%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU782^1 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 9 02:49:36 PM UTC 2025
% Result : Theorem 275.35s 274.78s
% Output : Proof 276.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SEU782^1 : TPTP v9.2.0. Released v3.7.0.
% 0.08/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Oct 8 21:41:53 EDT 2025
% 0.13/0.34 % CPUTime :
% 275.35/274.78 % SZS status Theorem
% 275.35/274.78 % Mode: mode498:USE_SINE=true:SINE_TOLERANCE=1.5:SINE_GENERALITY_THRESHOLD=16:SINE_RANK_LIMIT=2.:SINE_DEPTH=2
% 275.35/274.78 % Inferences: 305
% 275.35/274.78 % SZS output start Proof
% 275.35/274.78 thf(ty_kfst, type, kfst : ($i>$i)).
% 275.35/274.78 thf(ty_binintersect, type, binintersect : ($i>$i>$i)).
% 275.35/274.78 thf(ty_singleton, type, singleton : ($i>$o)).
% 275.35/274.78 thf(ty_if, type, if : ($i>$o>$i>$i>$i)).
% 275.35/274.78 thf(ty_subset, type, subset : ($i>$i>$o)).
% 275.35/274.78 thf(ty_eigen__2, type, eigen__2 : $i).
% 275.35/274.78 thf(ty_setunion, type, setunion : ($i>$i)).
% 275.35/274.78 thf(ty_iskpair, type, iskpair : ($i>$o)).
% 275.35/274.78 thf(ty_breln1invset, type, breln1invset : ($i>$i>$i)).
% 275.35/274.78 thf(ty_eigen__1, type, eigen__1 : $i).
% 275.35/274.78 thf(ty_eigen__0, type, eigen__0 : $i).
% 275.35/274.78 thf(ty_cartprod, type, cartprod : ($i>$i>$i)).
% 275.35/274.78 thf(ty_emptyset, type, emptyset : $i).
% 275.35/274.78 thf(ty_setminus, type, setminus : ($i>$i>$i)).
% 275.35/274.78 thf(ty_kpair, type, kpair : ($i>$i>$i)).
% 275.35/274.78 thf(ty_descr, type, descr : (($i>$o)>$i)).
% 275.35/274.78 thf(ty_reflwellordering, type, reflwellordering : ($i>$i>$o)).
% 275.35/274.78 thf(ty_breln1compset, type, breln1compset : ($i>$i>$i>$i)).
% 275.35/274.78 thf(ty_breln1Set, type, breln1Set : ($i>$i)).
% 275.35/274.78 thf(ty_ap, type, ap : ($i>$i>$i>$i>$i)).
% 275.35/274.78 thf(ty_funcSet, type, funcSet : ($i>$i>$i)).
% 275.35/274.78 thf(ty_symdiff, type, symdiff : ($i>$i>$i)).
% 275.35/274.78 thf(ty_dsetconstr, type, dsetconstr : ($i>($i>$o)>$i)).
% 275.35/274.78 thf(ty_powerset, type, powerset : ($i>$i)).
% 275.35/274.78 thf(ty_omega, type, omega : $i).
% 275.35/274.78 thf(ty_ex1, type, ex1 : ($i>($i>$o)>$o)).
% 275.35/274.78 thf(ty_ksnd, type, ksnd : ($i>$i)).
% 275.35/274.78 thf(ty_prop2set, type, prop2set : ($o>$i)).
% 275.35/274.78 thf(ty_set2prop, type, set2prop : ($i>$o)).
% 275.35/274.78 thf(ty_lam, type, lam : ($i>$i>($i>$i)>$i)).
% 275.35/274.78 thf(ty_in, type, in : ($i>$i>$o)).
% 275.35/274.78 thf(ty_func, type, func : ($i>$i>$i>$o)).
% 275.35/274.78 thf(ty_binunion, type, binunion : ($i>$i>$i)).
% 275.35/274.78 thf(ty_dpsetconstr, type, dpsetconstr : ($i>$i>($i>$i>$o)>$i)).
% 275.35/274.78 thf(ty_setadjoin, type, setadjoin : ($i>$i>$i)).
% 275.35/274.78 thf(def_exu,definition,(exu = (^[X1:$i>$o]:(~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3)))))))))))).
% 275.35/274.78 thf(def_setextAx,definition,(setextAx = (![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) = ((in @ X3) @ X2))) => (X1 = X2)))))).
% 275.35/274.78 thf(def_emptysetAx,definition,(emptysetAx = (![X1:$i]:(~(((in @ X1) @ emptyset)))))).
% 275.35/274.78 thf(def_setadjoinAx,definition,(setadjoinAx = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ X2)) = ((~((X3 = X1))) => ((in @ X3) @ X2)))))))).
% 275.35/274.78 thf(def_powersetAx,definition,(powersetAx = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) = (![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1)))))))).
% 275.35/274.78 thf(def_setunionAx,definition,(setunionAx = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) = (~((![X3:$i]:(((in @ X2) @ X3) => (~(((in @ X3) @ X1)))))))))))).
% 275.35/274.78 thf(def_omega0Ax,definition,(omega0Ax = ((in @ emptyset) @ omega))).
% 275.35/274.78 thf(def_omegaSAx,definition,(omegaSAx = (![X1:$i]:(((in @ X1) @ omega) => ((in @ ((setadjoin @ X1) @ X1)) @ omega))))).
% 275.35/274.78 thf(def_omegaIndAx,definition,(omegaIndAx = (![X1:$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))))))).
% 275.35/274.78 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))))))))))))))))))).
% 275.35/274.78 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))))))))))))))).
% 275.35/274.78 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:$i]:(((in @ X7) @ X6) => ((in @ X7) @ X4))))) => ((in @ X5) @ X6)))))))))))))))))))))).
% 275.35/274.78 thf(def_descrp,definition,(descrp = (![X1:$i>$o]:((exu @ X1) => (X1 @ (descr @ X1)))))).
% 275.35/274.78 thf(def_dsetconstrI,definition,(dsetconstrI = (![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((in @ X3) @ ((dsetconstr @ X1) @ X2))))))))).
% 275.35/274.78 thf(def_dsetconstrEL,definition,(dsetconstrEL = (![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ ((dsetconstr @ X1) @ X2)) => ((in @ X3) @ X1))))))).
% 275.35/274.78 thf(def_dsetconstrER,definition,(dsetconstrER = (![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ ((dsetconstr @ X1) @ X2)) => (X2 @ X3))))))).
% 275.35/274.78 thf(def_exuE1,definition,(exuE1 = (![X1:$i>$o]:((exu @ X1) => (~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))))))).
% 275.35/274.78 thf(def_prop2setE,definition,(prop2setE = (![X1:$o]:(![X2:$i]:(((in @ X2) @ (prop2set @ X1)) => X1))))).
% 275.35/274.78 thf(def_emptysetE,definition,(emptysetE = (![X1:$i]:(((in @ X1) @ emptyset) => (![X2:$o]:X2))))).
% 275.35/274.78 thf(def_emptysetimpfalse,definition,(emptysetimpfalse = (![X1:$i]:(~(((in @ X1) @ emptyset)))))).
% 275.35/274.78 thf(def_notinemptyset,definition,(notinemptyset = (![X1:$i]:(~(((in @ X1) @ emptyset)))))).
% 275.35/274.78 thf(def_exuE3e,definition,(exuE3e = (![X1:$i>$o]:((exu @ X1) => (~((![X2:$i]:(~((X1 @ X2)))))))))).
% 275.35/274.78 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))))))).
% 275.35/274.78 thf(def_emptyI,definition,(emptyI = (![X1:$i]:((![X2:$i]:(~(((in @ X2) @ X1)))) => (X1 = emptyset))))).
% 275.35/274.78 thf(def_noeltsimpempty,definition,(noeltsimpempty = (![X1:$i]:((![X2:$i]:(~(((in @ X2) @ X1)))) => (X1 = emptyset))))).
% 275.35/274.78 thf(def_setbeta,definition,(setbeta = (![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ ((dsetconstr @ X1) @ X2)) = (X2 @ X3)))))))).
% 275.35/274.78 thf(def_nonempty,definition,(nonempty = (^[X1:$i]:(~((X1 = emptyset)))))).
% 275.35/274.78 thf(def_nonemptyE1,definition,(nonemptyE1 = (![X1:$i]:((nonempty @ X1) => (~((![X2:$i]:(~(((in @ X2) @ X1)))))))))).
% 275.35/274.78 thf(def_nonemptyI,definition,(nonemptyI = (![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => (nonempty @ ((dsetconstr @ X1) @ X2))))))))).
% 275.35/274.78 thf(def_nonemptyI1,definition,(nonemptyI1 = (![X1:$i]:((~((![X2:$i]:(~(((in @ X2) @ X1)))))) => (nonempty @ X1))))).
% 275.35/274.78 thf(def_setadjoinIL,definition,(setadjoinIL = (![X1:$i]:(![X2:$i]:((in @ X1) @ ((setadjoin @ X1) @ X2)))))).
% 275.35/274.78 thf(def_emptyinunitempty,definition,(emptyinunitempty = ((in @ emptyset) @ ((setadjoin @ emptyset) @ emptyset)))).
% 275.35/274.78 thf(def_setadjoinIR,definition,(setadjoinIR = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ ((setadjoin @ X1) @ X2)))))))).
% 275.35/274.78 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))))))))).
% 275.35/274.78 thf(def_setadjoinOr,definition,(setadjoinOr = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ X2)) => ((~((X3 = X1))) => ((in @ X3) @ X2)))))))).
% 275.35/274.78 thf(def_setoftrueEq,definition,(setoftrueEq = (![X1:$i]:(((dsetconstr @ X1) @ (^[X2:$i]:(~($false)))) = X1)))).
% 275.35/274.78 thf(def_powersetI,definition,(powersetI = (![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1))) => ((in @ X2) @ (powerset @ X1))))))).
% 275.35/274.78 thf(def_emptyinPowerset,definition,(emptyinPowerset = (![X1:$i]:((in @ emptyset) @ (powerset @ X1))))).
% 275.35/274.78 thf(def_emptyInPowerset,definition,(emptyInPowerset = (![X1:$i]:((in @ emptyset) @ (powerset @ X1))))).
% 275.35/274.78 thf(def_powersetE,definition,(powersetE = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X2) @ (powerset @ X1)) => (((in @ X3) @ X2) => ((in @ X3) @ X1)))))))).
% 275.35/274.78 thf(def_setunionI,definition,(setunionI = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X2) @ X3) => (((in @ X3) @ X1) => ((in @ X2) @ (setunion @ X1))))))))).
% 275.35/274.78 thf(def_setunionE,definition,(setunionE = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) => (![X3:$o]:((![X4:$i]:(((in @ X2) @ X4) => (((in @ X4) @ X1) => X3))) => X3))))))).
% 275.35/274.78 thf(def_subPowSU,definition,(subPowSU = (![X1:$i]:(![X2:$i]:(((in @ X2) @ X1) => ((in @ X2) @ (powerset @ (setunion @ X1)))))))).
% 275.35/274.78 thf(def_exuE2,definition,(exuE2 = (![X1:$i>$o]:((exu @ X1) => (~((![X2:$i]:(~((![X3:$i]:((X1 @ X3) = (X3 = X2)))))))))))).
% 275.35/274.78 thf(def_nonemptyImpWitness,definition,(nonemptyImpWitness = (![X1:$i]:((nonempty @ X1) => (~((![X2:$i]:(~(((in @ X2) @ X1)))))))))).
% 275.35/274.78 thf(def_uniqinunit,definition,(uniqinunit = (![X1:$i]:(![X2:$i]:(((in @ X1) @ ((setadjoin @ X2) @ emptyset)) => (X1 = X2)))))).
% 275.35/274.78 thf(def_notinsingleton,definition,(notinsingleton = (![X1:$i]:(![X2:$i]:((~((X1 = X2))) => (~(((in @ X2) @ ((setadjoin @ X1) @ emptyset))))))))).
% 275.35/274.78 thf(def_eqinunit,definition,(eqinunit = (![X1:$i]:(![X2:$i]:((X1 = X2) => ((in @ X1) @ ((setadjoin @ X2) @ emptyset))))))).
% 275.35/274.78 thf(def_singletonsswitch,definition,(singletonsswitch = (![X1:$i]:(![X2:$i]:(((in @ X1) @ ((setadjoin @ X2) @ emptyset)) => ((in @ X2) @ ((setadjoin @ X1) @ emptyset))))))).
% 275.35/274.78 thf(def_upairsetE,definition,(upairsetE = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) => ((~((X3 = X1))) => (X3 = X2)))))))).
% 275.35/274.78 thf(def_upairsetIL,definition,(upairsetIL = (![X1:$i]:(![X2:$i]:((in @ X1) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))))).
% 275.35/274.78 thf(def_upairsetIR,definition,(upairsetIR = (![X1:$i]:(![X2:$i]:((in @ X2) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))))).
% 275.35/274.78 thf(def_emptyE1,definition,(emptyE1 = (![X1:$i]:(![X2:$i>$o]:((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => (~((((dsetconstr @ X1) @ X2) = emptyset)))))))).
% 275.35/274.78 thf(def_vacuousDall,definition,(vacuousDall = (![X1:$i>$o]:(![X2:$i]:(((in @ X2) @ emptyset) => (X1 @ X2)))))).
% 275.35/274.78 thf(def_quantDeMorgan1,definition,(quantDeMorgan1 = (![X1:$i]:(![X2:$i>$o]:((~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3))))) => (~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3)))))))))).
% 275.35/274.78 thf(def_quantDeMorgan2,definition,(quantDeMorgan2 = (![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))) => (![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))))).
% 275.35/274.78 thf(def_quantDeMorgan3,definition,(quantDeMorgan3 = (![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))) => (![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))))).
% 275.35/274.78 thf(def_quantDeMorgan4,definition,(quantDeMorgan4 = (![X1:$i]:(![X2:$i>$o]:((~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3))))) => (~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3)))))))))).
% 275.35/274.78 thf(def_prop2setI,definition,(prop2setI = (![X1:$o]:(X1 => ((in @ emptyset) @ (prop2set @ X1)))))).
% 275.35/274.78 thf(def_prop2set2propI,definition,(prop2set2propI = (![X1:$o]:(X1 => (set2prop @ (prop2set @ X1)))))).
% 275.35/274.78 thf(def_notdexE,definition,(notdexE = (![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))) => (![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))))).
% 275.35/274.78 thf(def_notdallE,definition,(notdallE = (![X1:$i]:(![X2:$i>$o]:((~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3))))) => (~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3)))))))))).
% 275.35/274.78 thf(def_exuI1,definition,(exuI1 = (![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (exu @ X1))))).
% 275.35/274.78 thf(def_exuI3,definition,(exuI3 = (![X1:$i>$o]:((~((![X2:$i]:(~((X1 @ X2)))))) => ((![X2:$i]:(![X3:$i]:((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))) => (exu @ X1)))))).
% 275.35/274.78 thf(def_exuI2,definition,(exuI2 = (![X1:$i>$o]:((~((![X2:$i]:(~((![X3:$i]:((X1 @ X3) = (X3 = X2)))))))) => (exu @ X1))))).
% 275.35/274.78 thf(def_inCongP,definition,(inCongP = (![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((in @ X3) @ X1) => ((in @ X4) @ X2)))))))))).
% 275.35/274.78 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)))))))))).
% 275.35/274.78 thf(def_exuE3u,definition,(exuE3u = (![X1:$i>$o]:((exu @ X1) => (![X2:$i]:(![X3:$i]:((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))))))).
% 275.35/274.78 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))))))).
% 275.35/274.78 thf(def_emptyset__Cong,definition,(emptyset__Cong = (emptyset = emptyset))).
% 275.35/274.78 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)))))))))).
% 275.35/274.78 thf(def_powerset__Cong,definition,(powerset__Cong = (![X1:$i]:(![X2:$i]:((X1 = X2) => ((powerset @ X1) = (powerset @ X2))))))).
% 275.35/274.78 thf(def_setunion__Cong,definition,(setunion__Cong = (![X1:$i]:(![X2:$i]:((X1 = X2) => ((setunion @ X1) = (setunion @ X2))))))).
% 275.35/274.78 thf(def_omega__Cong,definition,(omega__Cong = (omega = omega))).
% 275.35/274.78 thf(def_exuEu,definition,(exuEu = (![X1:$i>$o]:((exu @ X1) => (![X2:$i]:(![X3:$i]:((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))))))).
% 275.35/274.78 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))))))))).
% 275.35/274.78 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)))))))))).
% 275.35/274.78 thf(def_subsetI1,definition,(subsetI1 = (![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((subset @ X1) @ X2)))))).
% 275.35/274.78 thf(def_eqimpsubset2,definition,(eqimpsubset2 = (![X1:$i]:(![X2:$i]:((X1 = X2) => ((subset @ X2) @ X1)))))).
% 275.35/274.78 thf(def_eqimpsubset1,definition,(eqimpsubset1 = (![X1:$i]:(![X2:$i]:((X1 = X2) => ((subset @ X1) @ X2)))))).
% 275.35/274.78 thf(def_subsetI2,definition,(subsetI2 = (![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((subset @ X1) @ X2)))))).
% 275.35/274.78 thf(def_emptysetsubset,definition,(emptysetsubset = ((!!) @ (subset @ emptyset)))).
% 275.35/274.78 thf(def_subsetE,definition,(subsetE = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X2) => (((in @ X3) @ X1) => ((in @ X3) @ X2)))))))).
% 275.35/274.78 thf(def_subsetE2,definition,(subsetE2 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X2) => ((~(((in @ X3) @ X2))) => (~(((in @ X3) @ X1)))))))))).
% 275.35/274.78 thf(def_notsubsetI,definition,(notsubsetI = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => (~(((subset @ X1) @ X2)))))))))).
% 275.35/274.78 thf(def_notequalI1,definition,(notequalI1 = (![X1:$i]:(![X2:$i]:((~(((subset @ X1) @ X2))) => (~((X1 = X2)))))))).
% 275.35/274.78 thf(def_notequalI2,definition,(notequalI2 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => (~((X1 = X2)))))))))).
% 275.35/274.78 thf(def_subsetRefl,definition,(subsetRefl = (![X1:$i]:((subset @ X1) @ X1)))).
% 275.35/274.78 thf(def_subsetTrans,definition,(subsetTrans = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X2) => (((subset @ X2) @ X3) => ((subset @ X1) @ X3)))))))).
% 275.35/274.78 thf(def_setadjoinSub,definition,(setadjoinSub = (![X1:$i]:(![X2:$i]:((subset @ X2) @ ((setadjoin @ X1) @ X2)))))).
% 275.35/274.78 thf(def_setadjoinSub2,definition,(setadjoinSub2 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X3) => ((subset @ X1) @ ((setadjoin @ X2) @ X3)))))))).
% 275.35/274.78 thf(def_subset2powerset,definition,(subset2powerset = (![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => ((in @ X1) @ (powerset @ X2))))))).
% 275.35/274.78 thf(def_setextsub,definition,(setextsub = (![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((subset @ X2) @ X1) => (X1 = X2))))))).
% 275.35/274.78 thf(def_subsetemptysetimpeq,definition,(subsetemptysetimpeq = (![X1:$i]:(((subset @ X1) @ emptyset) => (X1 = emptyset))))).
% 275.35/274.78 thf(def_powersetI1,definition,(powersetI1 = (![X1:$i]:(![X2:$i]:(((subset @ X2) @ X1) => ((in @ X2) @ (powerset @ X1))))))).
% 275.35/274.78 thf(def_powersetE1,definition,(powersetE1 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ X2) @ X1)))))).
% 275.35/274.78 thf(def_inPowerset,definition,(inPowerset = (![X1:$i]:((in @ X1) @ (powerset @ X1))))).
% 275.35/274.78 thf(def_powersetsubset,definition,(powersetsubset = (![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => ((subset @ (powerset @ X1)) @ (powerset @ X2))))))).
% 275.35/274.78 thf(def_sepInPowerset,definition,(sepInPowerset = (![X1:$i]:(![X2:$i>$o]:((in @ ((dsetconstr @ X1) @ X2)) @ (powerset @ X1)))))).
% 275.35/274.78 thf(def_sepSubset,definition,(sepSubset = (![X1:$i]:(![X2:$i>$o]:((subset @ ((dsetconstr @ X1) @ X2)) @ X1))))).
% 275.35/274.78 thf(def_binunionIL,definition,(binunionIL = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ ((binunion @ X1) @ X2)))))))).
% 275.35/274.78 thf(def_upairset2IR,definition,(upairset2IR = (![X1:$i]:(![X2:$i]:((in @ X2) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))))).
% 275.35/274.78 thf(def_binunionIR,definition,(binunionIR = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ ((binunion @ X1) @ X2)))))))).
% 275.35/274.78 thf(def_binunionEcases,definition,(binunionEcases = (![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$o]:(((in @ X3) @ ((binunion @ X1) @ X2)) => ((((in @ X3) @ X1) => X4) => ((((in @ X3) @ X2) => X4) => X4))))))))).
% 275.35/274.78 thf(def_binunionE,definition,(binunionE = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((binunion @ X1) @ X2)) => ((~(((in @ X3) @ X1))) => ((in @ X3) @ X2)))))))).
% 275.35/274.78 thf(def_binunionLsub,definition,(binunionLsub = (![X1:$i]:(![X2:$i]:((subset @ X1) @ ((binunion @ X1) @ X2)))))).
% 275.35/274.78 thf(def_binunionRsub,definition,(binunionRsub = (![X1:$i]:(![X2:$i]:((subset @ X2) @ ((binunion @ X1) @ X2)))))).
% 275.35/274.78 thf(def_binintersectI,definition,(binintersectI = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => ((in @ X3) @ ((binintersect @ X1) @ X2))))))))).
% 275.35/274.78 thf(def_binintersectSubset5,definition,(binintersectSubset5 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X3) @ X1) => (((subset @ X3) @ X2) => ((subset @ X3) @ ((binintersect @ X1) @ X2))))))))).
% 275.35/274.78 thf(def_binintersectEL,definition,(binintersectEL = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((binintersect @ X1) @ X2)) => ((in @ X3) @ X1))))))).
% 275.35/274.78 thf(def_binintersectLsub,definition,(binintersectLsub = (![X1:$i]:(![X2:$i]:((subset @ ((binintersect @ X1) @ X2)) @ X1))))).
% 275.35/274.78 thf(def_binintersectSubset2,definition,(binintersectSubset2 = (![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((binintersect @ X1) @ X2) = X1)))))).
% 275.35/274.78 thf(def_binintersectSubset3,definition,(binintersectSubset3 = (![X1:$i]:(![X2:$i]:((((binintersect @ X1) @ X2) = X2) => ((subset @ X2) @ X1)))))).
% 275.35/274.78 thf(def_binintersectER,definition,(binintersectER = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((binintersect @ X1) @ X2)) => ((in @ X3) @ X2))))))).
% 275.35/274.78 thf(def_disjointsetsI1,definition,(disjointsetsI1 = (![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => (~(((in @ X3) @ X2))))) => (((binintersect @ X1) @ X2) = emptyset)))))).
% 275.35/274.78 thf(def_binintersectRsub,definition,(binintersectRsub = (![X1:$i]:(![X2:$i]:((subset @ ((binintersect @ X1) @ X2)) @ X2))))).
% 275.35/274.78 thf(def_binintersectSubset4,definition,(binintersectSubset4 = (![X1:$i]:(![X2:$i]:(((subset @ X2) @ X1) => (((binintersect @ X1) @ X2) = X2)))))).
% 275.35/274.78 thf(def_binintersectSubset1,definition,(binintersectSubset1 = (![X1:$i]:(![X2:$i]:((((binintersect @ X1) @ X2) = X1) => ((subset @ X1) @ X2)))))).
% 275.35/274.78 thf(def_bs114d,definition,(bs114d = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((binintersect @ X1) @ ((binunion @ X2) @ X3)) = ((binunion @ ((binintersect @ X1) @ X2)) @ ((binintersect @ X1) @ X3)))))))).
% 275.35/274.78 thf(def_setminusI,definition,(setminusI = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => ((in @ X3) @ ((setminus @ X1) @ X2))))))))).
% 275.35/274.78 thf(def_setminusEL,definition,(setminusEL = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setminus @ X1) @ X2)) => ((in @ X3) @ X1))))))).
% 275.35/274.78 thf(def_setminusER,definition,(setminusER = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setminus @ X1) @ X2)) => (~(((in @ X3) @ X2))))))))).
% 275.35/274.78 thf(def_setminusSubset2,definition,(setminusSubset2 = (![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((setminus @ X1) @ X2) = emptyset)))))).
% 275.35/274.78 thf(def_setminusERneg,definition,(setminusERneg = (![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ ((setminus @ X1) @ X2)))) => (((in @ X3) @ X1) => ((in @ X3) @ X2)))))))).
% 275.35/274.78 thf(def_setminusELneg,definition,(setminusELneg = (![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ ((setminus @ X1) @ X2)))) => ((~(((in @ X3) @ X2))) => (~(((in @ X3) @ X1)))))))))).
% 275.35/274.78 thf(def_setminusILneg,definition,(setminusILneg = (![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))))).
% 275.35/274.78 thf(def_setminusIRneg,definition,(setminusIRneg = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X2) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))))).
% 275.35/274.78 thf(def_setminusLsub,definition,(setminusLsub = (![X1:$i]:(![X2:$i]:((subset @ ((setminus @ X1) @ X2)) @ X1))))).
% 275.35/274.78 thf(def_setminusSubset1,definition,(setminusSubset1 = (![X1:$i]:(![X2:$i]:((((setminus @ X1) @ X2) = emptyset) => ((subset @ X1) @ X2)))))).
% 275.35/274.78 thf(def_symdiffE,definition,(symdiffE = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((symdiff @ X1) @ X2)) => (![X4:$o]:((((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => X4)) => (((~(((in @ X3) @ X1))) => (((in @ X3) @ X2) => X4)) => X4))))))))).
% 275.35/274.78 thf(def_symdiffI1,definition,(symdiffI1 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => ((in @ X3) @ ((symdiff @ X1) @ X2))))))))).
% 275.35/274.78 thf(def_symdiffI2,definition,(symdiffI2 = (![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => (((in @ X3) @ X2) => ((in @ X3) @ ((symdiff @ X1) @ X2))))))))).
% 275.35/274.78 thf(def_symdiffIneg1,definition,(symdiffIneg1 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => (~(((in @ X3) @ ((symdiff @ X1) @ X2))))))))))).
% 275.35/274.78 thf(def_symdiffIneg2,definition,(symdiffIneg2 = (![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => ((~(((in @ X3) @ X2))) => (~(((in @ X3) @ ((symdiff @ X1) @ X2))))))))))).
% 275.35/274.78 thf(def_secondinupair,definition,(secondinupair = (![X1:$i]:(![X2:$i]:((in @ X2) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))))).
% 275.35/274.78 thf(def_setukpairIL,definition,(setukpairIL = (![X1:$i]:(![X2:$i]:((in @ X1) @ (setunion @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)))))))).
% 275.35/274.78 thf(def_setukpairIR,definition,(setukpairIR = (![X1:$i]:(![X2:$i]:((in @ X2) @ (setunion @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)))))))).
% 275.35/274.78 thf(def_kpairiskpair,definition,(kpairiskpair = (![X1:$i]:(![X2:$i]:(iskpair @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))))))).
% 275.35/274.78 thf(def_kpairp,definition,(kpairp = (![X1:$i]:(![X2:$i]:(iskpair @ ((kpair @ X1) @ X2)))))).
% 275.35/274.78 thf(def_singletonsubset,definition,(singletonsubset = (![X1:$i]:(![X2:$i]:(((in @ X2) @ X1) => ((subset @ ((setadjoin @ X2) @ emptyset)) @ X1)))))).
% 275.35/274.78 thf(def_singletoninpowerset,definition,(singletoninpowerset = (![X1:$i]:(![X2:$i]:(((in @ X2) @ X1) => ((in @ ((setadjoin @ X2) @ emptyset)) @ (powerset @ X1))))))).
% 275.35/274.78 thf(def_singletoninpowunion,definition,(singletoninpowunion = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((in @ ((setadjoin @ X3) @ emptyset)) @ (powerset @ ((binunion @ X1) @ X2))))))))).
% 275.35/274.78 thf(def_upairset2E,definition,(upairset2E = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) => ((~((X3 = X1))) => (X3 = X2)))))))).
% 275.35/274.78 thf(def_upairsubunion,definition,(upairsubunion = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((subset @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ ((binunion @ X1) @ X2)))))))))).
% 275.35/274.78 thf(def_upairinpowunion,definition,(upairinpowunion = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))))).
% 275.35/274.78 thf(def_ubforcartprodlem1,definition,(ubforcartprodlem1 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((subset @ ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))))).
% 275.35/274.78 thf(def_ubforcartprodlem2,definition,(ubforcartprodlem2 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) @ (powerset @ (powerset @ ((binunion @ X1) @ X2)))))))))))).
% 275.35/274.78 thf(def_ubforcartprodlem3,definition,(ubforcartprodlem3 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ (powerset @ (powerset @ ((binunion @ X1) @ X2)))))))))))).
% 275.35/274.78 thf(def_cartprodpairin,definition,(cartprodpairin = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)))))))))).
% 275.35/274.78 thf(def_cartprodmempair1,definition,(cartprodmempair1 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (~((X3 = ((kpair @ X4) @ X5)))))))))))))))).
% 275.35/274.78 thf(def_cartprodmempair,definition,(cartprodmempair = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (iskpair @ X3))))))).
% 275.35/274.78 thf(def_setunionE2,definition,(setunionE2 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) => (~((![X3:$i]:(((in @ X3) @ X1) => (~(((in @ X2) @ X3)))))))))))).
% 275.35/274.78 thf(def_setunionsingleton1,definition,(setunionsingleton1 = (![X1:$i]:((subset @ (setunion @ ((setadjoin @ X1) @ emptyset))) @ X1)))).
% 275.35/274.78 thf(def_setunionsingleton2,definition,(setunionsingleton2 = (![X1:$i]:((subset @ X1) @ (setunion @ ((setadjoin @ X1) @ emptyset)))))).
% 275.35/274.78 thf(def_setunionsingleton,definition,(setunionsingleton = (![X1:$i]:((setunion @ ((setadjoin @ X1) @ emptyset)) = X1)))).
% 275.35/274.78 thf(def_singletonprop,definition,(singletonprop = (![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => ((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => (singleton @ ((dsetconstr @ X1) @ X2)))))))).
% 275.35/274.78 thf(def_ex1E1,definition,(ex1E1 = (![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))))))).
% 275.35/274.78 thf(def_ex1I,definition,(ex1I = (![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X4) => (X4 = X3)))) => ((ex1 @ X1) @ X2))))))))).
% 275.35/274.78 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))))))).
% 275.35/274.78 thf(def_singletonsuniq,definition,(singletonsuniq = (![X1:$i]:(![X2:$i]:((((setadjoin @ X1) @ emptyset) = ((setadjoin @ X2) @ emptyset)) => (X1 = X2)))))).
% 275.35/274.78 thf(def_setukpairinjL1,definition,(setukpairinjL1 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) => (X1 = X3))))))).
% 275.35/274.78 thf(def_kfstsingleton,definition,(kfstsingleton = (![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:((in @ ((setadjoin @ X2) @ emptyset)) @ X1)))))))).
% 275.35/274.78 thf(def_theprop,definition,(theprop = (![X1:$i]:((singleton @ X1) => ((in @ (setunion @ X1)) @ X1))))).
% 275.35/274.78 thf(def_kfstpairEq,definition,(kfstpairEq = (![X1:$i]:(![X2:$i]:((kfst @ ((kpair @ X1) @ X2)) = X1))))).
% 275.35/274.78 thf(def_cartprodfstin,definition,(cartprodfstin = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (kfst @ X3)) @ X1))))))).
% 275.35/274.78 thf(def_setukpairinjL2,definition,(setukpairinjL2 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X1 = X3)))))))).
% 275.35/274.78 thf(def_setukpairinjL,definition,(setukpairinjL = (![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X1 = X3)))))))).
% 275.35/274.78 thf(def_setukpairinjR11,definition,(setukpairinjR11 = (![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X1) @ emptyset))))))).
% 275.35/274.78 thf(def_setukpairinjR12,definition,(setukpairinjR12 = (![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ emptyset))))))).
% 275.35/274.78 thf(def_setukpairinjR1,definition,(setukpairinjR1 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => ((X3 = X4) => (X2 = X4))))))))).
% 275.35/274.78 thf(def_upairequniteq,definition,(upairequniteq = (![X1:$i]:(![X2:$i]:(![X3:$i]:((((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X3) @ emptyset)) => (X1 = X2))))))).
% 275.35/274.78 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)))))))).
% 275.35/274.78 thf(def_setukpairinjR,definition,(setukpairinjR = (![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X2 = X4)))))))).
% 275.35/274.78 thf(def_ksndsingleton,definition,(ksndsingleton = (![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:(X1 = ((kpair @ (kfst @ X1)) @ X2))))))))).
% 275.35/274.78 thf(def_ksndpairEq,definition,(ksndpairEq = (![X1:$i]:(![X2:$i]:((ksnd @ ((kpair @ X1) @ X2)) = X2))))).
% 275.35/274.78 thf(def_kpairsurjEq,definition,(kpairsurjEq = (![X1:$i]:((iskpair @ X1) => (((kpair @ (kfst @ X1)) @ (ksnd @ X1)) = X1))))).
% 275.35/274.78 thf(def_cartprodsndin,definition,(cartprodsndin = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))))).
% 275.35/274.78 thf(def_cartprodpairmemEL,definition,(cartprodpairmemEL = (![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))))).
% 275.35/274.78 thf(def_cartprodpairmemER,definition,(cartprodpairmemER = (![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X4) @ X2)))))))).
% 275.35/274.78 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)))))))))).
% 275.35/274.78 thf(def_cartprodfstpairEq,definition,(cartprodfstpairEq = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))))).
% 275.35/274.78 thf(def_cartprodsndpairEq,definition,(cartprodsndpairEq = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))))).
% 275.35/274.78 thf(def_cartprodpairsurjEq,definition,(cartprodpairsurjEq = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))))).
% 275.35/274.78 thf(def_breln,definition,(breln = (^[X1:$i]:(^[X2:$i]:(^[X3:$i]:((subset @ X3) @ ((cartprod @ X1) @ X2))))))).
% 275.35/274.78 thf(def_dpsetconstrI,definition,(dpsetconstrI = (![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((X3 @ X4) @ X5) => ((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)))))))))))).
% 275.35/274.78 thf(def_dpsetconstrSub,definition,(dpsetconstrSub = (![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))))).
% 275.35/274.78 thf(def_setOfPairsIsBReln,definition,(setOfPairsIsBReln = (![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(((breln @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ X3))))))).
% 275.35/274.78 thf(def_dpsetconstrERa,definition,(dpsetconstrERa = (![X1:$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))))))))))).
% 275.35/274.78 thf(def_dpsetconstrEL1,definition,(dpsetconstrEL1 = (![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))))).
% 275.35/274.78 thf(def_dpsetconstrEL2,definition,(dpsetconstrEL2 = (![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))))).
% 275.35/274.78 thf(def_dpsetconstrER,definition,(dpsetconstrER = (![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))).
% 275.35/274.78 thf(def_funcImageSingleton,definition,(funcImageSingleton = (![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))))).
% 275.35/274.78 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:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))))).
% 275.35/274.78 thf(def_app,definition,(app = (![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))))).
% 275.35/274.78 thf(def_infuncsetfunc,definition,(infuncsetfunc = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))))).
% 275.35/274.78 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))))))))).
% 275.35/274.78 thf(def_funcinfuncset,definition,(funcinfuncset = (![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))))).
% 275.35/274.78 thf(def_lamProp,definition,(lamProp = (![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((dpsetconstr @ X1) @ X2) @ (^[X4:$i]:((=) @ (X3 @ X4))))))))))).
% 275.35/274.78 thf(def_lamp,definition,(lamp = (![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))))).
% 275.35/274.78 thf(def_lam2p,definition,(lam2p = (![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))))).
% 275.35/274.78 thf(def_brelnall1,definition,(brelnall1 = (![X1:$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:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))))).
% 275.35/274.78 thf(def_brelnall2,definition,(brelnall2 = (![X1:$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:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))))).
% 275.35/274.78 thf(def_ex1E2,definition,(ex1E2 = (![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))))).
% 275.35/274.78 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))))))))).
% 275.35/274.78 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))))))))).
% 275.35/274.78 thf(def_funcGraphProp2,definition,(funcGraphProp2 = (![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))))).
% 275.35/274.79 thf(def_funcextLem,definition,(funcextLem = (![X1:$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))))))))))))))).
% 275.35/274.79 thf(def_funcGraphProp4,definition,(funcGraphProp4 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))))).
% 275.35/274.79 thf(def_subbreln,definition,(subbreln = (![X1:$i]:(![X2:$i]:(![X3:$i]:((((breln @ X1) @ X2) @ X3) => (![X4:$i]:((((breln @ X1) @ X2) @ X4) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))))).
% 275.35/274.79 thf(def_eqbreln,definition,(eqbreln = (![X1:$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:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3)))))) => (X3 = X4))))))))))).
% 275.35/274.79 thf(def_funcext,definition,(funcext = (![X1:$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)))))))))).
% 275.35/274.79 thf(def_funcext2,definition,(funcext2 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))))).
% 275.35/274.79 thf(def_ap2apEq1,definition,(ap2apEq1 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))))).
% 275.35/274.79 thf(def_ap2apEq2,definition,(ap2apEq2 = (![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))))).
% 275.35/274.79 thf(def_beta1,definition,(beta1 = (![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))))).
% 275.35/274.79 thf(def_eta1,definition,(eta1 = (![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))))).
% 275.35/274.79 thf(def_lam2lamEq,definition,(lam2lamEq = (![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((((lam @ X1) @ X2) @ X3) = (((lam @ X1) @ X2) @ X3)))))))).
% 275.35/274.79 thf(def_beta2,definition,(beta2 = (![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))))).
% 275.35/274.79 thf(def_eta2,definition,(eta2 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))))).
% 275.35/274.79 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:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))))).
% 275.35/274.79 thf(def_iffalseProp2,definition,(iffalseProp2 = (![X1:$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))))))))))).
% 275.35/274.79 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:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))))))))))))).
% 275.35/274.79 thf(def_iftrueProp2,definition,(iftrueProp2 = (![X1:$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))))))))))).
% 275.35/274.79 thf(def_ifSingleton,definition,(ifSingleton = (![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4)))))))))))))))))).
% 275.35/274.79 thf(def_ifp,definition,(ifp = (![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ X1))))))))).
% 275.35/274.79 thf(def_theeq,definition,(theeq = (![X1:$i]:((singleton @ X1) => (![X2:$i]:(((in @ X2) @ X1) => ((setunion @ X1) = X2))))))).
% 275.35/274.79 thf(def_iftrue,definition,(iftrue = (![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((((if @ X1) @ X2) @ X3) @ X4) = X3)))))))))).
% 275.35/274.79 thf(def_iffalse,definition,(iffalse = (![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((((if @ X1) @ X2) @ X3) @ X4) = X4)))))))))).
% 275.35/274.79 thf(def_iftrueorfalse,definition,(iftrueorfalse = (![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))))))))))).
% 275.35/274.79 thf(def_binintersectT_lem,definition,(binintersectT_lem = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))))).
% 275.35/274.79 thf(def_binunionT_lem,definition,(binunionT_lem = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binunion @ X2) @ X3)) @ (powerset @ X1))))))))).
% 275.35/274.79 thf(def_powersetT_lem,definition,(powersetT_lem = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((in @ (powerset @ X2)) @ (powerset @ (powerset @ X1)))))))).
% 275.35/274.79 thf(def_setminusT_lem,definition,(setminusT_lem = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X2) @ X3)) @ (powerset @ X1))))))))).
% 275.35/274.79 thf(def_complementT_lem,definition,(complementT_lem = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ X1))))))).
% 275.35/274.79 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:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X3) => ((in @ X4) @ X2)))) => (X2 = X3)))))))))).
% 275.35/274.79 thf(def_subsetTI,definition,(subsetTI = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))) => ((subset @ X2) @ X3))))))))).
% 275.35/274.79 thf(def_powersetTI1,definition,(powersetTI1 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))) => ((in @ X2) @ (powerset @ X3)))))))))).
% 275.35/274.79 thf(def_powersetTE1,definition,(powersetTE1 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X2) @ (powerset @ X3)) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))))))))))).
% 275.35/274.79 thf(def_complementTI1,definition,(complementTI1 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))))))).
% 275.35/274.79 thf(def_complementTE1,definition,(complementTE1 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ ((setminus @ X1) @ X2)))) => ((in @ X3) @ X2))))))))).
% 275.35/274.79 thf(def_binintersectTELcontra,definition,(binintersectTELcontra = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X2))) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))))).
% 275.35/274.79 thf(def_binintersectTERcontra,definition,(binintersectTERcontra = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))))).
% 275.35/274.79 thf(def_contrasubsetT,definition,(contrasubsetT = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => (((in @ X4) @ X3) => (~(((in @ X4) @ X2)))))))))))))).
% 275.35/274.79 thf(def_contrasubsetT1,definition,(contrasubsetT1 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((subset @ X2) @ X3) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ X2)))))))))))))).
% 275.35/274.79 thf(def_contrasubsetT2,definition,(contrasubsetT2 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ X3) => ((subset @ ((setminus @ X1) @ X3)) @ ((setminus @ X1) @ X2)))))))))).
% 275.35/274.79 thf(def_contrasubsetT3,definition,(contrasubsetT3 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ ((setminus @ X1) @ X3)) @ ((setminus @ X1) @ X2)) => ((subset @ X2) @ X3))))))))).
% 275.35/274.79 thf(def_doubleComplementI1,definition,(doubleComplementI1 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => ((in @ X3) @ ((setminus @ X1) @ ((setminus @ X1) @ X2))))))))))).
% 275.35/274.79 thf(def_doubleComplementE1,definition,(doubleComplementE1 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ ((setminus @ X1) @ ((setminus @ X1) @ X2))) => ((in @ X3) @ X2))))))))).
% 275.35/274.79 thf(def_doubleComplementSub1,definition,(doubleComplementSub1 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ X2) @ ((setminus @ X1) @ ((setminus @ X1) @ X2)))))))).
% 275.35/274.79 thf(def_doubleComplementSub2,definition,(doubleComplementSub2 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ ((setminus @ X1) @ X2))) @ X2)))))).
% 275.35/274.79 thf(def_doubleComplementEq,definition,(doubleComplementEq = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (X2 = ((setminus @ X1) @ ((setminus @ X1) @ X2)))))))).
% 275.35/274.79 thf(def_complementTnotintersectT,definition,(complementTnotintersectT = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))))).
% 275.35/274.79 thf(def_complementImpComplementIntersect,definition,(complementImpComplementIntersect = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))))).
% 275.35/274.79 thf(def_complementSubsetComplementIntersect,definition,(complementSubsetComplementIntersect = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))))).
% 275.35/274.79 thf(def_complementInPowersetComplementIntersect,definition,(complementInPowersetComplementIntersect = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))).
% 275.35/274.79 thf(def_contraSubsetComplement,definition,(contraSubsetComplement = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X3) => ((in @ X4) @ ((setminus @ X1) @ X2))))))))))))).
% 275.35/274.79 thf(def_complementTcontraSubset,definition,(complementTcontraSubset = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))))).
% 275.35/274.79 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))))))))))))).
% 275.35/274.79 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))))))))))))).
% 275.35/274.79 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:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binintersect @ X2) @ X3)) => ((in @ X5) @ ((binunion @ X2) @ X4)))))))))))))).
% 275.35/274.79 thf(def_inIntersectImpInUnion2,definition,(inIntersectImpInUnion2 = (![X1:$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)))))))))))))).
% 275.35/274.79 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:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binintersect @ X2) @ X3)) => ((in @ X5) @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))))))).
% 275.35/274.79 thf(def_intersectInPowersetIntersectUnions,definition,(intersectInPowersetIntersectUnions = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))))).
% 275.35/274.79 thf(def_inComplementUnionImpNotIn1,definition,(inComplementUnionImpNotIn1 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => (~(((in @ X4) @ X2))))))))))))).
% 275.35/274.79 thf(def_inComplementUnionImpInComplement1,definition,(inComplementUnionImpInComplement1 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X2)))))))))))).
% 275.35/274.79 thf(def_binunionTE,definition,(binunionTE = (![X1:$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))))))))))))).
% 275.35/274.79 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))))))))))))))).
% 275.35/274.79 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)))))))))))).
% 275.35/274.79 thf(def_complementUnionInPowersetComplement,definition,(complementUnionInPowersetComplement = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))))).
% 275.35/274.79 thf(def_demorgan2a2,definition,(demorgan2a2 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))))).
% 275.35/274.79 thf(def_demorgan1a,definition,(demorgan1a = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))) => ((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))))).
% 275.35/274.79 thf(def_demorgan1b,definition,(demorgan1b = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))))).
% 275.35/274.79 thf(def_demorgan1,definition,(demorgan1 = (![X1:$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)))))))))).
% 275.35/274.79 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))))))))))))).
% 275.35/274.79 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)))))))))))))).
% 275.35/274.79 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))))))))))))).
% 275.35/274.79 thf(def_demorgan2,definition,(demorgan2 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binunion @ X2) @ X3)) = ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))))).
% 275.35/274.79 thf(def_woz13rule0,definition,(woz13rule0 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))))).
% 275.35/274.79 thf(def_woz13rule1,definition,(woz13rule1 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))))).
% 275.35/274.79 thf(def_woz13rule2,definition,(woz13rule2 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))))).
% 275.35/274.79 thf(def_woz13rule3,definition,(woz13rule3 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X2) @ X3) => (((subset @ X2) @ X4) => ((subset @ X2) @ ((binintersect @ X3) @ X4))))))))))))).
% 275.35/274.79 thf(def_woz13rule4,definition,(woz13rule4 = (![X1:$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))))))))))))))).
% 275.35/274.79 thf(def_woz1_1,definition,(woz1_1 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))).
% 275.35/274.79 thf(def_woz1_2,definition,(woz1_2 = (![X1:$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))))))))))))))).
% 275.35/274.79 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))))))))))))).
% 275.35/274.79 thf(def_woz1_4,definition,(woz1_4 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))))).
% 275.35/274.79 thf(def_woz1_5,definition,(woz1_5 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))))).
% 275.35/274.79 thf(def_breln1,definition,(breln1 = (^[X1:$i]:((breln @ X1) @ X1)))).
% 275.35/274.79 thf(def_breln1all2,definition,(breln1all2 = (![X1:$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)))))))))).
% 275.35/274.79 thf(def_breln1SetBreln1,definition,(breln1SetBreln1 = (![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((breln1 @ X1) @ X2)))))).
% 275.35/274.79 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:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))))).
% 275.35/274.79 thf(def_setOfPairsIsBReln1,definition,(setOfPairsIsBReln1 = (![X1:$i]:(![X2:$i>$i>$o]:((breln1 @ X1) @ (((dpsetconstr @ X1) @ X1) @ X2)))))).
% 275.35/274.79 thf(def_breln1all1,definition,(breln1all1 = (![X1:$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)))))))))).
% 275.35/274.79 thf(def_subbreln1,definition,(subbreln1 = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))))).
% 275.35/274.79 thf(def_eqbreln1,definition,(eqbreln1 = (![X1:$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)))))))))).
% 275.35/274.79 thf(def_breln1invprop,definition,(breln1invprop = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => ((breln1 @ X1) @ ((breln1invset @ X1) @ X2))))))).
% 275.35/274.79 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)))))))))))).
% 275.35/274.79 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))))))))))).
% 275.35/274.79 thf(def_breln1compprop,definition,(breln1compprop = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => ((breln1 @ X1) @ (((breln1compset @ X1) @ X2) @ X3))))))))).
% 275.35/274.79 thf(def_breln1compI,definition,(breln1compI = (![X1:$i]:(![X2:$i]:(((breln1 @ X1) @ X2) => (![X3:$i]:(((breln1 @ X1) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))))).
% 275.35/274.79 thf(def_breln1compE,definition,(breln1compE = (![X1:$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:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))))).
% 275.35/274.79 thf(def_breln1compEex,definition,(breln1compEex = (![X1:$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)))))))))))))).
% 275.35/274.79 thf(breln1unionprop,conjecture,((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) = ((in @ X3) @ X2))) => (X1 = X2)))) => ((![X1:$i]:(~(((in @ X1) @ emptyset)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ X2)) = ((~((X3 = X1))) => ((in @ X3) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) = (![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) = (~((![X3:$i]:(((in @ X2) @ X3) => (~(((in @ X3) @ X1)))))))))) => (((in @ emptyset) @ omega) => ((![X1:$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))))) => ((![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:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1))) => (X1 = X2))))) => ((![X1:$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:$i]:(((in @ X4) @ X2) => ((subset @ ((setadjoin @ X3) @ ((setadjoin 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@ X3) @ X1) => (![X4:$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>$o]:(((ex1 @ X1) @ 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X1) => (((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))) => ((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))).
% 275.35/274.79 thf(h0,negated_conjecture,(~(((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) = ((in @ X3) @ X2))) => (X1 = X2)))) => ((![X1:$i]:(~(((in @ X1) @ emptyset)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ X2)) = ((~((X3 = X1))) => ((in @ X3) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) = (![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) = (~((![X3:$i]:(((in @ X2) @ X3) => (~(((in @ X3) @ X1)))))))))) => (((in @ emptyset) @ omega) => ((![X1:$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))))) => ((![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:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1))) => (X1 = X2))))) => ((![X1:$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 @ 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(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)))))) => 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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 @ 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) @ ((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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),inference(assume_negation,[status(cth)],[breln1unionprop])).
% 275.35/274.79 thf(h1,assumption,(![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) = ((in @ X3) @ X2))) => (X1 = X2)))),introduced(assumption,[])).
% 275.35/274.79 thf(h2,assumption,(~(((![X1:$i]:(~(((in @ X1) @ emptyset)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ X2)) = ((~((X3 = X1))) => ((in @ X3) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) = (![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) = (~((![X3:$i]:(((in @ X2) @ X3) => (~(((in @ X3) @ X1)))))))))) => (((in @ emptyset) @ omega) => ((![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:$i]:(((in @ X3) @ ((dsetconstr @ X1) @ X2)) => ((in @ X3) @ X1))))) => ((![X1:$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))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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))))))) => ((![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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.35/274.80 thf(h3,assumption,(![X1:$i]:(~(((in @ X1) @ emptyset)))),introduced(assumption,[])).
% 275.35/274.80 thf(h4,assumption,(~(((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ X2)) = ((~((X3 = X1))) => ((in @ X3) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) = (![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) = (~((![X3:$i]:(((in @ X2) @ X3) => (~(((in @ X3) @ X1)))))))))) => (((in @ emptyset) @ omega) => ((![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:$i]:(((in @ X3) @ ((dsetconstr @ X1) @ X2)) => ((in @ X3) @ X1))))) => ((![X1:$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))))) => ((![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:$o]:(((X3 = X1) => X4) => ((((in @ X3) @ X2) => X4) => 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((![X1:$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:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => ((in @ X3) @ ((setminus @ X1) @ X2))))))) => 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X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.35/274.80 thf(h5,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ X2)) = ((~((X3 = X1))) => ((in @ X3) @ X2)))))),introduced(assumption,[])).
% 275.35/274.80 thf(h6,assumption,(~(((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) = (![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) = (~((![X3:$i]:(((in @ X2) @ X3) => (~(((in @ X3) @ X1)))))))))) => (((in @ emptyset) @ omega) => ((![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:$i]:(((in @ X3) @ ((dsetconstr @ X1) @ X2)) => ((in @ X3) @ X1))))) => ((![X1:$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))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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))))))) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.35/274.80 thf(h7,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) = (![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1)))))),introduced(assumption,[])).
% 275.35/274.80 thf(h8,assumption,(~(((![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) = (~((![X3:$i]:(((in @ X2) @ X3) => (~(((in @ X3) @ X1)))))))))) => (((in @ emptyset) @ omega) => ((![X1:$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))))) => ((![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:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1))) => (X1 = X2))))) => ((![X1:$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:$i]:(iskpair @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))))) => 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((![X1:$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>$o]:((subset @ 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(![X4:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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 @ 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((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.35/274.81 thf(h9,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) = (~((![X3:$i]:(((in @ X2) @ X3) => (~(((in @ X3) @ X1)))))))))),introduced(assumption,[])).
% 275.35/274.81 thf(h10,assumption,(~((((in @ emptyset) @ omega) => ((![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:$i]:(((in @ X3) @ ((dsetconstr @ X1) @ X2)) => ((in @ X3) @ X1))))) => ((![X1:$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))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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:$i]:(((in @ X5) @ X1) => (((((ap @ 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X2))))))))))) => ((![X1:$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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.35/274.81 thf(h11,assumption,((in @ emptyset) @ omega),introduced(assumption,[])).
% 275.35/274.81 thf(h12,assumption,(~(((![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:$i]:(((in @ X3) @ ((dsetconstr @ X1) @ X2)) => ((in @ X3) @ X1))))) => ((![X1:$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))))) => ((![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:$i]:(((in @ X3) @ 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@ X3))))) @ X2))))))) => ((![X1:$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:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ 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emptyset))))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.35/274.81 thf(h13,assumption,(![X1:$i]:(((in @ X1) @ omega) => ((in @ ((setadjoin @ X1) @ X1)) @ omega))),introduced(assumption,[])).
% 275.35/274.81 thf(h14,assumption,(~(((![X1:$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:$i]:(((in @ X3) @ ((dsetconstr @ X1) @ X2)) => ((in @ X3) @ X1))))) => ((![X1:$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))))) => ((![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:$i]:(((in @ 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((![X1:$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:$i]:(((in @ X3) @ X1) => 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=> (![X3:$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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.35/274.81 thf(h15,assumption,(![X1:$i]:((~((((in @ emptyset) @ X1) => (~((![X2:$i]:((~((((in @ X2) @ omega) => (~(((in @ X2) @ X1)))))) => ((in @ ((setadjoin @ X2) @ X2)) @ X1)))))))) => (![X2:$i]:(((in @ X2) @ omega) => ((in @ X2) @ X1))))),introduced(assumption,[])).
% 275.35/274.81 thf(h16,assumption,(~(((![X1:$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))))) => ((![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:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1))) => (X1 = X2))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)) => (((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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:(((in @ X4) @ X1) => (~((![X5:$i]:(((in @ X5) @ X2) => (~(((X3 @ X4) @ X5))))))))) => (![X4:$i]:(((in @ X4) @ (breln1Set @ X2)) => 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@ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) 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((X5 = X6) => ((X3 @ X5) = (X4 @ X6))))))) => (((dsetconstr @ X1) @ X3) = ((dsetconstr @ X2) @ X4)))))))) => ((![X1:$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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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))))))) => ((![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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.41/274.82 thf(h19,assumption,(![X1:$i]:((~((![X2:$i]:(~(((in @ X2) @ X1)))))) => (~((![X2:$i]:(((in @ X2) @ X1) => (~((![X3:$i]:(((in @ X3) @ X2) => (~(((in @ X3) @ X1))))))))))))),introduced(assumption,[])).
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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))))) => ((![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:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1))) => (X1 = X2))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.41/274.82 thf(h21,assumption,(![X1:$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)))))))))))))))))))),introduced(assumption,[])).
% 275.41/274.82 thf(h22,assumption,(~(((![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))))) => ((![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:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1))) => (X1 = X2))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ 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((![X1:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:((X2 => (~((X5 = X3)))) => 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=> ((subset @ X2) @ ((setminus @ X1) @ ((setminus @ X1) @ X2)))))) => ((![X1:$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) @ 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((~(((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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.41/274.83 thf(h23,assumption,(![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (X1 @ (descr @ X1)))),introduced(assumption,[])).
% 275.41/274.83 thf(h24,assumption,(~(((![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))))) => ((![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:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1))) => (X1 = X2))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X2) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ X1))))) => 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X1) => (((subset @ X2) @ X3) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ X2)))))))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.41/274.83 thf(h25,assumption,(![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((in @ X3) @ ((dsetconstr @ X1) @ X2))))))),introduced(assumption,[])).
% 275.41/274.83 thf(h26,assumption,(~(((![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ ((dsetconstr @ X1) @ X2)) => ((in @ X3) @ X1))))) => ((![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:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1))) => (X1 = X2))))) => ((![X1:$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:$i]:(((in @ X3) @ 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((![X1:$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>$o]:((subset @ 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(![X4:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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 @ 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((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.41/274.83 thf(h27,assumption,(![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ ((dsetconstr @ X1) @ X2)) => ((in @ X3) @ X1))))),introduced(assumption,[])).
% 275.41/274.83 thf(h28,assumption,(~(((![X1:$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))))) => ((![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:$i]:(((in @ X3) @ ((binintersect @ X1) @ X2)) => ((in @ X3) @ 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=> (![X3:$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) @ 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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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.41/274.83 thf(h29,assumption,(![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ ((dsetconstr @ X1) @ X2)) => (X2 @ X3))))),introduced(assumption,[])).
% 275.41/274.83 thf(h30,assumption,(~(((![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:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1))) => (X1 = X2))))) => ((![X1:$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 @ 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((![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:$i]:((((setadjoin @ X1) @ 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((![X1:$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 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((![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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:((X2 => (~((X5 = 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((![X1:$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)))))))) => 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(![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:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.41/274.84 thf(h31,assumption,(![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))))),introduced(assumption,[])).
% 275.41/274.84 thf(h32,assumption,(~(((![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:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1))) => (X1 = X2))))) => ((![X1:$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) @ 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(![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:$i]:((~(((in @ X3) @ X1))) => ((~(((in 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((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ ((setminus @ X1) @ X3)) @ ((setminus 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((![X1:$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) @ 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((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:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus 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X2)))))))) => ((![X1:$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) @ 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@ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.41/274.84 thf(h33,assumption,(![X1:$o]:(![X2:$i]:(((in @ X2) @ (prop2set @ X1)) => X1))),introduced(assumption,[])).
% 275.41/274.84 thf(h34,assumption,(~(((![X1:$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))))) => ((![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 = 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((![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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.41/274.84 thf(h35,assumption,(![X1:$i]:(((in @ X1) @ emptyset) => (![X2:$o]:X2))),introduced(assumption,[])).
% 275.41/274.84 thf(h36,assumption,(~(((![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:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1))) => (X1 = X2))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.44/274.85 thf(h37,assumption,(~(((![X1:$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:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1))) => (X1 = X2))))) => ((![X1:$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))))))) => 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((![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:$i]:((iskpair @ X1) => 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((![X1:$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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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 @ 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((![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => 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(powerset @ X1)) => (![X3:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.44/274.85 thf(h39,assumption,(![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (~((![X2:$i]:(~((X1 @ X2)))))))),introduced(assumption,[])).
% 275.44/274.85 thf(h40,assumption,(~(((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1))) => (X1 = X2))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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))))))) => ((![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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.44/274.86 thf(h41,assumption,(![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1))) => (X1 = X2))))),introduced(assumption,[])).
% 275.44/274.86 thf(h42,assumption,(~(((![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 @ 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=> (~((![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:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ 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@ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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:$i]:(((in @ X4) @ X1) => (singleton @ 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(((ap @ X1) @ X2) @ X3)) = X3))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.44/274.86 thf(h43,assumption,(![X1:$i]:((![X2:$i]:(~(((in @ X2) @ X1)))) => (X1 = emptyset))),introduced(assumption,[])).
% 275.44/274.86 thf(h44,assumption,(~(((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ X1) => (((in @ 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=> ((subset @ ((setminus @ X1) @ ((setminus @ X1) @ X2))) @ X2)))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ 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X3) @ X4))))))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => 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(~((![X2:$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:$i]:((X3 = X4) => (((setadjoin @ X1) @ X3) = ((setadjoin @ 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=> ((subset @ X2) @ X1)))) => ((![X1:$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:$i]:(iskpair @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ 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(![X4:$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) @ 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@ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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:$i]:((((func @ 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((![X1:$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:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.44/274.87 thf(h46,assumption,(![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ ((dsetconstr @ X1) @ X2)) = (X2 @ X3)))))),introduced(assumption,[])).
% 275.44/274.87 thf(h47,assumption,(~(((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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:$i]:(((in @ X5) @ X1) => (((((ap @ 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=> (![X3:$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)) => 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((![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:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ 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(![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ 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@ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.44/274.87 thf(h48,assumption,(![X1:$i]:((~((X1 = emptyset))) => (~((![X2:$i]:(~(((in @ X2) @ X1)))))))),introduced(assumption,[])).
% 275.44/274.87 thf(h49,assumption,(~(((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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 @ 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((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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) @ 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((![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 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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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.44/274.87 thf(h50,assumption,(![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => (~((((dsetconstr @ X1) @ X2) = emptyset)))))))),introduced(assumption,[])).
% 275.44/274.87 thf(h51,assumption,(~(((![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))) => 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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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.44/274.88 thf(h52,assumption,(![X1:$i]:((~((![X2:$i]:(~(((in @ X2) @ X1)))))) => (~((X1 = emptyset))))),introduced(assumption,[])).
% 275.44/274.88 thf(h53,assumption,(~(((![X1:$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) @ 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((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) 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((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => 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@ X1)) => (![X3:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.44/274.88 thf(h54,assumption,(![X1:$i]:(![X2:$i]:((in @ X1) @ ((setadjoin @ X1) @ X2)))),introduced(assumption,[])).
% 275.44/274.88 thf(h55,assumption,(~((((in @ emptyset) @ ((setadjoin @ emptyset) @ emptyset)) => ((![X1:$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 @ 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((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:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.44/274.88 thf(h56,assumption,((in @ emptyset) @ ((setadjoin @ emptyset) @ emptyset)),introduced(assumption,[])).
% 275.44/274.88 thf(h57,assumption,(~(((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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) @ 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((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.44/274.89 thf(h58,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ ((setadjoin @ X1) @ X2)))))),introduced(assumption,[])).
% 275.44/274.89 thf(h59,assumption,(~(((![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:$i]:(((in @ 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X1) => (singleton @ ((dsetconstr @ X2) @ (^[X6:$i]:(~((((X3 @ X5) @ X6) => (~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.44/274.89 thf(h60,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ X2)) => (![X4:$o]:(((X3 = X1) => X4) => ((((in @ X3) @ X2) => X4) => X4))))))),introduced(assumption,[])).
% 275.44/274.89 thf(h61,assumption,(~(((![X1:$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:$i]:((X1 @ X2) => 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((X5 = X6) => ((X3 @ X5) = (X4 @ X6))))))) => (((dsetconstr @ X1) @ X3) = ((dsetconstr @ X2) @ X4)))))))) => ((![X1:$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) @ 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((![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))) 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((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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.44/274.89 thf(h62,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ X2)) => ((~((X3 = X1))) => ((in @ X3) @ X2)))))),introduced(assumption,[])).
% 275.44/274.89 thf(h63,assumption,(~(((![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) => 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((![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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))))))) => ((![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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.44/274.89 thf(h64,assumption,(![X1:$i]:(((dsetconstr @ X1) @ (^[X2:$i]:(~($false)))) = X1)),introduced(assumption,[])).
% 275.44/274.89 thf(h65,assumption,(~(((![X1:$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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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))))))) => ((![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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=> ((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 @ 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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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.44/274.89 thf(h66,assumption,(![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1))) => ((in @ X2) @ (powerset @ X1))))),introduced(assumption,[])).
% 275.44/274.89 thf(h67,assumption,(~(((![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:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))) => 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X1) @ X2)))))) => ((![X1:$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) @ 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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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.44/274.90 thf(h68,assumption,(![X1:$i]:((in @ emptyset) @ (powerset @ X1))),introduced(assumption,[])).
% 275.44/274.90 thf(h69,assumption,(~(((![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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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 @ 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=> (![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:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ X3) => ((subset @ ((setminus @ X1) @ X3)) @ ((setminus @ X1) @ 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X1)) => (![X4:$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) @ ((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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.44/274.90 thf(h70,assumption,(~(((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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 @ 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((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.44/274.90 thf(h71,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X2) @ (powerset @ X1)) => (((in @ X3) @ X2) => ((in @ X3) @ X1)))))),introduced(assumption,[])).
% 275.44/274.90 thf(h72,assumption,(~(((![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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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) @ 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((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 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((![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:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ 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X2)))))))) => ((![X1:$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) @ 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@ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.44/274.91 thf(h73,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X2) @ X3) => (((in @ X3) @ X1) => ((in @ X2) @ (setunion @ X1))))))),introduced(assumption,[])).
% 275.44/274.91 thf(h74,assumption,(~(((![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:$i]:((X3 = X4) => (((in @ 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X3) @ X1)))))))) => ((![X1:$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:$i]:((~(((in @ X3) @ X1))) => (~(((in @ X3) @ ((setminus @ X1) @ 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@ X2) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))) => ((![X1:$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:$i]:((X1 = 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((![X1:$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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => 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((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.44/274.91 thf(h75,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) => (![X3:$o]:((![X4:$i]:(((in @ X2) @ X4) => (((in @ X4) @ X1) => X3))) => X3))))),introduced(assumption,[])).
% 275.44/274.91 thf(h76,assumption,(~(((![X1:$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:$i]:((X1 = X2) => (((setadjoin @ ((setadjoin @ X1) @ 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(![X4:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in 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((![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 @ 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((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:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.44/274.91 thf(h77,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ X1) => ((in @ X2) @ (powerset @ (setunion @ X1)))))),introduced(assumption,[])).
% 275.44/274.91 thf(h78,assumption,(~(((![X1:$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:$i]:((in @ X1) @ (setunion @ 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((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.44/274.92 thf(h79,assumption,(![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (~((![X2:$i]:(~((![X3:$i]:((X1 @ X3) = (X3 = X2)))))))))),introduced(assumption,[])).
% 275.44/274.92 thf(h80,assumption,(~(((![X1:$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 @ 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@ 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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.44/274.92 thf(h81,assumption,(~(((![X1:$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 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(![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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 @ 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((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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.44/274.92 thf(h82,assumption,(![X1:$i]:(![X2:$i]:(((in @ X1) @ ((setadjoin @ X2) @ emptyset)) => (X1 = X2)))),introduced(assumption,[])).
% 275.44/274.92 thf(h83,assumption,(~(((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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))))))) => ((![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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=> ((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 @ 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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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.44/274.93 thf(h84,assumption,(![X1:$i]:(![X2:$i]:((~((X1 = X2))) => (~(((in @ X2) @ ((setadjoin @ X1) @ emptyset))))))),introduced(assumption,[])).
% 275.44/274.93 thf(h85,assumption,(~(((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((in @ X4) @ X1) => ((in @ 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(((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => (~(((in @ X4) @ X2))))))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.44/274.93 thf(h86,assumption,(![X1:$i]:(![X2:$i]:((X1 = X2) => ((in @ X1) @ ((setadjoin @ X2) @ emptyset))))),introduced(assumption,[])).
% 275.44/274.93 thf(h87,assumption,(~(((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => 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X1)) => (![X4:$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) @ ((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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.52/274.93 thf(h88,assumption,(![X1:$i]:(![X2:$i]:(((in @ X1) @ ((setadjoin @ X2) @ emptyset)) => ((in @ X2) @ ((setadjoin @ X1) @ emptyset))))),introduced(assumption,[])).
% 275.52/274.93 thf(h89,assumption,(~(((![X1:$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 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@ 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:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ 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@ X2)) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))) => ((![X1:$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:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.52/274.94 thf(h90,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) => ((~((X3 = X1))) => (X3 = X2)))))),introduced(assumption,[])).
% 275.52/274.94 thf(h91,assumption,(~(((![X1:$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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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))))) => 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(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:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.52/274.94 thf(h92,assumption,(![X1:$i]:(![X2:$i]:((in @ X1) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))),introduced(assumption,[])).
% 275.52/274.94 thf(h93,assumption,(~(((![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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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) => 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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) @ ((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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.52/274.94 thf(h94,assumption,(![X1:$i]:(![X2:$i]:((in @ X2) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))),introduced(assumption,[])).
% 275.52/274.94 thf(h95,assumption,(~(((![X1:$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) => 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(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) @ ((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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.52/274.94 thf(h96,assumption,(![X1:$i]:(![X2:$i>$o]:((~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))))) => (~((((dsetconstr @ X1) @ X2) = emptyset)))))),introduced(assumption,[])).
% 275.52/274.94 thf(h97,assumption,(~(((![X1:$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:$i]:((ksnd @ ((kpair @ X1) @ 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((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => 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=> (![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:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.52/274.94 thf(h98,assumption,(![X1:$i>$o]:(![X2:$i]:(((in @ X2) @ emptyset) => (X1 @ X2)))),introduced(assumption,[])).
% 275.52/274.94 thf(h99,assumption,(~(((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.52/274.95 thf(h100,assumption,(![X1:$i]:(![X2:$i>$o]:((~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3))))) => (~((![X3:$i]:(((in @ X3) @ X1) => (X2 @ X3)))))))),introduced(assumption,[])).
% 275.52/274.95 thf(h101,assumption,(~(((![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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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 @ 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(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:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.52/274.95 thf(h102,assumption,(![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3))))) => (![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))),introduced(assumption,[])).
% 275.52/274.95 thf(h103,assumption,(~(((![X1:$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]:((subset @ 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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) @ 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% 275.52/274.95 thf(h104,assumption,(~(((![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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((in @ X4) @ 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(![X4:$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)))))))) => ((![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:$i]:(((in @ X5) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ ((binunion @ X2) @ X3)) @ ((binunion @ X4) @ X5))) = ((binunion @ ((binintersect @ ((setminus @ X1) @ 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(![X4:$i]:(((in @ X4) @ X2) => (X3 @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ 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@ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.52/274.96 thf(h105,assumption,(~(((![X1:$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)) = 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@ 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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ 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((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.52/274.96 thf(h106,assumption,(![X1:$o]:(X1 => ((in @ emptyset) @ (prop2set @ X1)))),introduced(assumption,[])).
% 275.52/274.96 thf(h107,assumption,(~(((![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) @ 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(![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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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))))))))) => 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((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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.52/274.96 thf(h108,assumption,(![X1:$o]:(X1 => (set2prop @ (prop2set @ X1)))),introduced(assumption,[])).
% 275.52/274.96 thf(h109,assumption,(~(((![X1:$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)))))) => 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((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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 @ 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(~((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.52/274.97 thf(h110,assumption,(~(((![X1:$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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))) => 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(![X4:$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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.52/274.97 thf(h111,assumption,(~(((![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))))) => 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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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.52/274.97 thf(h112,assumption,(~(((![X1:$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:$i]:((in @ X2) @ (setunion @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ 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@ X3)))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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:$i]:(((in @ X4) @ X1) => (singleton @ 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=> ((![X1:$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 @ 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@ ((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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.52/274.97 thf(h113,assumption,(![X1:$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)))))))))))),introduced(assumption,[])).
% 275.52/274.97 thf(h114,assumption,(~(((![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:$i]:(((subset @ X1) @ X3) => ((subset @ X1) @ 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X2)))))) => ((![X1:$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:$i]:(iskpair @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ 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((![X1:$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:$i]:(((in @ X3) @ X1) => 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((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.52/274.97 thf(h115,assumption,(![X1:$i>$o]:((~((![X2:$i]:(~((![X3:$i]:((X1 @ X3) = (X3 = X2)))))))) => (~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))))),introduced(assumption,[])).
% 275.52/274.97 thf(h116,assumption,(~(((![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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:((X2 => (~((X5 = 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((![X1:$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)) => 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((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.59/274.98 thf(h117,assumption,(![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((in @ X3) @ X1) => ((in @ X4) @ X2)))))))),introduced(assumption,[])).
% 275.59/274.98 thf(h118,assumption,(~(((![X1:$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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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) => 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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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.59/274.98 thf(h119,assumption,(![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((in @ X3) @ X1) = ((in @ X4) @ X2)))))))),introduced(assumption,[])).
% 275.59/274.98 thf(h120,assumption,(~(((![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:$i]:((X1 = 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@ X2)) => ((![X5:$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:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => 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((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.59/274.98 thf(h121,assumption,(![X1:$i>$o]:((~((![X2:$i]:((X1 @ X2) => (~((![X3:$i]:((X1 @ X3) => (X2 = X3))))))))) => (![X2:$i]:(![X3:$i]:((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))))),introduced(assumption,[])).
% 275.59/274.98 thf(h122,assumption,(~(((![X1:$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 @ 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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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ 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((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => ((![X1:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.59/274.99 thf(h123,assumption,(![X1:$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:$i]:((X2 @ X4) => (X3 = X4))))))))))))),introduced(assumption,[])).
% 275.59/274.99 thf(h124,assumption,(~(((emptyset = emptyset) => ((![X1:$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:$i]:(((in @ 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((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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 @ 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((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.59/274.99 thf(h125,assumption,(emptyset = emptyset),introduced(assumption,[])).
% 275.59/274.99 thf(h126,assumption,(~(((![X1:$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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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))))))) => ((![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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.59/274.99 thf(h127,assumption,(![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((setadjoin @ X1) @ X3) = ((setadjoin @ X2) @ X4)))))))),introduced(assumption,[])).
% 275.59/274.99 thf(h128,assumption,(~(((![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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.59/274.99 thf(h129,assumption,(![X1:$i]:(![X2:$i]:((X1 = X2) => ((powerset @ X1) = (powerset @ X2))))),introduced(assumption,[])).
% 275.59/274.99 thf(h130,assumption,(~(((![X1:$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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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:$i]:(((in @ X4) @ 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((setminus @ X1) @ X3)) => (![X4:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.59/275.00 thf(h131,assumption,(![X1:$i]:(![X2:$i]:((X1 = X2) => ((setunion @ X1) = (setunion @ X2))))),introduced(assumption,[])).
% 275.59/275.00 thf(h132,assumption,(~(((omega = omega) => ((![X1:$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:$i]:(((in @ X3) @ ((binintersect @ X1) @ X2)) => ((in @ X3) @ 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=> (![X3:$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) @ 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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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.59/275.00 thf(h133,assumption,(omega = omega),introduced(assumption,[])).
% 275.59/275.00 thf(h134,assumption,(~(((![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:$i]:(((in @ X2) @ X1) => ((subset @ 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(![X4:$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 @ 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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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.59/275.00 thf(h135,assumption,(~(((![X1:$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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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 @ 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((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 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((![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:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ 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((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.59/275.01 thf(h136,assumption,(![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))))))),introduced(assumption,[])).
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((![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)))))))) => 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((![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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ 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((![X1:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => 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@ (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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.59/275.01 thf(h138,assumption,(![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i>$o]:(![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => ((X5 = X6) => ((X3 @ X5) = (X4 @ X6))))))) => (((dsetconstr @ X1) @ X3) = ((dsetconstr @ X2) @ X4)))))))),introduced(assumption,[])).
% 275.59/275.01 thf(h139,assumption,(~(((![X1:$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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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:$i]:((=) @ (X3 @ X4))))))))) => 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=> ((![X1:$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 @ 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@ ((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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.59/275.01 thf(h140,assumption,(![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((subset @ X1) @ X2)))),introduced(assumption,[])).
% 275.59/275.01 thf(h141,assumption,(~(((![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 @ 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(![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) 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((![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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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) 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((![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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))))))) => ((![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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.59/275.01 thf(h142,assumption,(![X1:$i]:(![X2:$i]:((X1 = X2) => ((subset @ X2) @ X1)))),introduced(assumption,[])).
% 275.59/275.01 thf(h143,assumption,(~(((![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:$i]:(((in @ X5) @ X2) => (~((X3 = ((kpair @ X4) @ X5)))))))))))))) => 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((![X1:$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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.59/275.01 thf(h144,assumption,(![X1:$i]:(![X2:$i]:((X1 = X2) => ((subset @ X1) @ X2)))),introduced(assumption,[])).
% 275.59/275.01 thf(h145,assumption,(~(((![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:$i]:((((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = 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X4)))))))))))) => ((![X1:$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:$i]:(((in @ X4) @ X1) => 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((![X1:$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 @ 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((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.59/275.02 thf(h146,assumption,(~((((!!) @ (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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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 @ 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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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.59/275.02 thf(h147,assumption,((!!) @ (subset @ emptyset)),introduced(assumption,[])).
% 275.59/275.02 thf(h148,assumption,(~(((![X1:$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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ 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((![X1:$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:$i]:(((in 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((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => 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((![X1:$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 @ 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@ 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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.59/275.02 thf(h149,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X2) => (((in @ X3) @ X1) => ((in @ X3) @ X2)))))),introduced(assumption,[])).
% 275.59/275.02 thf(h150,assumption,(~(((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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 @ 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((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 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((![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:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ 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(powerset @ X1)) => (![X3:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.59/275.02 thf(h151,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X2) => ((~(((in @ X3) @ X2))) => (~(((in @ X3) @ X1)))))))),introduced(assumption,[])).
% 275.59/275.02 thf(h152,assumption,(~(((![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)))))) => 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((![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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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)))))))) => 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((![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) @ 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(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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.59/275.03 thf(h153,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => (~(((subset @ X1) @ X2)))))))),introduced(assumption,[])).
% 275.59/275.03 thf(h154,assumption,(~(((![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:$i]:((((kpair @ 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@ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X4) @ X1) => ((~(X2)) => ((in @ X4) @ 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((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binunion @ X2) @ X3)) @ (powerset @ 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=> (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.59/275.03 thf(h155,assumption,(![X1:$i]:(![X2:$i]:((~(((subset @ X1) @ X2))) => (~((X1 = X2)))))),introduced(assumption,[])).
% 275.59/275.03 thf(h156,assumption,(~(((![X1:$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:$i]:(((in @ 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X2) @ X3) @ X4)) @ X1))))))) => ((![X1:$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)))))))) => ((![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) @ 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((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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.59/275.03 thf(h157,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => (~((X1 = X2)))))))),introduced(assumption,[])).
% 275.59/275.03 thf(h158,assumption,(~(((![X1:$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) @ 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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 @ 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) @ ((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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.59/275.04 thf(h159,assumption,(![X1:$i]:((subset @ X1) @ X1)),introduced(assumption,[])).
% 275.59/275.04 thf(h160,assumption,(~(((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => 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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) @ 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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.59/275.04 thf(h161,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X2) => (((subset @ X2) @ X3) => ((subset @ X1) @ X3)))))),introduced(assumption,[])).
% 275.59/275.04 thf(h162,assumption,(~(((![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:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ 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((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.59/275.04 thf(h163,assumption,(![X1:$i]:(![X2:$i]:((subset @ X2) @ ((setadjoin @ X1) @ X2)))),introduced(assumption,[])).
% 275.59/275.04 thf(h164,assumption,(~(((![X1:$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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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))))))) => ((![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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.59/275.04 thf(h165,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X1) @ X3) => ((subset @ X1) @ ((setadjoin @ X2) @ X3)))))),introduced(assumption,[])).
% 275.59/275.04 thf(h166,assumption,(~(((![X1:$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:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => ((X3 = X4) => (X2 = X4))))))) => 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X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))) => ((![X1:$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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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:$i]:((((func @ 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((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.65/275.04 thf(h167,assumption,(![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => ((in @ X1) @ (powerset @ X2))))),introduced(assumption,[])).
% 275.65/275.04 thf(h168,assumption,(~(((![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 @ 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((![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:$i]:(((in @ X3) @ 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@ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X1 = X3)))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((in @ X4) @ 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(![X4:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.65/275.05 thf(h169,assumption,(![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((subset @ X2) @ X1) => (X1 = X2))))),introduced(assumption,[])).
% 275.65/275.05 thf(h170,assumption,(~(((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:((X2 => (~((X5 = 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((![X1:$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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.65/275.05 thf(h171,assumption,(![X1:$i]:(((subset @ X1) @ emptyset) => (X1 = emptyset))),introduced(assumption,[])).
% 275.65/275.05 thf(h172,assumption,(~(((![X1:$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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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))))))) => ((![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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.65/275.05 thf(h173,assumption,(![X1:$i]:(![X2:$i]:(((subset @ X2) @ X1) => ((in @ X2) @ (powerset @ X1))))),introduced(assumption,[])).
% 275.65/275.05 thf(h174,assumption,(~(((![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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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) @ 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((((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:$i]:(((in @ X3) @ X1) => 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((subset @ X2) @ X3))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ ((setminus @ X1) @ X3)) @ ((setminus 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((binunion @ X3) @ X4)))))))))))) => ((![X1:$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 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((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.65/275.05 thf(h175,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ X2) @ X1)))),introduced(assumption,[])).
% 275.65/275.05 thf(h176,assumption,(~(((![X1:$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:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X2 = X4)))))) => 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((![X1:$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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))) => 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((![X1:$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:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X1) @ 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(powerset @ X1)) => (![X3:$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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.65/275.06 thf(h177,assumption,(![X1:$i]:((in @ X1) @ (powerset @ X1))),introduced(assumption,[])).
% 275.65/275.06 thf(h178,assumption,(~(((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.65/275.06 thf(h179,assumption,(![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => ((subset @ (powerset @ X1)) @ (powerset @ X2))))),introduced(assumption,[])).
% 275.65/275.06 thf(h180,assumption,(~(((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)) => (((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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.67/275.06 thf(h181,assumption,(![X1:$i]:(![X2:$i>$o]:((in @ ((dsetconstr @ X1) @ X2)) @ (powerset @ X1)))),introduced(assumption,[])).
% 275.67/275.06 thf(h182,assumption,(~(((![X1:$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 @ 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((![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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) => 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@ 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) @ ((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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.67/275.06 thf(h183,assumption,(![X1:$i]:(![X2:$i>$o]:((subset @ ((dsetconstr @ X1) @ X2)) @ X1))),introduced(assumption,[])).
% 275.67/275.06 thf(h184,assumption,(~(((![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:$i]:((ksnd @ ((kpair @ X1) @ 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(![X5:$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) => 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=> (![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:$i]:(((in @ X3) @ X1) => (((in @ X3) @ ((setminus @ X1) @ ((setminus @ 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X1) => (((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))) => ((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.67/275.07 thf(h185,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ ((binunion @ X1) @ X2)))))),introduced(assumption,[])).
% 275.67/275.07 thf(h186,assumption,(~(((![X1:$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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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))))))) => ((![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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.67/275.07 thf(h187,assumption,(~(((![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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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 @ 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=> ((![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:$i]:(((in @ X2) @ (powerset @ X1)) => ((in @ ((setminus @ 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@ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => ((![X1:$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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.67/275.07 thf(h188,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ ((binunion @ X1) @ X2)))))),introduced(assumption,[])).
% 275.67/275.07 thf(h189,assumption,(~(((![X1:$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:$i]:(iskpair @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ 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((![X1:$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:$i]:(((in @ X3) @ X1) => 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@ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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 @ 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((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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:$i]:(((in @ X3) @ 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((![X1:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.67/275.08 thf(h190,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$o]:(((in @ X3) @ ((binunion @ X1) @ X2)) => ((((in @ X3) @ X1) => X4) => ((((in @ X3) @ X2) => X4) => X4))))))),introduced(assumption,[])).
% 275.67/275.08 thf(h191,assumption,(~(((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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 @ 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((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.67/275.08 thf(h192,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((binunion @ X1) @ X2)) => ((~(((in @ X3) @ X1))) => ((in @ X3) @ X2)))))),introduced(assumption,[])).
% 275.67/275.08 thf(h193,assumption,(~(((![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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((in @ X4) @ X1) => 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X2)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.67/275.08 thf(h194,assumption,(![X1:$i]:(![X2:$i]:((subset @ X1) @ ((binunion @ X1) @ X2)))),introduced(assumption,[])).
% 275.67/275.08 thf(h195,assumption,(~(((![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:$i]:(((in @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin 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((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) 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((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.67/275.08 thf(h196,assumption,(![X1:$i]:(![X2:$i]:((subset @ X2) @ ((binunion @ X1) @ X2)))),introduced(assumption,[])).
% 275.67/275.08 thf(h197,assumption,(~(((![X1:$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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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:$i]:(((in @ X3) @ 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(![X4:$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) @ ((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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.67/275.09 thf(h198,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => ((in @ X3) @ ((binintersect @ X1) @ X2))))))),introduced(assumption,[])).
% 275.67/275.09 thf(h199,assumption,(~(((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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))))))) => ((![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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.67/275.09 thf(h200,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X3) @ X1) => (((subset @ X3) @ X2) => ((subset @ X3) @ ((binintersect @ X1) @ X2))))))),introduced(assumption,[])).
% 275.67/275.09 thf(h201,assumption,(~(((![X1:$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:$i]:(X1 = ((kpair @ 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(kfst @ X3)) @ (ksnd @ X3)) = X3))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => 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(![X5:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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 @ 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=> (![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) => 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@ (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:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.67/275.09 thf(h202,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((binintersect @ X1) @ X2)) => ((in @ X3) @ X1))))),introduced(assumption,[])).
% 275.67/275.09 thf(h203,assumption,(~(((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X2) @ X3)) @ (powerset @ 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((in @ X4) @ X3)))))))))) => ((![X1:$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) @ 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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:$i]:(((in @ X4) @ 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((~(((in @ X4) @ X2))) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ ((binunion @ X2) @ X3))))))))))))) => ((![X1:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.67/275.09 thf(h204,assumption,(![X1:$i]:(![X2:$i]:((subset @ ((binintersect @ X1) @ X2)) @ X1))),introduced(assumption,[])).
% 275.67/275.09 thf(h205,assumption,(~(((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.67/275.09 thf(h206,assumption,(![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((binintersect @ X1) @ X2) = X1)))),introduced(assumption,[])).
% 275.67/275.09 thf(h207,assumption,(~(((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.67/275.10 thf(h208,assumption,(![X1:$i]:(![X2:$i]:((((binintersect @ X1) @ X2) = X2) => ((subset @ X2) @ X1)))),introduced(assumption,[])).
% 275.67/275.10 thf(h209,assumption,(~(((![X1:$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:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => ((X3 = X4) => (X2 = X4))))))) => 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@ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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 @ 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((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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)) @ 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((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.67/275.10 thf(h210,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((binintersect @ X1) @ X2)) => ((in @ X3) @ X2))))),introduced(assumption,[])).
% 275.67/275.10 thf(h211,assumption,(~(((![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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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 @ 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((![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:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ X3) => ((subset @ ((setminus @ X1) @ X3)) @ ((setminus @ X1) @ 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((![X1:$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 @ 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@ 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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.67/275.10 thf(h212,assumption,(![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => (~(((in @ X3) @ X2))))) => (((binintersect @ X1) @ X2) = emptyset)))),introduced(assumption,[])).
% 275.67/275.10 thf(h213,assumption,(~(((![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:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ 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(powerset @ X1)) => ((![X4:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.67/275.10 thf(h214,assumption,(![X1:$i]:(![X2:$i]:((subset @ ((binintersect @ X1) @ X2)) @ X2))),introduced(assumption,[])).
% 275.67/275.10 thf(h215,assumption,(~(((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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) @ 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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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.67/275.11 thf(h216,assumption,(![X1:$i]:(![X2:$i]:(((subset @ X2) @ X1) => (((binintersect @ X1) @ X2) = X2)))),introduced(assumption,[])).
% 275.67/275.11 thf(h217,assumption,(~(((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ 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((![X1:$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:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X1) @ 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(powerset @ X1)) => (![X3:$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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.67/275.11 thf(h218,assumption,(![X1:$i]:(![X2:$i]:((((binintersect @ X1) @ X2) = X1) => ((subset @ X1) @ X2)))),introduced(assumption,[])).
% 275.67/275.11 thf(h219,assumption,(~(((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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))))))) => ((![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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.67/275.11 thf(h220,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((binintersect @ X1) @ ((binunion @ X2) @ X3)) = ((binunion @ ((binintersect @ X1) @ X2)) @ ((binintersect @ X1) @ X3)))))),introduced(assumption,[])).
% 275.67/275.11 thf(h221,assumption,(~(((![X1:$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:$i]:(X1 = ((kpair @ 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(kfst @ X3)) @ (ksnd @ X3)) = X3))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:((singleton @ X1) => 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@ (powerset @ X1)) => (![X4:$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) @ ((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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.67/275.11 thf(h222,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => ((in @ X3) @ ((setminus @ X1) @ X2))))))),introduced(assumption,[])).
% 275.67/275.11 thf(h223,assumption,(~(((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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))))))) => ((![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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.73/275.12 thf(h224,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setminus @ X1) @ X2)) => ((in @ X3) @ X1))))),introduced(assumption,[])).
% 275.73/275.12 thf(h225,assumption,(~(((![X1:$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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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:$i]:(((in @ X4) @ X1) => (singleton @ 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(powerset @ X1)) => (![X4:$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) @ ((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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.73/275.12 thf(h226,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setminus @ X1) @ X2)) => (~(((in @ X3) @ X2))))))),introduced(assumption,[])).
% 275.73/275.12 thf(h227,assumption,(~(((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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))))))) => ((![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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.73/275.12 thf(h228,assumption,(![X1:$i]:(![X2:$i]:(((subset @ X1) @ X2) => (((setminus @ X1) @ X2) = emptyset)))),introduced(assumption,[])).
% 275.73/275.12 thf(h229,assumption,(~(((![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>$o]:((subset @ 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((setminus @ X1) @ X3)) => (![X4:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.73/275.12 thf(h230,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ ((setminus @ X1) @ X2)))) => (((in @ X3) @ X1) => ((in @ X3) @ X2)))))),introduced(assumption,[])).
% 275.73/275.12 thf(h231,assumption,(~(((![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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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 @ 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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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.73/275.13 thf(h232,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ ((setminus @ X1) @ X2)))) => ((~(((in @ X3) @ X2))) => (~(((in @ X3) @ X1)))))))),introduced(assumption,[])).
% 275.73/275.13 thf(h233,assumption,(~(((![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:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = 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@ X4)))))))) => ((![X1:$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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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) @ 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((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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.73/275.13 thf(h234,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))),introduced(assumption,[])).
% 275.73/275.13 thf(h235,assumption,(~(((![X1:$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)) = 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@ 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 = 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((![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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.73/275.13 thf(h236,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X2) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))),introduced(assumption,[])).
% 275.73/275.13 thf(h237,assumption,(~(((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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)) => 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=> (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in 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((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))) => ((![X1:$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:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.73/275.13 thf(h238,assumption,(![X1:$i]:(![X2:$i]:((subset @ ((setminus @ X1) @ X2)) @ X1))),introduced(assumption,[])).
% 275.73/275.13 thf(h239,assumption,(~(((![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:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4))))))) => 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((![X1:$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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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 @ 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((![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => 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((![X1:$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) @ 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((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.73/275.14 thf(h240,assumption,(![X1:$i]:(![X2:$i]:((((setminus @ X1) @ X2) = emptyset) => ((subset @ X1) @ X2)))),introduced(assumption,[])).
% 275.73/275.14 thf(h241,assumption,(~(((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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))))))) => 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@ 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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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 @ 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(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) => 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(![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.73/275.14 thf(h242,assumption,(![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))))))),introduced(assumption,[])).
% 275.73/275.14 thf(h243,assumption,(~(((![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 @ 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=> (~((![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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.73/275.14 thf(h244,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ X2))) => ((in @ X3) @ ((symdiff @ X1) @ X2))))))),introduced(assumption,[])).
% 275.73/275.14 thf(h245,assumption,(~(((![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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))) => 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@ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$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)))))))))) => 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@ 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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.73/275.14 thf(h246,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => (((in @ X3) @ X2) => ((in @ X3) @ ((symdiff @ X1) @ X2))))))),introduced(assumption,[])).
% 275.73/275.14 thf(h247,assumption,(~(((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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 @ 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=> (![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) @ ((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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.73/275.14 thf(h248,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => (~(((in @ X3) @ ((symdiff @ X1) @ X2))))))))),introduced(assumption,[])).
% 275.73/275.14 thf(h249,assumption,(~(((![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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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) => 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((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 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((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:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus 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((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.73/275.14 thf(h250,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((in @ X3) @ X1))) => ((~(((in @ X3) @ X2))) => (~(((in @ X3) @ ((symdiff @ X1) @ X2))))))))),introduced(assumption,[])).
% 275.73/275.14 thf(h251,assumption,(~(((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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)) @ 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=> ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.15 thf(h252,assumption,(~(((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.15 thf(h253,assumption,(![X1:$i]:(![X2:$i]:((in @ X1) @ (setunion @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)))))),introduced(assumption,[])).
% 275.77/275.15 thf(h254,assumption,(~(((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.15 thf(h255,assumption,(![X1:$i]:(![X2:$i]:((in @ X2) @ (setunion @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)))))),introduced(assumption,[])).
% 275.77/275.15 thf(h256,assumption,(~(((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X2) @ (powerset @ X1)) => ((in @ ((setminus @ 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((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.15 thf(h257,assumption,(![X1:$i]:(![X2:$i]:(iskpair @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))))),introduced(assumption,[])).
% 275.77/275.15 thf(h258,assumption,(~(((![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:$i]:(((in @ ((kpair @ 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@ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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 @ 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((![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) @ ((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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.16 thf(h259,assumption,(![X1:$i]:(![X2:$i]:(iskpair @ ((kpair @ X1) @ X2)))),introduced(assumption,[])).
% 275.77/275.16 thf(h260,assumption,(~(((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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 @ 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((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.16 thf(h261,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ X1) => ((subset @ ((setadjoin @ X2) @ emptyset)) @ X1)))),introduced(assumption,[])).
% 275.77/275.16 thf(h262,assumption,(~(((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((in @ X4) @ 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((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.16 thf(h263,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ X1) => ((in @ ((setadjoin @ X2) @ emptyset)) @ (powerset @ X1))))),introduced(assumption,[])).
% 275.77/275.16 thf(h264,assumption,(~(((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ 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((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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) @ 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((![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) @ ((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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.16 thf(h265,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((in @ ((setadjoin @ X3) @ emptyset)) @ (powerset @ ((binunion @ X1) @ X2))))))),introduced(assumption,[])).
% 275.77/275.16 thf(h266,assumption,(~(((![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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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)))))))) => 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((![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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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)) @ 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((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.17 thf(h268,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((subset @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ ((binunion @ X1) @ X2)))))))),introduced(assumption,[])).
% 275.77/275.17 thf(h269,assumption,(~(((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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) @ 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@ ((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:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.17 thf(h270,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))),introduced(assumption,[])).
% 275.77/275.17 thf(h271,assumption,(~(((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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))))))) => ((![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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.17 thf(h272,assumption,(![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))))))))),introduced(assumption,[])).
% 275.77/275.17 thf(h273,assumption,(~(((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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:$i]:(((in @ X4) @ X1) => 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((![X1:$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:$i]:(((in 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((![X1:$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) @ 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((![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 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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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.17 thf(h274,assumption,(![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)))))))))),introduced(assumption,[])).
% 275.77/275.17 thf(h275,assumption,(~(((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => 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@ (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) @ ((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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.17 thf(h276,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ (powerset @ (powerset @ ((binunion @ X1) @ X2)))))))))),introduced(assumption,[])).
% 275.77/275.17 thf(h277,assumption,(~(((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))) => 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(![X3:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.18 thf(h278,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)))))))),introduced(assumption,[])).
% 275.77/275.18 thf(h279,assumption,(~(((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.18 thf(h280,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (~((X3 = ((kpair @ X4) @ X5)))))))))))))),introduced(assumption,[])).
% 275.77/275.18 thf(h281,assumption,(~(((![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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.18 thf(h282,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (iskpair @ X3))))),introduced(assumption,[])).
% 275.77/275.18 thf(h283,assumption,(~(((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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))))))) => ((![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)))))))) => ((![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:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ 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((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))) => ((![X1:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.18 thf(h284,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) => (~((![X3:$i]:(((in @ X3) @ X1) => (~(((in @ X2) @ X3)))))))))),introduced(assumption,[])).
% 275.77/275.18 thf(h285,assumption,(~(((![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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => 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=> (![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:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ X3) => ((subset @ ((setminus @ X1) @ X3)) @ ((setminus @ X1) @ 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X2) @ (powerset @ X1)) => (![X3:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.19 thf(h286,assumption,(![X1:$i]:((subset @ (setunion @ ((setadjoin @ X1) @ emptyset))) @ X1)),introduced(assumption,[])).
% 275.77/275.19 thf(h287,assumption,(~(((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ 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((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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) @ 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((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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.19 thf(h288,assumption,(![X1:$i]:((subset @ X1) @ (setunion @ ((setadjoin @ X1) @ emptyset)))),introduced(assumption,[])).
% 275.77/275.19 thf(h289,assumption,(~(((![X1:$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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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:$i]:(((in @ X4) @ 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((![X1:$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:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.19 thf(h290,assumption,(![X1:$i]:((setunion @ ((setadjoin @ X1) @ emptyset)) = X1)),introduced(assumption,[])).
% 275.77/275.19 thf(h291,assumption,(~(((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((in @ X3) @ 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(~((![X5:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.19 thf(h292,assumption,(![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)))))),introduced(assumption,[])).
% 275.77/275.19 thf(h293,assumption,(~(((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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))))))) => ((![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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.19 thf(h294,assumption,(![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (~((![X3:$i]:(((in @ X3) @ X1) => (~((X2 @ X3)))))))))),introduced(assumption,[])).
% 275.77/275.19 thf(h295,assumption,(~(((![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 @ 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((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => 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X4) @ X1) => ((~(X2)) => (((dsetconstr @ X1) @ (^[X5:$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:$i]:(((in @ X3) @ X1) => (((in @ X3) @ ((setminus @ X1) @ ((setminus @ 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@ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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) @ ((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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.20 thf(h296,assumption,(![X1:$i]:(![X2:$i>$o]:(![X3:$i]:(((in @ X3) @ X1) => ((X2 @ X3) => ((![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X4) => (X4 = X3)))) => ((ex1 @ X1) @ X2))))))),introduced(assumption,[])).
% 275.77/275.20 thf(h297,assumption,(~(((![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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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 @ 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((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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.20 thf(h298,assumption,(![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))))),introduced(assumption,[])).
% 275.77/275.20 thf(h299,assumption,(~(((![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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((in @ X4) @ 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((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.20 thf(h300,assumption,(![X1:$i]:(![X2:$i]:((((setadjoin @ X1) @ emptyset) = ((setadjoin @ X2) @ emptyset)) => (X1 = X2)))),introduced(assumption,[])).
% 275.77/275.20 thf(h301,assumption,(~(((![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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => 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=> (![X3:$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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.20 thf(h302,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) => (X1 = X3))))),introduced(assumption,[])).
% 275.77/275.20 thf(h303,assumption,(~(((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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 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@ (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) @ ((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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.20 thf(h304,assumption,(![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:((in @ ((setadjoin @ X2) @ emptyset)) @ X1)))))),introduced(assumption,[])).
% 275.77/275.20 thf(h305,assumption,(~(((![X1:$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))))))) => 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@ 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) @ ((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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.20 thf(h306,assumption,(![X1:$i]:((singleton @ X1) => ((in @ (setunion @ X1)) @ X1))),introduced(assumption,[])).
% 275.77/275.20 thf(h307,assumption,(~(((![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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.21 thf(h308,assumption,(![X1:$i]:(![X2:$i]:((kfst @ ((kpair @ X1) @ X2)) = X1))),introduced(assumption,[])).
% 275.77/275.21 thf(h309,assumption,(~(((![X1:$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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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))))))) => ((![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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.21 thf(h310,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (kfst @ X3)) @ X1))))),introduced(assumption,[])).
% 275.77/275.21 thf(h311,assumption,(~(((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.21 thf(h312,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X1 = X3)))))),introduced(assumption,[])).
% 275.77/275.21 thf(h313,assumption,(~(((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.21 thf(h314,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X1 = X3)))))),introduced(assumption,[])).
% 275.77/275.21 thf(h315,assumption,(~(((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X3) @ emptyset))))))))) => 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@ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.21 thf(h316,assumption,(![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X1) @ emptyset))))),introduced(assumption,[])).
% 275.77/275.21 thf(h317,assumption,(~(((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.22 thf(h318,assumption,(![X1:$i]:(![X2:$i]:((X1 = X2) => (((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ emptyset))))),introduced(assumption,[])).
% 275.77/275.22 thf(h319,assumption,(~(((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.22 thf(h320,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => ((X3 = X4) => (X2 = X4))))))),introduced(assumption,[])).
% 275.77/275.22 thf(h321,assumption,(~(((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.22 thf(h322,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:((((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset)) = ((setadjoin @ X3) @ emptyset)) => (X1 = X2))))),introduced(assumption,[])).
% 275.77/275.22 thf(h323,assumption,(~(((![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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.22 thf(h324,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X2 = X4)))))),introduced(assumption,[])).
% 275.77/275.22 thf(h325,assumption,(~(((![X1:$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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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))))))) => ((![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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.22 thf(h326,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X2 = X4)))))),introduced(assumption,[])).
% 275.77/275.22 thf(h327,assumption,(~(((![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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.23 thf(h328,assumption,(![X1:$i]:((iskpair @ X1) => (singleton @ ((dsetconstr @ (setunion @ X1)) @ (^[X2:$i]:(X1 = ((kpair @ (kfst @ X1)) @ X2))))))),introduced(assumption,[])).
% 275.77/275.23 thf(h329,assumption,(~(((![X1:$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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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))))))) => ((![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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.23 thf(h330,assumption,(![X1:$i]:(![X2:$i]:((ksnd @ ((kpair @ X1) @ X2)) = X2))),introduced(assumption,[])).
% 275.77/275.23 thf(h331,assumption,(~(((![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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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)))))) => 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@ ((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:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.23 thf(h332,assumption,(![X1:$i]:((iskpair @ X1) => (((kpair @ (kfst @ X1)) @ (ksnd @ X1)) = X1))),introduced(assumption,[])).
% 275.77/275.23 thf(h333,assumption,(~(((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ 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((![X1:$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:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ 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(powerset @ X1)) => (![X3:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.23 thf(h334,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (ksnd @ X3)) @ X2))))),introduced(assumption,[])).
% 275.77/275.23 thf(h335,assumption,(~(((![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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.23 thf(h336,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))),introduced(assumption,[])).
% 275.77/275.23 thf(h337,assumption,(~(((![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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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) @ 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((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.24 thf(h338,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X4) @ X2)))))),introduced(assumption,[])).
% 275.77/275.24 thf(h339,assumption,(~(((![X1:$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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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) @ 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=> (![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:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ X3) => ((subset @ ((setminus @ X1) @ X3)) @ ((setminus @ X1) @ 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X2) @ (powerset @ X1)) => (![X3:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.24 thf(h340,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => (((kpair @ X3) @ X4) = ((kpair @ X3) @ X4)))))))),introduced(assumption,[])).
% 275.77/275.24 thf(h341,assumption,(~(((![X1:$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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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:$i]:((((func @ X1) @ X2) @ X3) => 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((subset @ X3) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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) @ 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=> (((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:$i]:(((in @ X4) @ X1) => (((in @ 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((setminus @ X1) @ X2)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.24 thf(h342,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))),introduced(assumption,[])).
% 275.77/275.24 thf(h343,assumption,(~(((![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]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.24 thf(h344,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))),introduced(assumption,[])).
% 275.77/275.24 thf(h345,assumption,(~(((![X1:$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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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) @ 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@ 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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.77/275.24 thf(h346,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))),introduced(assumption,[])).
% 275.77/275.24 thf(h347,assumption,(~(((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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) => 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(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:$i]:(((in @ X3) 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((![X1:$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:$i]:(((in @ X5) @ (powerset @ X1)) => (((subset @ X2) @ X4) => (((subset @ X3) @ X5) => ((subset @ ((binintersect @ X2) @ X3)) @ ((binintersect @ X4) @ X5))))))))))))) => 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(~((![X7:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))) => ((![X1:$i]:(![X2:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ 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% 275.88/275.25 thf(h348,assumption,(![X1:$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)))))))))),introduced(assumption,[])).
% 275.88/275.25 thf(h349,assumption,(~(((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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) @ 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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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.88/275.25 thf(h350,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))),introduced(assumption,[])).
% 275.88/275.25 thf(h351,assumption,(~(((![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X2))))) => ((![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:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ 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=> ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))) => ((![X1:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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 = 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((![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)))))))) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ 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=> ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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:$i]:(((in @ X3) @ ((funcSet @ 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X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ 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X3) => ((in @ X4) @ X2)))) => (X2 = X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.88/275.25 thf(h353,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))))),introduced(assumption,[])).
% 275.88/275.25 thf(h354,assumption,(~(((![X1:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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 @ 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((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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.88/275.25 thf(h355,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X4) @ X1))))))),introduced(assumption,[])).
% 275.88/275.25 thf(h356,assumption,(~(((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((in @ 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(~((![X5:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ 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X3))))))))))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.88/275.25 thf(h357,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((in @ X5) @ X2))))))),introduced(assumption,[])).
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@ (powerset @ X1)))))) => ((![X1:$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:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))) => ((in @ X2) @ (powerset @ X3)))))))) => 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@ X1)) => (![X3:$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:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.88/275.25 thf(h359,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i>$i>$o]:(![X4:$i]:(![X5:$i]:(((in @ ((kpair @ X4) @ X5)) @ (((dpsetconstr @ X1) @ X2) @ X3)) => ((X3 @ X4) @ X5))))))),introduced(assumption,[])).
% 275.88/275.25 thf(h360,assumption,(~(((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))) => 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@ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))) => ((![X1:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:((X2 => (~((X5 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@ X1) => (![X4:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X2) @ X3)) @ (powerset 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=> ((subset @ X2) @ ((setminus @ X1) @ ((setminus @ X1) @ X2)))))) => ((![X1:$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) @ 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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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.88/275.25 thf(h361,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3)))))))))),introduced(assumption,[])).
% 275.88/275.25 thf(h362,assumption,(~(((![X1:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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) 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(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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.88/275.26 thf(h363,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ (setunion @ ((dsetconstr @ X2) @ (^[X5:$i]:((in @ ((kpair @ X4) @ X5)) @ X3))))) @ X2))))))),introduced(assumption,[])).
% 275.88/275.26 thf(h364,assumption,(~(((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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))))))) => ((![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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ 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@ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.88/275.26 thf(h365,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))),introduced(assumption,[])).
% 275.88/275.26 thf(h366,assumption,(~(((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => 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(powerset @ X1)) => ((![X4:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.88/275.26 thf(h367,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (((func @ X1) @ X2) @ X3))))),introduced(assumption,[])).
% 275.88/275.26 thf(h368,assumption,(~(((![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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))))))) => ((![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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.88/275.26 thf(h369,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((ap @ X1) @ X2) @ X3) @ X4)) @ X2))))))),introduced(assumption,[])).
% 275.88/275.26 thf(h370,assumption,(~(((![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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:$i]:((X2 => (~((X5 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X3) @ X4))))))))))) => ((![X1:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.88/275.26 thf(h371,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((in @ X3) @ ((funcSet @ X1) @ X2)))))),introduced(assumption,[])).
% 275.88/275.26 thf(h372,assumption,(~(((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:((singleton @ X1) => 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(powerset @ X1)) => (![X3:$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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.88/275.27 thf(h373,assumption,(![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))))))))),introduced(assumption,[])).
% 275.88/275.27 thf(h374,assumption,(~(((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ 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((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.88/275.27 thf(h375,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (((func @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)))))),introduced(assumption,[])).
% 275.88/275.27 thf(h376,assumption,(~(((![X1:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.88/275.27 thf(h377,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((in @ (((lam @ X1) @ X2) @ X3)) @ ((funcSet @ X1) @ X2)))))),introduced(assumption,[])).
% 275.88/275.27 thf(h378,assumption,(~(((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.88/275.27 thf(h379,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i>$o]:((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => (X4 @ ((kpair @ X5) @ X6))))))) => (![X5:$i]:(((in @ X5) @ X3) => (X4 @ X5))))))))),introduced(assumption,[])).
% 275.88/275.27 thf(h380,assumption,(~(((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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))))))) => ((![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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.88/275.27 thf(h381,assumption,(~(((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.88/275.27 thf(h382,assumption,(![X1:$i]:(![X2:$i>$o]:(((ex1 @ X1) @ X2) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((X2 @ X3) => ((X2 @ X4) => (X3 = X4)))))))))),introduced(assumption,[])).
% 275.88/275.27 thf(h383,assumption,(~(((![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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))))))) => ((![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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.88/275.28 thf(h384,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((kpair @ X4) @ ((((ap @ X1) @ X2) @ X3) @ X4))) @ X3))))))),introduced(assumption,[])).
% 275.88/275.28 thf(h385,assumption,(~(((![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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))))))) => ((![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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.88/275.28 thf(h386,assumption,(![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))))))),introduced(assumption,[])).
% 275.88/275.28 thf(h387,assumption,(~(((![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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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))))))) => ((![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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.88/275.28 thf(h388,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))),introduced(assumption,[])).
% 275.88/275.28 thf(h389,assumption,(~(((![X1:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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))))))) => ((![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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.88/275.28 thf(h390,assumption,(![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:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X4) => ((in @ ((kpair @ X5) @ X6)) @ X3))))))))))))),introduced(assumption,[])).
% 275.88/275.28 thf(h391,assumption,(~(((![X1:$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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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) => 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((![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:$i]:(((in @ X2) @ 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((~(((in @ X4) @ X2))) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ ((binunion @ X2) @ X3))))))))))))) => ((![X1:$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 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@ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.88/275.28 thf(h392,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (((in @ ((kpair @ X4) @ X5)) @ X3) => (((((ap @ X1) @ X2) @ X3) @ X4) = X5)))))))))),introduced(assumption,[])).
% 275.88/275.28 thf(h393,assumption,(~(((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((((if @ X1) @ X2) @ X3) @ X4) = 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((![X4:$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:$i]:(((in @ X4) @ X1) => (((subset @ X2) @ X3) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ X2)))))))))))) => 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((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))) => 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(![X5:$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))))))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.88/275.28 thf(h394,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X2) => (((in @ ((kpair @ X5) @ X6)) @ X3) => ((in @ ((kpair @ X5) @ X6)) @ X4)))))) => ((subset @ X3) @ X4)))))))),introduced(assumption,[])).
% 275.88/275.28 thf(h395,assumption,(~(((![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![X5:$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))))))) => ((![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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.88/275.28 thf(h396,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X2)) => (![X4:$i]:(((subset @ X4) @ ((cartprod @ X1) @ X2)) => ((![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))))))))),introduced(assumption,[])).
% 275.88/275.28 thf(h397,assumption,(~(((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.88/275.28 thf(h398,assumption,(![X1:$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)))))))),introduced(assumption,[])).
% 275.88/275.28 thf(h399,assumption,(~(((![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))))))) => ((![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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.88/275.28 thf(h400,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => (![X4:$i]:(((in @ X4) @ ((funcSet @ X1) @ X2)) => ((![X5:$i]:(((in @ X5) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X5) = ((((ap @ X1) @ X2) @ X4) @ X5)))) => (X3 = X4)))))))),introduced(assumption,[])).
% 275.88/275.28 thf(h401,assumption,(~(((![X1:$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))))))) => ((![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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.88/275.29 thf(h402,assumption,(![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)))))))),introduced(assumption,[])).
% 275.88/275.29 thf(h403,assumption,(~(((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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))))))) => 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((![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)) @ 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@ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.88/275.29 thf(h404,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ X3) @ X4) = ((((ap @ X1) @ X2) @ X3) @ X4)))))))),introduced(assumption,[])).
% 275.88/275.29 thf(h405,assumption,(~(((![X1:$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:$i]:((X2 => 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(((in @ X5) @ ((binunion @ X2) @ X3)) => ((((in @ X5) @ X2) => X4) => ((((in @ X5) @ X3) => X4) => X4))))))))))) => ((![X1:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.88/275.29 thf(h406,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => (![X4:$i]:(((in @ X4) @ X1) => (((((ap @ X1) @ X2) @ (((lam @ X1) @ X2) @ X3)) @ X4) = (X3 @ X4)))))))),introduced(assumption,[])).
% 275.88/275.29 thf(h407,assumption,(~(((![X1:$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))))))) => ((![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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.88/275.29 thf(h408,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:((((func @ X1) @ X2) @ X3) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))),introduced(assumption,[])).
% 275.88/275.29 thf(h409,assumption,(~(((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.29 thf(h410,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i]:(((in @ X4) @ X1) => ((in @ (X3 @ X4)) @ X2))) => ((((lam @ X1) @ X2) @ X3) = (((lam @ X1) @ X2) @ X3)))))),introduced(assumption,[])).
% 275.93/275.29 thf(h411,assumption,(~(((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))) => ((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.29 thf(h412,assumption,(~(((![X1:$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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.29 thf(h413,assumption,(![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((funcSet @ X1) @ X2)) => ((((lam @ X1) @ X2) @ (((ap @ X1) @ X2) @ X3)) = X3))))),introduced(assumption,[])).
% 275.93/275.29 thf(h414,assumption,(~(((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.30 thf(h415,assumption,(![X1:$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))))))))))))))))),introduced(assumption,[])).
% 275.93/275.30 thf(h416,assumption,(~(((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ ((binunion @ X2) @ X3)))) => (~(((in @ X4) @ 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((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.30 thf(h417,assumption,(![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4))))))))) = ((setadjoin @ X4) @ emptyset))))))))),introduced(assumption,[])).
% 275.93/275.30 thf(h418,assumption,(~(((![X1:$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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.30 thf(h419,assumption,(![X1:$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))))))))))))))))),introduced(assumption,[])).
% 275.93/275.30 thf(h420,assumption,(~(((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.30 thf(h421,assumption,(![X1:$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))))))))),introduced(assumption,[])).
% 275.93/275.30 thf(h422,assumption,(~(((![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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.30 thf(h423,assumption,(![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (singleton @ ((dsetconstr @ X1) @ (^[X5:$i]:((X2 => (~((X5 = X3)))) => (~(((~(X2)) => (~((X5 = X4)))))))))))))))),introduced(assumption,[])).
% 275.93/275.30 thf(h424,assumption,(~(((![X1:$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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.30 thf(h425,assumption,(![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((in @ ((((if @ X1) @ X2) @ X3) @ X4)) @ X1))))))),introduced(assumption,[])).
% 275.93/275.30 thf(h426,assumption,(~(((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.30 thf(h427,assumption,(![X1:$i]:((singleton @ X1) => (![X2:$i]:(((in @ X2) @ X1) => ((setunion @ X1) = X2))))),introduced(assumption,[])).
% 275.93/275.30 thf(h428,assumption,(~(((![X1:$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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.31 thf(h429,assumption,(![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (X2 => (((((if @ X1) @ X2) @ X3) @ X4) = X3)))))))),introduced(assumption,[])).
% 275.93/275.31 thf(h430,assumption,(~(((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.31 thf(h431,assumption,(![X1:$i]:(![X2:$o]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => ((~(X2)) => (((((if @ X1) @ X2) @ X3) @ X4) = X4)))))))),introduced(assumption,[])).
% 275.93/275.31 thf(h432,assumption,(~(((![X1:$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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.31 thf(h433,assumption,(![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))))))))),introduced(assumption,[])).
% 275.93/275.31 thf(h434,assumption,(~(((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.31 thf(h435,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ X1))))))),introduced(assumption,[])).
% 275.93/275.31 thf(h436,assumption,(~(((![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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.31 thf(h437,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((binunion @ X2) @ X3)) @ (powerset @ X1))))))),introduced(assumption,[])).
% 275.93/275.31 thf(h438,assumption,(~(((![X1:$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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.31 thf(h439,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((in @ (powerset @ X2)) @ (powerset @ (powerset @ X1)))))),introduced(assumption,[])).
% 275.93/275.31 thf(h440,assumption,(~(((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.31 thf(h441,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X2) @ X3)) @ (powerset @ X1))))))),introduced(assumption,[])).
% 275.93/275.31 thf(h442,assumption,(~(((![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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.31 thf(h443,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ X1))))),introduced(assumption,[])).
% 275.93/275.31 thf(h444,assumption,(~(((![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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.32 thf(h445,assumption,(![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:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X3) => ((in @ X4) @ X2)))) => (X2 = X3)))))))),introduced(assumption,[])).
% 275.93/275.32 thf(h446,assumption,(~(((![X1:$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)))))))) => ((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.32 thf(h447,assumption,(![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))))))),introduced(assumption,[])).
% 275.93/275.32 thf(h448,assumption,(~(((![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:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))) => ((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.32 thf(h449,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ X2) => ((in @ X4) @ X3)))) => ((in @ X2) @ (powerset @ X3)))))))),introduced(assumption,[])).
% 275.93/275.32 thf(h450,assumption,(~(((![X1:$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:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.32 thf(h451,assumption,(![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)))))))))),introduced(assumption,[])).
% 275.93/275.32 thf(h452,assumption,(~(((![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) @ ((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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.32 thf(h453,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => (~(((in @ X3) @ ((setminus @ X1) @ X2)))))))))),introduced(assumption,[])).
% 275.93/275.32 thf(h454,assumption,(~(((![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:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.32 thf(h455,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => ((~(((in @ X3) @ ((setminus @ X1) @ X2)))) => ((in @ X3) @ X2))))))),introduced(assumption,[])).
% 275.93/275.32 thf(h456,assumption,(~(((![X1:$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:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.32 thf(h457,assumption,(![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)))))))))))),introduced(assumption,[])).
% 275.93/275.32 thf(h458,assumption,(~(((![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) @ ((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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.32 thf(h459,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))),introduced(assumption,[])).
% 275.93/275.32 thf(h460,assumption,(~(((![X1:$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:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.32 thf(h461,assumption,(![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)))))))))))),introduced(assumption,[])).
% 275.93/275.32 thf(h462,assumption,(~(((![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) @ ((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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.32 thf(h463,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((subset @ X2) @ X3) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ X2)))))))))))),introduced(assumption,[])).
% 275.93/275.32 thf(h464,assumption,(~(((![X1:$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:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.32 thf(h465,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ X3) => ((subset @ ((setminus @ X1) @ X3)) @ ((setminus @ X1) @ X2)))))))),introduced(assumption,[])).
% 275.93/275.32 thf(h466,assumption,(~(((![X1:$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) @ ((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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.32 thf(h467,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ ((setminus @ X1) @ X3)) @ ((setminus @ X1) @ X2)) => ((subset @ X2) @ X3))))))),introduced(assumption,[])).
% 275.93/275.32 thf(h468,assumption,(~(((![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) @ ((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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.32 thf(h469,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ X2) => ((in @ X3) @ ((setminus @ X1) @ ((setminus @ X1) @ X2))))))))),introduced(assumption,[])).
% 275.93/275.32 thf(h470,assumption,(~(((![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:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.33 thf(h471,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (((in @ X3) @ ((setminus @ X1) @ ((setminus @ X1) @ X2))) => ((in @ X3) @ X2))))))),introduced(assumption,[])).
% 275.93/275.33 thf(h472,assumption,(~(((![X1:$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:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.33 thf(h473,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ X2) @ ((setminus @ X1) @ ((setminus @ X1) @ X2)))))),introduced(assumption,[])).
% 275.93/275.33 thf(h474,assumption,(~(((![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) @ ((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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.33 thf(h475,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ ((setminus @ X1) @ X2))) @ X2)))),introduced(assumption,[])).
% 275.93/275.33 thf(h476,assumption,(~(((![X1:$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:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.33 thf(h477,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (X2 = ((setminus @ X1) @ ((setminus @ X1) @ X2)))))),introduced(assumption,[])).
% 275.93/275.33 thf(h478,assumption,(~(((![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) @ ((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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.33 thf(h479,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (~(((in @ X4) @ ((binintersect @ X2) @ X3)))))))))))),introduced(assumption,[])).
% 275.93/275.33 thf(h480,assumption,(~(((![X1:$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:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.33 thf(h481,assumption,(![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))))))))))),introduced(assumption,[])).
% 275.93/275.33 thf(h482,assumption,(~(((![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) @ ((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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.33 thf(h483,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((subset @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3)))))))),introduced(assumption,[])).
% 275.93/275.33 thf(h484,assumption,(~(((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.33 thf(h485,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))),introduced(assumption,[])).
% 275.93/275.33 thf(h486,assumption,(~(((![X1:$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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.33 thf(h487,assumption,(![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))))))))))),introduced(assumption,[])).
% 275.93/275.33 thf(h488,assumption,(~(((![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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.33 thf(h489,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((subset @ X2) @ ((setminus @ X1) @ X3)) => ((subset @ X3) @ ((setminus @ X1) @ X2)))))))),introduced(assumption,[])).
% 275.93/275.33 thf(h490,assumption,(~(((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.34 thf(h491,assumption,(![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))))))))))),introduced(assumption,[])).
% 275.93/275.34 thf(h492,assumption,(~(((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.34 thf(h493,assumption,(![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))))))))))),introduced(assumption,[])).
% 275.93/275.34 thf(h494,assumption,(~(((![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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.34 thf(h495,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binintersect @ X2) @ X3)) => ((in @ X5) @ ((binunion @ X2) @ X4)))))))))))),introduced(assumption,[])).
% 275.93/275.34 thf(h496,assumption,(~(((![X1:$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:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))) => ((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.34 thf(h497,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binintersect @ X2) @ X3)) => ((in @ X5) @ ((binunion @ X3) @ X4)))))))))))),introduced(assumption,[])).
% 275.93/275.34 thf(h498,assumption,(~(((![X1:$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)))))))) => ((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.34 thf(h499,assumption,(![X1:$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))))))))))))),introduced(assumption,[])).
% 275.93/275.34 thf(h500,assumption,(~(((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.34 thf(h501,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => ((in @ ((binintersect @ X2) @ X3)) @ (powerset @ ((binintersect @ ((binunion @ X2) @ X4)) @ ((binunion @ X3) @ X4))))))))))),introduced(assumption,[])).
% 275.93/275.34 thf(h502,assumption,(~(((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.34 thf(h503,assumption,(![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))))))))))),introduced(assumption,[])).
% 275.93/275.34 thf(h504,assumption,(~(((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.34 thf(h505,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X2)))))))))),introduced(assumption,[])).
% 275.93/275.34 thf(h506,assumption,(~(((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.34 thf(h507,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$o]:(![X5:$i]:(((in @ X5) @ X1) => (((in @ X5) @ ((binunion @ X2) @ X3)) => ((((in @ X5) @ X2) => X4) => ((((in @ X5) @ X3) => X4) => X4))))))))))),introduced(assumption,[])).
% 275.93/275.34 thf(h508,assumption,(~(((![X1:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.34 thf(h509,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => ((~(((in @ X4) @ X2))) => ((~(((in @ X4) @ X3))) => (~(((in @ X4) @ ((binunion @ X2) @ X3))))))))))))),introduced(assumption,[])).
% 275.93/275.34 thf(h510,assumption,(~(((![X1:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.34 thf(h511,assumption,(~(((![X1:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.34 thf(h512,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => ((in @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) @ (powerset @ ((setminus @ X1) @ X2)))))))),introduced(assumption,[])).
% 275.93/275.34 thf(h513,assumption,(~(((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.34 thf(h514,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ X3)))))))))),introduced(assumption,[])).
% 275.93/275.34 thf(h515,assumption,(~(((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.35 thf(h516,assumption,(![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))))))))))),introduced(assumption,[])).
% 275.93/275.35 thf(h517,assumption,(~(((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.35 thf(h518,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binintersect @ X2) @ X3))))))))))),introduced(assumption,[])).
% 275.93/275.35 thf(h519,assumption,(~(((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.35 thf(h520,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (((setminus @ X1) @ ((binintersect @ X2) @ X3)) = ((binunion @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3)))))))),introduced(assumption,[])).
% 275.93/275.35 thf(h521,assumption,(~(((![X1:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.35 thf(h522,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))) => ((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))))))))))),introduced(assumption,[])).
% 275.93/275.35 thf(h523,assumption,(~(((![X1:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.35 thf(h524,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((setminus @ X1) @ X2)) => (((in @ X4) @ ((setminus @ X1) @ X3)) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3)))))))))))),introduced(assumption,[])).
% 275.93/275.35 thf(h525,assumption,(~(((![X1:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.35 thf(h526,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ X4) @ ((binintersect @ ((setminus @ X1) @ X2)) @ ((setminus @ X1) @ X3))) => ((in @ X4) @ ((setminus @ X1) @ ((binunion @ X2) @ X3))))))))))),introduced(assumption,[])).
% 275.93/275.35 thf(h527,assumption,(~(((![X1:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.35 thf(h528,assumption,(![X1:$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)))))))),introduced(assumption,[])).
% 275.93/275.35 thf(h529,assumption,(~(((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.35 thf(h530,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ ((binintersect @ X2) @ X3)) => ((in @ X4) @ X1)))))))),introduced(assumption,[])).
% 275.93/275.35 thf(h531,assumption,(~(((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.35 thf(h532,assumption,(![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))))))))),introduced(assumption,[])).
% 275.93/275.35 thf(h533,assumption,(~(((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.35 thf(h534,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) => (![X3:$i]:(((in @ X3) @ (powerset @ X1)) => (![X4:$i]:(((in @ X4) @ (powerset @ X1)) => (((subset @ X3) @ X4) => ((subset @ ((binintersect @ X2) @ X3)) @ X4))))))))),introduced(assumption,[])).
% 275.93/275.35 thf(h535,assumption,(~(((![X1:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.35 thf(h536,assumption,(![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))))))))))),introduced(assumption,[])).
% 275.93/275.35 thf(h537,assumption,(~(((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.35 thf(h538,assumption,(![X1:$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))))))))))))),introduced(assumption,[])).
% 275.93/275.35 thf(h539,assumption,(~(((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.35 thf(h540,assumption,(~(((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.35 thf(h541,assumption,(![X1:$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))))))))))))),introduced(assumption,[])).
% 275.93/275.35 thf(h542,assumption,(~(((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.35 thf(h543,assumption,(~(((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.35 thf(h544,assumption,(~(((![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.35 thf(h545,assumption,(~(((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.35 thf(h546,assumption,(![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)))))))),introduced(assumption,[])).
% 275.93/275.35 thf(h547,assumption,(~(((![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.35 thf(h548,assumption,(![X1:$i]:(![X2:$i]:(((in @ X2) @ (breln1Set @ X1)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))),introduced(assumption,[])).
% 275.93/275.35 thf(h549,assumption,(~(((![X1:$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]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.35 thf(h550,assumption,(![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:$i]:(((in @ X7) @ X2) => (((X3 @ X5) @ X7) => ((in @ ((kpair @ X6) @ X7)) @ X4))))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.35 thf(h551,assumption,(~(((![X1:$i]:(![X2:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.35 thf(h552,assumption,(![X1:$i]:(![X2:$i>$i>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))),introduced(assumption,[])).
% 275.93/275.35 thf(h553,assumption,(~(((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))),introduced(assumption,[])).
% 275.93/275.35 thf(h554,assumption,(~(((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))))),introduced(assumption,[])).
% 276.01/275.37 thf(h555,assumption,(![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => ((in @ ((kpair @ X4) @ X5)) @ X3)))))) => ((subset @ X2) @ X3))))))),introduced(assumption,[])).
% 276.01/275.37 thf(h556,assumption,(~(((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))),introduced(assumption,[])).
% 276.01/275.37 thf(h557,assumption,(![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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)))))))),introduced(assumption,[])).
% 276.01/275.37 thf(h558,assumption,(~(((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))))),introduced(assumption,[])).
% 276.01/275.37 thf(h559,assumption,(![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))),introduced(assumption,[])).
% 276.01/275.37 thf(h560,assumption,(~(((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))),introduced(assumption,[])).
% 276.01/275.37 thf(h561,assumption,(![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ X2) => ((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)))))))))),introduced(assumption,[])).
% 276.01/275.37 thf(h562,assumption,(~(((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))))),introduced(assumption,[])).
% 276.01/275.37 thf(h563,assumption,(![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X1) => (((in @ ((kpair @ X4) @ X3)) @ ((breln1invset @ X1) @ X2)) => ((in @ ((kpair @ X3) @ X4)) @ X2))))))))),introduced(assumption,[])).
% 276.01/275.37 thf(h564,assumption,(~(((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))),introduced(assumption,[])).
% 276.01/275.37 thf(h565,assumption,(![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))),introduced(assumption,[])).
% 276.01/275.37 thf(h566,assumption,(~(((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))))),introduced(assumption,[])).
% 276.01/275.37 thf(h567,assumption,(![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (![X6:$i]:(((in @ X6) @ X1) => (((in @ ((kpair @ X4) @ X6)) @ X2) => (((in @ ((kpair @ X6) @ X5)) @ X3) => ((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3))))))))))))))),introduced(assumption,[])).
% 276.01/275.37 thf(h568,assumption,(~(((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))),introduced(assumption,[])).
% 276.01/275.37 thf(h569,assumption,(![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ (((breln1compset @ X1) @ X2) @ X3)) => (~((![X6:$i]:((~((((in @ X6) @ X1) => (~(((in @ ((kpair @ X4) @ X6)) @ X2)))))) => (~(((in @ ((kpair @ X6) @ X5)) @ X3))))))))))))))))),introduced(assumption,[])).
% 276.01/275.37 thf(h570,assumption,(~(((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1)))))))))),introduced(assumption,[])).
% 276.01/275.37 thf(h571,assumption,(![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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)))))))))))),introduced(assumption,[])).
% 276.01/275.37 thf(h572,assumption,(~((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))),introduced(assumption,[])).
% 276.01/275.37 thf(h573,assumption,(~((![X1:$i]:(((subset @ X1) @ ((cartprod @ eigen__0) @ eigen__0)) => (![X2:$i]:(((subset @ X2) @ ((cartprod @ eigen__0) @ eigen__0)) => ((subset @ ((binunion @ X1) @ X2)) @ ((cartprod @ eigen__0) @ eigen__0)))))))),introduced(assumption,[])).
% 276.01/275.37 thf(h574,assumption,(~((((subset @ eigen__1) @ ((cartprod @ eigen__0) @ eigen__0)) => (![X1:$i]:(((subset @ X1) @ ((cartprod @ eigen__0) @ eigen__0)) => ((subset @ ((binunion @ eigen__1) @ X1)) @ ((cartprod @ eigen__0) @ eigen__0))))))),introduced(assumption,[])).
% 276.01/275.37 thf(h575,assumption,((subset @ eigen__1) @ ((cartprod @ eigen__0) @ eigen__0)),introduced(assumption,[])).
% 276.01/275.37 thf(h576,assumption,(~((![X1:$i]:(((subset @ X1) @ ((cartprod @ eigen__0) @ eigen__0)) => ((subset @ ((binunion @ eigen__1) @ X1)) @ ((cartprod @ eigen__0) @ eigen__0)))))),introduced(assumption,[])).
% 276.01/275.37 thf(h577,assumption,(~((((subset @ eigen__2) @ ((cartprod @ eigen__0) @ eigen__0)) => ((subset @ ((binunion @ eigen__1) @ eigen__2)) @ ((cartprod @ eigen__0) @ eigen__0))))),introduced(assumption,[])).
% 276.01/275.37 thf(h578,assumption,((subset @ eigen__2) @ ((cartprod @ eigen__0) @ eigen__0)),introduced(assumption,[])).
% 276.01/275.37 thf(h579,assumption,(~(((subset @ ((binunion @ eigen__1) @ eigen__2)) @ ((cartprod @ eigen__0) @ eigen__0)))),introduced(assumption,[])).
% 276.01/275.37 thf(ax599, axiom, (~(p178)|p1752), file('<stdin>', ax599)).
% 276.01/275.37 thf(ax521, axiom, (~(p213)|p1829), file('<stdin>', ax521)).
% 276.01/275.37 thf(ax569, axiom, (~(p1752)|p1782), file('<stdin>', ax569)).
% 276.01/275.37 thf(ax2180, axiom, p178, file('<stdin>', ax2180)).
% 276.01/275.37 thf(ax523, axiom, (~(p1828)|~(p1827)|p1), file('<stdin>', ax523)).
% 276.01/275.37 thf(ax2357, axiom, ~(p1), file('<stdin>', ax2357)).
% 276.01/275.37 thf(ax522, axiom, (~(p1829)|p1828), file('<stdin>', ax522)).
% 276.01/275.37 thf(ax2145, axiom, p213, file('<stdin>', ax2145)).
% 276.01/275.37 thf(pax3, axiom, (p3=>fsubset @ f__1 @ (fcartprod @ f__0 @ f__0)), file('<stdin>', pax3)).
% 276.01/275.37 thf(ax570, axiom, (~(p1782)|~(p2)|p1781), file('<stdin>', ax570)).
% 276.01/275.37 thf(pax1751, axiom, (p1751=>(fsubset @ f__1 @ (fcartprod @ f__0 @ f__0)=>(fbinintersect @ (fcartprod @ f__0 @ f__0) @ f__1)=(f__1))), file('<stdin>', pax1751)).
% 276.01/275.37 thf(ax2355, axiom, p3, file('<stdin>', ax2355)).
% 276.01/275.37 thf(ax600, axiom, (~(p1752)|p1751), file('<stdin>', ax600)).
% 276.01/275.37 thf(pax185, axiom, (p185=>![X31:$i, X30:$i, X3:$i]:(fin @ X3 @ (fbinintersect @ X31 @ X30)=>fin @ X3 @ X31)), file('<stdin>', pax185)).
% 276.01/275.37 thf(pax1781, axiom, (p1781=>(fbinintersect @ (fcartprod @ f__0 @ f__0) @ f__2)=(f__2)), file('<stdin>', pax1781)).
% 276.01/275.37 thf(ax2356, axiom, p2, file('<stdin>', ax2356)).
% 276.01/275.37 thf(pax190, axiom, (p190=>![X31:$i, X30:$i, X3:$i]:(fin @ X3 @ (fbinunion @ X31 @ X30)=>(~(fin @ X3 @ X31)=>fin @ X3 @ X30))), file('<stdin>', pax190)).
% 276.01/275.37 thf(nax1827, axiom, (p1827<=![X1:$i]:(fin @ X1 @ (fbinunion @ f__1 @ f__2)=>fin @ X1 @ (fcartprod @ f__0 @ f__0))), file('<stdin>', nax1827)).
% 276.01/275.37 thf(ax2173, axiom, p185, file('<stdin>', ax2173)).
% 276.01/275.37 thf(ax2168, axiom, p190, file('<stdin>', ax2168)).
% 276.01/275.37 thf(c_0_20, plain, (~p178|p1752), inference(fof_simplification,[status(thm)],[ax599])).
% 276.01/275.37 thf(c_0_21, plain, (~p213|p1829), inference(fof_simplification,[status(thm)],[ax521])).
% 276.01/275.37 thf(c_0_22, plain, (~p1752|p1782), inference(fof_simplification,[status(thm)],[ax569])).
% 276.01/275.37 thf(c_0_23, plain, (p1752|~p178), inference(split_conjunct,[status(thm)],[c_0_20])).
% 276.01/275.37 thf(c_0_24, plain, p178, inference(split_conjunct,[status(thm)],[ax2180])).
% 276.01/275.37 thf(c_0_25, plain, (~p1828|~p1827|p1), inference(fof_simplification,[status(thm)],[ax523])).
% 276.01/275.37 thf(c_0_26, plain, ~p1, inference(fof_simplification,[status(thm)],[ax2357])).
% 276.01/275.37 thf(c_0_27, plain, (~p1829|p1828), inference(fof_simplification,[status(thm)],[ax522])).
% 276.01/275.37 thf(c_0_28, plain, (p1829|~p213), inference(split_conjunct,[status(thm)],[c_0_21])).
% 276.01/275.37 thf(c_0_29, plain, p213, inference(split_conjunct,[status(thm)],[ax2145])).
% 276.01/275.37 thf(c_0_30, plain, (~p3|fsubset @ f__1 @ (fcartprod @ f__0 @ f__0)), inference(fof_nnf,[status(thm)],[pax3])).
% 276.01/275.37 thf(c_0_31, plain, (~p1782|~p2|p1781), inference(fof_simplification,[status(thm)],[ax570])).
% 276.01/275.37 thf(c_0_32, plain, (p1782|~p1752), inference(split_conjunct,[status(thm)],[c_0_22])).
% 276.01/275.37 thf(c_0_33, plain, p1752, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23, c_0_24])])).
% 276.01/275.37 thf(c_0_34, plain, (p1|~p1828|~p1827), inference(split_conjunct,[status(thm)],[c_0_25])).
% 276.01/275.37 thf(c_0_35, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_26])).
% 276.01/275.37 thf(c_0_36, plain, (p1828|~p1829), inference(split_conjunct,[status(thm)],[c_0_27])).
% 276.01/275.37 thf(c_0_37, plain, p1829, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28, c_0_29])])).
% 276.01/275.37 thf(c_0_38, plain, (~p1751|(~fsubset @ f__1 @ (fcartprod @ f__0 @ f__0)|(fbinintersect @ (fcartprod @ f__0 @ f__0) @ f__1)=(f__1))), inference(fof_nnf,[status(thm)],[pax1751])).
% 276.01/275.37 thf(c_0_39, plain, (fsubset @ f__1 @ (fcartprod @ f__0 @ f__0)|~p3), inference(split_conjunct,[status(thm)],[c_0_30])).
% 276.01/275.37 thf(c_0_40, plain, p3, inference(split_conjunct,[status(thm)],[ax2355])).
% 276.01/275.37 thf(c_0_41, plain, (~p1752|p1751), inference(fof_simplification,[status(thm)],[ax600])).
% 276.01/275.37 thf(c_0_42, plain, ![X3027:$i, X3028:$i, X3029:$i]:(~p185|(~fin @ X3029 @ (fbinintersect @ X3027 @ X3028)|fin @ X3029 @ X3027)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax185])])])).
% 276.01/275.37 thf(c_0_43, plain, (~p1781|(fbinintersect @ (fcartprod @ f__0 @ f__0) @ f__2)=(f__2)), inference(fof_nnf,[status(thm)],[pax1781])).
% 276.01/275.37 thf(c_0_44, plain, (p1781|~p1782|~p2), inference(split_conjunct,[status(thm)],[c_0_31])).
% 276.01/275.37 thf(c_0_45, plain, p2, inference(split_conjunct,[status(thm)],[ax2356])).
% 276.01/275.37 thf(c_0_46, plain, p1782, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32, c_0_33])])).
% 276.01/275.37 thf(c_0_47, plain, ![X3001:$i, X3002:$i, X3003:$i]:(~p190|(~fin @ X3003 @ (fbinunion @ X3001 @ X3002)|(fin @ X3003 @ X3001|fin @ X3003 @ X3002))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax190])])])])).
% 276.01/275.37 thf(c_0_48, plain, ((fin @ esk856_0 @ (fbinunion @ f__1 @ f__2)|p1827)&(~fin @ esk856_0 @ (fcartprod @ f__0 @ f__0)|p1827)), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1827])])])])])).
% 276.01/275.37 thf(c_0_49, plain, (~p1827|~p1828), inference(sr,[status(thm)],[c_0_34, c_0_35])).
% 276.01/275.37 thf(c_0_50, plain, p1828, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36, c_0_37])])).
% 276.01/275.37 thf(c_0_51, plain, ((fbinintersect @ (fcartprod @ f__0 @ f__0) @ f__1)=(f__1)|~p1751|~fsubset @ f__1 @ (fcartprod @ f__0 @ f__0)), inference(split_conjunct,[status(thm)],[c_0_38])).
% 276.01/275.37 thf(c_0_52, plain, fsubset @ f__1 @ (fcartprod @ f__0 @ f__0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39, c_0_40])])).
% 276.01/275.37 thf(c_0_53, plain, (p1751|~p1752), inference(split_conjunct,[status(thm)],[c_0_41])).
% 276.01/275.37 thf(c_0_54, plain, ![X1:$i, X2:$i, X3:$i]:(fin @ X1 @ X2|~p185|~fin @ X1 @ (fbinintersect @ X2 @ X3)), inference(split_conjunct,[status(thm)],[c_0_42])).
% 276.01/275.37 thf(c_0_55, plain, p185, inference(split_conjunct,[status(thm)],[ax2173])).
% 276.01/275.37 thf(c_0_56, plain, ((fbinintersect @ (fcartprod @ f__0 @ f__0) @ f__2)=(f__2)|~p1781), inference(split_conjunct,[status(thm)],[c_0_43])).
% 276.01/275.37 thf(c_0_57, plain, p1781, inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44, c_0_45]), c_0_46])])).
% 276.01/275.37 thf(c_0_58, plain, ![X1:$i, X2:$i, X3:$i]:(fin @ X1 @ X2|fin @ X1 @ X3|~p190|~fin @ X1 @ (fbinunion @ X2 @ X3)), inference(split_conjunct,[status(thm)],[c_0_47])).
% 276.01/275.37 thf(c_0_59, plain, p190, inference(split_conjunct,[status(thm)],[ax2168])).
% 276.01/275.37 thf(c_0_60, plain, (fin @ esk856_0 @ (fbinunion @ f__1 @ f__2)|p1827), inference(split_conjunct,[status(thm)],[c_0_48])).
% 276.01/275.37 thf(c_0_61, plain, ~p1827, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49, c_0_50])])).
% 276.01/275.37 thf(c_0_62, plain, ((fbinintersect @ (fcartprod @ f__0 @ f__0) @ f__1)=(f__1)|~p1751), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51, c_0_52])])).
% 276.01/275.37 thf(c_0_63, plain, p1751, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53, c_0_33])])).
% 276.01/275.37 thf(c_0_64, plain, ![X1:$i, X2:$i, X3:$i]:(fin @ X1 @ X2|~fin @ X1 @ (fbinintersect @ X2 @ X3)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54, c_0_55])])).
% 276.01/275.37 thf(c_0_65, plain, (fbinintersect @ (fcartprod @ f__0 @ f__0) @ f__2)=(f__2), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_56, c_0_57])])).
% 276.01/275.37 thf(c_0_66, plain, ![X1:$i, X2:$i, X3:$i]:(fin @ X1 @ X2|fin @ X1 @ X3|~fin @ X1 @ (fbinunion @ X2 @ X3)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58, c_0_59])])).
% 276.01/275.37 thf(c_0_67, plain, fin @ esk856_0 @ (fbinunion @ f__1 @ f__2), inference(sr,[status(thm)],[c_0_60, c_0_61])).
% 276.01/275.37 thf(c_0_68, plain, (p1827|~fin @ esk856_0 @ (fcartprod @ f__0 @ f__0)), inference(split_conjunct,[status(thm)],[c_0_48])).
% 276.01/275.37 thf(c_0_69, plain, (fbinintersect @ (fcartprod @ f__0 @ f__0) @ f__1)=(f__1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_62, c_0_63])])).
% 276.01/275.37 thf(c_0_70, plain, ![X1:$i]:(fin @ X1 @ (fcartprod @ f__0 @ f__0)|~fin @ X1 @ f__2), inference(spm,[status(thm)],[c_0_64, c_0_65])).
% 276.01/275.37 thf(c_0_71, plain, (fin @ esk856_0 @ f__1|fin @ esk856_0 @ f__2), inference(spm,[status(thm)],[c_0_66, c_0_67])).
% 276.01/275.37 thf(c_0_72, plain, ~fin @ esk856_0 @ (fcartprod @ f__0 @ f__0), inference(sr,[status(thm)],[c_0_68, c_0_61])).
% 276.01/275.37 thf(c_0_73, plain, ![X1:$i]:(fin @ X1 @ (fcartprod @ f__0 @ f__0)|~fin @ X1 @ f__1), inference(spm,[status(thm)],[c_0_64, c_0_69])).
% 276.01/275.37 thf(c_0_74, plain, fin @ esk856_0 @ f__1, inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_71]), c_0_72])).
% 276.01/275.37 thf(c_0_75, plain, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_73, c_0_74]), c_0_72]), ['proof']).
% 276.01/275.37 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h578,h579,h577,h575,h576,h574,h573,h571,h572,h569,h570,h567,h568,h565,h566,h563,h564,h561,h562,h559,h560,h557,h558,h555,h556,h546,h554,h552,h553,h550,h551,h548,h549,h546,h547,h512,h545,h489,h544,h501,h543,h541,h542,h485,h540,h538,h539,h536,h537,h534,h535,h532,h533,h530,h531,h528,h529,h526,h527,h524,h525,h522,h523,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h505,h511,h509,h510,h507,h508,h505,h506,h503,h504,h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[])).
% 276.01/275.37 thf(2,plain,$false,inference(tab_negimp,[status(thm),assumptions([h577,h575,h576,h574,h573,h571,h572,h569,h570,h567,h568,h565,h566,h563,h564,h561,h562,h559,h560,h557,h558,h555,h556,h546,h554,h552,h553,h550,h551,h548,h549,h546,h547,h512,h545,h489,h544,h501,h543,h541,h542,h485,h540,h538,h539,h536,h537,h534,h535,h532,h533,h530,h531,h528,h529,h526,h527,h524,h525,h522,h523,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h505,h511,h509,h510,h507,h508,h505,h506,h503,h504,h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h578,h579])],[h577,1,h578,h579])).
% 276.01/275.37 thf(3,plain,$false,inference(tab_negall,[status(thm),assumptions([h575,h576,h574,h573,h571,h572,h569,h570,h567,h568,h565,h566,h563,h564,h561,h562,h559,h560,h557,h558,h555,h556,h546,h554,h552,h553,h550,h551,h548,h549,h546,h547,h512,h545,h489,h544,h501,h543,h541,h542,h485,h540,h538,h539,h536,h537,h534,h535,h532,h533,h530,h531,h528,h529,h526,h527,h524,h525,h522,h523,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h505,h511,h509,h510,h507,h508,h505,h506,h503,h504,h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h577]),tab_negall(eigenvar,eigen__2)],[h576,2,h577])).
% 276.01/275.37 thf(4,plain,$false,inference(tab_negimp,[status(thm),assumptions([h574,h573,h571,h572,h569,h570,h567,h568,h565,h566,h563,h564,h561,h562,h559,h560,h557,h558,h555,h556,h546,h554,h552,h553,h550,h551,h548,h549,h546,h547,h512,h545,h489,h544,h501,h543,h541,h542,h485,h540,h538,h539,h536,h537,h534,h535,h532,h533,h530,h531,h528,h529,h526,h527,h524,h525,h522,h523,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h505,h511,h509,h510,h507,h508,h505,h506,h503,h504,h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h575,h576])],[h574,3,h575,h576])).
% 276.01/275.37 thf(5,plain,$false,inference(tab_negall,[status(thm),assumptions([h573,h571,h572,h569,h570,h567,h568,h565,h566,h563,h564,h561,h562,h559,h560,h557,h558,h555,h556,h546,h554,h552,h553,h550,h551,h548,h549,h546,h547,h512,h545,h489,h544,h501,h543,h541,h542,h485,h540,h538,h539,h536,h537,h534,h535,h532,h533,h530,h531,h528,h529,h526,h527,h524,h525,h522,h523,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h505,h511,h509,h510,h507,h508,h505,h506,h503,h504,h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h574]),tab_negall(eigenvar,eigen__1)],[h573,4,h574])).
% 276.01/275.37 thf(6,plain,$false,inference(tab_negall,[status(thm),assumptions([h571,h572,h569,h570,h567,h568,h565,h566,h563,h564,h561,h562,h559,h560,h557,h558,h555,h556,h546,h554,h552,h553,h550,h551,h548,h549,h546,h547,h512,h545,h489,h544,h501,h543,h541,h542,h485,h540,h538,h539,h536,h537,h534,h535,h532,h533,h530,h531,h528,h529,h526,h527,h524,h525,h522,h523,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h505,h511,h509,h510,h507,h508,h505,h506,h503,h504,h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h573]),tab_negall(eigenvar,eigen__0)],[h572,5,h573])).
% 276.01/275.37 thf(7,plain,$false,inference(tab_negimp,[status(thm),assumptions([h569,h570,h567,h568,h565,h566,h563,h564,h561,h562,h559,h560,h557,h558,h555,h556,h546,h554,h552,h553,h550,h551,h548,h549,h546,h547,h512,h545,h489,h544,h501,h543,h541,h542,h485,h540,h538,h539,h536,h537,h534,h535,h532,h533,h530,h531,h528,h529,h526,h527,h524,h525,h522,h523,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h505,h511,h509,h510,h507,h508,h505,h506,h503,h504,h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h571,h572])],[h570,6,h571,h572])).
% 276.01/275.37 thf(8,plain,$false,inference(tab_negimp,[status(thm),assumptions([h567,h568,h565,h566,h563,h564,h561,h562,h559,h560,h557,h558,h555,h556,h546,h554,h552,h553,h550,h551,h548,h549,h546,h547,h512,h545,h489,h544,h501,h543,h541,h542,h485,h540,h538,h539,h536,h537,h534,h535,h532,h533,h530,h531,h528,h529,h526,h527,h524,h525,h522,h523,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h505,h511,h509,h510,h507,h508,h505,h506,h503,h504,h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h569,h570])],[h568,7,h569,h570])).
% 276.01/275.37 thf(9,plain,$false,inference(tab_negimp,[status(thm),assumptions([h565,h566,h563,h564,h561,h562,h559,h560,h557,h558,h555,h556,h546,h554,h552,h553,h550,h551,h548,h549,h546,h547,h512,h545,h489,h544,h501,h543,h541,h542,h485,h540,h538,h539,h536,h537,h534,h535,h532,h533,h530,h531,h528,h529,h526,h527,h524,h525,h522,h523,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h505,h511,h509,h510,h507,h508,h505,h506,h503,h504,h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h567,h568])],[h566,8,h567,h568])).
% 276.01/275.37 thf(10,plain,$false,inference(tab_negimp,[status(thm),assumptions([h563,h564,h561,h562,h559,h560,h557,h558,h555,h556,h546,h554,h552,h553,h550,h551,h548,h549,h546,h547,h512,h545,h489,h544,h501,h543,h541,h542,h485,h540,h538,h539,h536,h537,h534,h535,h532,h533,h530,h531,h528,h529,h526,h527,h524,h525,h522,h523,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h505,h511,h509,h510,h507,h508,h505,h506,h503,h504,h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h565,h566])],[h564,9,h565,h566])).
% 276.01/275.37 thf(11,plain,$false,inference(tab_negimp,[status(thm),assumptions([h561,h562,h559,h560,h557,h558,h555,h556,h546,h554,h552,h553,h550,h551,h548,h549,h546,h547,h512,h545,h489,h544,h501,h543,h541,h542,h485,h540,h538,h539,h536,h537,h534,h535,h532,h533,h530,h531,h528,h529,h526,h527,h524,h525,h522,h523,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h505,h511,h509,h510,h507,h508,h505,h506,h503,h504,h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h563,h564])],[h562,10,h563,h564])).
% 276.01/275.37 thf(12,plain,$false,inference(tab_negimp,[status(thm),assumptions([h559,h560,h557,h558,h555,h556,h546,h554,h552,h553,h550,h551,h548,h549,h546,h547,h512,h545,h489,h544,h501,h543,h541,h542,h485,h540,h538,h539,h536,h537,h534,h535,h532,h533,h530,h531,h528,h529,h526,h527,h524,h525,h522,h523,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h505,h511,h509,h510,h507,h508,h505,h506,h503,h504,h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h561,h562])],[h560,11,h561,h562])).
% 276.01/275.37 thf(13,plain,$false,inference(tab_negimp,[status(thm),assumptions([h557,h558,h555,h556,h546,h554,h552,h553,h550,h551,h548,h549,h546,h547,h512,h545,h489,h544,h501,h543,h541,h542,h485,h540,h538,h539,h536,h537,h534,h535,h532,h533,h530,h531,h528,h529,h526,h527,h524,h525,h522,h523,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h505,h511,h509,h510,h507,h508,h505,h506,h503,h504,h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h559,h560])],[h558,12,h559,h560])).
% 276.01/275.37 thf(14,plain,$false,inference(tab_negimp,[status(thm),assumptions([h555,h556,h546,h554,h552,h553,h550,h551,h548,h549,h546,h547,h512,h545,h489,h544,h501,h543,h541,h542,h485,h540,h538,h539,h536,h537,h534,h535,h532,h533,h530,h531,h528,h529,h526,h527,h524,h525,h522,h523,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h505,h511,h509,h510,h507,h508,h505,h506,h503,h504,h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h557,h558])],[h556,13,h557,h558])).
% 276.04/275.40 thf(15,plain,$false,inference(tab_negimp,[status(thm),assumptions([h546,h554,h552,h553,h550,h551,h548,h549,h546,h547,h512,h545,h489,h544,h501,h543,h541,h542,h485,h540,h538,h539,h536,h537,h534,h535,h532,h533,h530,h531,h528,h529,h526,h527,h524,h525,h522,h523,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h505,h511,h509,h510,h507,h508,h505,h506,h503,h504,h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h555,h556])],[h554,14,h555,h556])).
% 276.04/275.40 thf(16,plain,$false,inference(tab_negimp,[status(thm),assumptions([h552,h553,h550,h551,h548,h549,h546,h547,h512,h545,h489,h544,h501,h543,h541,h542,h485,h540,h538,h539,h536,h537,h534,h535,h532,h533,h530,h531,h528,h529,h526,h527,h524,h525,h522,h523,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h505,h511,h509,h510,h507,h508,h505,h506,h503,h504,h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h546,h554])],[h553,15,h546,h554])).
% 276.04/275.40 thf(17,plain,$false,inference(tab_negimp,[status(thm),assumptions([h550,h551,h548,h549,h546,h547,h512,h545,h489,h544,h501,h543,h541,h542,h485,h540,h538,h539,h536,h537,h534,h535,h532,h533,h530,h531,h528,h529,h526,h527,h524,h525,h522,h523,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h505,h511,h509,h510,h507,h508,h505,h506,h503,h504,h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h552,h553])],[h551,16,h552,h553])).
% 276.04/275.40 thf(18,plain,$false,inference(tab_negimp,[status(thm),assumptions([h548,h549,h546,h547,h512,h545,h489,h544,h501,h543,h541,h542,h485,h540,h538,h539,h536,h537,h534,h535,h532,h533,h530,h531,h528,h529,h526,h527,h524,h525,h522,h523,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h505,h511,h509,h510,h507,h508,h505,h506,h503,h504,h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h550,h551])],[h549,17,h550,h551])).
% 276.04/275.40 thf(19,plain,$false,inference(tab_negimp,[status(thm),assumptions([h546,h547,h512,h545,h489,h544,h501,h543,h541,h542,h485,h540,h538,h539,h536,h537,h534,h535,h532,h533,h530,h531,h528,h529,h526,h527,h524,h525,h522,h523,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h505,h511,h509,h510,h507,h508,h505,h506,h503,h504,h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h548,h549])],[h547,18,h548,h549])).
% 276.04/275.40 thf(20,plain,$false,inference(tab_negimp,[status(thm),assumptions([h512,h545,h489,h544,h501,h543,h541,h542,h485,h540,h538,h539,h536,h537,h534,h535,h532,h533,h530,h531,h528,h529,h526,h527,h524,h525,h522,h523,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h505,h511,h509,h510,h507,h508,h505,h506,h503,h504,h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h546,h547])],[h545,19,h546,h547])).
% 276.04/275.40 thf(21,plain,$false,inference(tab_negimp,[status(thm),assumptions([h489,h544,h501,h543,h541,h542,h485,h540,h538,h539,h536,h537,h534,h535,h532,h533,h530,h531,h528,h529,h526,h527,h524,h525,h522,h523,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h505,h511,h509,h510,h507,h508,h505,h506,h503,h504,h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h512,h545])],[h544,20,h512,h545])).
% 276.04/275.40 thf(22,plain,$false,inference(tab_negimp,[status(thm),assumptions([h501,h543,h541,h542,h485,h540,h538,h539,h536,h537,h534,h535,h532,h533,h530,h531,h528,h529,h526,h527,h524,h525,h522,h523,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h505,h511,h509,h510,h507,h508,h505,h506,h503,h504,h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h489,h544])],[h543,21,h489,h544])).
% 276.04/275.40 thf(23,plain,$false,inference(tab_negimp,[status(thm),assumptions([h541,h542,h485,h540,h538,h539,h536,h537,h534,h535,h532,h533,h530,h531,h528,h529,h526,h527,h524,h525,h522,h523,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h505,h511,h509,h510,h507,h508,h505,h506,h503,h504,h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h501,h543])],[h542,22,h501,h543])).
% 276.04/275.40 thf(24,plain,$false,inference(tab_negimp,[status(thm),assumptions([h485,h540,h538,h539,h536,h537,h534,h535,h532,h533,h530,h531,h528,h529,h526,h527,h524,h525,h522,h523,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h505,h511,h509,h510,h507,h508,h505,h506,h503,h504,h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h541,h542])],[h540,23,h541,h542])).
% 276.04/275.40 thf(25,plain,$false,inference(tab_negimp,[status(thm),assumptions([h538,h539,h536,h537,h534,h535,h532,h533,h530,h531,h528,h529,h526,h527,h524,h525,h522,h523,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h505,h511,h509,h510,h507,h508,h505,h506,h503,h504,h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h485,h540])],[h539,24,h485,h540])).
% 276.04/275.40 thf(26,plain,$false,inference(tab_negimp,[status(thm),assumptions([h536,h537,h534,h535,h532,h533,h530,h531,h528,h529,h526,h527,h524,h525,h522,h523,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h505,h511,h509,h510,h507,h508,h505,h506,h503,h504,h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h538,h539])],[h537,25,h538,h539])).
% 276.04/275.40 thf(27,plain,$false,inference(tab_negimp,[status(thm),assumptions([h534,h535,h532,h533,h530,h531,h528,h529,h526,h527,h524,h525,h522,h523,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h505,h511,h509,h510,h507,h508,h505,h506,h503,h504,h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h536,h537])],[h535,26,h536,h537])).
% 276.04/275.40 thf(28,plain,$false,inference(tab_negimp,[status(thm),assumptions([h532,h533,h530,h531,h528,h529,h526,h527,h524,h525,h522,h523,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h505,h511,h509,h510,h507,h508,h505,h506,h503,h504,h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h534,h535])],[h533,27,h534,h535])).
% 276.04/275.40 thf(29,plain,$false,inference(tab_negimp,[status(thm),assumptions([h530,h531,h528,h529,h526,h527,h524,h525,h522,h523,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h505,h511,h509,h510,h507,h508,h505,h506,h503,h504,h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h532,h533])],[h531,28,h532,h533])).
% 276.04/275.40 thf(30,plain,$false,inference(tab_negimp,[status(thm),assumptions([h528,h529,h526,h527,h524,h525,h522,h523,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h505,h511,h509,h510,h507,h508,h505,h506,h503,h504,h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h530,h531])],[h529,29,h530,h531])).
% 276.04/275.40 thf(31,plain,$false,inference(tab_negimp,[status(thm),assumptions([h526,h527,h524,h525,h522,h523,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h505,h511,h509,h510,h507,h508,h505,h506,h503,h504,h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h528,h529])],[h527,30,h528,h529])).
% 276.04/275.40 thf(32,plain,$false,inference(tab_negimp,[status(thm),assumptions([h524,h525,h522,h523,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h505,h511,h509,h510,h507,h508,h505,h506,h503,h504,h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h526,h527])],[h525,31,h526,h527])).
% 276.04/275.40 thf(33,plain,$false,inference(tab_negimp,[status(thm),assumptions([h522,h523,h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h505,h511,h509,h510,h507,h508,h505,h506,h503,h504,h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h524,h525])],[h523,32,h524,h525])).
% 276.04/275.40 thf(34,plain,$false,inference(tab_negimp,[status(thm),assumptions([h520,h521,h518,h519,h516,h517,h514,h515,h512,h513,h505,h511,h509,h510,h507,h508,h505,h506,h503,h504,h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h522,h523])],[h521,33,h522,h523])).
% 276.04/275.40 thf(35,plain,$false,inference(tab_negimp,[status(thm),assumptions([h518,h519,h516,h517,h514,h515,h512,h513,h505,h511,h509,h510,h507,h508,h505,h506,h503,h504,h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h520,h521])],[h519,34,h520,h521])).
% 276.04/275.40 thf(36,plain,$false,inference(tab_negimp,[status(thm),assumptions([h516,h517,h514,h515,h512,h513,h505,h511,h509,h510,h507,h508,h505,h506,h503,h504,h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h518,h519])],[h517,35,h518,h519])).
% 276.04/275.40 thf(37,plain,$false,inference(tab_negimp,[status(thm),assumptions([h514,h515,h512,h513,h505,h511,h509,h510,h507,h508,h505,h506,h503,h504,h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h516,h517])],[h515,36,h516,h517])).
% 276.04/275.42 thf(38,plain,$false,inference(tab_negimp,[status(thm),assumptions([h512,h513,h505,h511,h509,h510,h507,h508,h505,h506,h503,h504,h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h514,h515])],[h513,37,h514,h515])).
% 276.04/275.42 thf(39,plain,$false,inference(tab_negimp,[status(thm),assumptions([h505,h511,h509,h510,h507,h508,h505,h506,h503,h504,h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h512,h513])],[h511,38,h512,h513])).
% 276.04/275.42 thf(40,plain,$false,inference(tab_negimp,[status(thm),assumptions([h509,h510,h507,h508,h505,h506,h503,h504,h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h505,h511])],[h510,39,h505,h511])).
% 276.04/275.42 thf(41,plain,$false,inference(tab_negimp,[status(thm),assumptions([h507,h508,h505,h506,h503,h504,h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h509,h510])],[h508,40,h509,h510])).
% 276.04/275.42 thf(42,plain,$false,inference(tab_negimp,[status(thm),assumptions([h505,h506,h503,h504,h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h507,h508])],[h506,41,h507,h508])).
% 276.04/275.42 thf(43,plain,$false,inference(tab_negimp,[status(thm),assumptions([h503,h504,h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h505,h506])],[h504,42,h505,h506])).
% 276.04/275.42 thf(44,plain,$false,inference(tab_negimp,[status(thm),assumptions([h501,h502,h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h503,h504])],[h502,43,h503,h504])).
% 276.04/275.42 thf(45,plain,$false,inference(tab_negimp,[status(thm),assumptions([h499,h500,h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h501,h502])],[h500,44,h501,h502])).
% 276.04/275.42 thf(46,plain,$false,inference(tab_negimp,[status(thm),assumptions([h497,h498,h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h499,h500])],[h498,45,h499,h500])).
% 276.04/275.42 thf(47,plain,$false,inference(tab_negimp,[status(thm),assumptions([h495,h496,h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h497,h498])],[h496,46,h497,h498])).
% 276.04/275.42 thf(48,plain,$false,inference(tab_negimp,[status(thm),assumptions([h493,h494,h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h495,h496])],[h494,47,h495,h496])).
% 276.04/275.42 thf(49,plain,$false,inference(tab_negimp,[status(thm),assumptions([h491,h492,h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h493,h494])],[h492,48,h493,h494])).
% 276.04/275.42 thf(50,plain,$false,inference(tab_negimp,[status(thm),assumptions([h489,h490,h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h491,h492])],[h490,49,h491,h492])).
% 276.04/275.42 thf(51,plain,$false,inference(tab_negimp,[status(thm),assumptions([h487,h488,h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h489,h490])],[h488,50,h489,h490])).
% 276.04/275.42 thf(52,plain,$false,inference(tab_negimp,[status(thm),assumptions([h485,h486,h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h487,h488])],[h486,51,h487,h488])).
% 276.04/275.42 thf(53,plain,$false,inference(tab_negimp,[status(thm),assumptions([h483,h484,h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h485,h486])],[h484,52,h485,h486])).
% 276.04/275.42 thf(54,plain,$false,inference(tab_negimp,[status(thm),assumptions([h481,h482,h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h483,h484])],[h482,53,h483,h484])).
% 276.04/275.42 thf(55,plain,$false,inference(tab_negimp,[status(thm),assumptions([h479,h480,h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h481,h482])],[h480,54,h481,h482])).
% 276.04/275.42 thf(56,plain,$false,inference(tab_negimp,[status(thm),assumptions([h477,h478,h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h479,h480])],[h478,55,h479,h480])).
% 276.04/275.42 thf(57,plain,$false,inference(tab_negimp,[status(thm),assumptions([h475,h476,h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h477,h478])],[h476,56,h477,h478])).
% 276.04/275.42 thf(58,plain,$false,inference(tab_negimp,[status(thm),assumptions([h473,h474,h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h475,h476])],[h474,57,h475,h476])).
% 276.04/275.42 thf(59,plain,$false,inference(tab_negimp,[status(thm),assumptions([h471,h472,h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h473,h474])],[h472,58,h473,h474])).
% 276.04/275.42 thf(60,plain,$false,inference(tab_negimp,[status(thm),assumptions([h469,h470,h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h471,h472])],[h470,59,h471,h472])).
% 276.04/275.42 thf(61,plain,$false,inference(tab_negimp,[status(thm),assumptions([h467,h468,h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h469,h470])],[h468,60,h469,h470])).
% 276.04/275.42 thf(62,plain,$false,inference(tab_negimp,[status(thm),assumptions([h465,h466,h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h467,h468])],[h466,61,h467,h468])).
% 276.04/275.42 thf(63,plain,$false,inference(tab_negimp,[status(thm),assumptions([h463,h464,h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h465,h466])],[h464,62,h465,h466])).
% 276.04/275.42 thf(64,plain,$false,inference(tab_negimp,[status(thm),assumptions([h461,h462,h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h463,h464])],[h462,63,h463,h464])).
% 276.04/275.42 thf(65,plain,$false,inference(tab_negimp,[status(thm),assumptions([h459,h460,h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h461,h462])],[h460,64,h461,h462])).
% 276.04/275.42 thf(66,plain,$false,inference(tab_negimp,[status(thm),assumptions([h457,h458,h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h459,h460])],[h458,65,h459,h460])).
% 276.04/275.42 thf(67,plain,$false,inference(tab_negimp,[status(thm),assumptions([h455,h456,h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h457,h458])],[h456,66,h457,h458])).
% 276.04/275.42 thf(68,plain,$false,inference(tab_negimp,[status(thm),assumptions([h453,h454,h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h455,h456])],[h454,67,h455,h456])).
% 276.04/275.42 thf(69,plain,$false,inference(tab_negimp,[status(thm),assumptions([h451,h452,h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h453,h454])],[h452,68,h453,h454])).
% 276.04/275.42 thf(70,plain,$false,inference(tab_negimp,[status(thm),assumptions([h449,h450,h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h451,h452])],[h450,69,h451,h452])).
% 276.04/275.42 thf(71,plain,$false,inference(tab_negimp,[status(thm),assumptions([h447,h448,h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h449,h450])],[h448,70,h449,h450])).
% 276.04/275.42 thf(72,plain,$false,inference(tab_negimp,[status(thm),assumptions([h445,h446,h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h447,h448])],[h446,71,h447,h448])).
% 276.04/275.42 thf(73,plain,$false,inference(tab_negimp,[status(thm),assumptions([h443,h444,h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h445,h446])],[h444,72,h445,h446])).
% 276.04/275.42 thf(74,plain,$false,inference(tab_negimp,[status(thm),assumptions([h441,h442,h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h443,h444])],[h442,73,h443,h444])).
% 276.04/275.42 thf(75,plain,$false,inference(tab_negimp,[status(thm),assumptions([h439,h440,h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h441,h442])],[h440,74,h441,h442])).
% 276.04/275.42 thf(76,plain,$false,inference(tab_negimp,[status(thm),assumptions([h437,h438,h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h439,h440])],[h438,75,h439,h440])).
% 276.04/275.42 thf(77,plain,$false,inference(tab_negimp,[status(thm),assumptions([h435,h436,h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h437,h438])],[h436,76,h437,h438])).
% 276.04/275.42 thf(78,plain,$false,inference(tab_negimp,[status(thm),assumptions([h433,h434,h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h435,h436])],[h434,77,h435,h436])).
% 276.04/275.42 thf(79,plain,$false,inference(tab_negimp,[status(thm),assumptions([h431,h432,h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h433,h434])],[h432,78,h433,h434])).
% 276.04/275.42 thf(80,plain,$false,inference(tab_negimp,[status(thm),assumptions([h429,h430,h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h431,h432])],[h430,79,h431,h432])).
% 276.04/275.42 thf(81,plain,$false,inference(tab_negimp,[status(thm),assumptions([h427,h428,h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h429,h430])],[h428,80,h429,h430])).
% 276.04/275.42 thf(82,plain,$false,inference(tab_negimp,[status(thm),assumptions([h425,h426,h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h427,h428])],[h426,81,h427,h428])).
% 276.04/275.42 thf(83,plain,$false,inference(tab_negimp,[status(thm),assumptions([h423,h424,h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h425,h426])],[h424,82,h425,h426])).
% 276.04/275.42 thf(84,plain,$false,inference(tab_negimp,[status(thm),assumptions([h421,h422,h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h423,h424])],[h422,83,h423,h424])).
% 276.04/275.42 thf(85,plain,$false,inference(tab_negimp,[status(thm),assumptions([h419,h420,h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h421,h422])],[h420,84,h421,h422])).
% 276.04/275.42 thf(86,plain,$false,inference(tab_negimp,[status(thm),assumptions([h417,h418,h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h419,h420])],[h418,85,h419,h420])).
% 276.04/275.42 thf(87,plain,$false,inference(tab_negimp,[status(thm),assumptions([h415,h416,h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h417,h418])],[h416,86,h417,h418])).
% 276.04/275.42 thf(88,plain,$false,inference(tab_negimp,[status(thm),assumptions([h413,h414,h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h415,h416])],[h414,87,h415,h416])).
% 276.04/275.42 thf(89,plain,$false,inference(tab_negimp,[status(thm),assumptions([h406,h412,h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h413,h414])],[h412,88,h413,h414])).
% 276.04/275.42 thf(90,plain,$false,inference(tab_negimp,[status(thm),assumptions([h410,h411,h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h406,h412])],[h411,89,h406,h412])).
% 276.04/275.42 thf(91,plain,$false,inference(tab_negimp,[status(thm),assumptions([h408,h409,h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h410,h411])],[h409,90,h410,h411])).
% 276.04/275.43 thf(92,plain,$false,inference(tab_negimp,[status(thm),assumptions([h406,h407,h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h408,h409])],[h407,91,h408,h409])).
% 276.04/275.43 thf(93,plain,$false,inference(tab_negimp,[status(thm),assumptions([h404,h405,h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h406,h407])],[h405,92,h406,h407])).
% 276.04/275.43 thf(94,plain,$false,inference(tab_negimp,[status(thm),assumptions([h402,h403,h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h404,h405])],[h403,93,h404,h405])).
% 276.04/275.43 thf(95,plain,$false,inference(tab_negimp,[status(thm),assumptions([h400,h401,h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h402,h403])],[h401,94,h402,h403])).
% 276.04/275.43 thf(96,plain,$false,inference(tab_negimp,[status(thm),assumptions([h398,h399,h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h400,h401])],[h399,95,h400,h401])).
% 276.04/275.43 thf(97,plain,$false,inference(tab_negimp,[status(thm),assumptions([h396,h397,h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h398,h399])],[h397,96,h398,h399])).
% 276.04/275.43 thf(98,plain,$false,inference(tab_negimp,[status(thm),assumptions([h394,h395,h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h396,h397])],[h395,97,h396,h397])).
% 276.04/275.43 thf(99,plain,$false,inference(tab_negimp,[status(thm),assumptions([h392,h393,h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h394,h395])],[h393,98,h394,h395])).
% 276.04/275.43 thf(100,plain,$false,inference(tab_negimp,[status(thm),assumptions([h390,h391,h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h392,h393])],[h391,99,h392,h393])).
% 276.04/275.43 thf(101,plain,$false,inference(tab_negimp,[status(thm),assumptions([h388,h389,h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h390,h391])],[h389,100,h390,h391])).
% 276.04/275.43 thf(102,plain,$false,inference(tab_negimp,[status(thm),assumptions([h386,h387,h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h388,h389])],[h387,101,h388,h389])).
% 276.04/275.43 thf(103,plain,$false,inference(tab_negimp,[status(thm),assumptions([h384,h385,h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h386,h387])],[h385,102,h386,h387])).
% 276.04/275.43 thf(104,plain,$false,inference(tab_negimp,[status(thm),assumptions([h382,h383,h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h384,h385])],[h383,103,h384,h385])).
% 276.04/275.43 thf(105,plain,$false,inference(tab_negimp,[status(thm),assumptions([h379,h381,h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h382,h383])],[h381,104,h382,h383])).
% 276.04/275.43 thf(106,plain,$false,inference(tab_negimp,[status(thm),assumptions([h379,h380,h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h379,h381])],[h380,105,h379,h381])).
% 276.04/275.43 thf(107,plain,$false,inference(tab_negimp,[status(thm),assumptions([h377,h378,h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h379,h380])],[h378,106,h379,h380])).
% 276.04/275.43 thf(108,plain,$false,inference(tab_negimp,[status(thm),assumptions([h375,h376,h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h377,h378])],[h376,107,h377,h378])).
% 276.04/275.43 thf(109,plain,$false,inference(tab_negimp,[status(thm),assumptions([h373,h374,h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h375,h376])],[h374,108,h375,h376])).
% 276.04/275.43 thf(110,plain,$false,inference(tab_negimp,[status(thm),assumptions([h371,h372,h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h373,h374])],[h372,109,h373,h374])).
% 276.04/275.43 thf(111,plain,$false,inference(tab_negimp,[status(thm),assumptions([h369,h370,h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h371,h372])],[h370,110,h371,h372])).
% 276.04/275.43 thf(112,plain,$false,inference(tab_negimp,[status(thm),assumptions([h367,h368,h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h369,h370])],[h368,111,h369,h370])).
% 276.04/275.43 thf(113,plain,$false,inference(tab_negimp,[status(thm),assumptions([h365,h366,h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h367,h368])],[h366,112,h367,h368])).
% 276.04/275.43 thf(114,plain,$false,inference(tab_negimp,[status(thm),assumptions([h363,h364,h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h365,h366])],[h364,113,h365,h366])).
% 276.04/275.43 thf(115,plain,$false,inference(tab_negimp,[status(thm),assumptions([h361,h362,h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h363,h364])],[h362,114,h363,h364])).
% 276.04/275.43 thf(116,plain,$false,inference(tab_negimp,[status(thm),assumptions([h359,h360,h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h361,h362])],[h360,115,h361,h362])).
% 276.04/275.43 thf(117,plain,$false,inference(tab_negimp,[status(thm),assumptions([h357,h358,h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h359,h360])],[h358,116,h359,h360])).
% 276.04/275.43 thf(118,plain,$false,inference(tab_negimp,[status(thm),assumptions([h355,h356,h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h357,h358])],[h356,117,h357,h358])).
% 276.04/275.43 thf(119,plain,$false,inference(tab_negimp,[status(thm),assumptions([h353,h354,h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h355,h356])],[h354,118,h355,h356])).
% 276.04/275.43 thf(120,plain,$false,inference(tab_negimp,[status(thm),assumptions([h350,h352,h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h353,h354])],[h352,119,h353,h354])).
% 276.04/275.43 thf(121,plain,$false,inference(tab_negimp,[status(thm),assumptions([h350,h351,h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h350,h352])],[h351,120,h350,h352])).
% 276.04/275.43 thf(122,plain,$false,inference(tab_negimp,[status(thm),assumptions([h348,h349,h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h350,h351])],[h349,121,h350,h351])).
% 276.04/275.43 thf(123,plain,$false,inference(tab_negimp,[status(thm),assumptions([h346,h347,h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h348,h349])],[h347,122,h348,h349])).
% 276.04/275.43 thf(124,plain,$false,inference(tab_negimp,[status(thm),assumptions([h344,h345,h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h346,h347])],[h345,123,h346,h347])).
% 276.04/275.43 thf(125,plain,$false,inference(tab_negimp,[status(thm),assumptions([h342,h343,h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h344,h345])],[h343,124,h344,h345])).
% 276.04/275.43 thf(126,plain,$false,inference(tab_negimp,[status(thm),assumptions([h340,h341,h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h342,h343])],[h341,125,h342,h343])).
% 276.04/275.43 thf(127,plain,$false,inference(tab_negimp,[status(thm),assumptions([h338,h339,h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h340,h341])],[h339,126,h340,h341])).
% 276.04/275.43 thf(128,plain,$false,inference(tab_negimp,[status(thm),assumptions([h336,h337,h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h338,h339])],[h337,127,h338,h339])).
% 276.04/275.43 thf(129,plain,$false,inference(tab_negimp,[status(thm),assumptions([h334,h335,h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h336,h337])],[h335,128,h336,h337])).
% 276.04/275.43 thf(130,plain,$false,inference(tab_negimp,[status(thm),assumptions([h332,h333,h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h334,h335])],[h333,129,h334,h335])).
% 276.04/275.43 thf(131,plain,$false,inference(tab_negimp,[status(thm),assumptions([h330,h331,h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h332,h333])],[h331,130,h332,h333])).
% 276.04/275.43 thf(132,plain,$false,inference(tab_negimp,[status(thm),assumptions([h328,h329,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h330,h331])],[h329,131,h330,h331])).
% 276.04/275.43 thf(133,plain,$false,inference(tab_negimp,[status(thm),assumptions([h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h328,h329])],[h327,132,h328,h329])).
% 276.04/275.43 thf(134,plain,$false,inference(tab_negimp,[status(thm),assumptions([h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h326,h327])],[h325,133,h326,h327])).
% 276.04/275.43 thf(135,plain,$false,inference(tab_negimp,[status(thm),assumptions([h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h324,h325])],[h323,134,h324,h325])).
% 276.04/275.43 thf(136,plain,$false,inference(tab_negimp,[status(thm),assumptions([h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h322,h323])],[h321,135,h322,h323])).
% 276.04/275.43 thf(137,plain,$false,inference(tab_negimp,[status(thm),assumptions([h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h320,h321])],[h319,136,h320,h321])).
% 276.04/275.43 thf(138,plain,$false,inference(tab_negimp,[status(thm),assumptions([h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h318,h319])],[h317,137,h318,h319])).
% 276.04/275.43 thf(139,plain,$false,inference(tab_negimp,[status(thm),assumptions([h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h316,h317])],[h315,138,h316,h317])).
% 276.04/275.43 thf(140,plain,$false,inference(tab_negimp,[status(thm),assumptions([h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h314,h315])],[h313,139,h314,h315])).
% 276.04/275.43 thf(141,plain,$false,inference(tab_negimp,[status(thm),assumptions([h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h312,h313])],[h311,140,h312,h313])).
% 276.04/275.43 thf(142,plain,$false,inference(tab_negimp,[status(thm),assumptions([h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h310,h311])],[h309,141,h310,h311])).
% 276.04/275.43 thf(143,plain,$false,inference(tab_negimp,[status(thm),assumptions([h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h308,h309])],[h307,142,h308,h309])).
% 276.04/275.43 thf(144,plain,$false,inference(tab_negimp,[status(thm),assumptions([h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h306,h307])],[h305,143,h306,h307])).
% 276.04/275.43 thf(145,plain,$false,inference(tab_negimp,[status(thm),assumptions([h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h304,h305])],[h303,144,h304,h305])).
% 276.04/275.43 thf(146,plain,$false,inference(tab_negimp,[status(thm),assumptions([h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h302,h303])],[h301,145,h302,h303])).
% 276.04/275.43 thf(147,plain,$false,inference(tab_negimp,[status(thm),assumptions([h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h300,h301])],[h299,146,h300,h301])).
% 276.04/275.43 thf(148,plain,$false,inference(tab_negimp,[status(thm),assumptions([h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h298,h299])],[h297,147,h298,h299])).
% 276.04/275.43 thf(149,plain,$false,inference(tab_negimp,[status(thm),assumptions([h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h296,h297])],[h295,148,h296,h297])).
% 276.04/275.43 thf(150,plain,$false,inference(tab_negimp,[status(thm),assumptions([h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h294,h295])],[h293,149,h294,h295])).
% 276.04/275.43 thf(151,plain,$false,inference(tab_negimp,[status(thm),assumptions([h290,h291,h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h292,h293])],[h291,150,h292,h293])).
% 276.04/275.43 thf(152,plain,$false,inference(tab_negimp,[status(thm),assumptions([h288,h289,h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h290,h291])],[h289,151,h290,h291])).
% 276.04/275.43 thf(153,plain,$false,inference(tab_negimp,[status(thm),assumptions([h286,h287,h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h288,h289])],[h287,152,h288,h289])).
% 276.04/275.43 thf(154,plain,$false,inference(tab_negimp,[status(thm),assumptions([h284,h285,h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h286,h287])],[h285,153,h286,h287])).
% 276.04/275.43 thf(155,plain,$false,inference(tab_negimp,[status(thm),assumptions([h282,h283,h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h284,h285])],[h283,154,h284,h285])).
% 276.04/275.43 thf(156,plain,$false,inference(tab_negimp,[status(thm),assumptions([h280,h281,h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h282,h283])],[h281,155,h282,h283])).
% 276.04/275.43 thf(157,plain,$false,inference(tab_negimp,[status(thm),assumptions([h278,h279,h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h280,h281])],[h279,156,h280,h281])).
% 276.04/275.43 thf(158,plain,$false,inference(tab_negimp,[status(thm),assumptions([h276,h277,h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h278,h279])],[h277,157,h278,h279])).
% 276.04/275.43 thf(159,plain,$false,inference(tab_negimp,[status(thm),assumptions([h274,h275,h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h276,h277])],[h275,158,h276,h277])).
% 276.04/275.43 thf(160,plain,$false,inference(tab_negimp,[status(thm),assumptions([h272,h273,h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h274,h275])],[h273,159,h274,h275])).
% 276.04/275.43 thf(161,plain,$false,inference(tab_negimp,[status(thm),assumptions([h270,h271,h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h272,h273])],[h271,160,h272,h273])).
% 276.04/275.43 thf(162,plain,$false,inference(tab_negimp,[status(thm),assumptions([h268,h269,h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h270,h271])],[h269,161,h270,h271])).
% 276.04/275.43 thf(163,plain,$false,inference(tab_negimp,[status(thm),assumptions([h90,h267,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h268,h269])],[h267,162,h268,h269])).
% 276.04/275.43 thf(164,plain,$false,inference(tab_negimp,[status(thm),assumptions([h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h90,h267])],[h266,163,h90,h267])).
% 276.04/275.43 thf(165,plain,$false,inference(tab_negimp,[status(thm),assumptions([h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h265,h266])],[h264,164,h265,h266])).
% 276.04/275.43 thf(166,plain,$false,inference(tab_negimp,[status(thm),assumptions([h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h263,h264])],[h262,165,h263,h264])).
% 276.04/275.43 thf(167,plain,$false,inference(tab_negimp,[status(thm),assumptions([h259,h260,h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h261,h262])],[h260,166,h261,h262])).
% 276.04/275.43 thf(168,plain,$false,inference(tab_negimp,[status(thm),assumptions([h257,h258,h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h259,h260])],[h258,167,h259,h260])).
% 276.04/275.43 thf(169,plain,$false,inference(tab_negimp,[status(thm),assumptions([h255,h256,h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h257,h258])],[h256,168,h257,h258])).
% 276.04/275.43 thf(170,plain,$false,inference(tab_negimp,[status(thm),assumptions([h253,h254,h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h255,h256])],[h254,169,h255,h256])).
% 276.04/275.43 thf(171,plain,$false,inference(tab_negimp,[status(thm),assumptions([h94,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h253,h254])],[h252,170,h253,h254])).
% 276.04/275.43 thf(172,plain,$false,inference(tab_negimp,[status(thm),assumptions([h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h94,h252])],[h251,171,h94,h252])).
% 276.04/275.43 thf(173,plain,$false,inference(tab_negimp,[status(thm),assumptions([h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h250,h251])],[h249,172,h250,h251])).
% 276.04/275.43 thf(174,plain,$false,inference(tab_negimp,[status(thm),assumptions([h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h248,h249])],[h247,173,h248,h249])).
% 276.04/275.43 thf(175,plain,$false,inference(tab_negimp,[status(thm),assumptions([h244,h245,h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h246,h247])],[h245,174,h246,h247])).
% 276.04/275.43 thf(176,plain,$false,inference(tab_negimp,[status(thm),assumptions([h242,h243,h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h244,h245])],[h243,175,h244,h245])).
% 276.04/275.43 thf(177,plain,$false,inference(tab_negimp,[status(thm),assumptions([h240,h241,h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h242,h243])],[h241,176,h242,h243])).
% 276.04/275.43 thf(178,plain,$false,inference(tab_negimp,[status(thm),assumptions([h238,h239,h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h240,h241])],[h239,177,h240,h241])).
% 276.04/275.43 thf(179,plain,$false,inference(tab_negimp,[status(thm),assumptions([h236,h237,h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h238,h239])],[h237,178,h238,h239])).
% 276.04/275.43 thf(180,plain,$false,inference(tab_negimp,[status(thm),assumptions([h234,h235,h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h236,h237])],[h235,179,h236,h237])).
% 276.04/275.43 thf(181,plain,$false,inference(tab_negimp,[status(thm),assumptions([h232,h233,h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h234,h235])],[h233,180,h234,h235])).
% 276.04/275.43 thf(182,plain,$false,inference(tab_negimp,[status(thm),assumptions([h230,h231,h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h232,h233])],[h231,181,h232,h233])).
% 276.04/275.43 thf(183,plain,$false,inference(tab_negimp,[status(thm),assumptions([h228,h229,h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h230,h231])],[h229,182,h230,h231])).
% 276.04/275.43 thf(184,plain,$false,inference(tab_negimp,[status(thm),assumptions([h226,h227,h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h228,h229])],[h227,183,h228,h229])).
% 276.04/275.43 thf(185,plain,$false,inference(tab_negimp,[status(thm),assumptions([h224,h225,h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h226,h227])],[h225,184,h226,h227])).
% 276.04/275.43 thf(186,plain,$false,inference(tab_negimp,[status(thm),assumptions([h222,h223,h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h224,h225])],[h223,185,h224,h225])).
% 276.04/275.43 thf(187,plain,$false,inference(tab_negimp,[status(thm),assumptions([h220,h221,h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h222,h223])],[h221,186,h222,h223])).
% 276.04/275.43 thf(188,plain,$false,inference(tab_negimp,[status(thm),assumptions([h218,h219,h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h220,h221])],[h219,187,h220,h221])).
% 276.04/275.43 thf(189,plain,$false,inference(tab_negimp,[status(thm),assumptions([h216,h217,h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h218,h219])],[h217,188,h218,h219])).
% 276.04/275.43 thf(190,plain,$false,inference(tab_negimp,[status(thm),assumptions([h214,h215,h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h216,h217])],[h215,189,h216,h217])).
% 276.04/275.43 thf(191,plain,$false,inference(tab_negimp,[status(thm),assumptions([h212,h213,h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h214,h215])],[h213,190,h214,h215])).
% 276.04/275.43 thf(192,plain,$false,inference(tab_negimp,[status(thm),assumptions([h210,h211,h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h212,h213])],[h211,191,h212,h213])).
% 276.04/275.43 thf(193,plain,$false,inference(tab_negimp,[status(thm),assumptions([h208,h209,h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h210,h211])],[h209,192,h210,h211])).
% 276.04/275.43 thf(194,plain,$false,inference(tab_negimp,[status(thm),assumptions([h206,h207,h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h208,h209])],[h207,193,h208,h209])).
% 276.04/275.43 thf(195,plain,$false,inference(tab_negimp,[status(thm),assumptions([h204,h205,h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h206,h207])],[h205,194,h206,h207])).
% 276.04/275.43 thf(196,plain,$false,inference(tab_negimp,[status(thm),assumptions([h202,h203,h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h204,h205])],[h203,195,h204,h205])).
% 276.04/275.43 thf(197,plain,$false,inference(tab_negimp,[status(thm),assumptions([h200,h201,h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h202,h203])],[h201,196,h202,h203])).
% 276.04/275.43 thf(198,plain,$false,inference(tab_negimp,[status(thm),assumptions([h198,h199,h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h200,h201])],[h199,197,h200,h201])).
% 276.04/275.43 thf(199,plain,$false,inference(tab_negimp,[status(thm),assumptions([h196,h197,h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h198,h199])],[h197,198,h198,h199])).
% 276.04/275.43 thf(200,plain,$false,inference(tab_negimp,[status(thm),assumptions([h194,h195,h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h196,h197])],[h195,199,h196,h197])).
% 276.04/275.43 thf(201,plain,$false,inference(tab_negimp,[status(thm),assumptions([h192,h193,h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h194,h195])],[h193,200,h194,h195])).
% 276.04/275.43 thf(202,plain,$false,inference(tab_negimp,[status(thm),assumptions([h190,h191,h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h192,h193])],[h191,201,h192,h193])).
% 276.04/275.43 thf(203,plain,$false,inference(tab_negimp,[status(thm),assumptions([h188,h189,h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h190,h191])],[h189,202,h190,h191])).
% 276.04/275.43 thf(204,plain,$false,inference(tab_negimp,[status(thm),assumptions([h94,h187,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h188,h189])],[h187,203,h188,h189])).
% 276.04/275.43 thf(205,plain,$false,inference(tab_negimp,[status(thm),assumptions([h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h94,h187])],[h186,204,h94,h187])).
% 276.04/275.43 thf(206,plain,$false,inference(tab_negimp,[status(thm),assumptions([h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h185,h186])],[h184,205,h185,h186])).
% 276.04/275.43 thf(207,plain,$false,inference(tab_negimp,[status(thm),assumptions([h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h183,h184])],[h182,206,h183,h184])).
% 276.04/275.43 thf(208,plain,$false,inference(tab_negimp,[status(thm),assumptions([h179,h180,h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h181,h182])],[h180,207,h181,h182])).
% 276.04/275.43 thf(209,plain,$false,inference(tab_negimp,[status(thm),assumptions([h177,h178,h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h179,h180])],[h178,208,h179,h180])).
% 276.04/275.43 thf(210,plain,$false,inference(tab_negimp,[status(thm),assumptions([h175,h176,h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h177,h178])],[h176,209,h177,h178])).
% 276.04/275.43 thf(211,plain,$false,inference(tab_negimp,[status(thm),assumptions([h173,h174,h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h175,h176])],[h174,210,h175,h176])).
% 276.04/275.43 thf(212,plain,$false,inference(tab_negimp,[status(thm),assumptions([h171,h172,h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h173,h174])],[h172,211,h173,h174])).
% 276.04/275.43 thf(213,plain,$false,inference(tab_negimp,[status(thm),assumptions([h169,h170,h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h171,h172])],[h170,212,h171,h172])).
% 276.04/275.43 thf(214,plain,$false,inference(tab_negimp,[status(thm),assumptions([h167,h168,h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h169,h170])],[h168,213,h169,h170])).
% 276.04/275.43 thf(215,plain,$false,inference(tab_negimp,[status(thm),assumptions([h165,h166,h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h167,h168])],[h166,214,h167,h168])).
% 276.04/275.43 thf(216,plain,$false,inference(tab_negimp,[status(thm),assumptions([h163,h164,h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h165,h166])],[h164,215,h165,h166])).
% 276.04/275.43 thf(217,plain,$false,inference(tab_negimp,[status(thm),assumptions([h161,h162,h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h163,h164])],[h162,216,h163,h164])).
% 276.04/275.43 thf(218,plain,$false,inference(tab_negimp,[status(thm),assumptions([h159,h160,h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h161,h162])],[h160,217,h161,h162])).
% 276.04/275.43 thf(219,plain,$false,inference(tab_negimp,[status(thm),assumptions([h157,h158,h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h159,h160])],[h158,218,h159,h160])).
% 276.04/275.43 thf(220,plain,$false,inference(tab_negimp,[status(thm),assumptions([h155,h156,h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h157,h158])],[h156,219,h157,h158])).
% 276.04/275.43 thf(221,plain,$false,inference(tab_negimp,[status(thm),assumptions([h153,h154,h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h155,h156])],[h154,220,h155,h156])).
% 276.04/275.43 thf(222,plain,$false,inference(tab_negimp,[status(thm),assumptions([h151,h152,h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h153,h154])],[h152,221,h153,h154])).
% 276.04/275.43 thf(223,plain,$false,inference(tab_negimp,[status(thm),assumptions([h149,h150,h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h151,h152])],[h150,222,h151,h152])).
% 276.04/275.43 thf(224,plain,$false,inference(tab_negimp,[status(thm),assumptions([h147,h148,h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h149,h150])],[h148,223,h149,h150])).
% 276.04/275.43 thf(225,plain,$false,inference(tab_negimp,[status(thm),assumptions([h140,h146,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h147,h148])],[h146,224,h147,h148])).
% 276.09/275.44 thf(226,plain,$false,inference(tab_negimp,[status(thm),assumptions([h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h140,h146])],[h145,225,h140,h146])).
% 276.09/275.44 thf(227,plain,$false,inference(tab_negimp,[status(thm),assumptions([h142,h143,h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h144,h145])],[h143,226,h144,h145])).
% 276.09/275.44 thf(228,plain,$false,inference(tab_negimp,[status(thm),assumptions([h140,h141,h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h142,h143])],[h141,227,h142,h143])).
% 276.09/275.44 thf(229,plain,$false,inference(tab_negimp,[status(thm),assumptions([h138,h139,h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h140,h141])],[h139,228,h140,h141])).
% 276.09/275.44 thf(230,plain,$false,inference(tab_negimp,[status(thm),assumptions([h136,h137,h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h138,h139])],[h137,229,h138,h139])).
% 276.09/275.44 thf(231,plain,$false,inference(tab_negimp,[status(thm),assumptions([h121,h135,h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h136,h137])],[h135,230,h136,h137])).
% 276.09/275.44 thf(232,plain,$false,inference(tab_negimp,[status(thm),assumptions([h133,h134,h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h121,h135])],[h134,231,h121,h135])).
% 276.09/275.44 thf(233,plain,$false,inference(tab_negimp,[status(thm),assumptions([h131,h132,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h133,h134])],[h132,232,h133,h134])).
% 276.09/275.44 thf(234,plain,$false,inference(tab_negimp,[status(thm),assumptions([h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h131,h132])],[h130,233,h131,h132])).
% 276.09/275.44 thf(235,plain,$false,inference(tab_negimp,[status(thm),assumptions([h127,h128,h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h129,h130])],[h128,234,h129,h130])).
% 276.09/275.44 thf(236,plain,$false,inference(tab_negimp,[status(thm),assumptions([h125,h126,h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h127,h128])],[h126,235,h127,h128])).
% 276.09/275.44 thf(237,plain,$false,inference(tab_negimp,[status(thm),assumptions([h123,h124,h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h125,h126])],[h124,236,h125,h126])).
% 276.09/275.44 thf(238,plain,$false,inference(tab_negimp,[status(thm),assumptions([h121,h122,h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h123,h124])],[h122,237,h123,h124])).
% 276.09/275.44 thf(239,plain,$false,inference(tab_negimp,[status(thm),assumptions([h119,h120,h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h121,h122])],[h120,238,h121,h122])).
% 276.09/275.44 thf(240,plain,$false,inference(tab_negimp,[status(thm),assumptions([h117,h118,h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h119,h120])],[h118,239,h119,h120])).
% 276.09/275.44 thf(241,plain,$false,inference(tab_negimp,[status(thm),assumptions([h115,h116,h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h117,h118])],[h116,240,h117,h118])).
% 276.09/275.44 thf(242,plain,$false,inference(tab_negimp,[status(thm),assumptions([h113,h114,h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h115,h116])],[h114,241,h115,h116])).
% 276.09/275.44 thf(243,plain,$false,inference(tab_negimp,[status(thm),assumptions([h31,h112,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h113,h114])],[h112,242,h113,h114])).
% 276.09/275.44 thf(244,plain,$false,inference(tab_negimp,[status(thm),assumptions([h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h31,h112])],[h111,243,h31,h112])).
% 276.09/275.44 thf(245,plain,$false,inference(tab_negimp,[status(thm),assumptions([h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h100,h111])],[h110,244,h100,h111])).
% 276.09/275.44 thf(246,plain,$false,inference(tab_negimp,[status(thm),assumptions([h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h102,h110])],[h109,245,h102,h110])).
% 276.09/275.44 thf(247,plain,$false,inference(tab_negimp,[status(thm),assumptions([h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h108,h109])],[h107,246,h108,h109])).
% 276.09/275.44 thf(248,plain,$false,inference(tab_negimp,[status(thm),assumptions([h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h106,h107])],[h105,247,h106,h107])).
% 276.09/275.44 thf(249,plain,$false,inference(tab_negimp,[status(thm),assumptions([h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h100,h105])],[h104,248,h100,h105])).
% 276.09/275.44 thf(250,plain,$false,inference(tab_negimp,[status(thm),assumptions([h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h102,h104])],[h103,249,h102,h104])).
% 276.09/275.44 thf(251,plain,$false,inference(tab_negimp,[status(thm),assumptions([h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h102,h103])],[h101,250,h102,h103])).
% 276.09/275.44 thf(252,plain,$false,inference(tab_negimp,[status(thm),assumptions([h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h100,h101])],[h99,251,h100,h101])).
% 276.09/275.44 thf(253,plain,$false,inference(tab_negimp,[status(thm),assumptions([h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h98,h99])],[h97,252,h98,h99])).
% 276.09/275.44 thf(254,plain,$false,inference(tab_negimp,[status(thm),assumptions([h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h96,h97])],[h95,253,h96,h97])).
% 276.09/275.44 thf(255,plain,$false,inference(tab_negimp,[status(thm),assumptions([h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h94,h95])],[h93,254,h94,h95])).
% 276.09/275.44 thf(256,plain,$false,inference(tab_negimp,[status(thm),assumptions([h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h92,h93])],[h91,255,h92,h93])).
% 276.09/275.44 thf(257,plain,$false,inference(tab_negimp,[status(thm),assumptions([h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h90,h91])],[h89,256,h90,h91])).
% 276.09/275.44 thf(258,plain,$false,inference(tab_negimp,[status(thm),assumptions([h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h88,h89])],[h87,257,h88,h89])).
% 276.09/275.44 thf(259,plain,$false,inference(tab_negimp,[status(thm),assumptions([h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h86,h87])],[h85,258,h86,h87])).
% 276.09/275.44 thf(260,plain,$false,inference(tab_negimp,[status(thm),assumptions([h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h84,h85])],[h83,259,h84,h85])).
% 276.09/275.44 thf(261,plain,$false,inference(tab_negimp,[status(thm),assumptions([h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h82,h83])],[h81,260,h82,h83])).
% 276.09/275.44 thf(262,plain,$false,inference(tab_negimp,[status(thm),assumptions([h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h48,h81])],[h80,261,h48,h81])).
% 276.09/275.44 thf(263,plain,$false,inference(tab_negimp,[status(thm),assumptions([h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h79,h80])],[h78,262,h79,h80])).
% 276.09/275.44 thf(264,plain,$false,inference(tab_negimp,[status(thm),assumptions([h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h77,h78])],[h76,263,h77,h78])).
% 276.09/275.44 thf(265,plain,$false,inference(tab_negimp,[status(thm),assumptions([h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h75,h76])],[h74,264,h75,h76])).
% 276.09/275.44 thf(266,plain,$false,inference(tab_negimp,[status(thm),assumptions([h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h73,h74])],[h72,265,h73,h74])).
% 276.09/275.44 thf(267,plain,$false,inference(tab_negimp,[status(thm),assumptions([h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h71,h72])],[h70,266,h71,h72])).
% 276.09/275.44 thf(268,plain,$false,inference(tab_negimp,[status(thm),assumptions([h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h68,h70])],[h69,267,h68,h70])).
% 276.09/275.44 thf(269,plain,$false,inference(tab_negimp,[status(thm),assumptions([h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h68,h69])],[h67,268,h68,h69])).
% 276.09/275.44 thf(270,plain,$false,inference(tab_negimp,[status(thm),assumptions([h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h66,h67])],[h65,269,h66,h67])).
% 276.09/275.44 thf(271,plain,$false,inference(tab_negimp,[status(thm),assumptions([h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h64,h65])],[h63,270,h64,h65])).
% 276.09/275.44 thf(272,plain,$false,inference(tab_negimp,[status(thm),assumptions([h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h62,h63])],[h61,271,h62,h63])).
% 276.09/275.44 thf(273,plain,$false,inference(tab_negimp,[status(thm),assumptions([h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h60,h61])],[h59,272,h60,h61])).
% 276.09/275.44 thf(274,plain,$false,inference(tab_negimp,[status(thm),assumptions([h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h58,h59])],[h57,273,h58,h59])).
% 276.09/275.44 thf(275,plain,$false,inference(tab_negimp,[status(thm),assumptions([h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h56,h57])],[h55,274,h56,h57])).
% 276.09/275.44 thf(276,plain,$false,inference(tab_negimp,[status(thm),assumptions([h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h54,h55])],[h53,275,h54,h55])).
% 276.09/275.44 thf(277,plain,$false,inference(tab_negimp,[status(thm),assumptions([h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h52,h53])],[h51,276,h52,h53])).
% 276.09/275.44 thf(278,plain,$false,inference(tab_negimp,[status(thm),assumptions([h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h50,h51])],[h49,277,h50,h51])).
% 276.09/275.44 thf(279,plain,$false,inference(tab_negimp,[status(thm),assumptions([h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h48,h49])],[h47,278,h48,h49])).
% 276.09/275.44 thf(280,plain,$false,inference(tab_negimp,[status(thm),assumptions([h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h46,h47])],[h45,279,h46,h47])).
% 276.09/275.44 thf(281,plain,$false,inference(tab_negimp,[status(thm),assumptions([h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h43,h45])],[h44,280,h43,h45])).
% 276.09/275.44 thf(282,plain,$false,inference(tab_negimp,[status(thm),assumptions([h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h43,h44])],[h42,281,h43,h44])).
% 276.09/275.44 thf(283,plain,$false,inference(tab_negimp,[status(thm),assumptions([h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h41,h42])],[h40,282,h41,h42])).
% 276.09/275.44 thf(284,plain,$false,inference(tab_negimp,[status(thm),assumptions([h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h39,h40])],[h38,283,h39,h40])).
% 276.09/275.44 thf(285,plain,$false,inference(tab_negimp,[status(thm),assumptions([h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h3,h38])],[h37,284,h3,h38])).
% 276.09/275.44 thf(286,plain,$false,inference(tab_negimp,[status(thm),assumptions([h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h3,h37])],[h36,285,h3,h37])).
% 276.09/275.44 thf(287,plain,$false,inference(tab_negimp,[status(thm),assumptions([h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h35,h36])],[h34,286,h35,h36])).
% 276.09/275.44 thf(288,plain,$false,inference(tab_negimp,[status(thm),assumptions([h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h33,h34])],[h32,287,h33,h34])).
% 276.09/275.44 thf(289,plain,$false,inference(tab_negimp,[status(thm),assumptions([h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h31,h32])],[h30,288,h31,h32])).
% 276.09/275.44 thf(290,plain,$false,inference(tab_negimp,[status(thm),assumptions([h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h29,h30])],[h28,289,h29,h30])).
% 276.09/275.44 thf(291,plain,$false,inference(tab_negimp,[status(thm),assumptions([h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h27,h28])],[h26,290,h27,h28])).
% 276.09/275.44 thf(292,plain,$false,inference(tab_negimp,[status(thm),assumptions([h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h25,h26])],[h24,291,h25,h26])).
% 276.09/275.44 thf(293,plain,$false,inference(tab_negimp,[status(thm),assumptions([h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h23,h24])],[h22,292,h23,h24])).
% 276.09/275.44 thf(294,plain,$false,inference(tab_negimp,[status(thm),assumptions([h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h21,h22])],[h20,293,h21,h22])).
% 276.09/275.44 thf(295,plain,$false,inference(tab_negimp,[status(thm),assumptions([h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h19,h20])],[h18,294,h19,h20])).
% 276.09/275.44 thf(296,plain,$false,inference(tab_negimp,[status(thm),assumptions([h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h17,h18])],[h16,295,h17,h18])).
% 276.09/275.44 thf(297,plain,$false,inference(tab_negimp,[status(thm),assumptions([h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h15,h16])],[h14,296,h15,h16])).
% 276.09/275.44 thf(298,plain,$false,inference(tab_negimp,[status(thm),assumptions([h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h13,h14])],[h12,297,h13,h14])).
% 276.09/275.44 thf(299,plain,$false,inference(tab_negimp,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h11,h12])],[h10,298,h11,h12])).
% 276.09/275.44 thf(300,plain,$false,inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h8,299,h9,h10])).
% 276.09/275.44 thf(301,plain,$false,inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h6,300,h7,h8])).
% 276.09/275.44 thf(302,plain,$false,inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,301,h5,h6])).
% 276.09/275.44 thf(303,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,302,h3,h4])).
% 276.09/275.44 thf(304,plain,$false,inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,303,h1,h2])).
% 276.09/275.44 thf(0,theorem,((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) = ((in @ X3) @ X2))) => (X1 = X2)))) => ((![X1:$i]:(~(((in @ X1) @ emptyset)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ X2)) = ((~((X3 = X1))) => ((in @ X3) @ X2)))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (powerset @ X1)) = (![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ X1)))))) => ((![X1:$i]:(![X2:$i]:(((in @ X2) @ (setunion @ X1)) = (~((![X3:$i]:(((in @ X2) @ X3) => (~(((in @ X3) @ X1)))))))))) => (((in @ emptyset) @ omega) => ((![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:$i]:(((in @ X3) @ ((dsetconstr @ X1) @ X2)) => ((in @ X3) @ X1))))) => ((![X1:$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))))) => ((![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:$i]:((kfst @ 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=> (![X4:$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) @ ((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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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)) => ((subset @ X2) @ ((cartprod @ X1) @ X1))))) => ((![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>$o]:((subset @ (((dpsetconstr @ X1) @ X1) @ X2)) @ ((cartprod @ X1) @ X1)))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![X4:$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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => ((subset @ ((breln1invset @ X1) @ X2)) @ ((cartprod @ X1) @ X1))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ (((breln1compset @ X1) @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))) => ((![X1:$i]:(![X2:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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:$i]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => (![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]:(((subset @ X2) @ ((cartprod @ X1) @ X1)) => (![X3:$i]:(((subset @ X3) @ ((cartprod @ X1) @ X1)) => ((subset @ ((binunion @ X2) @ X3)) @ ((cartprod @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[304,h0])).
% 276.09/275.44 % SZS output end Proof
%------------------------------------------------------------------------------