X1)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((binintersect @ X1) @ X2)) => ((in @ X3) @ X2))))) => ((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => (~(((in @ X3) @ X2))))) => (((binintersect @ X1) @ X2) = emptyset)))) => ((![X1:$i]:(![X2:$i]:((subset @ ((binintersect @ X1) @ X2)) @ X2))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ X1) => (((binintersect @ X1) @ X2) = X2)))) => ((![X1:$i]:(![X2:$i]:((((binintersect @ X1) @ X2) = X1) => ((subset @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((binintersect @ X1) @ ((binunion @ X2) @ X3)) = ((binunion @ ((binintersect @ X1) @ X2)) @ ((binintersect @ X1) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => ((in @ X3) @ ((setminus @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setminus @ X1) @ X2)) => ((in @ X3) @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setminus @ X1) @ X2)) => (~(((in @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((setminus @ X1) @ X2) = emptyset)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ ((setminus @ X1) @ X2)))) => (((in @ X3) @ X1) => ((in @ X3) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ ((setminus @ X1) @ X2)))) => ((~(((in @ X3) @ X2))) => (~(((in @ X3) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X2) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))) => sP5))))))))))))))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP12])])). 107.79/107.75 thf(sP13,plain,sP13 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X2 = X4)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X2 = X4)))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:(X1 = ((kpair @ (kfst @ X1)) @ X2))))))) => ((![X1:$i]:(![X2:$i]:((ksnd @ ((kpair @ X1) @ X2)) = X2))) => ((![X1:$i]:((iskpair @ X1) => (((kpair @ (kfst @ X1)) @ (ksnd @ X1)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))) => sP8)))))),introduced(definition,[new_symbols(definition,[sP13])])). 107.79/107.75 thf(sP14,plain,sP14 <=> ((![X1:$i]:(![X2:$i]:((in @ X1) @ (setunion @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)))))) => ((![X1:$i]:(![X2:$i]:((in @ X2) @ (setunion @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)))))) => ((![X1:$i]:(![X2:$i]:(iskpair @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(iskpair @ ((kpair @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ X1) => ((subset @ ((setadjoin @ X2) @ emptyset)) @ X1)))) => sP7))))),introduced(definition,[new_symbols(definition,[sP14])])). 107.79/107.75 thf(sP15,plain,sP15 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => sP3))))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP15])])). 107.79/107.75 thf(sP16,plain,sP16 <=> ((![X1:$i>$o]:((~((![X2:$i]:(~((![X3:$i]:((X1 @ X3) = (X3 = X2)))))))) => (~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((in @ X3) @ X1) => ((in @ X4) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((in @ X3) @ X1) = ((in @ X4) @ X2)))))))) => ((![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (![X2:$i]:(![X3:$i]:((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))))) => ((![X1:$i>$o]:(![X2:$i>$o]:((![X3:$i]:(![X4:$i]:((X3 = X4) => ((X1 @ X3) = (X2 @ X4))))) => ((~((![X3:$i]:((X1 @ X3) => (~((![X4:$i]:((X1 @ X4) => (X3 = X4))))))))) = (~((![X3:$i]:((X2 @ X3) => (~((![X4:$i]:((X2 @ X4) => (X3 = X4))))))))))))) => ((emptyset = emptyset) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((setadjoin @ X1) @ X3) = ((setadjoin @ X2) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => ((powerset @ X1) = (powerset @ X2))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => ((setunion @ X1) = (setunion @ X2))))) => ((omega = omega) => ((![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (![X2:$i]:(![X3:$i]:((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))))) => ((![X1:$i>$o]:(![X2:$i>$o]:((![X3:$i]:(![X4:$i]:((X3 = X4) => ((X1 @ X3) = (X2 @ X4))))) => ((~((![X3:$i]:((X1 @ X3) => (~((![X4:$i]:((X1 @ X4) => (X3 = X4))))))))) => ((~((![X3:$i]:((X2 @ X3) => (~((![X4:$i]:((X2 @ X4) => (X3 = X4))))))))) => ((descr @ X1) = (descr @ X2))))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i>$o]:(![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => ((X5 = X6) => ((X3 @ X5) = (X4 @ X6))))))) => (((dsetconstr @ X1) @ X3) = ((dsetconstr @ X2) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((subset @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => ((subset @ X2) @ X1)))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => ((subset @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((subset @ X1) @ X2)))) => (((!!) @ (subset @ emptyset)) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X2) => (((in @ X3) @ X1) => ((in @ X3) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X2) => ((~(((in @ X3) @ X2))) => (~(((in @ X3) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => (~(((subset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:((~(((subset @ X1) @ X2))) => (~((X1 = X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => (~((X1 = X2)))))))) => ((![X1:$i]:((subset @ X1) @ X1)) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X2) => (((subset @ X2) @ X3) => ((subset @ X1) @ X3)))))) => ((![X1:$i]:(![X2:$i]:((subset @ X2) @ ((setadjoin @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X3) => ((subset @ X1) @ ((setadjoin @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => ((in @ X1) @ (powerset @ X2))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((subset @ X2) @ X1) => (X1 = X2))))) => ((![X1:$i]:(((subset @ X1) @ emptyset) => (X1 = emptyset))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ X1) => ((in @ X2) @ (powerset @ X1))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ X2) @ X1)))) => sP12)))))))))))))))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP16])])). 107.79/107.75 thf(sP17,plain,sP17 <=> ((![X1:$i]:((setunion @ ((setadjoin @ X1) @ emptyset)) = X1)) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => (singleton @ ((dsetconstr @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))))) => ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X4) => (X4 = X3)))) => ((ex1 @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => ((ex1 @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:((((setadjoin @ X1) @ emptyset) = ((setadjoin @ X2) @ emptyset)) => (X1 = X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) => (X1 = X3))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:((in @ ((setadjoin @ X2) @ emptyset)) @ X1)))))) => ((![X1:$i]:((singleton @ X1) => ((in @ (setunion @ X1)) @ X1))) => ((![X1:$i]:(![X2:$i]:((kfst @ ((kpair @ X1) @ X2)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (kfst @ X3)) @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X1) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => ((X3 = X4) => (X2 = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X3) @ emptyset)) => (X1 = X2))))) => sP13))))))))))))))))),introduced(definition,[new_symbols(definition,[sP17])])). 107.79/107.75 thf(sP18,plain,sP18 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X2) => (((in @ X3) @ X1) => ((in @ X3) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X2) => ((~(((in @ X3) @ X2))) => (~(((in @ X3) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => (~(((subset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:((~(((subset @ X1) @ X2))) => (~((X1 = X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => (~((X1 = X2)))))))) => ((![X1:$i]:((subset @ X1) @ X1)) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X2) => (((subset @ X2) @ X3) => ((subset @ X1) @ X3)))))) => ((![X1:$i]:(![X2:$i]:((subset @ X2) @ ((setadjoin @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X3) => ((subset @ X1) @ ((setadjoin @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => ((in @ X1) @ (powerset @ X2))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((subset @ X2) @ X1) => (X1 = X2))))) => ((![X1:$i]:(((subset @ X1) @ emptyset) => (X1 = emptyset))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ X1) => ((in @ X2) @ (powerset @ X1))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ X2) @ X1)))) => sP12)))))))))))))),introduced(definition,[new_symbols(definition,[sP18])])). 107.79/107.75 thf(sP19,plain,sP19 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => ((in @ X3) @ ((binintersect @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X3) @ X1) => (((subset @ X3) @ X2) => ((subset @ X3) @ ((binintersect @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((binintersect @ X1) @ X2)) => ((in @ X3) @ X1))))) => ((![X1:$i]:(![X2:$i]:((subset @ ((binintersect @ X1) @ X2)) @ X1))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((binintersect @ X1) @ X2) = X1)))) => ((![X1:$i]:(![X2:$i]:((((binintersect @ X1) @ X2) = X2) => ((subset @ X2) @ X1)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((binintersect @ X1) @ X2)) => ((in @ X3) @ X2))))) => ((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => (~(((in @ X3) @ X2))))) => (((binintersect @ X1) @ X2) = emptyset)))) => ((![X1:$i]:(![X2:$i]:((subset @ ((binintersect @ X1) @ X2)) @ X2))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ X1) => (((binintersect @ X1) @ X2) = X2)))) => ((![X1:$i]:(![X2:$i]:((((binintersect @ X1) @ X2) = X1) => ((subset @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((binintersect @ X1) @ ((binunion @ X2) @ X3)) = ((binunion @ ((binintersect @ X1) @ X2)) @ ((binintersect @ X1) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => ((in @ X3) @ ((setminus @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setminus @ X1) @ X2)) => ((in @ X3) @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setminus @ X1) @ X2)) => (~(((in @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((setminus @ X1) @ X2) = emptyset)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ ((setminus @ X1) @ X2)))) => (((in @ X3) @ X1) => ((in @ X3) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ ((setminus @ X1) @ X2)))) => ((~(((in @ X3) @ X2))) => (~(((in @ X3) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X2) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))) => sP5)))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP19])])). 107.79/107.75 thf(sP20,plain,sP20 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ ((setminus @ X1) @ X2)))) => ((~(((in @ X3) @ X2))) => (~(((in @ X3) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X2) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))) => sP5))),introduced(definition,[new_symbols(definition,[sP20])])). 107.79/107.75 thf(sP21,plain,sP21 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X3) => ((in @ X4) @ ((setminus @ X1) @ X2))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ ((binunion @ X2) @ X3)))) => (~(((in @ X4) @ X2))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ ((binunion @ X2) @ X3)))) => (~(((in @ X4) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binintersect @ X2) @ X3)) => ((in @ X5) @ ((binunion @ X2) @ X4)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binintersect @ X2) @ X3)) => ((in @ X5) @ ((binunion @ X3) @ X4)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binintersect @ X2) @ X3)) => ((in @ X5) @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => (~(((in @ X4) @ X2))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$o]:(![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binunion @ X2) @ X3)) => ((((in @ X5) @ X2) => X4) => ((((in @ X5) @ X3) => X4) => X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X2))) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ ((binunion @ X2) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))) => ((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ X2) @ X3)) = ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (((in @ X4) @ ((setminus @ X1) @ X3)) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => sP15)))))))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP21])])). 107.79/107.75 thf(sP22,plain,sP22 <=> (![X1:$i]:(((in @ X1) @ ((image1 @ eigen__0) @ eigen__1)) = (~((![X2:$i]:(((in @ X2) @ eigen__0) => (~((X1 = (eigen__1 @ X2)))))))))),introduced(definition,[new_symbols(definition,[sP22])])). 107.79/107.75 thf(sP23,plain,sP23 <=> ((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1))) => (X1 = X2))))) => sP1),introduced(definition,[new_symbols(definition,[sP23])])). 107.79/107.75 thf(sP24,plain,sP24 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => (~(((in @ X3) @ ((symdiff @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => ((~(((in @ X3) @ X2))) => (~(((in @ X3) @ ((symdiff @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:((in @ X2) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))) => sP14))),introduced(definition,[new_symbols(definition,[sP24])])). 107.79/107.75 thf(sP25,plain,sP25 <=> ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => 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(powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ ((setminus @ X1) @ ((setminus @ X1) @ X2))) => ((in @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ X2) @ ((setminus @ X1) @ ((setminus @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ ((setminus @ X1) @ X2))) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (X2 = ((setminus @ X1) @ ((setminus @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => sP21)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP28])])). 107.79/107.75 thf(sP29,plain,sP29 <=> ((![X1:$i]:(~(((in @ X1) @ emptyset)))) => ((![X1:$i]:(~(((in @ X1) @ emptyset)))) => ((![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (~((![X2:$i]:(~((X1 @ X2)))))))) => sP23))),introduced(definition,[new_symbols(definition,[sP29])])). 107.79/107.75 thf(sP30,plain,sP30 <=> ((![X1:$i]:(![X2:$i]:((subset @ X2) @ ((setadjoin @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X3) => ((subset @ X1) @ ((setadjoin @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => ((in @ X1) @ (powerset @ X2))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((subset @ X2) @ X1) => (X1 = X2))))) => ((![X1:$i]:(((subset @ X1) @ emptyset) => (X1 = emptyset))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ X1) => ((in @ X2) @ (powerset @ X1))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ X2) @ X1)))) => sP12))))))),introduced(definition,[new_symbols(definition,[sP30])])). 107.79/107.75 thf(sP31,plain,sP31 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ ((setminus @ X1) @ X2)))) => (((in @ X3) @ X1) => ((in @ X3) @ X2)))))) => sP20),introduced(definition,[new_symbols(definition,[sP31])])). 107.79/107.75 thf(sP32,plain,sP32 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X2))) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ ((binunion @ X2) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))) => ((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ X2) @ X3)) = ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (((in @ X4) @ ((setminus @ X1) @ X3)) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => sP15)))))))))))),introduced(definition,[new_symbols(definition,[sP32])])). 107.79/107.76 thf(sP33,plain,sP33 <=> ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))) => ((![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))) => (~((![X4:$i]:((![X5:$i]:(((in @ X5) @ X4) = (~((![X6:$i]:(((in @ X6) @ X1) => (~((X5 = (X2 @ X6)))))))))) => (X3 = X4))))))))))) => ((![X1:$i]:(![X2:$i>$i]:(![X3:$i]:(((in @ X3) @ ((image1 @ X1) @ X2)) = (~((![X4:$i]:(((in @ X4) @ X1) => (~((X3 = (X2 @ X4)))))))))))) => ((![X1:$i]:(![X2:$i>$i]:(![X3:$i]:(((in @ X3) @ ((image1 @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (~((X3 = (X2 @ X4)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(![X3:$i]:((~((![X4:$i]:((X3 = (X2 @ X4)) => (~(((in @ X4) @ X1))))))) => ((in @ X3) @ ((image1 @ X1) @ X2))))))))))),introduced(definition,[new_symbols(definition,[sP33])])). 107.79/107.76 thf(sP34,plain,sP34 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (iskpair @ X3))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) => (~((![X3:$i]:(((in @ X3) @ X1) => (~(((in @ X2) @ X3)))))))))) => ((![X1:$i]:((subset @ (setunion @ ((setadjoin @ X1) @ emptyset))) @ X1)) => ((![X1:$i]:((subset @ X1) @ (setunion @ ((setadjoin @ X1) @ emptyset)))) => sP17)))),introduced(definition,[new_symbols(definition,[sP34])])). 107.79/107.76 thf(sP35,plain,sP35 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X2) @ X3) => (((in @ X3) @ X1) => ((in @ X2) @ (setunion @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) => (![X3:$o]:((![X4:$i]:(((in @ X2) @ X4) => (((in @ X4) @ X1) => X3))) => X3))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ X1) => ((in @ X2) @ (powerset @ (setunion @ X1)))))) => ((![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (~((![X2:$i]:(~((![X3:$i]:((X1 @ X3) = (X3 = X2)))))))))) => ((![X1:$i]:((~((X1 = emptyset))) => (~((![X2:$i]:(~(((in @ X2) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X1) @ ((setadjoin @ X2) @ emptyset)) => (X1 = X2)))) => ((![X1:$i]:(![X2:$i]:((~((X1 = X2))) => (~(((in @ X2) @ ((setadjoin @ X1) @ emptyset))))))) => sP2))))))),introduced(definition,[new_symbols(definition,[sP35])])). 107.79/107.76 thf(sP36,plain,sP36 <=> ((![X1:$i]:(![X2:$i]:((((binintersect @ X1) @ X2) = X1) => ((subset @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((binintersect @ X1) @ ((binunion @ X2) @ X3)) = ((binunion @ ((binintersect @ X1) @ X2)) @ ((binintersect @ X1) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => ((in @ X3) @ ((setminus @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setminus @ X1) @ X2)) => ((in @ X3) @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setminus @ X1) @ X2)) => (~(((in @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((setminus @ X1) @ X2) = emptyset)))) => sP31)))))),introduced(definition,[new_symbols(definition,[sP36])])). 107.79/107.76 thf(sP37,plain,sP37 <=> ((![X1:$i]:(![X2:$i]:((((setminus @ X1) @ X2) = emptyset) => ((subset @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((symdiff @ X1) @ X2)) => (![X4:$o]:((((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => X4)) => (((~(((in @ X3) @ X1))) => (((in @ X3) @ X2) => X4)) => X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => ((in @ X3) @ ((symdiff @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => (((in @ X3) @ X2) => ((in @ X3) @ ((symdiff @ X1) @ X2))))))) => sP24)))),introduced(definition,[new_symbols(definition,[sP37])])). 107.79/107.76 thf(sP38,plain,sP38 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ 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((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((((lam @ X1) @ X2) @ X3) = (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => ((in @ X4) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => 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=> (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((((if @ X1) @ X2) @ X3) @ X4) = X4)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binunion @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((in @ (powerset @ X2)) @ (powerset @ (powerset @ X1)))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ X1))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))) => ((![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X3) => ((in @ X4) @ X2)))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))) => ((in @ X2) @ (powerset @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X2) @ (powerset @ X3)) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ 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X1) => (((subset @ X2) @ X3) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ X2)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ X3) => ((subset @ ((setminus @ X1) @ X3)) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ ((setminus @ X1) @ X3)) @ ((setminus @ X1) @ X2)) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => ((in @ X3) @ ((setminus @ X1) @ ((setminus @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ ((setminus @ X1) @ ((setminus @ X1) @ X2))) => ((in @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ X2) @ ((setminus @ X1) @ ((setminus @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ ((setminus @ X1) @ X2))) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (X2 = ((setminus @ X1) @ ((setminus @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => sP21)))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP38])])). 107.79/107.76 thf(sP39,plain,sP39 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@ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ 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X4) = (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => ((in @ X4) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => ((in @ X3) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X3) @ emptyset))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4)))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ X1))))))) => ((![X1:$i]:((singleton @ X1) => (![X2:$i]:(((in @ X2) @ X1) => ((setunion @ X1) = X2))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((((if @ X1) @ X2) @ X3) @ X4) = X3)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((((if @ X1) @ X2) @ X3) @ X4) = X4)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binunion @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((in @ (powerset @ X2)) @ (powerset @ (powerset @ X1)))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ X1))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))) => ((![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X3) => ((in @ X4) @ X2)))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))) => ((in @ X2) @ (powerset @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X2) @ (powerset @ X3)) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ ((setminus @ X1) @ X2)))) => ((in @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X2))) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => (((in @ X4) @ X3) => (~(((in @ X4) @ X2)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((subset @ X2) @ X3) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ X2)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ X3) => ((subset @ ((setminus @ X1) @ X3)) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ ((setminus @ X1) @ X3)) @ ((setminus @ X1) @ X2)) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => ((in @ X3) @ ((setminus @ X1) @ ((setminus @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ ((setminus @ X1) @ ((setminus @ X1) @ X2))) => ((in @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ X2) @ ((setminus @ X1) @ ((setminus @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ ((setminus @ X1) @ X2))) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (X2 = ((setminus @ X1) @ ((setminus @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => sP21)))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP39])])). 107.79/107.76 thf(sP40,plain,sP40 <=> ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => sP33)))),introduced(definition,[new_symbols(definition,[sP40])])). 107.79/107.76 thf(sP41,plain,sP41 <=> ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ X1) => ((in @ X2) @ (powerset @ X1))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ X2) @ X1)))) => sP12)),introduced(definition,[new_symbols(definition,[sP41])])). 107.79/107.76 thf(sP42,plain,sP42 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ X1))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))) => ((![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X3) => ((in @ X4) @ X2)))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))) => ((in @ X2) @ (powerset @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X2) @ (powerset @ X3)) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ ((setminus @ X1) @ X2)))) => ((in @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X2))) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => (((in @ X4) @ X3) => (~(((in @ X4) @ X2)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((subset @ X2) @ X3) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ X2)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ X3) => ((subset @ ((setminus @ X1) @ X3)) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ ((setminus @ X1) @ X3)) @ ((setminus @ X1) @ X2)) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => ((in @ X3) @ ((setminus @ X1) @ ((setminus @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ ((setminus @ X1) @ ((setminus @ X1) @ X2))) => ((in @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ X2) @ ((setminus @ X1) @ ((setminus @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ ((setminus @ X1) @ X2))) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (X2 = ((setminus @ X1) @ ((setminus @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => sP21)))))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP42])])). 107.79/107.76 thf(sP43,plain,sP43 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X2) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))) => sP5)),introduced(definition,[new_symbols(definition,[sP43])])). 107.79/107.76 thf(sP44,plain,sP44 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X2) @ (powerset @ X1)) => (((in @ X3) @ X2) => ((in @ X3) @ X1)))))) => sP35),introduced(definition,[new_symbols(definition,[sP44])])). 107.79/107.76 thf(sP45,plain,sP45 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => (((in @ X4) @ X3) => (~(((in @ X4) @ X2)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((subset @ X2) @ X3) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ X2)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ X3) => ((subset @ ((setminus @ X1) @ X3)) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ ((setminus @ X1) @ X3)) @ ((setminus @ X1) @ X2)) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => ((in @ X3) @ ((setminus @ X1) @ ((setminus @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ ((setminus @ X1) @ ((setminus @ X1) @ X2))) => ((in @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ X2) @ ((setminus @ X1) @ ((setminus @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ ((setminus @ X1) @ X2))) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (X2 = ((setminus @ X1) @ ((setminus @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => sP21)))))))))))),introduced(definition,[new_symbols(definition,[sP45])])). 107.79/107.76 thf(sP46,plain,sP46 <=> (((!!) @ (subset @ emptyset)) => sP18),introduced(definition,[new_symbols(definition,[sP46])])). 107.79/107.76 thf(sP47,plain,sP47 <=> ((![X1:$i]:((~((X1 = emptyset))) => (~((![X2:$i]:(~(((in @ X2) @ X1)))))))) => ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => (~((((dsetconstr @ X1) @ X2) = emptyset)))))))) => ((![X1:$i]:((~((![X2:$i]:(~(((in @ X2) @ X1)))))) => (~((X1 = emptyset))))) => ((![X1:$i]:(![X2:$i]:((in @ X1) @ ((setadjoin @ X1) @ X2)))) => (((in @ emptyset) @ ((setadjoin @ emptyset) @ emptyset)) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ ((setadjoin @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ X2)) => (![X4:$o]:(((X3 = X1) => X4) => ((((in @ X3) @ X2) => X4) => X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ X2)) => ((~((X3 = X1))) => ((in @ X3) @ X2)))))) => ((![X1:$i]:(((dsetconstr @ X1) @ (^[X2:$i]:(~($false)))) = X1)) => sP10))))))))),introduced(definition,[new_symbols(definition,[sP47])])). 107.79/107.76 thf(sP48,plain,sP48 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => sP28))),introduced(definition,[new_symbols(definition,[sP48])])). 107.79/107.76 thf(sP49,plain,sP49 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ ((binunion @ X2) @ X3)))) => (~(((in @ X4) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binintersect @ X2) @ X3)) => ((in @ X5) @ ((binunion @ X2) @ X4)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binintersect @ X2) @ X3)) => ((in @ X5) @ ((binunion @ X3) @ X4)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binintersect @ X2) @ X3)) => ((in @ X5) @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => (~(((in @ X4) @ X2))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$o]:(![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binunion @ X2) @ X3)) => ((((in @ X5) @ X2) => X4) => ((((in @ X5) @ X3) => X4) => X4))))))))))) => sP32)))))))),introduced(definition,[new_symbols(definition,[sP49])])). 107.79/107.76 thf(sP50,plain,sP50 <=> ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => sP3)))))),introduced(definition,[new_symbols(definition,[sP50])])). 107.79/107.76 thf(sP51,plain,sP51 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) => (![X3:$o]:((![X4:$i]:(((in @ X2) @ X4) => (((in @ X4) @ X1) => X3))) => X3))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ X1) => ((in @ X2) @ (powerset @ (setunion @ X1)))))) => ((![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (~((![X2:$i]:(~((![X3:$i]:((X1 @ X3) = (X3 = X2)))))))))) => ((![X1:$i]:((~((X1 = emptyset))) => (~((![X2:$i]:(~(((in @ X2) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X1) @ ((setadjoin @ X2) @ emptyset)) => (X1 = X2)))) => ((![X1:$i]:(![X2:$i]:((~((X1 = X2))) => (~(((in @ X2) @ ((setadjoin @ X1) @ emptyset))))))) => sP2)))))),introduced(definition,[new_symbols(definition,[sP51])])). 107.79/107.76 thf(sP52,plain,sP52 <=> ((![X1:$i>$o]:(![X2:$i>$o]:((![X3:$i]:(![X4:$i]:((X3 = X4) => ((X1 @ X3) = (X2 @ X4))))) => ((~((![X3:$i]:((X1 @ X3) => (~((![X4:$i]:((X1 @ X4) => (X3 = X4))))))))) = (~((![X3:$i]:((X2 @ X3) => (~((![X4:$i]:((X2 @ X4) => (X3 = X4))))))))))))) => ((emptyset = emptyset) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((setadjoin @ X1) @ X3) = ((setadjoin @ X2) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => ((powerset @ X1) = (powerset @ X2))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => ((setunion @ X1) = (setunion @ X2))))) => ((omega = omega) => ((![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (![X2:$i]:(![X3:$i]:((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))))) => ((![X1:$i>$o]:(![X2:$i>$o]:((![X3:$i]:(![X4:$i]:((X3 = X4) => ((X1 @ X3) = (X2 @ X4))))) => ((~((![X3:$i]:((X1 @ X3) => (~((![X4:$i]:((X1 @ X4) => (X3 = X4))))))))) => ((~((![X3:$i]:((X2 @ X3) => (~((![X4:$i]:((X2 @ X4) => (X3 = X4))))))))) => ((descr @ X1) = (descr @ X2))))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i>$o]:(![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => ((X5 = X6) => ((X3 @ X5) = (X4 @ X6))))))) => (((dsetconstr @ X1) @ X3) = ((dsetconstr @ X2) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((subset @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => ((subset @ X2) @ X1)))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => ((subset @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((subset @ X1) @ X2)))) => sP46))))))))))))),introduced(definition,[new_symbols(definition,[sP52])])). 107.79/107.76 thf(sP53,plain,sP53 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) => ((~((X3 = X1))) => (X3 = X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((subset @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ ((binunion @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((subset @ ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) @ (powerset @ (powerset @ ((binunion @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ (powerset @ (powerset @ ((binunion @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (~((X3 = ((kpair @ X4) @ X5)))))))))))))) => sP34)))))))),introduced(definition,[new_symbols(definition,[sP53])])). 107.79/107.76 thf(sP54,plain,sP54 <=> (((in @ eigen__2) @ ((image1 @ eigen__0) @ eigen__1)) = (~((![X1:$i]:(((in @ X1) @ eigen__0) => (~((eigen__2 = (eigen__1 @ X1))))))))),introduced(definition,[new_symbols(definition,[sP54])])). 107.79/107.76 thf(sP55,plain,sP55 <=> ((![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))))) => ((![X1:$i>$o]:((~((![X2:$i]:(~((X1 @ X2)))))) => ((![X2:$i]:(![X3:$i]:((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))) => (~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3)))))))))))) => sP16)),introduced(definition,[new_symbols(definition,[sP55])])). 107.79/107.76 thf(sP56,plain,sP56 <=> ((![X1:$i]:(![X2:$i]:((in @ X2) @ (setunion @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)))))) => ((![X1:$i]:(![X2:$i]:(iskpair @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(iskpair @ ((kpair @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ X1) => ((subset @ ((setadjoin @ X2) @ emptyset)) @ X1)))) => sP7)))),introduced(definition,[new_symbols(definition,[sP56])])). 107.79/107.76 thf(sP57,plain,sP57 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ ((setminus @ X1) @ X3)) @ ((setminus @ X1) @ X2)) => ((subset @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => ((in @ X3) @ ((setminus @ X1) @ ((setminus @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ ((setminus @ X1) @ ((setminus @ X1) @ X2))) => ((in @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ X2) @ ((setminus @ X1) @ ((setminus @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ ((setminus @ X1) @ X2))) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (X2 = ((setminus @ X1) @ ((setminus @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => sP21))))))))),introduced(definition,[new_symbols(definition,[sP57])])). 107.79/107.76 thf(sP58,plain,sP58 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ ((setadjoin @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ X2)) => (![X4:$o]:(((X3 = X1) => X4) => ((((in @ X3) @ X2) => X4) => X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ X2)) => ((~((X3 = X1))) => ((in @ X3) @ X2)))))) => ((![X1:$i]:(((dsetconstr @ X1) @ (^[X2:$i]:(~($false)))) = X1)) => sP10)))),introduced(definition,[new_symbols(definition,[sP58])])). 107.79/107.76 thf(sP59,plain,sP59 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (~((X3 = ((kpair @ X4) @ X5)))))))))))))) => sP34)),introduced(definition,[new_symbols(definition,[sP59])])). 107.79/107.76 thf(sP60,plain,sP60 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => sP15),introduced(definition,[new_symbols(definition,[sP60])])). 107.79/107.76 thf(sP61,plain,sP61 <=> ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))) => sP40),introduced(definition,[new_symbols(definition,[sP61])])). 107.79/107.76 thf(sP62,plain,sP62 <=> ((![X1:$i>$o]:((~((![X2:$i]:(~((X1 @ X2)))))) => ((![X2:$i]:(![X3:$i]:((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))) => (~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3)))))))))))) => sP16),introduced(definition,[new_symbols(definition,[sP62])])). 107.79/107.76 thf(sP63,plain,sP63 <=> ((![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i>$o]:(![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => ((X5 = X6) => ((X3 @ X5) = (X4 @ X6))))))) => (((dsetconstr @ X1) @ X3) = ((dsetconstr @ X2) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((subset @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => ((subset @ X2) @ X1)))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => ((subset @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((subset @ X1) @ X2)))) => sP46))))),introduced(definition,[new_symbols(definition,[sP63])])). 107.79/107.76 thf(sP64,plain,sP64 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => sP39))),introduced(definition,[new_symbols(definition,[sP64])])). 107.79/107.76 thf(sP65,plain,sP65 <=> ((![X1:$i]:(~(((in @ X1) @ emptyset)))) => ((![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (~((![X2:$i]:(~((X1 @ X2)))))))) => sP23)),introduced(definition,[new_symbols(definition,[sP65])])). 107.79/107.76 thf(sP66,plain,sP66 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ ((setminus @ X1) @ ((setminus @ X1) @ X2))) => ((in @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ X2) @ ((setminus @ X1) @ ((setminus @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ ((setminus @ X1) @ X2))) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (X2 = ((setminus @ X1) @ ((setminus @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => sP21))))))),introduced(definition,[new_symbols(definition,[sP66])])). 107.79/107.76 thf(sP67,plain,sP67 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X2) => ((~(((in @ X3) @ X2))) => (~(((in @ X3) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => (~(((subset @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:((~(((subset @ X1) @ X2))) => (~((X1 = X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => (~((X1 = X2)))))))) => ((![X1:$i]:((subset @ X1) @ X1)) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X2) => (((subset @ X2) @ X3) => ((subset @ X1) @ X3)))))) => sP30)))))),introduced(definition,[new_symbols(definition,[sP67])])). 107.79/107.76 thf(sP68,plain,sP68 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => sP48)))))))))),introduced(definition,[new_symbols(definition,[sP68])])). 107.79/107.76 thf(sP69,plain,sP69 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => sP48))))))),introduced(definition,[new_symbols(definition,[sP69])])). 107.79/107.76 thf(sP70,plain,sP70 <=> ((![X1:$i]:(![X2:$i]:((((setadjoin @ X1) @ emptyset) = ((setadjoin @ X2) @ emptyset)) => (X1 = X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) => (X1 = X3))))) => ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:((in @ ((setadjoin @ X2) @ emptyset)) @ X1)))))) => ((![X1:$i]:((singleton @ X1) => ((in @ (setunion @ X1)) @ X1))) => ((![X1:$i]:(![X2:$i]:((kfst @ ((kpair @ X1) @ X2)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (kfst @ X3)) @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X1) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => ((X3 = X4) => (X2 = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X3) @ emptyset)) => (X1 = X2))))) => sP13)))))))))))),introduced(definition,[new_symbols(definition,[sP70])])). 107.79/107.76 thf(sP71,plain,sP71 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => sP50))))),introduced(definition,[new_symbols(definition,[sP71])])). 107.79/107.76 thf(sP72,plain,sP72 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binunion @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((in @ (powerset @ X2)) @ (powerset @ (powerset @ X1)))))) => sP42)),introduced(definition,[new_symbols(definition,[sP72])])). 107.79/107.76 thf(sP73,plain,sP73 <=> ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))) => sP33),introduced(definition,[new_symbols(definition,[sP73])])). 107.79/107.76 thf(sP74,plain,sP74 <=> ((![X1:$i]:(![X2:$i]:((~(((subset @ X1) @ X2))) => (~((X1 = X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => (~((X1 = X2)))))))) => ((![X1:$i]:((subset @ X1) @ X1)) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X2) => (((subset @ X2) @ X3) => ((subset @ X1) @ X3)))))) => sP30)))),introduced(definition,[new_symbols(definition,[sP74])])). 107.79/107.76 thf(sP75,plain,sP75 <=> ((![X1:$i]:(![X2:$i]:((kfst @ ((kpair @ X1) @ X2)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (kfst @ X3)) @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X1) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => ((X3 = X4) => (X2 = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X3) @ emptyset)) => (X1 = X2))))) => sP13)))))))),introduced(definition,[new_symbols(definition,[sP75])])). 107.79/107.76 thf(sP76,plain,sP76 <=> ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((((lam @ X1) @ X2) @ X3) = (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => ((in @ X4) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => ((in @ X3) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X3) @ emptyset))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4)))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ X1))))))) => ((![X1:$i]:((singleton @ X1) => (![X2:$i]:(((in @ X2) @ X1) => ((setunion @ X1) = X2))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((((if @ X1) @ X2) @ X3) @ X4) = X3)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((((if @ X1) @ X2) @ X3) @ X4) = X4)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => sP72)))))))))))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP76])])). 107.79/107.77 thf(sP77,plain,sP77 <=> ((in @ eigen__2) @ ((image1 @ eigen__0) @ eigen__1)),introduced(definition,[new_symbols(definition,[sP77])])). 107.79/107.77 thf(sP78,plain,sP78 <=> ((![X1:$i]:(![X2:$i]:((subset @ X2) @ ((binunion @ X1) @ X2)))) => sP19),introduced(definition,[new_symbols(definition,[sP78])])). 107.79/107.77 thf(sP79,plain,sP79 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X1 = X3)))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X1) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => ((X3 = X4) => (X2 = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X3) @ emptyset)) => (X1 = X2))))) => sP13))))),introduced(definition,[new_symbols(definition,[sP79])])). 107.79/107.77 thf(sP80,plain,sP80 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((((lam @ X1) @ X2) @ X3) = (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => ((in @ X4) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => ((in @ X3) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X3) @ emptyset))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4)))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ X1))))))) => ((![X1:$i]:((singleton @ X1) => (![X2:$i]:(((in @ X2) @ X1) => ((setunion @ X1) = X2))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((((if @ X1) @ X2) @ X3) @ X4) = X3)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((((if @ X1) @ X2) @ X3) @ X4) = X4)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => sP72))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP80])])). 107.79/107.77 thf(sP81,plain,sP81 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ X3) => ((subset @ ((setminus @ X1) @ X3)) @ ((setminus @ X1) @ X2)))))))) => sP57),introduced(definition,[new_symbols(definition,[sP81])])). 107.79/107.77 thf(sP82,plain,sP82 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X3) => ((subset @ X1) @ ((setadjoin @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => ((in @ X1) @ (powerset @ X2))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((subset @ X2) @ X1) => (X1 = X2))))) => ((![X1:$i]:(((subset @ X1) @ emptyset) => (X1 = emptyset))) => sP41)))),introduced(definition,[new_symbols(definition,[sP82])])). 107.79/107.77 thf(sP83,plain,sP83 <=> ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))) => (![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))) => ((![X1:$i]:(![X2:$i>$o]:((~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3))))) => (~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3)))))))) => sP55)),introduced(definition,[new_symbols(definition,[sP83])])). 107.79/107.77 thf(sP84,plain,sP84 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => sP60)),introduced(definition,[new_symbols(definition,[sP84])])). 107.79/107.77 thf(sP85,plain,sP85 <=> (((in @ eigen__3) @ eigen__0) => (~((eigen__2 = (eigen__1 @ eigen__3))))),introduced(definition,[new_symbols(definition,[sP85])])). 107.79/107.77 thf(sP86,plain,sP86 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((binintersect @ X1) @ X2)) => ((in @ X3) @ X2))))) => ((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => (~(((in @ X3) @ X2))))) => (((binintersect @ X1) @ X2) = emptyset)))) => ((![X1:$i]:(![X2:$i]:((subset @ ((binintersect @ X1) @ X2)) @ X2))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ X1) => (((binintersect @ X1) @ X2) = X2)))) => sP36)))),introduced(definition,[new_symbols(definition,[sP86])])). 107.79/107.77 thf(sP87,plain,sP87 <=> ((![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))) => (~((![X4:$i]:((![X5:$i]:(((in @ X5) @ X4) = (~((![X6:$i]:(((in @ X6) @ X1) => (~((X5 = (X2 @ X6)))))))))) => (X3 = X4))))))))))) => ((![X1:$i]:(![X2:$i>$i]:(![X3:$i]:(((in @ X3) @ ((image1 @ X1) @ X2)) = (~((![X4:$i]:(((in @ X4) @ X1) => (~((X3 = (X2 @ X4)))))))))))) => ((![X1:$i]:(![X2:$i>$i]:(![X3:$i]:(((in @ X3) @ ((image1 @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (~((X3 = (X2 @ X4)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(![X3:$i]:((~((![X4:$i]:((X3 = (X2 @ X4)) => (~(((in @ X4) @ X1))))))) => ((in @ X3) @ ((image1 @ X1) @ X2))))))))),introduced(definition,[new_symbols(definition,[sP87])])). 107.79/107.77 thf(sP88,plain,sP88 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((subset @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ ((binunion @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((subset @ ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) @ (powerset @ (powerset @ ((binunion @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ (powerset @ (powerset @ ((binunion @ X1) @ X2)))))))))) => sP59))))),introduced(definition,[new_symbols(definition,[sP88])])). 107.79/107.77 thf(sP89,plain,sP89 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) => ((~((X3 = X1))) => (X3 = X2)))))) => ((![X1:$i]:(![X2:$i]:((in @ X1) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:((in @ X2) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))) => ((![X1:$i]:(![X2:$i>$o]:((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => (~((((dsetconstr @ X1) @ X2) = emptyset)))))) => ((![X1:$i>$o]:(![X2:$i]:(((in @ X2) @ emptyset) => (X1 @ X2)))) => ((![X1:$i]:(![X2:$i>$o]:((~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3))))) => (~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3)))))))) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))) => (![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))) => (![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))) => ((![X1:$i]:(![X2:$i>$o]:((~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3))))) => (~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3)))))))) => ((![X1:$o]:(X1 => ((in @ emptyset) @ (prop2set @ X1)))) => ((![X1:$o]:(X1 => (set2prop @ (prop2set @ X1)))) => sP83))))))))))),introduced(definition,[new_symbols(definition,[sP89])])). 107.79/107.77 thf(sP90,plain,sP90 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X3) @ emptyset)) => (X1 = X2))))) => sP13),introduced(definition,[new_symbols(definition,[sP90])])). 107.79/107.77 thf(sP91,plain,sP91 <=> (![X1:$i]:(![X2:$i>$i]:(![X3:$i]:(((in @ X3) @ ((image1 @ X1) @ X2)) = (~((![X4:$i]:(((in @ X4) @ X1) => (~((X3 = (X2 @ X4)))))))))))),introduced(definition,[new_symbols(definition,[sP91])])). 107.79/107.77 thf(sP92,plain,sP92 <=> ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:((in @ ((setadjoin @ X2) @ emptyset)) @ X1)))))) => ((![X1:$i]:((singleton @ X1) => ((in @ (setunion @ X1)) @ X1))) => sP75)),introduced(definition,[new_symbols(definition,[sP92])])). 107.79/107.77 thf(sP93,plain,sP93 <=> ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))) => sP61),introduced(definition,[new_symbols(definition,[sP93])])). 107.79/107.77 thf(sP94,plain,sP94 <=> (eigen__2 = (eigen__1 @ eigen__3)),introduced(definition,[new_symbols(definition,[sP94])])). 107.79/107.77 thf(sP95,plain,sP95 <=> ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X1) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => ((X3 = X4) => (X2 = X4))))))) => sP90))),introduced(definition,[new_symbols(definition,[sP95])])). 107.79/107.77 thf(sP96,plain,sP96 <=> ((in @ eigen__3) @ eigen__0),introduced(definition,[new_symbols(definition,[sP96])])). 107.79/107.77 thf(sP97,plain,sP97 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binintersect @ X2) @ X3)) => ((in @ X5) @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => (~(((in @ X4) @ X2))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$o]:(![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binunion @ X2) @ X3)) => ((((in @ X5) @ X2) => X4) => ((((in @ X5) @ X3) => X4) => X4))))))))))) => sP32))))),introduced(definition,[new_symbols(definition,[sP97])])). 107.79/107.77 thf(sP98,plain,sP98 <=> ((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((subset @ X1) @ X2)))) => sP46),introduced(definition,[new_symbols(definition,[sP98])])). 107.79/107.77 thf(sP99,plain,sP99 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))) => ((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ X2) @ X3)) = ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (((in @ X4) @ ((setminus @ X1) @ X3)) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3)))))))))))) => sP84))))),introduced(definition,[new_symbols(definition,[sP99])])). 107.79/107.77 thf(sP100,plain,sP100 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X1 = X3)))))) => sP79),introduced(definition,[new_symbols(definition,[sP100])])). 107.79/107.77 thf(sP101,plain,sP101 <=> ((![X1:$i]:(((in @ X1) @ omega) => ((in @ ((setadjoin @ X1) @ X1)) @ omega))) => ((![X1:$i]:((~((((in @ emptyset) @ X1) => (~((![X2:$i]:((~((((in @ X2) @ omega) => (~(((in @ X2) @ X1)))))) => ((in @ ((setadjoin @ X2) @ X2)) @ X1)))))))) => (![X2:$i]:(((in @ X2) @ omega) => ((in @ X2) @ X1))))) => ((![X1:$i>$i>$o]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X2) => (~((![X4:$i]:(((X1 @ X3) @ X4) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (X4 = X5))))))))))) => (~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X1 @ X5) @ X4))))))))))))))))) => ((![X1:$i]:((~((![X2:$i]:(~(((in @ X2) @ X1)))))) => (~((![X2:$i]:(((in @ X2) @ X1) => (~((![X3:$i]:(((in @ X3) @ X2) => (~(((in @ X3) @ X1))))))))))))) => ((![X1:$i]:(~((![X2:$i]:((~(((~(((![X3:$i]:(((in @ X3) @ X2) => (![X4:$i]:(((in @ X4) @ X3) => ((in @ X4) @ X1))))) => (~((![X3:$i]:(![X4:$i]:((~((((in @ X3) @ X1) => (~(((in @ X4) @ X1)))))) => ((![X5:$i]:(((in @ X5) @ X2) => (((in @ X3) @ X5) = ((in @ X4) @ X5)))) => (X3 = X4)))))))))) => (~((![X3:$i]:(![X4:$i]:((~((((in @ X3) @ X2) => (~(((in @ X4) @ X2)))))) => ((~((![X5:$i]:(((in @ X5) @ X3) => ((in @ X5) @ X4))))) => (![X5:$i]:(((in @ X5) @ X4) => ((in @ X5) @ X3)))))))))))) => (~((![X3:$i]:((~(((![X4:$i]:(((in @ X4) @ X3) => ((in @ X4) @ X1))) => (![X4:$i]:(~(((in @ X4) @ X3))))))) => (~((![X4:$i]:(![X5:$i]:((~(((~((((in @ X4) @ X2) => (~(((in @ X5) @ X3)))))) => (~((![X6:$i]:(((in @ X6) @ X4) => (~(((in @ X6) @ X3)))))))))) => (~((![X6:$i]:(((in @ X6) @ X2) => ((~((![X7:$i]:(((in @ X7) @ X6) => ((in @ X7) @ X4))))) => ((in @ X5) @ X6)))))))))))))))))))) => ((![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (X1 @ (descr @ X1)))) => ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((in @ X3) @ ((dsetconstr @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ ((dsetconstr @ X1) @ X2)) => ((in @ X3) @ X1))))) => sP4)))))))),introduced(definition,[new_symbols(definition,[sP101])])). 107.79/107.77 thf(sP102,plain,sP102 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((binintersect @ X1) @ ((binunion @ X2) @ X3)) = ((binunion @ ((binintersect @ X1) @ X2)) @ ((binintersect @ X1) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => ((in @ X3) @ ((setminus @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setminus @ X1) @ X2)) => ((in @ X3) @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setminus @ X1) @ X2)) => (~(((in @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((setminus @ X1) @ X2) = emptyset)))) => sP31))))),introduced(definition,[new_symbols(definition,[sP102])])). 107.79/107.77 thf(sP103,plain,sP103 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))) => sP69)),introduced(definition,[new_symbols(definition,[sP103])])). 107.79/107.77 thf(sP104,plain,sP104 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))) => ((in @ X2) @ (powerset @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X2) @ (powerset @ X3)) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ ((setminus @ X1) @ X2)))) => ((in @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X2))) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))) => sP45)))))),introduced(definition,[new_symbols(definition,[sP104])])). 107.79/107.77 thf(sP105,plain,sP105 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) = (~((![X3:$i]:(((in @ X2) @ X3) => (~(((in @ X3) @ X1)))))))))) => (((in @ emptyset) @ omega) => sP101)),introduced(definition,[new_symbols(definition,[sP105])])). 107.79/107.77 thf(sP106,plain,sP106 <=> ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => ((in @ X3) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X3) @ emptyset))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4)))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ X1))))))) => ((![X1:$i]:((singleton @ X1) => (![X2:$i]:(((in @ X2) @ X1) => ((setunion @ X1) = X2))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((((if @ X1) @ X2) @ X3) @ X4) = X3)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((((if @ X1) @ X2) @ X3) @ X4) = X4)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => sP72))))))))),introduced(definition,[new_symbols(definition,[sP106])])). 107.79/107.77 thf(sP107,plain,sP107 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((binintersect @ X1) @ X2)) => ((in @ X3) @ X1))))) => ((![X1:$i]:(![X2:$i]:((subset @ ((binintersect @ X1) @ X2)) @ X1))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((binintersect @ X1) @ X2) = X1)))) => ((![X1:$i]:(![X2:$i]:((((binintersect @ X1) @ X2) = X2) => ((subset @ X2) @ X1)))) => sP86)))),introduced(definition,[new_symbols(definition,[sP107])])). 107.79/107.77 thf(sP108,plain,sP108 <=> (((in @ emptyset) @ omega) => sP101),introduced(definition,[new_symbols(definition,[sP108])])). 107.79/107.77 thf(sP109,plain,sP109 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => sP25)))))))),introduced(definition,[new_symbols(definition,[sP109])])). 107.79/107.77 thf(sP110,plain,sP110 <=> ((![X1:$i>$o]:(![X2:$i]:(((in @ X2) @ emptyset) => (X1 @ X2)))) => ((![X1:$i]:(![X2:$i>$o]:((~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3))))) => (~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3)))))))) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))) => (![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))) => (![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))) => ((![X1:$i]:(![X2:$i>$o]:((~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3))))) => (~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3)))))))) => ((![X1:$o]:(X1 => ((in @ emptyset) @ (prop2set @ X1)))) => ((![X1:$o]:(X1 => (set2prop @ (prop2set @ X1)))) => sP83))))))),introduced(definition,[new_symbols(definition,[sP110])])). 107.79/107.77 thf(sP111,plain,sP111 <=> ((![X1:$i]:(![X2:$i]:((subset @ ((binintersect @ X1) @ X2)) @ X2))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ X1) => (((binintersect @ X1) @ X2) = X2)))) => sP36)),introduced(definition,[new_symbols(definition,[sP111])])). 107.79/107.77 thf(sP112,plain,sP112 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => sP60),introduced(definition,[new_symbols(definition,[sP112])])). 107.79/107.77 thf(sP113,plain,sP113 <=> ((![X1:$i]:(![X2:$i]:(iskpair @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(iskpair @ ((kpair @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ X1) => ((subset @ ((setadjoin @ X2) @ emptyset)) @ X1)))) => sP7))),introduced(definition,[new_symbols(definition,[sP113])])). 107.79/107.77 thf(sP114,plain,sP114 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))) => sP48),introduced(definition,[new_symbols(definition,[sP114])])). 107.79/107.77 thf(sP115,plain,sP115 <=> ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => sP3)),introduced(definition,[new_symbols(definition,[sP115])])). 107.79/107.77 thf(sP116,plain,sP116 <=> (sP94 => (~(sP96))),introduced(definition,[new_symbols(definition,[sP116])])). 107.79/107.77 thf(sP117,plain,sP117 <=> ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => ((in @ X1) @ (powerset @ X2))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((subset @ X2) @ X1) => (X1 = X2))))) => ((![X1:$i]:(((subset @ X1) @ emptyset) => (X1 = emptyset))) => sP41))),introduced(definition,[new_symbols(definition,[sP117])])). 107.79/107.77 thf(sP118,plain,sP118 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => sP80)))),introduced(definition,[new_symbols(definition,[sP118])])). 107.79/107.77 thf(sP119,plain,sP119 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((((lam @ X1) @ X2) @ X3) = (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => ((in @ X4) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X4) @ emptyset))))))))) => sP106))))))),introduced(definition,[new_symbols(definition,[sP119])])). 107.79/107.77 thf(sP120,plain,sP120 <=> ((![X1:$i]:(![X2:$i]:((in @ X2) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))) => ((![X1:$i]:(![X2:$i>$o]:((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => (~((((dsetconstr @ X1) @ X2) = emptyset)))))) => sP110)),introduced(definition,[new_symbols(definition,[sP120])])). 107.79/107.77 thf(sP121,plain,sP121 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$o]:(((in @ X3) @ ((binunion @ X1) @ X2)) => ((((in @ X3) @ X1) => X4) => ((((in @ X3) @ X2) => X4) => X4))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((binunion @ X1) @ X2)) => ((~(((in @ X3) @ X1))) => ((in @ X3) @ X2)))))) => ((![X1:$i]:(![X2:$i]:((subset @ X1) @ ((binunion @ X1) @ X2)))) => sP78))),introduced(definition,[new_symbols(definition,[sP121])])). 107.79/107.77 thf(sP122,plain,sP122 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))) => sP80),introduced(definition,[new_symbols(definition,[sP122])])). 107.79/107.77 thf(sP123,plain,sP123 <=> ((![X1:$i]:((in @ emptyset) @ (powerset @ X1))) => sP44),introduced(definition,[new_symbols(definition,[sP123])])). 107.79/107.77 thf(sP124,plain,sP124 <=> ((![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (X1 @ (descr @ X1)))) => ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((in @ X3) @ ((dsetconstr @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ ((dsetconstr @ X1) @ X2)) => ((in @ X3) @ X1))))) => sP4))),introduced(definition,[new_symbols(definition,[sP124])])). 107.79/107.77 thf(sP125,plain,sP125 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((((lam @ X1) @ X2) @ X3) = (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => ((in @ X4) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X4) @ emptyset))))))))) => sP106))))),introduced(definition,[new_symbols(definition,[sP125])])). 107.79/107.77 thf(sP126,plain,sP126 <=> ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => sP93))))),introduced(definition,[new_symbols(definition,[sP126])])). 107.79/107.77 thf(sP127,plain,sP127 <=> ((![X1:$i]:((~((X1 = emptyset))) => (~((![X2:$i]:(~(((in @ X2) @ X1)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X1) @ ((setadjoin @ X2) @ emptyset)) => (X1 = X2)))) => ((![X1:$i]:(![X2:$i]:((~((X1 = X2))) => (~(((in @ X2) @ ((setadjoin @ X1) @ emptyset))))))) => sP2))),introduced(definition,[new_symbols(definition,[sP127])])). 107.79/107.77 thf(sP128,plain,sP128 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X2) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))) => sP5),introduced(definition,[new_symbols(definition,[sP128])])). 107.79/107.77 thf(sP129,plain,sP129 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => sP114)),introduced(definition,[new_symbols(definition,[sP129])])). 107.79/107.77 thf(sP130,plain,sP130 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ ((setminus @ X1) @ X2))) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (X2 = ((setminus @ X1) @ ((setminus @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => sP21))))),introduced(definition,[new_symbols(definition,[sP130])])). 107.79/107.77 thf(sP131,plain,sP131 <=> ((![X1:$i]:((![X2:$i]:(~(((in @ X2) @ X1)))) => (X1 = emptyset))) => sP11),introduced(definition,[new_symbols(definition,[sP131])])). 107.79/107.77 thf(sP132,plain,sP132 <=> ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))) => sP50),introduced(definition,[new_symbols(definition,[sP132])])). 107.79/107.77 thf(sP133,plain,sP133 <=> (![X1:$i>$i]:(![X2:$i]:(((in @ X2) @ ((image1 @ eigen__0) @ X1)) = (~((![X3:$i]:(((in @ X3) @ eigen__0) => (~((X2 = (X1 @ X3))))))))))),introduced(definition,[new_symbols(definition,[sP133])])). 107.79/107.77 thf(sP134,plain,sP134 <=> ((![X1:$i]:((subset @ X1) @ (setunion @ ((setadjoin @ X1) @ emptyset)))) => sP17),introduced(definition,[new_symbols(definition,[sP134])])). 107.79/107.77 thf(sP135,plain,sP135 <=> ((![X1:$i]:(![X2:$i>$o]:((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => (~((((dsetconstr @ X1) @ X2) = emptyset)))))) => sP110),introduced(definition,[new_symbols(definition,[sP135])])). 107.79/107.77 thf(sP136,plain,sP136 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))) => sP69),introduced(definition,[new_symbols(definition,[sP136])])). 107.79/107.77 thf(sP137,plain,sP137 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => sP28),introduced(definition,[new_symbols(definition,[sP137])])). 107.79/107.77 thf(sP138,plain,sP138 <=> ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => sP93)))),introduced(definition,[new_symbols(definition,[sP138])])). 107.79/107.77 thf(sP139,plain,sP139 <=> ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))) => sP73),introduced(definition,[new_symbols(definition,[sP139])])). 107.79/107.77 thf(sP140,plain,sP140 <=> ((![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))))) => ((![X1:$o]:(![X2:$i]:(((in @ X2) @ (prop2set @ X1)) => X1))) => sP6)),introduced(definition,[new_symbols(definition,[sP140])])). 107.79/107.77 thf(sP141,plain,sP141 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((subset @ ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) @ (powerset @ (powerset @ ((binunion @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ (powerset @ (powerset @ ((binunion @ X1) @ X2)))))))))) => sP59)))),introduced(definition,[new_symbols(definition,[sP141])])). 107.79/107.77 thf(sP142,plain,sP142 <=> ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X3) @ emptyset))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4)))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ X1))))))) => ((![X1:$i]:((singleton @ X1) => (![X2:$i]:(((in @ X2) @ X1) => ((setunion @ X1) = X2))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((((if @ X1) @ X2) @ X3) @ X4) = X3)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((((if @ X1) @ X2) @ X3) @ X4) = X4)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => sP72)))))))),introduced(definition,[new_symbols(definition,[sP142])])). 107.79/107.77 thf(sP143,plain,sP143 <=> (((in @ emptyset) @ ((setadjoin @ emptyset) @ emptyset)) => sP58),introduced(definition,[new_symbols(definition,[sP143])])). 107.79/107.77 thf(sP144,plain,sP144 <=> ((![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (~((![X2:$i]:(~((![X3:$i]:((X1 @ X3) = (X3 = X2)))))))))) => sP127),introduced(definition,[new_symbols(definition,[sP144])])). 107.79/107.77 thf(sP145,plain,sP145 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => ((in @ X3) @ ((setminus @ X1) @ ((setminus @ X1) @ X2))))))))) => sP66),introduced(definition,[new_symbols(definition,[sP145])])). 107.79/107.77 thf(sP146,plain,sP146 <=> ((omega = omega) => ((![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (![X2:$i]:(![X3:$i]:((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))))) => ((![X1:$i>$o]:(![X2:$i>$o]:((![X3:$i]:(![X4:$i]:((X3 = X4) => ((X1 @ X3) = (X2 @ X4))))) => ((~((![X3:$i]:((X1 @ X3) => (~((![X4:$i]:((X1 @ X4) => (X3 = X4))))))))) => ((~((![X3:$i]:((X2 @ X3) => (~((![X4:$i]:((X2 @ X4) => (X3 = X4))))))))) => ((descr @ X1) = (descr @ X2))))))) => sP63))),introduced(definition,[new_symbols(definition,[sP146])])). 107.79/107.77 thf(sP147,plain,sP147 <=> ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => sP93)),introduced(definition,[new_symbols(definition,[sP147])])). 107.79/107.77 thf(sP148,plain,sP148 <=> ((![X1:$i]:(![X2:$i]:(((in @ X1) @ ((setadjoin @ X2) @ emptyset)) => (X1 = X2)))) => ((![X1:$i]:(![X2:$i]:((~((X1 = X2))) => (~(((in @ X2) @ ((setadjoin @ X1) @ emptyset))))))) => sP2)),introduced(definition,[new_symbols(definition,[sP148])])). 107.79/107.77 thf(sP149,plain,sP149 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => sP132))),introduced(definition,[new_symbols(definition,[sP149])])). 107.79/107.77 thf(sP150,plain,sP150 <=> ((![X1:$i]:(![X2:$i>$o]:((~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3))))) => (~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3)))))))) => sP55),introduced(definition,[new_symbols(definition,[sP150])])). 107.79/107.77 thf(sP151,plain,sP151 <=> ((![X1:$o]:(X1 => ((in @ emptyset) @ (prop2set @ X1)))) => ((![X1:$o]:(X1 => (set2prop @ (prop2set @ X1)))) => sP83)),introduced(definition,[new_symbols(definition,[sP151])])). 107.79/107.77 thf(sP152,plain,sP152 <=> ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((binintersect @ X1) @ X2) = X1)))) => ((![X1:$i]:(![X2:$i]:((((binintersect @ X1) @ X2) = X2) => ((subset @ X2) @ X1)))) => sP86)),introduced(definition,[new_symbols(definition,[sP152])])). 107.79/107.77 thf(sP153,plain,sP153 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))) => ((![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X3) => ((in @ X4) @ X2)))) => (X2 = X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))) => ((subset @ X2) @ X3))))))) => sP104)),introduced(definition,[new_symbols(definition,[sP153])])). 107.79/107.77 thf(sP154,plain,sP154 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ X2)) => ((~((X3 = X1))) => ((in @ 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@ X2))))))))) => sP26),introduced(definition,[new_symbols(definition,[sP157])])). 107.79/107.77 thf(sP158,plain,sP158 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => sP72),introduced(definition,[new_symbols(definition,[sP158])])). 107.79/107.77 thf(sP159,plain,sP159 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X3) @ X1) => (((subset @ X3) @ X2) => ((subset @ X3) @ ((binintersect @ X1) @ X2))))))) => sP107),introduced(definition,[new_symbols(definition,[sP159])])). 107.79/107.77 thf(sP160,plain,sP160 <=> ((![X1:$i]:((~((![X2:$i]:(~(((in @ X2) @ X1)))))) => (~((X1 = emptyset))))) => ((![X1:$i]:(![X2:$i]:((in @ X1) @ ((setadjoin @ X1) @ X2)))) => sP143)),introduced(definition,[new_symbols(definition,[sP160])])). 107.79/107.77 thf(sP161,plain,sP161 <=> ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((in @ X3) @ ((dsetconstr @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ ((dsetconstr @ X1) @ X2)) => ((in @ X3) @ X1))))) => sP4)),introduced(definition,[new_symbols(definition,[sP161])])). 107.79/107.77 thf(sP162,plain,sP162 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (kfst @ X3)) @ X1))))) => sP100),introduced(definition,[new_symbols(definition,[sP162])])). 107.79/107.77 thf(sP163,plain,sP163 <=> ((![X1:$o]:(X1 => (set2prop @ (prop2set @ X1)))) => sP83),introduced(definition,[new_symbols(definition,[sP163])])). 107.79/107.77 thf(sP164,plain,sP164 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => sP114),introduced(definition,[new_symbols(definition,[sP164])])). 107.79/107.77 thf(sP165,plain,sP165 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => sP39)),introduced(definition,[new_symbols(definition,[sP165])])). 107.79/107.77 thf(sP166,plain,sP166 <=> ((![X1:$i]:(![X2:$i]:((X1 = X2) => ((powerset @ X1) = (powerset @ X2))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => ((setunion @ X1) = (setunion @ X2))))) => sP146)),introduced(definition,[new_symbols(definition,[sP166])])). 107.79/107.77 thf(sP167,plain,sP167 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))) => sP122),introduced(definition,[new_symbols(definition,[sP167])])). 107.79/107.77 thf(sP168,plain,sP168 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => sP125),introduced(definition,[new_symbols(definition,[sP168])])). 107.79/107.77 thf(sP169,plain,sP169 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ ((binunion @ X2) @ X3)))) => (~(((in @ X4) @ X2))))))))))) => sP49),introduced(definition,[new_symbols(definition,[sP169])])). 107.79/107.77 thf(sP170,plain,sP170 <=> ((![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))))) => ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X4) => (X4 = X3)))) => ((ex1 @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => ((ex1 @ X1) @ X2))))) => sP70))),introduced(definition,[new_symbols(definition,[sP170])])). 107.79/107.77 thf(sP171,plain,sP171 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => sP129)),introduced(definition,[new_symbols(definition,[sP171])])). 107.79/107.77 thf(sP172,plain,sP172 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => sP171),introduced(definition,[new_symbols(definition,[sP172])])). 107.79/107.77 thf(sP173,plain,sP173 <=> ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => ((subset @ (powerset @ X1)) @ (powerset @ X2))))) => ((![X1:$i]:(![X2:$i>$o]:((in @ ((dsetconstr @ X1) @ X2)) @ (powerset @ X1)))) => ((![X1:$i]:(![X2:$i>$o]:((subset @ ((dsetconstr @ X1) @ X2)) @ X1))) => sP155))),introduced(definition,[new_symbols(definition,[sP173])])). 107.79/107.77 thf(sP174,plain,sP174 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binintersect @ X2) @ X3)) => ((in @ X5) @ ((binunion @ X3) @ X4)))))))))))) => sP97),introduced(definition,[new_symbols(definition,[sP174])])). 107.79/107.77 thf(sP175,plain,sP175 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) = (![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1)))))) => sP105),introduced(definition,[new_symbols(definition,[sP175])])). 107.79/107.77 thf(sP176,plain,sP176 <=> ((![X1:$i]:(![X2:$i]:(((in @ X1) @ ((setadjoin @ X2) @ emptyset)) => ((in @ X2) @ ((setadjoin @ X1) @ emptyset))))) => sP89),introduced(definition,[new_symbols(definition,[sP176])])). 107.79/107.77 thf(sP177,plain,sP177 <=> (![X1:$i>$i]:(![X2:$i]:((~((![X3:$i]:((X2 = (X1 @ X3)) => (~(((in @ X3) @ eigen__0))))))) => ((in @ X2) @ ((image1 @ eigen__0) @ X1))))),introduced(definition,[new_symbols(definition,[sP177])])). 107.79/107.77 thf(sP178,plain,sP178 <=> ((![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (~((![X2:$i]:(~((X1 @ X2)))))))) => sP23),introduced(definition,[new_symbols(definition,[sP178])])). 107.79/107.77 thf(sP179,plain,sP179 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => sP118))),introduced(definition,[new_symbols(definition,[sP179])])). 107.79/107.77 thf(sP180,plain,sP180 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ ((setminus @ X1) @ X2)))) => ((in @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X2))) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))) => sP45))),introduced(definition,[new_symbols(definition,[sP180])])). 107.79/107.77 thf(sP181,plain,sP181 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => (~(((subset @ X1) @ X2)))))))) => sP74),introduced(definition,[new_symbols(definition,[sP181])])). 107.79/107.77 thf(sP182,plain,sP182 <=> ((![X1:$i>$o]:(![X2:$i>$o]:((![X3:$i]:(![X4:$i]:((X3 = X4) => ((X1 @ X3) = (X2 @ X4))))) => ((~((![X3:$i]:((X1 @ X3) => (~((![X4:$i]:((X1 @ X4) => (X3 = X4))))))))) => ((~((![X3:$i]:((X2 @ X3) => (~((![X4:$i]:((X2 @ X4) => (X3 = X4))))))))) => ((descr @ X1) = (descr @ X2))))))) => sP63),introduced(definition,[new_symbols(definition,[sP182])])). 107.79/107.77 thf(sP183,plain,sP183 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setminus @ X1) @ X2)) => ((in @ X3) @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setminus @ X1) @ X2)) => (~(((in @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((setminus @ X1) @ X2) = emptyset)))) => sP31))),introduced(definition,[new_symbols(definition,[sP183])])). 107.79/107.77 thf(sP184,plain,sP184 <=> ((![X1:$i]:(![X2:$i]:((in @ X1) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))) => sP120),introduced(definition,[new_symbols(definition,[sP184])])). 107.79/107.77 thf(sP185,plain,sP185 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ (powerset @ (powerset @ ((binunion @ X1) @ X2)))))))))) => sP59),introduced(definition,[new_symbols(definition,[sP185])])). 107.79/107.77 thf(sP186,plain,sP186 <=> ((![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((in @ X3) @ X1) = ((in @ X4) @ X2)))))))) => ((![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (![X2:$i]:(![X3:$i]:((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))))) => sP52)),introduced(definition,[new_symbols(definition,[sP186])])). 107.79/107.77 thf(sP187,plain,sP187 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ X2) @ X1)))) => sP12),introduced(definition,[new_symbols(definition,[sP187])])). 107.79/107.77 thf(sP188,plain,sP188 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X4) @ X2)))))) => sP9),introduced(definition,[new_symbols(definition,[sP188])])). 107.79/107.77 thf(sP189,plain,sP189 <=> ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => (singleton @ ((dsetconstr @ X1) @ X2)))))) => sP170),introduced(definition,[new_symbols(definition,[sP189])])). 107.79/107.77 thf(sP190,plain,sP190 <=> ((![X1:$o]:(![X2:$i]:(((in @ X2) @ (prop2set @ X1)) => X1))) => sP6),introduced(definition,[new_symbols(definition,[sP190])])). 107.79/107.77 thf(sP191,plain,sP191 <=> ((![X1:$i]:(((dsetconstr @ X1) @ (^[X2:$i]:(~($false)))) = X1)) => sP10),introduced(definition,[new_symbols(definition,[sP191])])). 107.79/107.77 thf(sP192,plain,sP192 <=> ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => sP115),introduced(definition,[new_symbols(definition,[sP192])])). 107.79/107.77 thf(sP193,plain,sP193 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ X1) => ((subset @ ((setadjoin @ X2) @ emptyset)) @ X1)))) => sP7),introduced(definition,[new_symbols(definition,[sP193])])). 107.79/107.77 thf(sP194,plain,sP194 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => sP25)))))),introduced(definition,[new_symbols(definition,[sP194])])). 107.79/107.77 thf(sP195,plain,sP195 <=> ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4)))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ X1))))))) => ((![X1:$i]:((singleton @ X1) => (![X2:$i]:(((in @ X2) @ X1) => ((setunion @ X1) = X2))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((((if @ X1) @ X2) @ X3) @ X4) = X3)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ 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sP42),introduced(definition,[new_symbols(definition,[sP198])])). 107.79/107.77 thf(sP199,plain,sP199 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (~((X3 = ((kpair @ X4) @ X5)))))))))))))) => sP34),introduced(definition,[new_symbols(definition,[sP199])])). 107.79/107.77 thf(sP200,plain,sP200 <=> (sP91 => ((![X1:$i]:(![X2:$i>$i]:(![X3:$i]:(((in @ X3) @ ((image1 @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (~((X3 = (X2 @ X4)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(![X3:$i]:((~((![X4:$i]:((X3 = (X2 @ X4)) => (~(((in @ X4) @ X1))))))) => ((in @ X3) @ ((image1 @ X1) @ X2)))))))),introduced(definition,[new_symbols(definition,[sP200])])). 107.79/107.77 thf(sP201,plain,sP201 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => sP21)),introduced(definition,[new_symbols(definition,[sP201])])). 107.79/107.77 thf(sP202,plain,sP202 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X2))) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))) => sP45)),introduced(definition,[new_symbols(definition,[sP202])])). 107.79/107.77 thf(sP203,plain,sP203 <=> ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => sP147),introduced(definition,[new_symbols(definition,[sP203])])). 107.79/107.77 thf(sP204,plain,sP204 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => ((in @ X3) @ ((setminus @ X1) @ X2))))))) => sP183),introduced(definition,[new_symbols(definition,[sP204])])). 107.79/107.77 thf(sP205,plain,sP205 <=> ((![X1:$i]:((subset @ (setunion @ ((setadjoin @ X1) @ emptyset))) @ X1)) => sP134),introduced(definition,[new_symbols(definition,[sP205])])). 107.79/107.77 thf(sP206,plain,sP206 <=> ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => ((ex1 @ X1) @ X2))))) => sP70),introduced(definition,[new_symbols(definition,[sP206])])). 107.79/107.77 thf(sP207,plain,sP207 <=> ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))) => sP93),introduced(definition,[new_symbols(definition,[sP207])])). 107.79/107.77 thf(sP208,plain,sP208 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => ((in @ X4) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X4) @ emptyset))))))))) => sP106)))),introduced(definition,[new_symbols(definition,[sP208])])). 107.79/107.78 thf(sP209,plain,sP209 <=> ((![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((setadjoin @ X1) @ X3) = ((setadjoin @ X2) @ X4)))))))) => sP166),introduced(definition,[new_symbols(definition,[sP209])])). 107.79/107.78 thf(sP210,plain,sP210 <=> ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((subset @ X2) @ X1) => (X1 = X2))))) => ((![X1:$i]:(((subset @ X1) @ emptyset) => (X1 = emptyset))) => sP41)),introduced(definition,[new_symbols(definition,[sP210])])). 107.79/107.78 thf(sP211,plain,sP211 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))) => sP201),introduced(definition,[new_symbols(definition,[sP211])])). 107.79/107.78 thf(sP212,plain,sP212 <=> ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => sP192),introduced(definition,[new_symbols(definition,[sP212])])). 107.79/107.78 thf(sP213,plain,sP213 <=> ((![X1:$i]:(![X2:$i]:((ksnd @ ((kpair @ X1) @ X2)) = X2))) => ((![X1:$i]:((iskpair @ X1) => (((kpair @ (kfst @ X1)) @ (ksnd @ X1)) = X1))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))) => sP8))),introduced(definition,[new_symbols(definition,[sP213])])). 107.79/107.78 thf(sP214,plain,sP214 <=> ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((((if @ X1) @ X2) @ X3) @ X4) = X4)))))))) => ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))))))))) => sP158)),introduced(definition,[new_symbols(definition,[sP214])])). 107.79/107.78 thf(sP215,plain,sP215 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) @ (powerset @ (powerset @ ((binunion @ X1) @ X2)))))))))) => sP185),introduced(definition,[new_symbols(definition,[sP215])])). 107.79/107.78 thf(sP216,plain,sP216 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))) => sP137),introduced(definition,[new_symbols(definition,[sP216])])). 107.79/107.78 thf(sP217,plain,sP217 <=> ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X4) @ emptyset))))))))) => sP106),introduced(definition,[new_symbols(definition,[sP217])])). 107.79/107.78 thf(sP218,plain,sP218 <=> ((![X1:$i]:(((subset @ X1) @ emptyset) => (X1 = emptyset))) => sP41),introduced(definition,[new_symbols(definition,[sP218])])). 107.79/107.78 thf(sP219,plain,sP219 <=> ((![X1:$i]:(![X2:$i]:((~((X1 = X2))) => (~(((in @ X2) @ ((setadjoin @ X1) @ emptyset))))))) => sP2),introduced(definition,[new_symbols(definition,[sP219])])). 107.79/107.78 thf(sP220,plain,sP220 <=> ((![X1:$i]:(![X2:$i>$o]:((subset @ ((dsetconstr @ X1) @ X2)) @ X1))) => sP155),introduced(definition,[new_symbols(definition,[sP220])])). 107.79/107.78 thf(sP221,plain,sP221 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => sP169),introduced(definition,[new_symbols(definition,[sP221])])). 107.79/107.78 thf(sP222,plain,sP222 <=> ((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => (~(((in @ X3) @ X2))))) => (((binintersect @ X1) @ X2) = emptyset)))) => sP111),introduced(definition,[new_symbols(definition,[sP222])])). 107.79/107.78 thf(sP223,plain,sP223 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))) => sP167),introduced(definition,[new_symbols(definition,[sP223])])). 107.79/107.78 thf(sP224,plain,sP224 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))) => sP45),introduced(definition,[new_symbols(definition,[sP224])])). 107.79/107.78 thf(sP225,plain,sP225 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => (~((X1 = X2)))))))) => ((![X1:$i]:((subset @ X1) @ X1)) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X2) => (((subset @ X2) @ X3) => ((subset @ X1) @ X3)))))) => sP30))),introduced(definition,[new_symbols(definition,[sP225])])). 107.79/107.78 thf(sP226,plain,sP226 <=> ((![X1:$i]:(![X2:$i]:((subset @ X1) @ ((binunion @ X1) @ X2)))) => sP78),introduced(definition,[new_symbols(definition,[sP226])])). 107.79/107.78 thf(sP227,plain,sP227 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))) => sP8),introduced(definition,[new_symbols(definition,[sP227])])). 107.79/107.78 thf(sP228,plain,sP228 <=> ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ ((dsetconstr @ X1) @ X2)) => ((in @ X3) @ X1))))) => sP4),introduced(definition,[new_symbols(definition,[sP228])])). 107.79/107.78 thf(sP229,plain,sP229 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => sP118)),introduced(definition,[new_symbols(definition,[sP229])])). 107.79/107.78 thf(sP230,plain,sP230 <=> ((![X1:$i]:(![X2:$i]:((X1 = X2) => ((subset @ X2) @ X1)))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => ((subset @ X1) @ X2)))) => sP98)),introduced(definition,[new_symbols(definition,[sP230])])). 107.79/107.78 thf(sP231,plain,sP231 <=> ((![X1:$i]:(![X2:$i]:((X1 = X2) => ((subset @ X1) @ X2)))) => sP98),introduced(definition,[new_symbols(definition,[sP231])])). 107.79/107.78 thf(sP232,plain,sP232 <=> ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => ((in @ X4) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))) => sP217),introduced(definition,[new_symbols(definition,[sP232])])). 107.79/107.78 thf(sP233,plain,sP233 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X2) => (((subset @ X2) @ X3) => ((subset @ X1) @ X3)))))) => sP30),introduced(definition,[new_symbols(definition,[sP233])])). 107.79/107.78 thf(sP234,plain,sP234 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => sP119),introduced(definition,[new_symbols(definition,[sP234])])). 107.79/107.78 thf(sP235,plain,sP235 <=> ((![X1:$i]:(![X2:$i]:((in @ X2) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ ((binunion @ X1) @ X2)))))) => sP121)),introduced(definition,[new_symbols(definition,[sP235])])). 107.79/107.78 thf(sP236,plain,sP236 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => ((in @ X3) @ ((symdiff @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => (((in @ X3) @ X2) => ((in @ X3) @ ((symdiff @ X1) @ X2))))))) => sP24)),introduced(definition,[new_symbols(definition,[sP236])])). 107.79/107.78 thf(sP237,plain,sP237 <=> ((~((![X1:$i]:((eigen__2 = (eigen__1 @ X1)) => (~(((in @ X1) @ eigen__0))))))) => sP77),introduced(definition,[new_symbols(definition,[sP237])])). 107.79/107.78 thf(sP238,plain,sP238 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ X2)) => (![X4:$o]:(((X3 = X1) => X4) => ((((in @ X3) @ X2) => X4) => X4))))))) => sP154),introduced(definition,[new_symbols(definition,[sP238])])). 107.79/107.78 thf(sP239,plain,sP239 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (((in @ X4) @ ((setminus @ X1) @ X3)) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3)))))))))))) => sP84),introduced(definition,[new_symbols(definition,[sP239])])). 107.79/107.78 thf(sP240,plain,sP240 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => sP25),introduced(definition,[new_symbols(definition,[sP240])])). 107.79/107.78 thf(sP241,plain,sP241 <=> ((![X1:$i]:(![X2:$i]:((((binintersect @ X1) @ X2) = X2) => ((subset @ X2) @ X1)))) => sP86),introduced(definition,[new_symbols(definition,[sP241])])). 107.79/107.78 thf(sP242,plain,sP242 <=> ((![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:(X1 = ((kpair @ (kfst @ X1)) @ X2))))))) => sP213),introduced(definition,[new_symbols(definition,[sP242])])). 107.79/107.78 thf(sP243,plain,sP243 <=> ((![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((in @ X3) @ X1) => ((in @ X4) @ X2)))))))) => sP186),introduced(definition,[new_symbols(definition,[sP243])])). 107.79/107.78 thf(sP244,plain,sP244 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setminus @ X1) @ X2)) => (~(((in @ X3) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((setminus @ X1) @ X2) = emptyset)))) => sP31)),introduced(definition,[new_symbols(definition,[sP244])])). 107.79/107.78 thf(sP245,plain,sP245 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => sP240),introduced(definition,[new_symbols(definition,[sP245])])). 107.79/107.78 thf(sP246,plain,sP246 <=> (![X1:$i]:((~((![X2:$i]:((X1 = (eigen__1 @ X2)) => (~(((in @ X2) @ eigen__0))))))) => ((in @ X1) @ ((image1 @ eigen__0) @ eigen__1)))),introduced(definition,[new_symbols(definition,[sP246])])). 107.79/107.78 thf(sP247,plain,sP247 <=> ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))))))))) => sP158),introduced(definition,[new_symbols(definition,[sP247])])). 107.79/107.78 thf(sP248,plain,sP248 <=> ((![X1:$i>$i>$o]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X2) => (~((![X4:$i]:(((X1 @ X3) @ X4) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (X4 = X5))))))))))) => (~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X1 @ X5) @ X4))))))))))))))))) => ((![X1:$i]:((~((![X2:$i]:(~(((in @ X2) @ X1)))))) => (~((![X2:$i]:(((in @ X2) @ X1) => (~((![X3:$i]:(((in @ X3) @ X2) => (~(((in @ X3) @ X1))))))))))))) => ((![X1:$i]:(~((![X2:$i]:((~(((~(((![X3:$i]:(((in @ X3) @ X2) => (![X4:$i]:(((in @ X4) @ X3) => ((in @ X4) @ X1))))) => (~((![X3:$i]:(![X4:$i]:((~((((in @ X3) @ X1) => (~(((in @ X4) @ X1)))))) => ((![X5:$i]:(((in @ X5) @ X2) => (((in @ X3) @ X5) = ((in @ X4) @ X5)))) => (X3 = X4)))))))))) => (~((![X3:$i]:(![X4:$i]:((~((((in @ X3) @ X2) => (~(((in @ X4) @ X2)))))) => ((~((![X5:$i]:(((in @ X5) @ X3) => ((in @ X5) @ X4))))) => (![X5:$i]:(((in @ X5) @ X4) => ((in @ X5) @ X3)))))))))))) => (~((![X3:$i]:((~(((![X4:$i]:(((in @ X4) @ X3) => ((in @ X4) @ X1))) => (![X4:$i]:(~(((in @ X4) @ X3))))))) => (~((![X4:$i]:(![X5:$i]:((~(((~((((in @ X4) @ X2) => (~(((in @ X5) @ X3)))))) => (~((![X6:$i]:(((in @ X6) @ X4) => (~(((in @ X6) @ X3)))))))))) => (~((![X6:$i]:(((in @ X6) @ X2) => ((~((![X7:$i]:(((in @ X7) @ X6) => ((in @ X7) @ X4))))) => ((in @ X5) @ X6)))))))))))))))))))) => sP124))),introduced(definition,[new_symbols(definition,[sP248])])). 107.79/107.78 thf(sP249,plain,sP249 <=> ((![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((setminus @ X1) @ X2) = emptyset)))) => sP31),introduced(definition,[new_symbols(definition,[sP249])])). 107.79/107.78 thf(sP250,plain,sP250 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => sP118),introduced(definition,[new_symbols(definition,[sP250])])). 107.79/107.78 thf(sP251,plain,sP251 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))))) => sP180),introduced(definition,[new_symbols(definition,[sP251])])). 107.79/107.78 thf(sP252,plain,sP252 <=> ((![X1:$i]:((~((![X2:$i]:(~(((in @ X2) @ X1)))))) => (~((![X2:$i]:(((in @ X2) @ X1) => (~((![X3:$i]:(((in @ X3) @ X2) => (~(((in @ X3) @ X1))))))))))))) => ((![X1:$i]:(~((![X2:$i]:((~(((~(((![X3:$i]:(((in @ X3) @ X2) => (![X4:$i]:(((in @ X4) @ X3) => ((in @ X4) @ X1))))) => (~((![X3:$i]:(![X4:$i]:((~((((in @ X3) @ X1) => (~(((in @ X4) @ X1)))))) => ((![X5:$i]:(((in @ X5) @ X2) => (((in @ X3) @ X5) = ((in @ X4) @ X5)))) => (X3 = X4)))))))))) => (~((![X3:$i]:(![X4:$i]:((~((((in @ X3) @ X2) => (~(((in @ X4) @ X2)))))) => ((~((![X5:$i]:(((in @ X5) @ X3) => ((in @ X5) @ X4))))) => (![X5:$i]:(((in @ X5) @ X4) => ((in @ X5) @ X3)))))))))))) => (~((![X3:$i]:((~(((![X4:$i]:(((in @ X4) @ X3) => ((in @ X4) @ X1))) => (![X4:$i]:(~(((in @ X4) @ X3))))))) => (~((![X4:$i]:(![X5:$i]:((~(((~((((in @ X4) @ X2) => (~(((in @ X5) @ X3)))))) => (~((![X6:$i]:(((in @ X6) @ X4) => (~(((in @ X6) @ X3)))))))))) => (~((![X6:$i]:(((in @ X6) @ X2) => ((~((![X7:$i]:(((in @ X7) @ X6) => ((in @ X7) @ X4))))) => ((in @ X5) @ X6)))))))))))))))))))) => sP124)),introduced(definition,[new_symbols(definition,[sP252])])). 107.79/107.78 thf(sP253,plain,sP253 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X2 = X4)))))) => sP242),introduced(definition,[new_symbols(definition,[sP253])])). 107.79/107.78 thf(sP254,plain,sP254 <=> ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((((if @ X1) @ X2) @ X3) @ X4) = X3)))))))) => sP214),introduced(definition,[new_symbols(definition,[sP254])])). 107.79/107.78 thf(sP255,plain,sP255 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => sP245)),introduced(definition,[new_symbols(definition,[sP255])])). 107.79/107.78 thf(sP256,plain,sP256 <=> ((emptyset = emptyset) => sP209),introduced(definition,[new_symbols(definition,[sP256])])). 107.79/107.78 thf(sP257,plain,sP257 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => ((X3 = X4) => (X2 = X4))))))) => sP90),introduced(definition,[new_symbols(definition,[sP257])])). 107.79/107.78 thf(sP258,plain,sP258 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => sP99),introduced(definition,[new_symbols(definition,[sP258])])). 107.79/107.78 thf(sP259,plain,sP259 <=> ((![X1:$i]:(![X2:$i]:(iskpair @ ((kpair @ X1) @ X2)))) => sP193),introduced(definition,[new_symbols(definition,[sP259])])). 107.79/107.78 thf(sP260,plain,sP260 <=> (![X1:$i]:(((in @ X1) @ eigen__0) => (~((eigen__2 = (eigen__1 @ X1)))))),introduced(definition,[new_symbols(definition,[sP260])])). 107.79/107.78 thf(sP261,plain,sP261 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((binunion @ X1) @ X2)) => ((~(((in @ X3) @ X1))) => ((in @ X3) @ X2)))))) => sP226),introduced(definition,[new_symbols(definition,[sP261])])). 107.79/107.78 thf(sP262,plain,sP262 <=> ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => sP132),introduced(definition,[new_symbols(definition,[sP262])])). 107.79/107.78 thf(sP263,plain,sP263 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))) => sP258),introduced(definition,[new_symbols(definition,[sP263])])). 107.79/107.78 thf(sP264,plain,sP264 <=> ((![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (![X2:$i]:(![X3:$i]:((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))))) => sP182),introduced(definition,[new_symbols(definition,[sP264])])). 107.79/107.78 thf(sP265,plain,sP265 <=> ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X4) => (X4 = X3)))) => ((ex1 @ X1) @ X2))))))) => sP206),introduced(definition,[new_symbols(definition,[sP265])])). 107.79/107.78 thf(sP266,plain,sP266 <=> ((![X1:$i]:(![X2:$i>$o]:((~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3))))) => (~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3)))))))) => sP151),introduced(definition,[new_symbols(definition,[sP266])])). 107.79/107.78 thf(sP267,plain,sP267 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ X2) @ X3)) = ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => sP239))),introduced(definition,[new_symbols(definition,[sP267])])). 107.79/107.78 thf(sP268,plain,sP268 <=> ((![X1:$i]:(![X2:$i>$o]:((~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3))))) => (~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3)))))))) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))) => (![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))) => (![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))) => sP266))),introduced(definition,[new_symbols(definition,[sP268])])). 107.79/107.78 thf(sP269,plain,sP269 <=> ((![X1:$i]:(![X2:$i>$o]:((in @ ((dsetconstr @ X1) @ X2)) @ (powerset @ X1)))) => sP220),introduced(definition,[new_symbols(definition,[sP269])])). 107.79/107.78 thf(sP270,plain,sP270 <=> ((![X1:$i]:((singleton @ X1) => ((in @ (setunion @ X1)) @ X1))) => sP75),introduced(definition,[new_symbols(definition,[sP270])])). 107.79/107.78 thf(sP271,plain,sP271 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => sP76),introduced(definition,[new_symbols(definition,[sP271])])). 107.79/107.78 thf(sP272,plain,sP272 <=> ((![X1:$i]:((in @ emptyset) @ (powerset @ X1))) => sP123),introduced(definition,[new_symbols(definition,[sP272])])). 107.79/107.78 thf(sP273,plain,sP273 <=> ((![X1:$i]:(![X2:$i]:((X1 = X2) => ((setunion @ X1) = (setunion @ X2))))) => sP146),introduced(definition,[new_symbols(definition,[sP273])])). 107.79/107.78 thf(sP274,plain,sP274 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ X2) @ X3)) = ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => sP239)),introduced(definition,[new_symbols(definition,[sP274])])). 107.79/107.78 thf(sP275,plain,sP275 <=> ((![X1:$i]:(~((![X2:$i]:((~(((~(((![X3:$i]:(((in @ X3) @ X2) => (![X4:$i]:(((in @ X4) @ X3) => ((in @ X4) @ X1))))) => (~((![X3:$i]:(![X4:$i]:((~((((in @ X3) @ X1) => (~(((in @ X4) @ X1)))))) => ((![X5:$i]:(((in @ X5) @ X2) => (((in @ X3) @ X5) = ((in @ X4) @ X5)))) => (X3 = X4)))))))))) => (~((![X3:$i]:(![X4:$i]:((~((((in @ X3) @ X2) => (~(((in @ X4) @ X2)))))) => ((~((![X5:$i]:(((in @ X5) @ X3) => ((in @ X5) @ X4))))) => (![X5:$i]:(((in @ X5) @ X4) => ((in @ X5) @ X3)))))))))))) => (~((![X3:$i]:((~(((![X4:$i]:(((in @ X4) @ X3) => ((in @ X4) @ X1))) => (![X4:$i]:(~(((in @ X4) @ X3))))))) => (~((![X4:$i]:(![X5:$i]:((~(((~((((in @ X4) @ X2) => (~(((in @ X5) @ X3)))))) => (~((![X6:$i]:(((in @ X6) @ X4) => (~(((in @ X6) @ X3)))))))))) => (~((![X6:$i]:(((in @ X6) @ X2) => ((~((![X7:$i]:(((in @ X7) @ X6) => ((in @ X7) @ X4))))) => ((in @ X5) @ X6)))))))))))))))))))) => sP124),introduced(definition,[new_symbols(definition,[sP275])])). 107.79/107.78 thf(sP276,plain,sP276 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => sP21),introduced(definition,[new_symbols(definition,[sP276])])). 107.79/107.78 thf(sP277,plain,sP277 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$o]:(![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binunion @ X2) @ X3)) => ((((in @ X5) @ X2) => X4) => ((((in @ X5) @ X3) => X4) => X4))))))))))) => sP32)),introduced(definition,[new_symbols(definition,[sP277])])). 107.79/107.78 thf(sP278,plain,sP278 <=> ((![X1:$i]:(![X2:$i>$i]:(![X3:$i]:(((in @ X3) @ ((image1 @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (~((X3 = (X2 @ X4)))))))))))) => (![X1:$i]:(![X2:$i>$i]:(![X3:$i]:((~((![X4:$i]:((X3 = (X2 @ X4)) => (~(((in @ X4) @ X1))))))) => ((in @ X3) @ ((image1 @ X1) @ X2))))))),introduced(definition,[new_symbols(definition,[sP278])])). 107.79/107.78 thf(sP279,plain,sP279 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => sP255),introduced(definition,[new_symbols(definition,[sP279])])). 107.79/107.78 thf(sP280,plain,sP280 <=> ((![X1:$i]:(~(((in @ X1) @ emptyset)))) => sP196),introduced(definition,[new_symbols(definition,[sP280])])). 107.79/107.78 thf(sP281,plain,sP281 <=> ((![X1:$i]:((subset @ X1) @ X1)) => sP233),introduced(definition,[new_symbols(definition,[sP281])])). 107.79/107.78 thf(sP282,plain,sP282 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))) => ((subset @ X2) @ X3))))))) => sP104),introduced(definition,[new_symbols(definition,[sP282])])). 107.79/107.78 thf(sP283,plain,sP283 <=> ((![X1:$i]:((iskpair @ X1) => (((kpair @ (kfst @ X1)) @ (ksnd @ X1)) = X1))) => sP227),introduced(definition,[new_symbols(definition,[sP283])])). 107.79/107.78 thf(sP284,plain,sP284 <=> (![X1:$i]:((eigen__2 = (eigen__1 @ X1)) => (~(((in @ X1) @ eigen__0))))),introduced(definition,[new_symbols(definition,[sP284])])). 107.79/107.78 thf(sP285,plain,sP285 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((symdiff @ X1) @ X2)) => (![X4:$o]:((((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => X4)) => (((~(((in @ X3) @ X1))) => (((in @ X3) @ X2) => X4)) => X4))))))) => sP236),introduced(definition,[new_symbols(definition,[sP285])])). 107.79/107.78 thf(sP286,plain,sP286 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ X1) => ((in @ X2) @ (powerset @ (setunion @ X1)))))) => sP144),introduced(definition,[new_symbols(definition,[sP286])])). 107.79/107.78 thf(sP287,plain,sP287 <=> ((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) = ((in @ X3) @ X2))) => (X1 = X2)))) => sP280),introduced(definition,[new_symbols(definition,[sP287])])). 107.79/107.78 thf(sP288,plain,sP288 <=> ((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((subset @ X1) @ X2)))) => sP230),introduced(definition,[new_symbols(definition,[sP288])])). 107.79/107.78 thf(sP289,plain,sP289 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => sP234),introduced(definition,[new_symbols(definition,[sP289])])). 107.79/107.78 thf(sP290,plain,sP290 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))) => sP38),introduced(definition,[new_symbols(definition,[sP290])])). 107.79/107.78 thf(sP291,plain,sP291 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ X2) @ ((setminus @ X1) @ ((setminus @ X1) @ X2)))))) => sP130),introduced(definition,[new_symbols(definition,[sP291])])). 107.79/107.78 thf(sP292,plain,sP292 <=> ((![X1:$i]:(![X2:$i]:((in @ X1) @ ((setadjoin @ X1) @ X2)))) => sP143),introduced(definition,[new_symbols(definition,[sP292])])). 107.79/107.78 thf(sP293,plain,sP293 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => (~(((in @ X4) @ X2))))))))))) => sP277),introduced(definition,[new_symbols(definition,[sP293])])). 107.79/107.78 thf(sP294,plain,sP294 <=> ((![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))) => sP262),introduced(definition,[new_symbols(definition,[sP294])])). 107.79/107.78 thf(sP295,plain,sP295 <=> ((![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ X1))))))) => ((![X1:$i]:((singleton @ X1) => (![X2:$i]:(((in @ X2) @ X1) => ((setunion @ X1) = X2))))) => sP254)),introduced(definition,[new_symbols(definition,[sP295])])). 107.79/107.78 thf(sP296,plain,sP296 <=> ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))) => sP212),introduced(definition,[new_symbols(definition,[sP296])])). 107.79/107.78 thf(sP297,plain,sP297 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => (((in @ X3) @ X2) => ((in @ X3) @ ((symdiff @ X1) @ X2))))))) => sP24),introduced(definition,[new_symbols(definition,[sP297])])). 107.79/107.78 thf(sP298,plain,sP298 <=> ((![X1:$i]:(![X2:$i]:((subset @ ((binintersect @ X1) @ X2)) @ X1))) => sP152),introduced(definition,[new_symbols(definition,[sP298])])). 107.79/107.78 thf(sP299,plain,sP299 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => sP293),introduced(definition,[new_symbols(definition,[sP299])])). 107.79/107.78 thf(sP300,plain,sP300 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => sP179),introduced(definition,[new_symbols(definition,[sP300])])). 107.79/107.78 thf(sP301,plain,sP301 <=> ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ X1) => (((binintersect @ X1) @ X2) = X2)))) => sP36),introduced(definition,[new_symbols(definition,[sP301])])). 107.79/107.78 thf(sP302,plain,sP302 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))) => sP232),introduced(definition,[new_symbols(definition,[sP302])])). 107.79/107.78 thf(sP303,plain,sP303 <=> ((![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (![X2:$i]:(![X3:$i]:((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))))) => sP52),introduced(definition,[new_symbols(definition,[sP303])])). 107.79/107.78 thf(sP304,plain,sP304 <=> ((![X1:$i]:((singleton @ X1) => (![X2:$i]:(((in @ X2) @ X1) => ((setunion @ X1) = X2))))) => sP254),introduced(definition,[new_symbols(definition,[sP304])])). 107.79/107.78 thf(sP305,plain,sP305 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => sP239),introduced(definition,[new_symbols(definition,[sP305])])). 107.79/107.78 thf(sP306,plain,sP306 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (X2 = ((setminus @ X1) @ ((setminus @ X1) @ X2)))))) => sP211),introduced(definition,[new_symbols(definition,[sP306])])). 107.79/107.78 thf(sP307,plain,sP307 <=> ((![X1:$i]:((~((((in @ emptyset) @ X1) => (~((![X2:$i]:((~((((in @ X2) @ omega) => (~(((in @ X2) @ X1)))))) => ((in @ ((setadjoin @ X2) @ X2)) @ X1)))))))) => (![X2:$i]:(((in @ X2) @ omega) => ((in @ X2) @ X1))))) => sP248),introduced(definition,[new_symbols(definition,[sP307])])). 107.79/107.78 thf(sP308,plain,sP308 <=> (![X1:$i]:(![X2:$i>$i]:(![X3:$i]:((~((![X4:$i]:((X3 = (X2 @ X4)) => (~(((in @ X4) @ X1))))))) => ((in @ X3) @ ((image1 @ X1) @ X2)))))),introduced(definition,[new_symbols(definition,[sP308])])). 107.79/107.78 thf(sP309,plain,sP309 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => sP245),introduced(definition,[new_symbols(definition,[sP309])])). 107.79/107.78 thf(sP310,plain,sP310 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => sP39),introduced(definition,[new_symbols(definition,[sP310])])). 107.79/107.78 thf(sP311,plain,sP311 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ X1))))) => sP153),introduced(definition,[new_symbols(definition,[sP311])])). 107.79/107.78 thf(sP312,plain,sP312 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$o]:(![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binunion @ X2) @ X3)) => ((((in @ X5) @ X2) => X4) => ((((in @ X5) @ X3) => X4) => X4))))))))))) => sP32),introduced(definition,[new_symbols(definition,[sP312])])). 107.79/107.78 thf(sP313,plain,sP313 <=> ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))) => (![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))) => ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))) => (![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))) => sP266)),introduced(definition,[new_symbols(definition,[sP313])])). 107.79/107.78 thf(sP314,plain,sP314 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((subset @ ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))) => sP215),introduced(definition,[new_symbols(definition,[sP314])])). 107.79/107.78 thf(sP315,plain,sP315 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X3) => ((in @ X4) @ ((setminus @ X1) @ X2))))))))))) => sP221),introduced(definition,[new_symbols(definition,[sP315])])). 107.79/107.78 thf(sP316,plain,sP316 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ ((binunion @ X1) @ X2)))))) => sP121),introduced(definition,[new_symbols(definition,[sP316])])). 107.79/107.78 thf(sP317,plain,sP317 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))) => sP194),introduced(definition,[new_symbols(definition,[sP317])])). 107.79/107.78 thf(sP318,plain,sP318 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))) => sP129),introduced(definition,[new_symbols(definition,[sP318])])). 107.79/107.78 thf(sP319,plain,sP319 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X2) @ (powerset @ X3)) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))))))))) => sP251),introduced(definition,[new_symbols(definition,[sP319])])). 107.79/107.78 thf(sP320,plain,sP320 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binintersect @ X2) @ X3)) => ((in @ X5) @ ((binunion @ X2) @ X4)))))))))))) => sP174),introduced(definition,[new_symbols(definition,[sP320])])). 107.79/107.78 thf(sP321,plain,sP321 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X2)))))))))) => sP263),introduced(definition,[new_symbols(definition,[sP321])])). 107.79/107.78 thf(sP322,plain,sP322 <=> ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))) => sP3),introduced(definition,[new_symbols(definition,[sP322])])). 107.79/107.78 thf(sP323,plain,sP323 <=> ((![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))) => (![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))) => sP266),introduced(definition,[new_symbols(definition,[sP323])])). 107.79/107.78 thf(sP324,plain,sP324 <=> ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) => (X1 = X3))))) => sP92),introduced(definition,[new_symbols(definition,[sP324])])). 107.79/107.78 thf(sP325,plain,sP325 <=> ((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => (~((((dsetconstr @ X1) @ X2) = emptyset)))))))) => sP160),introduced(definition,[new_symbols(definition,[sP325])])). 107.79/107.78 thf(sP326,plain,sP326 <=> ((![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))) => sP139),introduced(definition,[new_symbols(definition,[sP326])])). 107.79/107.78 thf(sP327,plain,sP327 <=> ((![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ emptyset))))) => sP257),introduced(definition,[new_symbols(definition,[sP327])])). 107.79/107.78 thf(sP328,plain,sP328 <=> ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((subset @ X2) @ X3) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ X2)))))))))))) => sP81),introduced(definition,[new_symbols(definition,[sP328])])). 107.79/107.78 thf(def_exu,definition,(exu = (^[X1:$i>$o]:(~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3)))))))))))). 107.79/107.78 thf(def_setextAx,definition,(setextAx = (![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) = ((in @ X3) @ X2))) => (X1 = X2)))))). 107.79/107.78 thf(def_emptysetAx,definition,(emptysetAx = (![X1:$i]:(~(((in @ X1) @ emptyset)))))). 107.79/107.78 thf(def_setadjoinAx,definition,(setadjoinAx = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ X2)) = ((~((X3 = X1))) => ((in @ X3) @ X2)))))))). 107.79/107.78 thf(def_powersetAx,definition,(powersetAx = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) = (![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1)))))))). 107.79/107.78 thf(def_setunionAx,definition,(setunionAx = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) = (~((![X3:$i]:(((in @ X2) @ X3) => (~(((in @ X3) @ X1)))))))))))). 107.79/107.78 thf(def_omega0Ax,definition,(omega0Ax = ((in @ emptyset) @ omega))). 107.79/107.78 thf(def_omegaSAx,definition,(omegaSAx = (![X1:$i]:(((in @ X1) @ omega) => ((in @ ((setadjoin @ X1) @ X1)) @ omega))))). 107.79/107.78 thf(def_omegaIndAx,definition,(omegaIndAx = (![X1:$i]:((~((((in @ emptyset) @ X1) => (~((![X2:$i]:((~((((in @ X2) @ omega) => (~(((in @ X2) @ X1)))))) => ((in @ ((setadjoin @ X2) @ X2)) @ X1)))))))) => (![X2:$i]:(((in @ X2) @ omega) => ((in @ X2) @ X1))))))). 107.79/107.78 thf(def_replAx,definition,(replAx = (![X1:$i>$i>$o]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X2) => (exu @ (X1 @ X3)))) => (~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X1 @ X5) @ X4))))))))))))))))))). 107.79/107.78 thf(def_foundationAx,definition,(foundationAx = (![X1:$i]:((~((![X2:$i]:(~(((in @ X2) @ X1)))))) => (~((![X2:$i]:(((in @ X2) @ X1) => (~((![X3:$i]:(((in @ X3) @ X2) => (~(((in @ X3) @ X1))))))))))))))). 107.79/107.78 thf(def_wellorderingAx,definition,(wellorderingAx = (![X1:$i]:(~((![X2:$i]:((~(((~(((![X3:$i]:(((in @ X3) @ X2) => (![X4:$i]:(((in @ X4) @ X3) => ((in @ X4) @ X1))))) => (~((![X3:$i]:(![X4:$i]:((~((((in @ X3) @ X1) => (~(((in @ X4) @ X1)))))) => ((![X5:$i]:(((in @ X5) @ X2) => (((in @ X3) @ X5) = ((in @ X4) @ X5)))) => (X3 = X4)))))))))) => (~((![X3:$i]:(![X4:$i]:((~((((in @ X3) @ X2) => (~(((in @ X4) @ X2)))))) => ((~((![X5:$i]:(((in @ X5) @ X3) => ((in @ X5) @ X4))))) => (![X5:$i]:(((in @ X5) @ X4) => ((in @ X5) @ X3)))))))))))) => (~((![X3:$i]:((~(((![X4:$i]:(((in @ X4) @ X3) => ((in @ X4) @ X1))) => (![X4:$i]:(~(((in @ X4) @ X3))))))) => (~((![X4:$i]:(![X5:$i]:((~(((~((((in @ X4) @ X2) => (~(((in @ X5) @ X3)))))) => (~((![X6:$i]:(((in @ X6) @ X4) => (~(((in @ X6) @ X3)))))))))) => (~((![X6:$i]:(((in @ X6) @ X2) => ((~((![X7:$i]:(((in @ X7) @ X6) => ((in @ X7) @ X4))))) => ((in @ X5) @ X6)))))))))))))))))))))). 107.79/107.78 thf(def_descrp,definition,(descrp = (![X1:$i>$o]:((exu @ X1) => (X1 @ (descr @ X1)))))). 107.79/107.78 thf(def_dsetconstrI,definition,(dsetconstrI = (![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((in @ X3) @ ((dsetconstr @ X1) @ X2))))))))). 107.79/107.78 thf(def_dsetconstrEL,definition,(dsetconstrEL = (![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ ((dsetconstr @ X1) @ X2)) => ((in @ X3) @ X1))))))). 107.79/107.78 thf(def_dsetconstrER,definition,(dsetconstrER = (![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ ((dsetconstr @ X1) @ X2)) => (X2 @ X3))))))). 107.79/107.78 thf(def_exuE1,definition,(exuE1 = (![X1:$i>$o]:((exu @ X1) => (~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))))))). 107.79/107.78 thf(def_prop2setE,definition,(prop2setE = (![X1:$o]:(![X2:$i]:(((in @ X2) @ (prop2set @ X1)) => X1))))). 107.79/107.78 thf(def_emptysetE,definition,(emptysetE = (![X1:$i]:(((in @ X1) @ emptyset) => (![X2:$o]:X2))))). 107.79/107.78 thf(def_emptysetimpfalse,definition,(emptysetimpfalse = (![X1:$i]:(~(((in @ X1) @ emptyset)))))). 107.79/107.78 thf(def_notinemptyset,definition,(notinemptyset = (![X1:$i]:(~(((in @ X1) @ emptyset)))))). 107.79/107.78 thf(def_exuE3e,definition,(exuE3e = (![X1:$i>$o]:((exu @ X1) => (~((![X2:$i]:(~((X1 @ X2)))))))))). 107.79/107.78 thf(def_setext,definition,(setext = (![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1))) => (X1 = X2))))))). 107.79/107.78 thf(def_emptyI,definition,(emptyI = (![X1:$i]:((![X2:$i]:(~(((in @ X2) @ X1)))) => (X1 = emptyset))))). 107.79/107.78 thf(def_noeltsimpempty,definition,(noeltsimpempty = (![X1:$i]:((![X2:$i]:(~(((in @ X2) @ X1)))) => (X1 = emptyset))))). 107.79/107.78 thf(def_setbeta,definition,(setbeta = (![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ ((dsetconstr @ X1) @ X2)) = (X2 @ X3)))))))). 107.79/107.78 thf(def_nonempty,definition,(nonempty = (^[X1:$i]:(~((X1 = emptyset)))))). 107.79/107.78 thf(def_nonemptyE1,definition,(nonemptyE1 = (![X1:$i]:((nonempty @ X1) => (~((![X2:$i]:(~(((in @ X2) @ X1)))))))))). 107.79/107.78 thf(def_nonemptyI,definition,(nonemptyI = (![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => (nonempty @ ((dsetconstr @ X1) @ X2))))))))). 107.79/107.78 thf(def_nonemptyI1,definition,(nonemptyI1 = (![X1:$i]:((~((![X2:$i]:(~(((in @ X2) @ X1)))))) => (nonempty @ X1))))). 107.79/107.78 thf(def_setadjoinIL,definition,(setadjoinIL = (![X1:$i]:(![X2:$i]:((in @ X1) @ ((setadjoin @ X1) @ X2)))))). 107.79/107.78 thf(def_emptyinunitempty,definition,(emptyinunitempty = ((in @ emptyset) @ ((setadjoin @ emptyset) @ emptyset)))). 107.79/107.78 thf(def_setadjoinIR,definition,(setadjoinIR = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ ((setadjoin @ X1) @ X2)))))))). 107.79/107.78 thf(def_setadjoinE,definition,(setadjoinE = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ X2)) => (![X4:$o]:(((X3 = X1) => X4) => ((((in @ X3) @ X2) => X4) => X4))))))))). 107.79/107.78 thf(def_setadjoinOr,definition,(setadjoinOr = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ X2)) => ((~((X3 = X1))) => ((in @ X3) @ X2)))))))). 107.79/107.78 thf(def_setoftrueEq,definition,(setoftrueEq = (![X1:$i]:(((dsetconstr @ X1) @ (^[X2:$i]:(~($false)))) = X1)))). 107.79/107.78 thf(def_powersetI,definition,(powersetI = (![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1))) => ((in @ X2) @ (powerset @ X1))))))). 107.79/107.78 thf(def_emptyinPowerset,definition,(emptyinPowerset = (![X1:$i]:((in @ emptyset) @ (powerset @ X1))))). 107.79/107.78 thf(def_emptyInPowerset,definition,(emptyInPowerset = (![X1:$i]:((in @ emptyset) @ (powerset @ X1))))). 107.79/107.78 thf(def_powersetE,definition,(powersetE = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X2) @ (powerset @ X1)) => (((in @ X3) @ X2) => ((in @ X3) @ X1)))))))). 107.79/107.78 thf(def_setunionI,definition,(setunionI = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X2) @ X3) => (((in @ X3) @ X1) => ((in @ X2) @ (setunion @ X1))))))))). 107.79/107.78 thf(def_setunionE,definition,(setunionE = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) => (![X3:$o]:((![X4:$i]:(((in @ X2) @ X4) => (((in @ X4) @ X1) => X3))) => X3))))))). 107.79/107.78 thf(def_subPowSU,definition,(subPowSU = (![X1:$i]:(![X2:$i]:(((in @ X2) @ X1) => ((in @ X2) @ (powerset @ (setunion @ X1)))))))). 107.79/107.78 thf(def_exuE2,definition,(exuE2 = (![X1:$i>$o]:((exu @ X1) => (~((![X2:$i]:(~((![X3:$i]:((X1 @ X3) = (X3 = X2)))))))))))). 107.79/107.78 thf(def_nonemptyImpWitness,definition,(nonemptyImpWitness = (![X1:$i]:((nonempty @ X1) => (~((![X2:$i]:(~(((in @ X2) @ X1)))))))))). 107.79/107.78 thf(def_uniqinunit,definition,(uniqinunit = (![X1:$i]:(![X2:$i]:(((in @ X1) @ ((setadjoin @ X2) @ emptyset)) => (X1 = X2)))))). 107.79/107.78 thf(def_notinsingleton,definition,(notinsingleton = (![X1:$i]:(![X2:$i]:((~((X1 = X2))) => (~(((in @ X2) @ ((setadjoin @ X1) @ emptyset))))))))). 107.79/107.78 thf(def_eqinunit,definition,(eqinunit = (![X1:$i]:(![X2:$i]:((X1 = X2) => ((in @ X1) @ ((setadjoin @ X2) @ emptyset))))))). 107.79/107.78 thf(def_singletonsswitch,definition,(singletonsswitch = (![X1:$i]:(![X2:$i]:(((in @ X1) @ ((setadjoin @ X2) @ emptyset)) => ((in @ X2) @ ((setadjoin @ X1) @ emptyset))))))). 107.79/107.78 thf(def_upairsetE,definition,(upairsetE = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) => ((~((X3 = X1))) => (X3 = X2)))))))). 107.79/107.78 thf(def_upairsetIL,definition,(upairsetIL = (![X1:$i]:(![X2:$i]:((in @ X1) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))))). 107.79/107.78 thf(def_upairsetIR,definition,(upairsetIR = (![X1:$i]:(![X2:$i]:((in @ X2) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))))). 107.79/107.78 thf(def_emptyE1,definition,(emptyE1 = (![X1:$i]:(![X2:$i>$o]:((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => (~((((dsetconstr @ X1) @ X2) = emptyset)))))))). 107.79/107.78 thf(def_vacuousDall,definition,(vacuousDall = (![X1:$i>$o]:(![X2:$i]:(((in @ X2) @ emptyset) => (X1 @ X2)))))). 107.79/107.78 thf(def_quantDeMorgan1,definition,(quantDeMorgan1 = (![X1:$i]:(![X2:$i>$o]:((~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3))))) => (~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3)))))))))). 107.79/107.78 thf(def_quantDeMorgan2,definition,(quantDeMorgan2 = (![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))) => (![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))))). 107.79/107.78 thf(def_quantDeMorgan3,definition,(quantDeMorgan3 = (![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))) => (![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))))). 107.79/107.78 thf(def_quantDeMorgan4,definition,(quantDeMorgan4 = (![X1:$i]:(![X2:$i>$o]:((~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3))))) => (~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3)))))))))). 107.79/107.78 thf(def_prop2setI,definition,(prop2setI = (![X1:$o]:(X1 => ((in @ emptyset) @ (prop2set @ X1)))))). 107.79/107.78 thf(def_prop2set2propI,definition,(prop2set2propI = (![X1:$o]:(X1 => (set2prop @ (prop2set @ X1)))))). 107.79/107.78 thf(def_notdexE,definition,(notdexE = (![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))) => (![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))))). 107.79/107.78 thf(def_notdallE,definition,(notdallE = (![X1:$i]:(![X2:$i>$o]:((~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3))))) => (~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3)))))))))). 107.79/107.78 thf(def_exuI1,definition,(exuI1 = (![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (exu @ X1))))). 107.79/107.78 thf(def_exuI3,definition,(exuI3 = (![X1:$i>$o]:((~((![X2:$i]:(~((X1 @ X2)))))) => ((![X2:$i]:(![X3:$i]:((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))) => (exu @ X1)))))). 107.79/107.78 thf(def_exuI2,definition,(exuI2 = (![X1:$i>$o]:((~((![X2:$i]:(~((![X3:$i]:((X1 @ X3) = (X3 = X2)))))))) => (exu @ X1))))). 107.79/107.78 thf(def_inCongP,definition,(inCongP = (![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((in @ X3) @ X1) => ((in @ X4) @ X2)))))))))). 107.79/107.78 thf(def_in__Cong,definition,(in__Cong = (![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((in @ X3) @ X1) = ((in @ X4) @ X2)))))))))). 107.79/107.78 thf(def_exuE3u,definition,(exuE3u = (![X1:$i>$o]:((exu @ X1) => (![X2:$i]:(![X3:$i]:((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))))))). 107.79/107.78 thf(def_exu__Cong,definition,(exu__Cong = (![X1:$i>$o]:(![X2:$i>$o]:((![X3:$i]:(![X4:$i]:((X3 = X4) => ((X1 @ X3) = (X2 @ X4))))) => ((exu @ X1) = (exu @ X2))))))). 107.79/107.78 thf(def_emptyset__Cong,definition,(emptyset__Cong = (emptyset = emptyset))). 107.79/107.78 thf(def_setadjoin__Cong,definition,(setadjoin__Cong = (![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((setadjoin @ X1) @ X3) = ((setadjoin @ X2) @ X4)))))))))). 107.79/107.78 thf(def_powerset__Cong,definition,(powerset__Cong = (![X1:$i]:(![X2:$i]:((X1 = X2) => ((powerset @ X1) = (powerset @ X2))))))). 107.79/107.78 thf(def_setunion__Cong,definition,(setunion__Cong = (![X1:$i]:(![X2:$i]:((X1 = X2) => ((setunion @ X1) = (setunion @ X2))))))). 107.79/107.78 thf(def_omega__Cong,definition,(omega__Cong = (omega = omega))). 107.79/107.78 thf(def_exuEu,definition,(exuEu = (![X1:$i>$o]:((exu @ X1) => (![X2:$i]:(![X3:$i]:((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))))))). 107.79/107.78 thf(def_descr__Cong,definition,(descr__Cong = (![X1:$i>$o]:(![X2:$i>$o]:((![X3:$i]:(![X4:$i]:((X3 = X4) => ((X1 @ X3) = (X2 @ X4))))) => ((exu @ X1) => ((exu @ X2) => ((descr @ X1) = (descr @ X2))))))))). 107.79/107.78 thf(def_dsetconstr__Cong,definition,(dsetconstr__Cong = (![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i>$o]:(![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => ((X5 = X6) => ((X3 @ X5) = (X4 @ X6))))))) => (((dsetconstr @ X1) @ X3) = ((dsetconstr @ X2) @ X4)))))))))). 107.79/107.78 thf(def_subsetI1,definition,(subsetI1 = (![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((subset @ X1) @ X2)))))). 107.79/107.78 thf(def_eqimpsubset2,definition,(eqimpsubset2 = (![X1:$i]:(![X2:$i]:((X1 = X2) => ((subset @ X2) @ X1)))))). 107.79/107.78 thf(def_eqimpsubset1,definition,(eqimpsubset1 = (![X1:$i]:(![X2:$i]:((X1 = X2) => ((subset @ X1) @ X2)))))). 107.79/107.78 thf(def_subsetI2,definition,(subsetI2 = (![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((subset @ X1) @ X2)))))). 107.79/107.78 thf(def_emptysetsubset,definition,(emptysetsubset = ((!!) @ (subset @ emptyset)))). 107.79/107.78 thf(def_subsetE,definition,(subsetE = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X2) => (((in @ X3) @ X1) => ((in @ X3) @ X2)))))))). 107.79/107.78 thf(def_subsetE2,definition,(subsetE2 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X2) => ((~(((in @ X3) @ X2))) => (~(((in @ X3) @ X1)))))))))). 107.79/107.78 thf(def_notsubsetI,definition,(notsubsetI = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => (~(((subset @ X1) @ X2)))))))))). 107.79/107.78 thf(def_notequalI1,definition,(notequalI1 = (![X1:$i]:(![X2:$i]:((~(((subset @ X1) @ X2))) => (~((X1 = X2)))))))). 107.79/107.78 thf(def_notequalI2,definition,(notequalI2 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => (~((X1 = X2)))))))))). 107.79/107.78 thf(def_subsetRefl,definition,(subsetRefl = (![X1:$i]:((subset @ X1) @ X1)))). 107.79/107.78 thf(def_subsetTrans,definition,(subsetTrans = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X2) => (((subset @ X2) @ X3) => ((subset @ X1) @ X3)))))))). 107.79/107.78 thf(def_setadjoinSub,definition,(setadjoinSub = (![X1:$i]:(![X2:$i]:((subset @ X2) @ ((setadjoin @ X1) @ X2)))))). 107.79/107.78 thf(def_setadjoinSub2,definition,(setadjoinSub2 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X3) => ((subset @ X1) @ ((setadjoin @ X2) @ X3)))))))). 107.79/107.78 thf(def_subset2powerset,definition,(subset2powerset = (![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => ((in @ X1) @ (powerset @ X2))))))). 107.79/107.78 thf(def_setextsub,definition,(setextsub = (![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((subset @ X2) @ X1) => (X1 = X2))))))). 107.79/107.78 thf(def_subsetemptysetimpeq,definition,(subsetemptysetimpeq = (![X1:$i]:(((subset @ X1) @ emptyset) => (X1 = emptyset))))). 107.79/107.78 thf(def_powersetI1,definition,(powersetI1 = (![X1:$i]:(![X2:$i]:(((subset @ X2) @ X1) => ((in @ X2) @ (powerset @ X1))))))). 107.79/107.78 thf(def_powersetE1,definition,(powersetE1 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ X2) @ X1)))))). 107.79/107.78 thf(def_inPowerset,definition,(inPowerset = (![X1:$i]:((in @ X1) @ (powerset @ X1))))). 107.79/107.78 thf(def_powersetsubset,definition,(powersetsubset = (![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => ((subset @ (powerset @ X1)) @ (powerset @ X2))))))). 107.79/107.78 thf(def_sepInPowerset,definition,(sepInPowerset = (![X1:$i]:(![X2:$i>$o]:((in @ ((dsetconstr @ X1) @ X2)) @ (powerset @ X1)))))). 107.79/107.78 thf(def_sepSubset,definition,(sepSubset = (![X1:$i]:(![X2:$i>$o]:((subset @ ((dsetconstr @ X1) @ X2)) @ X1))))). 107.79/107.78 thf(def_binunionIL,definition,(binunionIL = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ ((binunion @ X1) @ X2)))))))). 107.79/107.78 thf(def_upairset2IR,definition,(upairset2IR = (![X1:$i]:(![X2:$i]:((in @ X2) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))))). 107.79/107.78 thf(def_binunionIR,definition,(binunionIR = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ ((binunion @ X1) @ X2)))))))). 107.79/107.78 thf(def_binunionEcases,definition,(binunionEcases = (![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$o]:(((in @ X3) @ ((binunion @ X1) @ X2)) => ((((in @ X3) @ X1) => X4) => ((((in @ X3) @ X2) => X4) => X4))))))))). 107.79/107.78 thf(def_binunionE,definition,(binunionE = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((binunion @ X1) @ X2)) => ((~(((in @ X3) @ X1))) => ((in @ X3) @ X2)))))))). 107.79/107.78 thf(def_binunionLsub,definition,(binunionLsub = (![X1:$i]:(![X2:$i]:((subset @ X1) @ ((binunion @ X1) @ X2)))))). 107.79/107.78 thf(def_binunionRsub,definition,(binunionRsub = (![X1:$i]:(![X2:$i]:((subset @ X2) @ ((binunion @ X1) @ X2)))))). 107.79/107.78 thf(def_binintersectI,definition,(binintersectI = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => ((in @ X3) @ ((binintersect @ X1) @ X2))))))))). 107.79/107.78 thf(def_binintersectSubset5,definition,(binintersectSubset5 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X3) @ X1) => (((subset @ X3) @ X2) => ((subset @ X3) @ ((binintersect @ X1) @ X2))))))))). 107.79/107.78 thf(def_binintersectEL,definition,(binintersectEL = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((binintersect @ X1) @ X2)) => ((in @ X3) @ X1))))))). 107.79/107.78 thf(def_binintersectLsub,definition,(binintersectLsub = (![X1:$i]:(![X2:$i]:((subset @ ((binintersect @ X1) @ X2)) @ X1))))). 107.79/107.78 thf(def_binintersectSubset2,definition,(binintersectSubset2 = (![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((binintersect @ X1) @ X2) = X1)))))). 107.79/107.78 thf(def_binintersectSubset3,definition,(binintersectSubset3 = (![X1:$i]:(![X2:$i]:((((binintersect @ X1) @ X2) = X2) => ((subset @ X2) @ X1)))))). 107.79/107.78 thf(def_binintersectER,definition,(binintersectER = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((binintersect @ X1) @ X2)) => ((in @ X3) @ X2))))))). 107.79/107.78 thf(def_disjointsetsI1,definition,(disjointsetsI1 = (![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => (~(((in @ X3) @ X2))))) => (((binintersect @ X1) @ X2) = emptyset)))))). 107.79/107.78 thf(def_binintersectRsub,definition,(binintersectRsub = (![X1:$i]:(![X2:$i]:((subset @ ((binintersect @ X1) @ X2)) @ X2))))). 107.79/107.78 thf(def_binintersectSubset4,definition,(binintersectSubset4 = (![X1:$i]:(![X2:$i]:(((subset @ X2) @ X1) => (((binintersect @ X1) @ X2) = X2)))))). 107.79/107.78 thf(def_binintersectSubset1,definition,(binintersectSubset1 = (![X1:$i]:(![X2:$i]:((((binintersect @ X1) @ X2) = X1) => ((subset @ X1) @ X2)))))). 107.79/107.78 thf(def_bs114d,definition,(bs114d = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((binintersect @ X1) @ ((binunion @ X2) @ X3)) = ((binunion @ ((binintersect @ X1) @ X2)) @ ((binintersect @ X1) @ X3)))))))). 107.79/107.78 thf(def_setminusI,definition,(setminusI = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => ((in @ X3) @ ((setminus @ X1) @ X2))))))))). 107.79/107.78 thf(def_setminusEL,definition,(setminusEL = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setminus @ X1) @ X2)) => ((in @ X3) @ X1))))))). 107.79/107.78 thf(def_setminusER,definition,(setminusER = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setminus @ X1) @ X2)) => (~(((in @ X3) @ X2))))))))). 107.79/107.78 thf(def_setminusSubset2,definition,(setminusSubset2 = (![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((setminus @ X1) @ X2) = emptyset)))))). 107.79/107.78 thf(def_setminusERneg,definition,(setminusERneg = (![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ ((setminus @ X1) @ X2)))) => (((in @ X3) @ X1) => ((in @ X3) @ X2)))))))). 107.79/107.78 thf(def_setminusELneg,definition,(setminusELneg = (![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ ((setminus @ X1) @ X2)))) => ((~(((in @ X3) @ X2))) => (~(((in @ X3) @ X1)))))))))). 107.79/107.78 thf(def_setminusILneg,definition,(setminusILneg = (![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))))). 107.79/107.78 thf(def_setminusIRneg,definition,(setminusIRneg = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X2) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))))). 107.79/107.78 thf(def_setminusLsub,definition,(setminusLsub = (![X1:$i]:(![X2:$i]:((subset @ ((setminus @ X1) @ X2)) @ X1))))). 107.79/107.78 thf(def_setminusSubset1,definition,(setminusSubset1 = (![X1:$i]:(![X2:$i]:((((setminus @ X1) @ X2) = emptyset) => ((subset @ X1) @ X2)))))). 107.79/107.78 thf(def_symdiffE,definition,(symdiffE = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((symdiff @ X1) @ X2)) => (![X4:$o]:((((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => X4)) => (((~(((in @ X3) @ X1))) => (((in @ X3) @ X2) => X4)) => X4))))))))). 107.79/107.78 thf(def_symdiffI1,definition,(symdiffI1 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => ((in @ X3) @ ((symdiff @ X1) @ X2))))))))). 107.79/107.78 thf(def_symdiffI2,definition,(symdiffI2 = (![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => (((in @ X3) @ X2) => ((in @ X3) @ ((symdiff @ X1) @ X2))))))))). 107.79/107.78 thf(def_symdiffIneg1,definition,(symdiffIneg1 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => (~(((in @ X3) @ ((symdiff @ X1) @ X2))))))))))). 107.79/107.78 thf(def_symdiffIneg2,definition,(symdiffIneg2 = (![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => ((~(((in @ X3) @ X2))) => (~(((in @ X3) @ ((symdiff @ X1) @ X2))))))))))). 107.79/107.78 thf(def_secondinupair,definition,(secondinupair = (![X1:$i]:(![X2:$i]:((in @ X2) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))))). 107.79/107.78 thf(def_setukpairIL,definition,(setukpairIL = (![X1:$i]:(![X2:$i]:((in @ X1) @ (setunion @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)))))))). 107.79/107.78 thf(def_setukpairIR,definition,(setukpairIR = (![X1:$i]:(![X2:$i]:((in @ X2) @ (setunion @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)))))))). 107.79/107.78 thf(def_kpairiskpair,definition,(kpairiskpair = (![X1:$i]:(![X2:$i]:(iskpair @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))))))). 107.79/107.78 thf(def_kpairp,definition,(kpairp = (![X1:$i]:(![X2:$i]:(iskpair @ ((kpair @ X1) @ X2)))))). 107.79/107.78 thf(def_singletonsubset,definition,(singletonsubset = (![X1:$i]:(![X2:$i]:(((in @ X2) @ X1) => ((subset @ ((setadjoin @ X2) @ emptyset)) @ X1)))))). 107.79/107.78 thf(def_singletoninpowerset,definition,(singletoninpowerset = (![X1:$i]:(![X2:$i]:(((in @ X2) @ X1) => ((in @ ((setadjoin @ X2) @ emptyset)) @ (powerset @ X1))))))). 107.79/107.78 thf(def_singletoninpowunion,definition,(singletoninpowunion = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((in @ ((setadjoin @ X3) @ emptyset)) @ (powerset @ ((binunion @ X1) @ X2))))))))). 107.79/107.78 thf(def_upairset2E,definition,(upairset2E = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) => ((~((X3 = X1))) => (X3 = X2)))))))). 107.79/107.78 thf(def_upairsubunion,definition,(upairsubunion = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((subset @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ ((binunion @ X1) @ X2)))))))))). 107.79/107.78 thf(def_upairinpowunion,definition,(upairinpowunion = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))))). 107.79/107.78 thf(def_ubforcartprodlem1,definition,(ubforcartprodlem1 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((subset @ ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))))). 107.79/107.78 thf(def_ubforcartprodlem2,definition,(ubforcartprodlem2 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) @ (powerset @ (powerset @ ((binunion @ X1) @ X2)))))))))))). 107.79/107.78 thf(def_ubforcartprodlem3,definition,(ubforcartprodlem3 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ (powerset @ (powerset @ ((binunion @ X1) @ X2)))))))))))). 107.79/107.78 thf(def_cartprodpairin,definition,(cartprodpairin = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)))))))))). 107.79/107.78 thf(def_cartprodmempair1,definition,(cartprodmempair1 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (~((X3 = ((kpair @ X4) @ X5)))))))))))))))). 107.79/107.78 thf(def_cartprodmempair,definition,(cartprodmempair = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (iskpair @ X3))))))). 107.79/107.78 thf(def_setunionE2,definition,(setunionE2 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) => (~((![X3:$i]:(((in @ X3) @ X1) => (~(((in @ X2) @ X3)))))))))))). 107.79/107.78 thf(def_setunionsingleton1,definition,(setunionsingleton1 = (![X1:$i]:((subset @ (setunion @ ((setadjoin @ X1) @ emptyset))) @ X1)))). 107.79/107.78 thf(def_setunionsingleton2,definition,(setunionsingleton2 = (![X1:$i]:((subset @ X1) @ (setunion @ ((setadjoin @ X1) @ emptyset)))))). 107.79/107.78 thf(def_setunionsingleton,definition,(setunionsingleton = (![X1:$i]:((setunion @ ((setadjoin @ X1) @ emptyset)) = X1)))). 107.79/107.78 thf(def_singletonprop,definition,(singletonprop = (![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => (singleton @ ((dsetconstr @ X1) @ X2)))))))). 107.79/107.78 thf(def_ex1E1,definition,(ex1E1 = (![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))))))). 107.79/107.78 thf(def_ex1I,definition,(ex1I = (![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X4) => (X4 = X3)))) => ((ex1 @ X1) @ X2))))))))). 107.79/107.78 thf(def_ex1I2,definition,(ex1I2 = (![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => ((ex1 @ X1) @ X2))))))). 107.79/107.78 thf(def_singletonsuniq,definition,(singletonsuniq = (![X1:$i]:(![X2:$i]:((((setadjoin @ X1) @ emptyset) = ((setadjoin @ X2) @ emptyset)) => (X1 = X2)))))). 107.79/107.78 thf(def_setukpairinjL1,definition,(setukpairinjL1 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) => (X1 = X3))))))). 107.79/107.78 thf(def_kfstsingleton,definition,(kfstsingleton = (![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:((in @ ((setadjoin @ X2) @ emptyset)) @ X1)))))))). 107.79/107.78 thf(def_theprop,definition,(theprop = (![X1:$i]:((singleton @ X1) => ((in @ (setunion @ X1)) @ X1))))). 107.79/107.78 thf(def_kfstpairEq,definition,(kfstpairEq = (![X1:$i]:(![X2:$i]:((kfst @ ((kpair @ X1) @ X2)) = X1))))). 107.79/107.78 thf(def_cartprodfstin,definition,(cartprodfstin = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (kfst @ X3)) @ X1))))))). 107.79/107.78 thf(def_setukpairinjL2,definition,(setukpairinjL2 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X1 = X3)))))))). 107.79/107.78 thf(def_setukpairinjL,definition,(setukpairinjL = (![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X1 = X3)))))))). 107.79/107.78 thf(def_setukpairinjR11,definition,(setukpairinjR11 = (![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X1) @ emptyset))))))). 107.79/107.78 thf(def_setukpairinjR12,definition,(setukpairinjR12 = (![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ emptyset))))))). 107.79/107.78 thf(def_setukpairinjR1,definition,(setukpairinjR1 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => ((X3 = X4) => (X2 = X4))))))))). 107.79/107.78 thf(def_upairequniteq,definition,(upairequniteq = (![X1:$i]:(![X2:$i]:(![X3:$i]:((((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X3) @ emptyset)) => (X1 = X2))))))). 107.79/107.78 thf(def_setukpairinjR2,definition,(setukpairinjR2 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X2 = X4)))))))). 107.79/107.78 thf(def_setukpairinjR,definition,(setukpairinjR = (![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X2 = X4)))))))). 107.79/107.78 thf(def_ksndsingleton,definition,(ksndsingleton = (![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:(X1 = ((kpair @ (kfst @ X1)) @ X2))))))))). 107.79/107.78 thf(def_ksndpairEq,definition,(ksndpairEq = (![X1:$i]:(![X2:$i]:((ksnd @ ((kpair @ X1) @ X2)) = X2))))). 107.79/107.78 thf(def_kpairsurjEq,definition,(kpairsurjEq = (![X1:$i]:((iskpair @ X1) => (((kpair @ (kfst @ X1)) @ (ksnd @ X1)) = X1))))). 107.79/107.78 thf(def_cartprodsndin,definition,(cartprodsndin = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))))). 107.79/107.78 thf(def_cartprodpairmemEL,definition,(cartprodpairmemEL = (![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))))). 107.79/107.78 thf(def_cartprodpairmemER,definition,(cartprodpairmemER = (![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X4) @ X2)))))))). 107.79/107.78 thf(def_cartprodmempaircEq,definition,(cartprodmempaircEq = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => (((kpair @ X3) @ X4) = ((kpair @ X3) @ X4)))))))))). 107.79/107.78 thf(def_cartprodfstpairEq,definition,(cartprodfstpairEq = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))))). 107.89/107.79 thf(def_cartprodsndpairEq,definition,(cartprodsndpairEq = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))))). 107.89/107.79 thf(def_cartprodpairsurjEq,definition,(cartprodpairsurjEq = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))))). 107.89/107.79 thf(def_dpsetconstrI,definition,(dpsetconstrI = (![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)))))))))))). 107.89/107.79 thf(def_dpsetconstrSub,definition,(dpsetconstrSub = (![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))))). 107.89/107.79 thf(def_setOfPairsIsBReln,definition,(setOfPairsIsBReln = (![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))))). 107.89/107.79 thf(def_dpsetconstrERa,definition,(dpsetconstrERa = (![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))))). 107.89/107.79 thf(def_dpsetconstrEL1,definition,(dpsetconstrEL1 = (![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))))). 107.89/107.79 thf(def_dpsetconstrEL2,definition,(dpsetconstrEL2 = (![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))))). 107.89/107.79 thf(def_dpsetconstrER,definition,(dpsetconstrER = (![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))). 107.89/107.79 thf(def_funcImageSingleton,definition,(funcImageSingleton = (![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))). 107.89/107.79 thf(def_apProp,definition,(apProp = (![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))))). 107.89/107.79 thf(def_app,definition,(app = (![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))))). 107.89/107.79 thf(def_infuncsetfunc,definition,(infuncsetfunc = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))))). 107.89/107.79 thf(def_ap2p,definition,(ap2p = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))))). 107.89/107.79 thf(def_funcinfuncset,definition,(funcinfuncset = (![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))))). 107.89/107.79 thf(def_lamProp,definition,(lamProp = (![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))))). 107.89/107.79 thf(def_lamp,definition,(lamp = (![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))))). 107.89/107.79 thf(def_lam2p,definition,(lam2p = (![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))))). 107.89/107.79 thf(def_brelnall1,definition,(brelnall1 = (![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))))). 107.89/107.79 thf(def_brelnall2,definition,(brelnall2 = (![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))))). 107.89/107.79 thf(def_ex1E2,definition,(ex1E2 = (![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))))). 107.89/107.79 thf(def_funcGraphProp1,definition,(funcGraphProp1 = (![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))))). 107.89/107.79 thf(def_funcGraphProp3,definition,(funcGraphProp3 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))))). 107.89/107.79 thf(def_funcGraphProp2,definition,(funcGraphProp2 = (![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))))). 107.89/107.79 thf(def_funcextLem,definition,(funcextLem = (![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))))). 107.89/107.79 thf(def_funcGraphProp4,definition,(funcGraphProp4 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))))). 107.89/107.79 thf(def_subbreln,definition,(subbreln = (![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))))). 107.89/107.79 thf(def_eqbreln,definition,(eqbreln = (![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))))). 107.89/107.79 thf(def_funcext,definition,(funcext = (![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:((((func @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))))). 107.89/107.79 thf(def_funcext2,definition,(funcext2 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))))). 107.89/107.79 thf(def_ap2apEq1,definition,(ap2apEq1 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))))). 107.89/107.79 thf(def_ap2apEq2,definition,(ap2apEq2 = (![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))))). 107.89/107.79 thf(def_beta1,definition,(beta1 = (![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))))). 107.89/107.79 thf(def_eta1,definition,(eta1 = (![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))))). 107.89/107.79 thf(def_lam2lamEq,definition,(lam2lamEq = (![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((((lam @ X1) @ X2) @ X3) = (((lam @ X1) @ X2) @ X3)))))))). 107.89/107.79 thf(def_beta2,definition,(beta2 = (![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))))). 107.89/107.79 thf(def_eta2,definition,(eta2 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))))). 107.89/107.79 thf(def_iffalseProp1,definition,(iffalseProp1 = (![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => ((in @ X4) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))))). 107.89/107.79 thf(def_iffalseProp2,definition,(iffalseProp2 = (![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X4) @ emptyset))))))))))). 107.89/107.79 thf(def_iftrueProp1,definition,(iftrueProp1 = (![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => ((in @ X3) @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))))). 107.89/107.79 thf(def_iftrueProp2,definition,(iftrueProp2 = (![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X3) @ emptyset))))))))))). 107.89/107.79 thf(def_ifSingleton,definition,(ifSingleton = (![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4)))))))))))))))))). 107.89/107.79 thf(def_ifp,definition,(ifp = (![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ X1))))))))). 107.89/107.79 thf(def_theeq,definition,(theeq = (![X1:$i]:((singleton @ X1) => (![X2:$i]:(((in @ X2) @ X1) => ((setunion @ X1) = X2))))))). 107.89/107.79 thf(def_iftrue,definition,(iftrue = (![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((((if @ X1) @ X2) @ X3) @ X4) = X3)))))))))). 107.89/107.79 thf(def_iffalse,definition,(iffalse = (![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((((if @ X1) @ X2) @ X3) @ X4) = X4)))))))))). 107.89/107.79 thf(def_iftrueorfalse,definition,(iftrueorfalse = (![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))))))))))). 107.89/107.79 thf(def_binintersectT_lem,definition,(binintersectT_lem = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))))). 107.89/107.79 thf(def_binunionT_lem,definition,(binunionT_lem = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binunion @ X2) @ X3)) @ (powerset @ X1))))))))). 107.89/107.79 thf(def_powersetT_lem,definition,(powersetT_lem = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((in @ (powerset @ X2)) @ (powerset @ (powerset @ X1)))))))). 107.89/107.79 thf(def_setminusT_lem,definition,(setminusT_lem = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X2) @ X3)) @ (powerset @ X1))))))))). 107.89/107.79 thf(def_complementT_lem,definition,(complementT_lem = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ X1))))))). 107.89/107.79 thf(def_setextT,definition,(setextT = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))) => ((![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X3) => ((in @ X4) @ X2)))) => (X2 = X3)))))))))). 107.89/107.79 thf(def_subsetTI,definition,(subsetTI = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))) => ((subset @ X2) @ X3))))))))). 107.89/107.79 thf(def_powersetTI1,definition,(powersetTI1 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))) => ((in @ X2) @ (powerset @ X3)))))))))). 107.89/107.79 thf(def_powersetTE1,definition,(powersetTE1 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X2) @ (powerset @ X3)) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))))))))))). 107.89/107.79 thf(def_complementTI1,definition,(complementTI1 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))))))). 107.89/107.79 thf(def_complementTE1,definition,(complementTE1 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ ((setminus @ X1) @ X2)))) => ((in @ X3) @ X2))))))))). 107.89/107.79 thf(def_binintersectTELcontra,definition,(binintersectTELcontra = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X2))) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))))). 107.89/107.79 thf(def_binintersectTERcontra,definition,(binintersectTERcontra = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))))). 107.89/107.79 thf(def_contrasubsetT,definition,(contrasubsetT = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => (((in @ X4) @ X3) => (~(((in @ X4) @ X2)))))))))))))). 107.89/107.79 thf(def_contrasubsetT1,definition,(contrasubsetT1 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((subset @ X2) @ X3) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ X2)))))))))))))). 107.89/107.79 thf(def_contrasubsetT2,definition,(contrasubsetT2 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ X3) => ((subset @ ((setminus @ X1) @ X3)) @ ((setminus @ X1) @ X2)))))))))). 107.89/107.79 thf(def_contrasubsetT3,definition,(contrasubsetT3 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ ((setminus @ X1) @ X3)) @ ((setminus @ X1) @ X2)) => ((subset @ X2) @ X3))))))))). 107.89/107.79 thf(def_doubleComplementI1,definition,(doubleComplementI1 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => ((in @ X3) @ ((setminus @ X1) @ ((setminus @ X1) @ X2))))))))))). 107.89/107.79 thf(def_doubleComplementE1,definition,(doubleComplementE1 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ ((setminus @ X1) @ ((setminus @ X1) @ X2))) => ((in @ X3) @ X2))))))))). 107.89/107.79 thf(def_doubleComplementSub1,definition,(doubleComplementSub1 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ X2) @ ((setminus @ X1) @ ((setminus @ X1) @ X2)))))))). 107.89/107.79 thf(def_doubleComplementSub2,definition,(doubleComplementSub2 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ ((setminus @ X1) @ X2))) @ X2)))))). 107.89/107.79 thf(def_doubleComplementEq,definition,(doubleComplementEq = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (X2 = ((setminus @ X1) @ ((setminus @ X1) @ X2)))))))). 107.89/107.79 thf(def_complementTnotintersectT,definition,(complementTnotintersectT = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))))). 107.89/107.79 thf(def_complementImpComplementIntersect,definition,(complementImpComplementIntersect = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))))). 107.89/107.79 thf(def_complementSubsetComplementIntersect,definition,(complementSubsetComplementIntersect = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))))). 107.89/107.79 thf(def_complementInPowersetComplementIntersect,definition,(complementInPowersetComplementIntersect = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))). 107.89/107.79 thf(def_contraSubsetComplement,definition,(contraSubsetComplement = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X3) => ((in @ X4) @ ((setminus @ X1) @ X2))))))))))))). 107.89/107.79 thf(def_complementTcontraSubset,definition,(complementTcontraSubset = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))))). 107.89/107.79 thf(def_binunionTILcontra,definition,(binunionTILcontra = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ ((binunion @ X2) @ X3)))) => (~(((in @ X4) @ X2))))))))))))). 107.89/107.79 thf(def_binunionTIRcontra,definition,(binunionTIRcontra = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ ((binunion @ X2) @ X3)))) => (~(((in @ X4) @ X3))))))))))))). 107.89/107.79 thf(def_inIntersectImpInUnion,definition,(inIntersectImpInUnion = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binintersect @ X2) @ X3)) => ((in @ X5) @ ((binunion @ X2) @ X4)))))))))))))). 107.89/107.79 thf(def_inIntersectImpInUnion2,definition,(inIntersectImpInUnion2 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binintersect @ X2) @ X3)) => ((in @ X5) @ ((binunion @ X3) @ X4)))))))))))))). 107.89/107.79 thf(def_inIntersectImpInIntersectUnions,definition,(inIntersectImpInIntersectUnions = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binintersect @ X2) @ X3)) => ((in @ X5) @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))))))). 107.89/107.79 thf(def_intersectInPowersetIntersectUnions,definition,(intersectInPowersetIntersectUnions = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))))). 107.89/107.79 thf(def_inComplementUnionImpNotIn1,definition,(inComplementUnionImpNotIn1 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => (~(((in @ X4) @ X2))))))))))))). 107.89/107.79 thf(def_inComplementUnionImpInComplement1,definition,(inComplementUnionImpInComplement1 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X2)))))))))))). 107.89/107.79 thf(def_binunionTE,definition,(binunionTE = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$o]:(![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binunion @ X2) @ X3)) => ((((in @ X5) @ X2) => X4) => ((((in @ X5) @ X3) => X4) => X4))))))))))))). 107.89/107.79 thf(def_binunionTEcontra,definition,(binunionTEcontra = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X2))) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ ((binunion @ X2) @ X3))))))))))))))). 107.89/107.79 thf(def_demorgan2a1,definition,(demorgan2a1 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X2)))))))))))). 107.89/107.79 thf(def_complementUnionInPowersetComplement,definition,(complementUnionInPowersetComplement = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))))). 107.89/107.79 thf(def_demorgan2a2,definition,(demorgan2a2 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))))). 107.89/107.79 thf(def_demorgan1a,definition,(demorgan1a = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))) => ((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))))). 107.89/107.79 thf(def_demorgan1b,definition,(demorgan1b = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))))). 107.89/107.79 thf(def_demorgan1,definition,(demorgan1 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ X2) @ X3)) = ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))))). 107.89/107.79 thf(def_demorgan2a,definition,(demorgan2a = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))))). 107.89/107.79 thf(def_demorgan2b2,definition,(demorgan2b2 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (((in @ X4) @ ((setminus @ X1) @ X3)) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3)))))))))))))). 107.89/107.79 thf(def_demorgan2b,definition,(demorgan2b = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))))). 107.89/107.79 thf(def_demorgan2,definition,(demorgan2 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))))). 107.89/107.79 thf(def_woz13rule0,definition,(woz13rule0 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))))). 107.89/107.79 thf(def_woz13rule1,definition,(woz13rule1 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))))). 107.89/107.79 thf(def_woz13rule2,definition,(woz13rule2 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))))). 107.89/107.79 thf(def_woz13rule3,definition,(woz13rule3 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))))). 107.89/107.79 thf(def_woz13rule4,definition,(woz13rule4 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))))). 107.89/107.79 thf(def_woz1_1,definition,(woz1_1 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))). 107.89/107.79 thf(def_woz1_2,definition,(woz1_2 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) @ ((binintersect @ ((setminus @ X1) @ X4)) @ ((setminus @ X1) @ X5))))))))))))))). 107.89/107.79 thf(def_woz1_3,definition,(woz1_3 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))))). 107.89/107.79 thf(def_woz1_4,definition,(woz1_4 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))))). 107.89/107.79 thf(def_woz1_5,definition,(woz1_5 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))))). 107.89/107.79 thf(def_breln1all2,definition,(breln1all2 = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))))). 107.89/107.79 thf(def_breln1SetBreln1,definition,(breln1SetBreln1 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))))). 107.89/107.79 thf(def_choice2fnsingleton,definition,(choice2fnsingleton = (![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => (((reflwellordering @ X2) @ X4) => (![X5:$i]:(((in @ X5) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))))). 107.89/107.79 thf(def_setOfPairsIsBReln1,definition,(setOfPairsIsBReln1 = (![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))))). 107.89/107.79 thf(def_breln1all1,definition,(breln1all1 = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))))) => (![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))))). 107.89/107.79 thf(def_subbreln1,definition,(subbreln1 = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))))). 107.89/107.79 thf(def_eqbreln1,definition,(eqbreln1 = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ X2)))))) => (X2 = X3)))))))))). 107.89/107.79 thf(def_breln1invprop,definition,(breln1invprop = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))))). 107.89/107.79 thf(def_breln1invI,definition,(breln1invI = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))))). 107.89/107.79 thf(def_breln1invE,definition,(breln1invE = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))))). 107.89/107.79 thf(def_breln1compprop,definition,(breln1compprop = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))))). 107.89/107.79 thf(def_breln1compI,definition,(breln1compI = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))))). 107.89/107.79 thf(def_breln1compE,definition,(breln1compE = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))))). 107.89/107.79 thf(def_breln1compEex,definition,(breln1compEex = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (![X6:$o]:((![X7:$i]:(((in @ X7) @ X1) => (((in @ ((kpair @ X4) @ X7)) @ X2) => (((in @ ((kpair @ X7) @ X5)) @ X3) => X6)))) => X6)))))))))))))). 107.89/107.79 thf(def_breln1unionprop,definition,(breln1unionprop = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ ((binunion @ X2) @ X3))))))))). 107.89/107.79 thf(def_breln1unionIL,definition,(breln1unionIL = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))))). 107.89/107.79 thf(def_breln1unionIR,definition,(breln1unionIR = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))))). 107.89/107.79 thf(def_breln1unionI,definition,(breln1unionI = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)) => ((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)))))))))))))). 107.89/107.79 thf(def_breln1unionE,definition,(breln1unionE = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => ((~(((in @ ((kpair @ X4) @ X5)) @ X2))) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))))). 107.89/107.79 thf(def_breln1unionEcases,definition,(breln1unionEcases = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ ((binunion @ X2) @ X3)) => (![X6:$o]:((((in @ ((kpair @ X4) @ X5)) @ X2) => X6) => ((((in @ ((kpair @ X4) @ X5)) @ X3) => X6) => X6))))))))))))))). 107.89/107.79 thf(def_breln1unionCommutes,definition,(breln1unionCommutes = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((binunion @ X2) @ X3) = ((binunion @ X3) @ X2))))))))). 107.89/107.79 thf(def_woz2Ex,definition,(woz2Ex = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (X2 = ((breln1invset @ X1) @ ((breln1invset @ X1) @ X2)))))))). 107.89/107.79 thf(def_woz2W,definition,(woz2W = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (((breln1invset @ X1) @ (((breln1compset @ X1) @ X2) @ X3)) = (((breln1compset @ X1) @ ((breln1invset @ X1) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))). 107.89/107.79 thf(def_woz2A,definition,(woz2A = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ (((breln1compset @ X1) @ X2) @ X4)) @ (((breln1compset @ X1) @ X3) @ X4)))))))))))). 107.89/107.79 thf(def_woz2B,definition,(woz2B = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((breln1 @ X1) @ X4) => ((((breln1compset @ X1) @ ((binunion @ X2) @ X3)) @ X4) = ((binunion @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X3)))) @ ((breln1invset @ X1) @ (((breln1compset @ X1) @ ((breln1invset @ X1) @ X4)) @ ((breln1invset @ X1) @ X2)))))))))))))). 107.89/107.79 thf(def_image1Ex,definition,(image1Ex = (![X1:$i]:(![X2:$i>$i]:(~((![X3:$i]:(~((![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5))))))))))))))))))). 107.89/107.79 thf(def_image1Ex1,definition,(image1Ex1 = (![X1:$i]:(![X2:$i>$i]:(exu @ (^[X3:$i]:(![X4:$i]:(((in @ X4) @ X3) = (~((![X5:$i]:(((in @ X5) @ X1) => (~((X4 = (X2 @ X5)))))))))))))))). 107.89/107.79 thf(def_image1Equiv,definition,(image1Equiv = sP91)). 107.89/107.79 thf(def_image1E,definition,(image1E = (![X1:$i]:(![X2:$i>$i]:(![X3:$i]:(((in @ X3) @ ((image1 @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (~((X3 = (X2 @ X4)))))))))))))). 107.89/107.79 thf(image1I,conjecture,sP287). 107.89/107.79 thf(h2,negated_conjecture,(~(sP287)),inference(assume_negation,[status(cth)],[image1I])). 107.89/107.79 thf(1,plain,(~(sP260) | sP85),inference(all_rule,[status(thm)],[])). 107.89/107.79 thf(2,plain,((~(sP85) | ~(sP96)) | ~(sP94)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(3,plain,((~(sP54) | sP77) | sP260),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(4,plain,(~(sP91) | sP133),inference(all_rule,[status(thm)],[])). 107.89/107.79 thf(5,plain,(~(sP133) | sP22),inference(all_rule,[status(thm)],[])). 107.89/107.79 thf(6,plain,(~(sP22) | sP54),inference(all_rule,[status(thm)],[])). 107.89/107.79 thf(7,plain,(sP116 | sP96),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(8,plain,(sP116 | sP94),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(9,plain,(sP284 | ~(sP116)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3])). 107.89/107.79 thf(10,plain,(sP237 | ~(sP77)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(11,plain,(sP237 | ~(sP284)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(12,plain,(sP246 | ~(sP237)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2])). 107.89/107.79 thf(13,plain,(sP177 | ~(sP246)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__1])). 107.89/107.79 thf(14,plain,(sP308 | ~(sP177)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])). 107.89/107.79 thf(15,plain,(sP278 | ~(sP308)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(16,plain,(sP200 | ~(sP278)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(17,plain,(sP200 | sP91),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(18,plain,(sP87 | ~(sP200)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(19,plain,(sP197 | ~(sP87)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(20,plain,(sP33 | ~(sP197)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(21,plain,(sP73 | ~(sP33)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(22,plain,(sP139 | ~(sP73)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(23,plain,(sP326 | ~(sP139)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(24,plain,(sP40 | ~(sP326)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(25,plain,(sP61 | ~(sP40)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(26,plain,(sP93 | ~(sP61)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(27,plain,(sP207 | ~(sP93)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(28,plain,(sP147 | ~(sP207)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(29,plain,(sP203 | ~(sP147)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(30,plain,(sP138 | ~(sP203)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(31,plain,(sP126 | ~(sP138)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(32,plain,(sP3 | ~(sP126)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(33,plain,(sP322 | ~(sP3)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(34,plain,(sP115 | ~(sP322)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(35,plain,(sP192 | ~(sP115)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(36,plain,(sP212 | ~(sP192)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(37,plain,(sP296 | ~(sP212)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(38,plain,(sP50 | ~(sP296)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(39,plain,(sP132 | ~(sP50)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(40,plain,(sP262 | ~(sP132)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(41,plain,(sP294 | ~(sP262)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(42,plain,(sP149 | ~(sP294)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(43,plain,(sP71 | ~(sP149)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(44,plain,(sP25 | ~(sP71)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(45,plain,(sP240 | ~(sP25)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(46,plain,(sP245 | ~(sP240)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(47,plain,(sP309 | ~(sP245)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(48,plain,(sP255 | ~(sP309)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(49,plain,(sP279 | ~(sP255)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(50,plain,(sP194 | ~(sP279)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(51,plain,(sP317 | ~(sP194)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(52,plain,(sP109 | ~(sP317)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(53,plain,(sP15 | ~(sP109)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(54,plain,(sP60 | ~(sP15)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(55,plain,(sP112 | ~(sP60)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(56,plain,(sP84 | ~(sP112)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(57,plain,(sP239 | ~(sP84)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(58,plain,(sP305 | ~(sP239)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(59,plain,(sP274 | ~(sP305)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(60,plain,(sP267 | ~(sP274)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(61,plain,(sP99 | ~(sP267)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(62,plain,(sP258 | ~(sP99)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(63,plain,(sP263 | ~(sP258)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(64,plain,(sP321 | ~(sP263)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(65,plain,(sP32 | ~(sP321)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(66,plain,(sP312 | ~(sP32)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(67,plain,(sP277 | ~(sP312)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(68,plain,(sP293 | ~(sP277)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(69,plain,(sP299 | ~(sP293)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(70,plain,(sP97 | ~(sP299)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(71,plain,(sP174 | ~(sP97)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(72,plain,(sP320 | ~(sP174)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(73,plain,(sP49 | ~(sP320)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(74,plain,(sP169 | ~(sP49)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(75,plain,(sP221 | ~(sP169)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(76,plain,(sP315 | ~(sP221)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(77,plain,(sP21 | ~(sP315)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(78,plain,(sP276 | ~(sP21)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(79,plain,(sP201 | ~(sP276)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(80,plain,(sP211 | ~(sP201)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(81,plain,(sP306 | ~(sP211)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(82,plain,(sP130 | ~(sP306)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(83,plain,(sP291 | ~(sP130)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(84,plain,(sP66 | ~(sP291)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(85,plain,(sP145 | ~(sP66)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(86,plain,(sP57 | ~(sP145)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(87,plain,(sP81 | ~(sP57)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(88,plain,(sP328 | ~(sP81)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(89,plain,(sP45 | ~(sP328)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(90,plain,(sP224 | ~(sP45)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(91,plain,(sP202 | ~(sP224)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(92,plain,(sP180 | ~(sP202)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(93,plain,(sP251 | ~(sP180)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(94,plain,(sP319 | ~(sP251)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(95,plain,(sP104 | ~(sP319)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(96,plain,(sP282 | ~(sP104)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(97,plain,(sP153 | ~(sP282)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(98,plain,(sP311 | ~(sP153)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(99,plain,(sP42 | ~(sP311)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(100,plain,(sP198 | ~(sP42)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(101,plain,(sP72 | ~(sP198)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(102,plain,(sP158 | ~(sP72)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(103,plain,(sP247 | ~(sP158)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(104,plain,(sP214 | ~(sP247)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(105,plain,(sP254 | ~(sP214)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(106,plain,(sP304 | ~(sP254)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(107,plain,(sP295 | ~(sP304)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(108,plain,(sP195 | ~(sP295)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(109,plain,(sP142 | ~(sP195)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(110,plain,(sP106 | ~(sP142)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(111,plain,(sP217 | ~(sP106)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(112,plain,(sP232 | ~(sP217)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(113,plain,(sP302 | ~(sP232)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(114,plain,(sP208 | ~(sP302)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(115,plain,(sP125 | ~(sP208)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(116,plain,(sP168 | ~(sP125)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(117,plain,(sP119 | ~(sP168)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(118,plain,(sP234 | ~(sP119)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(119,plain,(sP289 | ~(sP234)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(120,plain,(sP80 | ~(sP289)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(121,plain,(sP122 | ~(sP80)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(122,plain,(sP167 | ~(sP122)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(123,plain,(sP223 | ~(sP167)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(124,plain,(sP118 | ~(sP223)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(125,plain,(sP250 | ~(sP118)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(126,plain,(sP229 | ~(sP250)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(127,plain,(sP179 | ~(sP229)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(128,plain,(sP300 | ~(sP179)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(129,plain,(sP76 | ~(sP300)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(130,plain,(sP271 | ~(sP76)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(131,plain,(sP39 | ~(sP271)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(132,plain,(sP310 | ~(sP39)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(133,plain,(sP165 | ~(sP310)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(134,plain,(sP64 | ~(sP165)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(135,plain,(sP38 | ~(sP64)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(136,plain,(sP290 | ~(sP38)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(137,plain,(sP28 | ~(sP290)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(138,plain,(sP137 | ~(sP28)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(139,plain,(sP216 | ~(sP137)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(140,plain,(sP48 | ~(sP216)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(141,plain,(sP114 | ~(sP48)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(142,plain,(sP164 | ~(sP114)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(143,plain,(sP129 | ~(sP164)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(144,plain,(sP318 | ~(sP129)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(145,plain,(sP171 | ~(sP318)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(146,plain,(sP172 | ~(sP171)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(147,plain,(sP69 | ~(sP172)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(148,plain,(sP136 | ~(sP69)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(149,plain,(sP103 | ~(sP136)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(150,plain,(sP68 | ~(sP103)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(151,plain,(sP9 | ~(sP68)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(152,plain,(sP188 | ~(sP9)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(153,plain,(sP8 | ~(sP188)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(154,plain,(sP227 | ~(sP8)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(155,plain,(sP283 | ~(sP227)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(156,plain,(sP213 | ~(sP283)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(157,plain,(sP242 | ~(sP213)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(158,plain,(sP253 | ~(sP242)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(159,plain,(sP13 | ~(sP253)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(160,plain,(sP90 | ~(sP13)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(161,plain,(sP257 | ~(sP90)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(162,plain,(sP327 | ~(sP257)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(163,plain,(sP95 | ~(sP327)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(164,plain,(sP79 | ~(sP95)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(165,plain,(sP100 | ~(sP79)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(166,plain,(sP162 | ~(sP100)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(167,plain,(sP75 | ~(sP162)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(168,plain,(sP270 | ~(sP75)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(169,plain,(sP92 | ~(sP270)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(170,plain,(sP324 | ~(sP92)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(171,plain,(sP70 | ~(sP324)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(172,plain,(sP206 | ~(sP70)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(173,plain,(sP265 | ~(sP206)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(174,plain,(sP170 | ~(sP265)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(175,plain,(sP189 | ~(sP170)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(176,plain,(sP17 | ~(sP189)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(177,plain,(sP134 | ~(sP17)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(178,plain,(sP205 | ~(sP134)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(179,plain,(sP156 | ~(sP205)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(180,plain,(sP34 | ~(sP156)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(181,plain,(sP199 | ~(sP34)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(182,plain,(sP59 | ~(sP199)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(183,plain,(sP185 | ~(sP59)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(184,plain,(sP215 | ~(sP185)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(185,plain,(sP314 | ~(sP215)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(186,plain,(sP141 | ~(sP314)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(187,plain,(sP88 | ~(sP141)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(188,plain,(sP53 | ~(sP88)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(189,plain,(sP27 | ~(sP53)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(190,plain,(sP7 | ~(sP27)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(191,plain,(sP193 | ~(sP7)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(192,plain,(sP259 | ~(sP193)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(193,plain,(sP113 | ~(sP259)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(194,plain,(sP56 | ~(sP113)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(195,plain,(sP14 | ~(sP56)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(196,plain,(sP26 | ~(sP14)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(197,plain,(sP157 | ~(sP26)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(198,plain,(sP24 | ~(sP157)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(199,plain,(sP297 | ~(sP24)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(200,plain,(sP236 | ~(sP297)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(201,plain,(sP285 | ~(sP236)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(202,plain,(sP37 | ~(sP285)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(203,plain,(sP5 | ~(sP37)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(204,plain,(sP128 | ~(sP5)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(205,plain,(sP43 | ~(sP128)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(206,plain,(sP20 | ~(sP43)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(207,plain,(sP31 | ~(sP20)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(208,plain,(sP249 | ~(sP31)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(209,plain,(sP244 | ~(sP249)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(210,plain,(sP183 | ~(sP244)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(211,plain,(sP204 | ~(sP183)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(212,plain,(sP102 | ~(sP204)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(213,plain,(sP36 | ~(sP102)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(214,plain,(sP301 | ~(sP36)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(215,plain,(sP111 | ~(sP301)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(216,plain,(sP222 | ~(sP111)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(217,plain,(sP86 | ~(sP222)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(218,plain,(sP241 | ~(sP86)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(219,plain,(sP152 | ~(sP241)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(220,plain,(sP298 | ~(sP152)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(221,plain,(sP107 | ~(sP298)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(222,plain,(sP159 | ~(sP107)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(223,plain,(sP19 | ~(sP159)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(224,plain,(sP78 | ~(sP19)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(225,plain,(sP226 | ~(sP78)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(226,plain,(sP261 | ~(sP226)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(227,plain,(sP121 | ~(sP261)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(228,plain,(sP316 | ~(sP121)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(229,plain,(sP235 | ~(sP316)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(230,plain,(sP155 | ~(sP235)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(231,plain,(sP220 | ~(sP155)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(232,plain,(sP269 | ~(sP220)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(233,plain,(sP173 | ~(sP269)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(234,plain,(sP12 | ~(sP173)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(235,plain,(sP187 | ~(sP12)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(236,plain,(sP41 | ~(sP187)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(237,plain,(sP218 | ~(sP41)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(238,plain,(sP210 | ~(sP218)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(239,plain,(sP117 | ~(sP210)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(240,plain,(sP82 | ~(sP117)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(241,plain,(sP30 | ~(sP82)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(242,plain,(sP233 | ~(sP30)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(243,plain,(sP281 | ~(sP233)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(244,plain,(sP225 | ~(sP281)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(245,plain,(sP74 | ~(sP225)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(246,plain,(sP181 | ~(sP74)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(247,plain,(sP67 | ~(sP181)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(248,plain,(sP18 | ~(sP67)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(249,plain,(sP46 | ~(sP18)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(250,plain,(sP98 | ~(sP46)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(251,plain,(sP231 | ~(sP98)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(252,plain,(sP230 | ~(sP231)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(253,plain,(sP288 | ~(sP230)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(254,plain,(sP63 | ~(sP288)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(255,plain,(sP182 | ~(sP63)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(256,plain,(sP264 | ~(sP182)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(257,plain,(sP146 | ~(sP264)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(258,plain,(sP273 | ~(sP146)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(259,plain,(sP166 | ~(sP273)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(260,plain,(sP209 | ~(sP166)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(261,plain,(sP256 | ~(sP209)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(262,plain,(sP52 | ~(sP256)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(263,plain,(sP303 | ~(sP52)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(264,plain,(sP186 | ~(sP303)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(265,plain,(sP243 | ~(sP186)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(266,plain,(sP16 | ~(sP243)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(267,plain,(sP62 | ~(sP16)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(268,plain,(sP55 | ~(sP62)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(269,plain,(sP150 | ~(sP55)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(270,plain,(sP83 | ~(sP150)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(271,plain,(sP163 | ~(sP83)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(272,plain,(sP151 | ~(sP163)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(273,plain,(sP266 | ~(sP151)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(274,plain,(sP323 | ~(sP266)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(275,plain,(sP313 | ~(sP323)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(276,plain,(sP268 | ~(sP313)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(277,plain,(sP110 | ~(sP268)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(278,plain,(sP135 | ~(sP110)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(279,plain,(sP120 | ~(sP135)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(280,plain,(sP184 | ~(sP120)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(281,plain,(sP89 | ~(sP184)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(282,plain,(sP176 | ~(sP89)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(283,plain,(sP2 | ~(sP176)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(284,plain,(sP219 | ~(sP2)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(285,plain,(sP148 | ~(sP219)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(286,plain,(sP127 | ~(sP148)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(287,plain,(sP144 | ~(sP127)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(288,plain,(sP286 | ~(sP144)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(289,plain,(sP51 | ~(sP286)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(290,plain,(sP35 | ~(sP51)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(291,plain,(sP44 | ~(sP35)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(292,plain,(sP123 | ~(sP44)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(293,plain,(sP272 | ~(sP123)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(294,plain,(sP10 | ~(sP272)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(295,plain,(sP191 | ~(sP10)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(296,plain,(sP154 | ~(sP191)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(297,plain,(sP238 | ~(sP154)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(298,plain,(sP58 | ~(sP238)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(299,plain,(sP143 | ~(sP58)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(300,plain,(sP292 | ~(sP143)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(301,plain,(sP160 | ~(sP292)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(302,plain,(sP325 | ~(sP160)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(303,plain,(sP47 | ~(sP325)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(304,plain,(sP11 | ~(sP47)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(305,plain,(sP131 | ~(sP11)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(306,plain,(sP1 | ~(sP131)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(307,plain,(sP23 | ~(sP1)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(308,plain,(sP178 | ~(sP23)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(309,plain,(sP65 | ~(sP178)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(310,plain,(sP29 | ~(sP65)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(311,plain,(sP6 | ~(sP29)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(312,plain,(sP190 | ~(sP6)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(313,plain,(sP140 | ~(sP190)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(314,plain,(sP4 | ~(sP140)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(315,plain,(sP228 | ~(sP4)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(316,plain,(sP161 | ~(sP228)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(317,plain,(sP124 | ~(sP161)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(318,plain,(sP275 | ~(sP124)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(319,plain,(sP252 | ~(sP275)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(320,plain,(sP248 | ~(sP252)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(321,plain,(sP307 | ~(sP248)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(322,plain,(sP101 | ~(sP307)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(323,plain,(sP108 | ~(sP101)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(324,plain,(sP105 | ~(sP108)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(325,plain,(sP175 | ~(sP105)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(326,plain,(sP196 | ~(sP175)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(327,plain,(sP280 | ~(sP196)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(328,plain,(sP287 | ~(sP280)),inference(prop_rule,[status(thm)],[])). 107.89/107.79 thf(329,plain,$false,inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,h2])). 107.89/107.79 thf(330,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[329,h1])). 107.89/107.79 thf(331,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[330,h0])). 107.89/107.79 thf(0,theorem,sP287,inference(contra,[status(thm),contra(discharge,[h2])],[329,h2])). 107.89/107.79 % SZS output end Proof 107.89/107.79 EOF